text:
Visitor $0.00 Login or Register
Fight Finance
Courses Tags Random All Recent Scores
Question 278 inflation, real and nominal returns and cash flows
Imagine that the interest rate on your savings account was 1% per year and inflation was 2% per year.
After one year, would you be able to buy , exactly the as or than today with the money in this account?
Question 279 diversification
Do you think that the following statement is or ? "Buying a single company stock usually provides a safer return than a stock mutual fund."
Question 1 NPV
Jan asks you for a loan. He wants $100 now and offers to pay you back $120 in 1 year. You can borrow and lend from the bank at an interest rate of 10% pa, given as an effective annual rate.
Ignore credit risk. Remember:
### V_0 = \frac{V_t}{(1+r_\text{eff})^t} ###
Will you or Jan's deal?
Question 4 DDM
For a price of $13, Carla will sell you a share which will pay a dividend of $1 in one year and every year after that forever. The required return of the stock is 10% pa.
Would you like to Carla's share or politely ?
For a price of $6, Carlos will sell you a share which will pay a dividend of $1 in one year and every year after that forever. The required return of the stock is 10% pa.
Would you like to his share or politely ?
For a price of $1040, Camille will sell you a share which just paid a dividend of $100, and is expected to pay dividends every year forever, growing at a rate of 5% pa.
So the next dividend will be ##100(1+0.05)^1=$105.00##, and the year after it will be ##100(1+0.05)^2=110.25## and so on.
The required return of the stock is 15% pa.
Would you like to the share or politely ?
Question 476 income and capital returns, idiom
The saying "buy low, sell high" suggests that investors should make a:
(a) Positive income return.
(b) Positive capital return.
(c) Negative income return.
(d) Negative capital return.
(e) Positive total return.
Question 478 income and capital returns
Total cash flows can be broken into income and capital cash flows. What is the name given to the income cash flow from owning shares?
(a) Dividends.
(b) Rent.
(c) Coupons.
(d) Loan payments.
(e) Capital gains.
Which of the following equations is NOT equal to the total return of an asset?
Let ##p_0## be the current price, ##p_1## the expected price in one year and ##c_1## the expected income in one year.
(a) ##r_\text{total} = \dfrac{c_1+p_1-p_0}{p_0} ##
(b) ##r_\text{total} = \dfrac{c_1+p_1}{p_0} - 1##
(c) ##r_\text{total} = \dfrac{c_1}{p_0} + \dfrac{p_1-p_0}{p_0}##
(d) ##r_\text{total} = \dfrac{c_1}{p_0} + \dfrac{p_1}{p_0} ##
(e) ##r_\text{total} = \dfrac{c_1}{p_0} + \dfrac{p_1}{p_0} - 1##
An asset's total expected return over the next year is given by:
###r_\text{total} = \dfrac{c_1+p_1-p_0}{p_0} ###
Where ##p_0## is the current price, ##c_1## is the expected income in one year and ##p_1## is the expected price in one year. The total return can be split into the income return and the capital return.
Which of the following is the expected capital return?
(a) ##c_1##
(b) ##p_1-p_0##
(c) ##\dfrac{c_1}{p_0} ##
(d) ##\dfrac{p_1}{p_0} -1##
(e) ##\dfrac{p_1}{p_0} ##
A stock was bought for $8 and paid a dividend of $0.50 one year later (at t=1 year). Just after the dividend was paid, the stock price was $7 (at t=1 year).
What were the total, capital and dividend returns given as effective annual rates? The choices are given in the same order:
##r_\text{total}##, ##r_\text{capital}##, ##r_\text{dividend}##.
(a) 0.0625, -0.0625, -0.125.
(b) 0.0625, 0.125, -0.0625.
(c) -0.0625, 0.0625, -0.125.
(d) -0.0625, -0.125, 0.0625.
(e) -0.125, -0.1875, 0.0625.
A share was bought for $30 (at t=0) and paid its annual dividend of $6 one year later (at t=1).
Just after the dividend was paid, the share price fell to $27 (at t=1). What were the total, capital and income returns given as effective annual rates?
The choices are given in the same order:
##r_\text{total}## , ##r_\text{capital}## , ##r_\text{dividend}##.
(a) -0.1, -0.3, 0.2.
(b) -0.1, 0.1, -0.2.
(c) 0.1, -0.1, 0.2.
(d) 0.1, 0.2, -0.1.
(e) 0.2, 0.1, -0.1.
Question 21 income and capital returns, bond pricing
A fixed coupon bond was bought for $90 and paid its annual coupon of $3 one year later (at t=1 year). Just after the coupon was paid, the bond price was $92 (at t=1 year). What was the total return, capital return and income return? Calculate your answers as effective annual rates.
The choices are given in the same order: ## r_\text{total},r_\text{capital},r_\text{income} ##.
(a) -0.0556, -0.0222, -0.0333
(b) 0.0222, -0.0111, 0.0333.
(c) 0.0333, 0.0556, 0.0222.
(d) 0.0556, 0.0222, 0.0333.
(e) 0.0556, 0.0333, 0.0222.
Question 295 inflation, real and nominal returns and cash flows, NPV
When valuing assets using discounted cash flow (net present value) methods, it is important to consider inflation. To properly deal with inflation:
(I) Discount nominal cash flows by nominal discount rates.
(II) Discount nominal cash flows by real discount rates.
(III) Discount real cash flows by nominal discount rates.
(IV) Discount real cash flows by real discount rates.
Which of the above statements is or are correct?
(a) I only.
(b) III only.
(c) IV only.
(d) I and IV only.
(e) II and III only.
Question 481 Annuity
This annuity formula ##\dfrac{C_1}{r}\left(1-\dfrac{1}{(1+r)^3} \right)## is equivalent to which of the following formulas? Note the 3.
In the below formulas, ##C_t## is a cash flow at time t. All of the cash flows are equal, but paid at different times.
(a) ##C_0+C_1+C_2+C_3##
(b) ##\dfrac{C_0+C_1+C_2+C_3}{(1+r)^3} ##
(c) ##C_0+\dfrac{C_1}{(1+r)^1} +\dfrac{C_2}{(1+r)^2} + \dfrac{C_3}{(1+r)^3} ##
(d) ##\dfrac{C_1}{(1+r)^1} +\dfrac{C_2}{(1+r)^2} + \dfrac{C_3}{(1+r)^3} ##
(e) ##\dfrac{C_1}{(1+r)^1} + \dfrac{C_2}{(1+r)^2} ##
Question 479 perpetuity with growth, DDM, NPV
Discounted cash flow (DCF) valuation prices assets by finding the present value of the asset's future cash flows. The single cash flow, annuity, and perpetuity equations are very useful for this.
Which of the following equations is the 'perpetuity with growth' equation?
(a) ##V_0=\dfrac{C_t}{(1+r)^t} ##
(b) ##V_0=\dfrac{C_1}{r}.\left(1-\dfrac{1}{(1+r)^T} \right)= \sum\limits_{t=1}^T \left( \dfrac{C_t}{(1+r)^t} \right) ##
(c) ##V_0=\dfrac{C_1}{r-g}.\left(1-\left(\dfrac{1+g}{1+r}\right)^T \right)= \sum\limits_{t=1}^T \left( \dfrac{C_t.(1+g)^t}{(1+r)^t} \right) ##
(d) ##V_0=\dfrac{C_1}{r} = \sum\limits_{t=1}^\infty \left( \dfrac{C_t}{(1+r)^t} \right) ##
(e) ##V_0=\dfrac{C_1}{r-g} = \sum\limits_{t=1}^\infty \left( \dfrac{C_t.(1+g)^t}{(1+r)^t} \right) ##
Question 517 DDM
A stock is expected to pay its next dividend of $1 in one year. Future annual dividends are expected to grow by 2% pa. So the first dividend of $1 will be in one year, the year after that $1.02 (=1*(1+0.02)^1), and a year later $1.0404 (=1*(1+0.02)^2) and so on forever.
Its required total return is 10% pa. The total required return and growth rate of dividends are given as effective annual rates.
Calculate the current stock price.
(a) $10
(b) $12.254902
(c) $12.5
(d) $12.75
(e) $13.75
A stock just paid a dividend of $1. Future annual dividends are expected to grow by 2% pa. The next dividend of $1.02 (=1*(1+0.02)^1) will be in one year, and the year after that the dividend will be $1.0404 (=1*(1+0.02)^2), and so on forever.
Question 528 DDM, income and capital returns
The perpetuity with growth formula, also known as the dividend discount model (DDM) or Gordon growth model, is appropriate for valuing a company's shares. ##P_0## is the current share price, ##C_1## is next year's expected dividend, ##r## is the total required return and ##g## is the expected growth rate of the dividend.
###P_0=\dfrac{C_1}{r-g}###
The below graph shows the expected future price path of the company's shares. Which of the following statements about the graph is NOT correct?
(a) Between points A and B, the share price is expected to grow by ##r##.
(b) Between points B and C, the share price is expected to instantaneously fall by ##C_1##.
(c) Between points A and C, the share price is expected to grow by ##g##.
(d) Between points B and D, the share price is expected to grow by ##g##.
(e) Between points D and E, the share price is expected to instantaneously fall by ##C_1.(1+r)^1##.
The following is the Dividend Discount Model (DDM) used to price stocks:
If the assumptions of the DDM hold, which one of the following statements is NOT correct? The long term expected:
(a) Dividend growth rate is equal to the long term expected growth rate of the stock price.
(b) Dividend growth rate is equal to the long term expected capital return of the stock.
(c) Dividend growth rate is equal to the long term expected dividend yield.
(d) Total return of the stock is equal to its long term required return.
(e) Total return of the stock is equal to the company's long term cost of equity.
Question 289 DDM, expected and historical returns, ROE
In the dividend discount model:
###P_0 = \dfrac{C_1}{r-g}###
The return ##r## is supposed to be the:
(a) Expected future total return of the market price of equity.
(b) Expected future total return of the book price of equity.
(c) Actual historical total return on the market price of equity.
(d) Actual historical total return on the book price of equity.
(e) Actual historical return on equity (ROE) defined as (Net Income / Owners Equity).
Question 36 DDM, perpetuity with growth
A stock pays annual dividends which are expected to continue forever. It just paid a dividend of $10. The growth rate in the dividend is 2% pa. You estimate that the stock's required return is 10% pa. Both the discount rate and growth rate are given as effective annual rates. Using the dividend discount model, what will be the share price?
(a) $127.5
(b) $125
(c) $102
(d) $101.98
(e) $100
A stock is expected to pay the following dividends:
Cash Flows of a Stock
Time (yrs) 0 1 2 3 4 ...
Dividend ($) 0.00 1.00 1.05 1.10 1.15 ...
After year 4, the annual dividend will grow in perpetuity at 5% pa, so;
the dividend at t=5 will be $1.15(1+0.05),
the dividend at t=6 will be $1.15(1+0.05)^2, and so on.
The required return on the stock is 10% pa. Both the growth rate and required return are given as effective annual rates.
What will be the price of the stock in three and a half years (t = 3.5)?
(a) $27.7567
(b) $24.1226
(c) $23.5680
(d) $22.4457
(e) $3.6341
Question 348 PE ratio, Multiples valuation
Estimate the US bank JP Morgan's share price using a price earnings (PE) multiples approach with the following assumptions and figures only:
The major US banks JP Morgan Chase (JPM), Citi Group (C) and Wells Fargo (WFC) are comparable companies;
JP Morgan Chase's historical earnings per share (EPS) is $4.37;
Citi Group's share price is $50.05 and historical EPS is $4.26;
Wells Fargo's share price is $48.98 and historical EPS is $3.89.
Note: Figures sourced from Google Finance on 24 March 2014.
A fairly valued share's current price is $4 and it has a total required return of 30%. Dividends are paid annually and next year's dividend is expected to be $1. After that, dividends are expected to grow by 5% pa in perpetuity. All rates are effective annual returns.
What is the expected dividend income paid at the end of the second year (t=2) and what is the expected capital gain from just after the first dividend (t=1) to just after the second dividend (t=2)? The answers are given in the same order, the dividend and then the capital gain.
(a) $1.3, $0.26
(b) $1.25, $0.25
(c) $1.1025, $0.2205
(d) $1.05, $0.21
(e) $1, $0.2
Question 488 income and capital returns, payout policy, payout ratio, DDM
Two companies BigDiv and ZeroDiv are exactly the same except for their dividend payouts.
BigDiv pays large dividends and ZeroDiv doesn't pay any dividends.
Currently the two firms have the same earnings, assets, number of shares, share price, expected total return and risk.
Assume a perfect world with no taxes, no transaction costs, no asymmetric information and that all assets including business projects are fairly priced and therefore zero-NPV.
All things remaining equal, which of the following statements is NOT correct?
(a) BigDiv is expected to have a lower capital return than ZeroDiv in the future.
(b) BigDiv is expected to have a lower total return than ZeroDiv in the future.
(c) ZeroDiv's assets are likely to grow faster than BigDiv's.
(d) ZeroDiv's share price will increase faster than BigDiv's.
(e) BigDiv currently has a higher payout ratio than ZeroDiv.
Question 341 Multiples valuation, PE ratio
Estimate Microsoft's (MSFT) share price using a price earnings (PE) multiples approach with the following assumptions and figures only:
Apple, Google and Microsoft are comparable companies,
Apple's (AAPL) share price is $526.24 and historical EPS is $40.32.
Google's (GOOG) share price is $1,215.65 and historical EPS is $36.23.
Micrsoft's (MSFT) historical earnings per share (EPS) is $2.71.
Source: Google Finance 28 Feb 2014.
(a) $63.15
(b) $61.67
(c) $30.83
(e) $8.60
Question 299 equivalent annual cash flow
Carlos and Edwin are brothers and they both love Holden Commodore cars.
Carlos likes to buy the latest Holden Commodore car for $40,000 every 4 years as soon as the new model is released. As soon as he buys the new car, he sells the old one on the second hand car market for $20,000. Carlos never has to bother with paying for repairs since his cars are brand new.
Edwin also likes Commodores, but prefers to buy 4-year old cars for $20,000 and keep them for 11 years until the end of their life (new ones last for 15 years in total but the 4-year old ones only last for another 11 years). Then he sells the old car for $2,000 and buys another 4-year old second hand car, and so on.
Every time Edwin buys a second hand 4 year old car he immediately has to spend $1,000 on repairs, and then $1,000 every year after that for the next 10 years. So there are 11 payments in total from when the second hand car is bought at t=0 to the last payment at t=10. One year later (t=11) the old car is at the end of its total 15 year life and can be scrapped for $2,000.
Assuming that Carlos and Edwin maintain their love of Commodores and keep up their habits of buying new ones and second hand ones respectively, how much larger is Carlos' equivalent annual cost of car ownership compared with Edwin's?
The real discount rate is 10% pa. All cash flows are real and are expected to remain constant. Inflation is forecast to be 3% pa. All rates are effective annual. Ignore capital gains tax and tax savings from depreciation since cars are tax-exempt for individuals.
(a) $13,848.99
(b) $13,106.61
(c) $8,547.50
(d) $4,238.08
(e) -$103.85
An industrial chicken farmer grows chickens for their meat. Chickens:
Cost $0.50 each to buy as chicks. They are bought on the day they're born, at t=0.
Grow at a rate of $0.70 worth of meat per chicken per week for the first 6 weeks (t=0 to t=6).
Grow at a rate of $0.40 worth of meat per chicken per week for the next 4 weeks (t=6 to t=10) since they're older and grow more slowly.
Feed costs are $0.30 per chicken per week for their whole life. Chicken feed is bought and fed to the chickens once per week at the beginning of the week. So the first amount of feed bought for a chicken at t=0 costs $0.30, and so on.
Can be slaughtered (killed for their meat) and sold at no cost at the end of the week. The price received for the chicken is their total value of meat (note that the chicken grows fast then slow, see above).
The required return of the chicken farm is 0.5% given as an effective weekly rate.
Ignore taxes and the fixed costs of the factory. Ignore the chicken's welfare and other environmental and ethical concerns.
Find the equivalent weekly cash flow of slaughtering a chicken at 6 weeks and at 10 weeks so the farmer can figure out the best time to slaughter his chickens. The choices below are given in the same order, 6 and 10 weeks.
(a) $0.3651, $0.2374
(b) $0.3172, $0.3506
(d) $0.3050, $0.2142
(e) $0.0157, $0.0491
There are many ways to write the ordinary annuity formula.
Which of the following is NOT equal to the ordinary annuity formula?
(a) ##V_0 = \dfrac{C_1}{r} \left(1-\dfrac{1}{(1+r)^T} \right) ##
(b) ##V_0 = \dfrac{C_1 \left(1-\dfrac{1}{(1+r)^T} \right)}{r}##
(c) ##V_0 = C_1\dfrac{\left(1-(1+r)^{-T} \right)}{r}##
(d) ##V_0 = C_1 \left(1-(1+r)^{-T} \right) r^{-1}##
(e) ##V_0 = C_1 \left(r^{-1}-(1+r)^{-T-1} \right)##
Question 137 NPV, Annuity
The following cash flows are expected:
10 yearly payments of $60, with the first payment in 3 years from now (first payment at t=3).
1 payment of $400 in 5 years and 6 months (t=5.5) from now.
What is the NPV of the cash flows if the discount rate is 10% given as an effective annual rate?
(a) $513.80
(b) $525.36
(c) $541.50
(e) $704.69
The first payment of a constant perpetual annual cash flow is received at time 5. Let this cash flow be ##C_5## and the required return be ##r##.
So there will be equal annual cash flows at time 5, 6, 7 and so on forever, and all of the cash flows will be equal so ##C_5 = C_6 = C_7 = ...##
When the perpetuity formula is used to value this stream of cash flows, it will give a value (V) at time:
(a) 0, so ##V_0=\dfrac{C_5}{r}##
(b) 1, so ##V_1=\dfrac{C_5}{r}##
(c) 4, so ##V_4=\dfrac{C_5}{r}##
(d) 5, so ##V_5=\dfrac{C_5}{r}##
(e) 6, so ##V_6=\dfrac{C_5}{r}##
A stock just paid its annual dividend of $9. The share price is $60. The required return of the stock is 10% pa as an effective annual rate.
What is the implied growth rate of the dividend per year?
(a) -0.8565
(b) -0.0500
(c) -0.0435
(d) 0.0000
(e) 0.1500
Question 352 income and capital returns, DDM, real estate
Two years ago Fred bought a house for $300,000.
Now it's worth $500,000, based on recent similar sales in the area.
Fred's residential property has an expected total return of 8% pa.
He rents his house out for $2,000 per month, paid in advance. Every 12 months he plans to increase the rental payments.
The present value of 12 months of rental payments is $23,173.86.
The future value of 12 months of rental payments one year ahead is $25,027.77.
What is the expected annual growth rate of the rental payments? In other words, by what percentage increase will Fred have to raise the monthly rent by each year to sustain the expected annual total return of 8%?
(a) -0.3426%
(b) 0%
(c) 0.2754%
(d) 2.9944%
(e) 3.3652%
A share just paid its semi-annual dividend of $10. The dividend is expected to grow at 2% every 6 months forever. This 2% growth rate is an effective 6 month rate. Therefore the next dividend will be $10.20 in six months. The required return of the stock 10% pa, given as an effective annual rate.
What is the price of the share now?
Question 51 DDM
A stock pays semi-annual dividends. It just paid a dividend of $10. The growth rate in the dividend is 1% every 6 months, given as an effective 6 month rate. You estimate that the stock's required return is 21% pa, as an effective annual rate.
Using the dividend discount model, what will be the share price?
Question 498 NPV, Annuity, perpetuity with growth, multi stage growth model
A business project is expected to cost $100 now (t=0), then pay $10 at the end of the third (t=3), fourth, fifth and sixth years, and then grow by 5% pa every year forever. So the cash flow will be $10.5 at the end of the seventh year (t=7), then $11.025 at the end of the eighth year (t=8) and so on perpetually. The total required return is 10℅ pa.
Which of the following formulas will NOT give the correct net present value of the project?
(a) ##-100+ \dfrac{ \dfrac{10}{0.1} \left(1-\dfrac{1}{(1+0.1)^3} \right)}{(1+0.1)^2} +\dfrac{\left(\dfrac{10}{0.1-0.05}\right)}{(1+0.1)^5} ##
(b) ##-100+ \dfrac{10}{(1+0.1)^3} +\dfrac{10}{(1+0.1)^4} +\dfrac{10}{(1+0.1)^5} +\dfrac{\left(\dfrac{10}{0.1-0.05}\right)}{(1+0.1)^5} ##
(c) ##-100+ \dfrac{ \dfrac{10}{0.1} \left(1-\dfrac{1}{(1+0.1)^4} \right)}{(1+0.1)^2} +\dfrac{\left(\dfrac{10.5}{0.1-0.05}\right)}{(1+0.1)^6} ##
(d) ##-100+ \dfrac{10}{(1+0.1)^3} +\dfrac{10}{(1+0.1)^4} +\dfrac{10}{(1+0.1)^5} +\dfrac{10}{(1+0.1)^6} +\dfrac{\left(\dfrac{10.5}{0.1-0.05}\right)}{(1+0.1)^6} ##
(e) ##-100+ \dfrac{ \dfrac{10}{0.1} \left(1-\dfrac{1}{(1+0.1)^3} \right)}{(1+0.1)^3} +\dfrac{\left(\dfrac{10}{0.1-0.05}\right)}{(1+0.1)^5} ##
Estimate the Chinese bank ICBC's share price using a backward-looking price earnings (PE) multiples approach with the following assumptions and figures only. Note that the renminbi (RMB) is the Chinese currency, also known as the yuan (CNY).
The 4 major Chinese banks ICBC, China Construction Bank (CCB), Bank of China (BOC) and Agricultural Bank of China (ABC) are comparable companies;
ICBC 's historical earnings per share (EPS) is RMB 0.74;
CCB's backward-looking PE ratio is 4.59;
BOC 's backward-looking PE ratio is 4.78;
ABC's backward-looking PE ratio is also 4.78;
Note: Figures sourced from Google Finance on 25 March 2014. Share prices are from the Shanghai stock exchange.
(a) RMB 6.4595
(b) RMB 6.3739
(c) RMB 6.3311
(d) RMB 3.4903
(e) RMB 3.3966
Which firms tend to have low forward-looking price-earnings (PE) ratios?
Only consider firms with positive earnings, disregard firms with negative earnings and therefore negative PE ratios.
(a) Illiquid small private companies.
(b) High growth technology firms.
(c) Firms expected to have temporarily low earnings over the next year, but with higher earnings later.
(d) Firms with a very low level of systematic risk.
(e) Firms whose assets include a very large proportion of cash.
Which of the following investable assets are NOT suitable for valuation using PE multiples techniques?
(a) Common equity in a listed public mining extraction company that will cease operations, wind up, and return all capital to shareholders in one year when its sole gold mine becomes depleted.
(b) Common equity in a small private owner-operated mining services company whose main asset is its sole tanker truck which delivers fuel to mines. The firm's shares are 100% owned by Bob, the driver of the tanker truck.
(c) Common equity in a large listed public company in the banking industry.
(d) Residential apartment real estate.
(e) Commercial warehouse real estate.
Which firms tend to have low forward-looking price-earnings (PE) ratios? Only consider firms with positive PE ratios.
(a) Highly liquid publically listed firms.
(b) Firms in a declining industry with very low or negative earnings growth.
(d) Firms whose returns have a very low level of systematic risk.
Question 26 APR, effective rate
A European bond paying annual coupons of 6% offers a yield of 10% pa.
Convert the yield into an effective monthly rate, an effective annual rate and an effective daily rate. Assume that there are 365 days in a year.
All answers are given in the same order:
### r_\text{eff, monthly} , r_\text{eff, yearly} , r_\text{eff, daily} ###
(a) 0.0041, 0.05, 0.0001.
(b) 0.0080, 0.1, 0.0003.
(c) 0.0083, 0.1, 0.0003.
Question 131 APR, effective rate
Calculate the effective annual rates of the following three APR's:
A credit card offering an interest rate of 18% pa, compounding monthly.
A bond offering a yield of 6% pa, compounding semi-annually.
An annual dividend-paying stock offering a return of 10% pa compounding annually.
##r_\text{credit card, eff yrly}##, ##r_\text{bond, eff yrly}##, ##r_\text{stock, eff yrly}##
(a) 0.1956, 0.0609, 0.1.
(b) 0.015, 0.09, 0.1.
(e) 6.2876, 0.1236, 0.1.
You're advising your superstar client 40-cent who is weighing up buying a private jet or a luxury yacht. 40-cent is just as happy with either, but he wants to go with the more cost-effective option. These are the cash flows of the two options:
The private jet can be bought for $6m now, which will cost $12,000 per month in fuel, piloting and airport costs, payable at the end of each month. The jet will last for 12 years.
Or the luxury yacht can be bought for $4m now, which will cost $20,000 per month in fuel, crew and berthing costs, payable at the end of each month. The yacht will last for 20 years.
What's unusual about 40-cent is that he is so famous that he will actually be able to sell his jet or yacht for the same price as it was bought since the next generation of superstar musicians will buy it from him as a status symbol.
Bank interest rates are 10% pa, given as an effective annual rate. You can assume that 40-cent will live for another 60 years and that when the jet or yacht's life is at an end, he will buy a new one with the same details as above.
Would you advise 40-cent to buy the or the ?
Note that the effective monthly rate is ##r_\text{eff monthly}=(1+0.1)^{1/12}-1=0.00797414##
Total cash flows can be broken into income and capital cash flows.
What is the name given to the cash flow generated from selling shares at a higher price than they were bought?
Question 543 price gains and returns over time, IRR, NPV, income and capital returns, effective return
For an asset price to triple every 5 years, what must be the expected future capital return, given as an effective annual rate?
(a) 0.6
(b) 0.319508
(c) 0.269705
(d) 0.245731
(e) 0.219755
Question 363 income and capital returns, inflation, real and nominal returns and cash flows, real estate
A residential investment property has an expected nominal total return of 8% pa and nominal capital return of 3% pa.
Inflation is expected to be 2% pa. All rates are given as effective annual rates.
What are the property's expected real total, capital and income returns? The answer choices below are given in the same order.
(a) 5.8824%, 0.9804%, 4.902%.
(b) 5.8824%, 0.9804%, 2.9412%.
(c) 4.0000%, 1.0000%, 3.0000%.
(d) 3.9412%, 1.0000%, 2.9412%.
(e) 3.9216%, 0.9804%, 2.9412%.
Question 526 real and nominal returns and cash flows, inflation, no explanation
How can a nominal cash flow be precisely converted into a real cash flow?
(a) ##C_\text{real, t}=C_\text{nominal,t}.(1+r_\text{inflation})^t##
(b) ##C_\text{real,t}=\dfrac{C_\text{nominal,t}}{(1+r_\text{inflation})^t} ##
(c) ##C_\text{real,t}=\dfrac{C_\text{nominal,t}}{r_\text{inflation}} ##
(d) ##C_\text{real,t}=C_\text{nominal,t}.r_\text{inflation} ##
(e) ##C_\text{real,t}=C_\text{nominal,t}.r_\text{inflation}.t##
What is the present value of a real payment of $500 in 2 years? The nominal discount rate is 7% pa and the inflation rate is 4% pa.
(a) $472.3557
(b) $471.298
(c) $436.7194
(d) $435.7415
(e) $405.8112
On his 20th birthday, a man makes a resolution. He will put $30 cash under his bed at the end of every month starting from today. His birthday today is the first day of the month. So the first addition to his cash stash will be in one month. He will write in his will that when he dies the cash under the bed should be given to charity.
If the man lives for another 60 years, how much money will be under his bed if he dies just after making his last (720th) addition?
Also, what will be the real value of that cash in today's prices if inflation is expected to 2.5% pa? Assume that the inflation rate is an effective annual rate and is not expected to change.
The answers are given in the same order, the amount of money under his bed in 60 years, and the real value of that money in today's prices.
(a) $21,600, $95,035.46
(b) $21,600, $49,515.44
(c) $21,600, $4,909.33
(d) $21,600, $2,557.86
(e) $11,254.05, $2,557.86
Apples and oranges currently cost $1 each. Inflation is 5% pa, and apples and oranges are equally affected by this inflation rate. Note that when payments are not specified as real, as in this question, they're conventionally assumed to be nominal.
Which of the following statements is NOT correct?
(a) A payment of $105 now has a real value of 105 apples or oranges now.
(b) A payment of $1 now has a real value of one apple or orange now.
(c) A payment of $105 in one year has a real value of 100 apples or oranges in one year.
(d) A payment of $105 in one year is worth $105 in real terms today.
(e) A payment of one apple now has a real value of one orange now.
What is the present value of a nominal payment of $100 in 5 years? The real discount rate is 10% pa and the inflation rate is 3% pa.
(d) $54.276
(e) $53.5612
What is the present value of a nominal payment of $1,000 in 4 years? The nominal discount rate is 8% pa and the inflation rate is 2% pa.
(b) $792.0937
Which of the following statements about inflation is NOT correct?
(a) Real returns approximately equal nominal returns less the inflation rate.
(b) Constant prices are the same as real prices.
(c) Current prices are the same as nominal prices.
(d) If your nominal wage grows by inflation, then your real wage won't change because you will be able to buy the same amount of goods and services as before.
(e) Interest rates advertised at the bank are usually quoted in real terms.
Question 466 limited liability, business structure
Which business structure or structures have the advantage of limited liability for equity investors?
(a) Sole traders.
(b) Partnerships.
(c) Corporations.
(d) All of the above.
(e) None of the above
Question 531 bankruptcy or insolvency, capital structure, risk, limited liability
Who is most in danger of being personally bankrupt? Assume that all of their businesses' assets are highly liquid and can therefore be sold immediately.
(a) Alice has $6,000 cash, owes $10,000 credit card debt due immediately and 100% owns a sole tradership business with assets worth $10,000 and liabilities of $3,000.
(b) Billy has $10,000 cash, owes $6,000 credit card debt due immediately and 100% owns a corporate business with assets worth $3,000 and liabilities of $10,000.
(c) Carla has $6,000 cash, owes $10,000 credit card debt due immediately and 100% owns a corporate business with assets worth $10,000 and liabilities of $3,000.
(d) Darren has $10,000 cash, owes $6,000 credit card debt due immediately and 100% owns a sole tradership business with assets worth $3,000 and liabilities of $10,000.
(e) Ernie has $1,000 cash, lent $3,000 to his friend, and doesn't have any personal debt or own any businesses.
Question 618 capital structure, no explanation
Who owns a company's shares? The:
(a) Company.
(b) Debt holders.
(c) Equity holders.
(d) Chief Executive Officer (CEO).
(e) Board of directors.
Question 452 limited liability, expected and historical returns
What is the lowest and highest expected share price and expected return from owning shares in a company over a finite period of time?
Let the current share price be ##p_0##, the expected future share price be ##p_1##, the expected future dividend be ##d_1## and the expected return be ##r##. Define the expected return as:
##r=\dfrac{p_1-p_0+d_1}{p_0} ##
The answer choices are stated using inequalities. As an example, the first answer choice "(a) ##0≤p<∞## and ##0≤r< 1##", states that the share price must be larger than or equal to zero and less than positive infinity, and that the return must be larger than or equal to zero and less than one.
(a) ##0≤p<∞## and ##0≤r< 1##
(b) ##0≤p<∞## and ##-1≤r< ∞##
(c) ##0≤p<∞## and ##0≤r< ∞##
(d) ##0≤p<∞## and ##-∞≤r< ∞##
(e) ##-∞<p<∞## and ##-∞<r< ∞##
Question 445 financing decision, corporate financial decision theory
The financing decision primarily affects which part of a business?
(a) Assets.
(b) Liabilities and owner's equity.
(c) Current assets and current liabilities.
(d) Dividends and buy backs.
(e) Net income, also known as earnings or net profit after tax.
Question 447 payout policy, corporate financial decision theory
Payout policy is most closely related to which part of a business?
Question 443 corporate financial decision theory, investment decision, financing decision, working capital decision, payout policy
Business people make lots of important decisions. Which of the following is the most important long term decision?
(a) Investment decision.
(b) Financing decision.
(c) Working capital decision.
(d) Payout policy decision.
(e) Capital or labour decision.
Question 515 corporate financial decision theory, idiom
The expression 'you have to spend money to make money' relates to which business decision?
(e) Diversification decision.
Question 516 corporate financial decision theory
Which of the following decisions relates to the current assets and current liabilities of the firm?
Question 467 book and market values
Which of the following statements about book and market equity is NOT correct?
(a) The market value of equity of a listed company's common stock is equal to the number of common shares multiplied by the share price.
(b) The book value of equity is the sum of contributed equity, retained profits and reserves.
(c) A company's book value of equity is recorded in its income statement, also known as the 'profit and loss' or the 'statement of financial performance'.
(d) A new company's market value of equity equals its book value of equity the moment that its shares are first sold. From then on, the market value changes continuously but the book value which is recorded at historical cost tends to only change due to retained profits.
(e) To buy all of the firm's shares, generally a price close to the market value of equity will have to be paid.
Question 482 market capitalisation of equity
The below screenshot of Microsoft's (MSFT) details were taken from the Google Finance website on 28 Nov 2014. Some information has been deliberately blanked out.
What was MSFT's market capitalisation of equity?
(a) $395.11 million
(b) $21.01 billion
(c) $121.92 billion
(d) $393.95 billion
(e) $1.02935 trillion
Question 44 NPV
The required return of a project is 10%, given as an effective annual rate. Assume that the cash flows shown in the table are paid all at once at the given point in time.
What is the Net Present Value (NPV) of the project?
Project Cash Flows
Time (yrs) Cash flow ($)
0 -100
(a) -100
(b) 0
(c) 10
(d) 21
(e) 121
Question 37 IRR
If a project's net present value (NPV) is zero, then its internal rate of return (IRR) will be:
(a) Positive infinity (##+\infty##)
(b) Zero (0).
(c) Less than the project's required return.
(d) More than the project's required return.
(e) Equal to the project's required return.
Question 182 NPV, IRR, pay back period
A project's NPV is positive. Select the most correct statement:
(a) The project should be rejected.
(b) The project's IRR is more than its required return.
(c) The project's IRR is less than its required return.
(d) The project's IRR is equal to its required return.
(e) The project will never pay itself off, assuming that the discount rate is positive.
Question 500 NPV, IRR
The below graph shows a project's net present value (NPV) against its annual discount rate.
For what discount rate or range of discount rates would you accept and commence the project?
All answer choices are given as approximations from reading off the graph.
(a) From 0 to 10% pa.
(b) From 0 to 5% pa.
(c) At 5.5% pa.
(d) From 6 to 20% pa.
(e) From 0 to 20% pa.
(a) When the project's discount rate is 18% pa, the NPV is approximately -$30m.
(b) The payback period is infinite, the project never pays itself off.
(c) The addition of the project's cash flows, ignoring the time value of money, is approximately $20m.
(d) The project's IRR is approximately 5.5% pa.
(e) As the discount rate rises, the NPV falls.
Question 489 NPV, IRR, pay back period, DDM
A firm is considering a business project which costs $11m now and is expected to pay a constant $1m at the end of every year forever.
Assume that the initial $11m cost is funded using the firm's existing cash so no new equity or debt will be raised. The cost of capital is 10% pa.
Which of the following statements about net present value (NPV), internal rate of return (IRR) and payback period is NOT correct?
(a) The NPV is negative $1m.
(b) The IRR is 9.09% pa, less than the 10% cost of capital.
(c) The payback period is infinite, the project will never pay itself off.
(d) The project should be rejected.
(e) If the project is accepted then the market value of the firm's assets will fall by $1m.
Question 128 debt terminology, needs refinement
An 'interest payment' is the same thing as a 'coupon payment'. or ?
Question 129 debt terminology
An 'interest rate' is the same thing as a 'coupon rate'. or ?
An 'interest rate' is the same thing as a 'yield'. or ?
Which of the following statements is NOT equivalent to the yield on debt?
Assume that the debt being referred to is fairly priced, but do not assume that it's priced at par.
(a) Debt coupon rate.
(b) Required return on debt.
(c) Total return on debt.
(d) Opportunity cost of debt.
(e) Cost of debt capital.
Which of the following statements is NOT correct? Borrowers:
(a) Receive cash at the start and promise to pay cash in the future, as set out in the debt contract.
(b) Are debtors.
(c) Owe money.
(d) Are funded by debt.
(e) Buy debt.
Which of the following statements is NOT correct? Lenders:
(a) Are long debt.
(b) Invest in debt.
(c) Are owed money.
(d) Provide debt funding.
(e) Have debt liabilities.
Question 87 fully amortising loan, APR
You want to buy an apartment worth $500,000. You have saved a deposit of $50,000. The bank has agreed to lend you the $450,000 as a fully amortising mortgage loan with a term of 25 years. The interest rate is 6% pa and is not expected to change.
What will be your monthly payments?
(a) 1,500.00
(b) 2,250.00
(c) 2,855.79
(d) 2,899.36
(e) 35,202.02
Question 134 fully amortising loan, APR
You want to buy an apartment worth $400,000. You have saved a deposit of $80,000. The bank has agreed to lend you the $320,000 as a fully amortising mortgage loan with a term of 30 years. The interest rate is 6% pa and is not expected to change. What will be your monthly payments?
(b) $1,600.00
(e) $23,247.65
You want to buy an apartment priced at $500,000. You have saved a deposit of $50,000. The bank has agreed to lend you the $450,000 as a fully amortising loan with a term of 30 years. The interest rate is 6% pa and is not expected to change. What will be your monthly payments?
(e) $1,250.00
You just signed up for a 30 year fully amortising mortgage with monthly payments of $1,000 per month. The interest rate is 6% pa which is not expected to change.
How much did you borrow? After 20 years, how much will be owing on the mortgage? The interest rate is still 6% and is not expected to change.
(a) 169,672.58, 90,724.32
(b) 166,791.61, 90,073.45
(c) 166,791.61, 139,580.77
(d) 165,177.97, 88,321.04
(e) 165,177.97, 137,639.05
You just signed up for a 30 year fully amortising mortgage loan with monthly payments of $1,500 per month. The interest rate is 9% pa which is not expected to change.
(a) 184,925.77, 164,313.82
(b) 184,925.77, 115,517.84
(d) 186,422.80, 118,412.54
You just agreed to a 30 year fully amortising mortgage loan with monthly payments of $2,500. The interest rate is 9% pa which is not expected to change.
How much did you borrow? After 10 years, how much will be owing on the mortgage? The interest rate is still 9% and is not expected to change. The below choices are given in the same order.
(a) $320,725.47, $284,977.19
(b) $310,704.66, $277,862.39
(c) $310,704.66, $197,354.23
(d) $308,209.62, $273,856.37
(e) $308,209.62, $192,529.73
You want to buy a house priced at $400,000. You have saved a deposit of $40,000. The bank has agreed to lend you $360,000 as a fully amortising loan with a term of 30 years. The interest rate is 8% pa payable monthly and is not expected to change.
(a) $1,000
(b) $1,106.6497
(c) $2,400
(d) $2,571.8327
(e) $2,641.5525
Question 29 interest only loan
You want to buy an apartment priced at $300,000. You have saved a deposit of $30,000. The bank has agreed to lend you the $270,000 as an interest only loan with a term of 25 years. The interest rate is 12% pa and is not expected to change.
What will be your monthly payments? Remember that mortgage payments are paid in arrears (at the end of the month).
(b) 2,700
(c) 2,722.1
You just signed up for a 30 year interest-only mortgage with monthly payments of $3,000 per month. The interest rate is 6% pa which is not expected to change.
How much did you borrow? After 15 years, just after the 180th payment at that time, how much will be owing on the mortgage? The interest rate is still 6% and is not expected to change. Remember that the mortgage is interest-only and that mortgage payments are paid in arrears (at the end of the month).
Question 107 interest only loan
You want to buy an apartment worth $300,000. You have saved a deposit of $60,000.
The bank has agreed to lend you $240,000 as an interest only mortgage loan with a term of 30 years. The interest rate is 6% pa and is not expected to change. What will be your monthly payments?
(a) 17,435.74
(e) 666.67
You want to buy an apartment priced at $500,000. You have saved a deposit of $50,000. The bank has agreed to lend you the $450,000 as an interest only loan with a term of 30 years. The interest rate is 6% pa and is not expected to change. What will be your monthly payments?
(a) $ 1,250.00
(b) $ 2,250.00
(c) $ 2,652.17
(d) $ 2,697.98
(e) $ 32,692.01
A prospective home buyer can afford to pay $2,000 per month in mortgage loan repayments. The central bank recently lowered its policy rate by 0.25%, and residential home lenders cut their mortgage loan rates from 4.74% to 4.49%.
How much more can the prospective home buyer borrow now that interest rates are 4.49% rather than 4.74%? Give your answer as a proportional increase over the original amount he could borrow (##V_\text{before}##), so:
###\text{Proportional increase} = \frac{V_\text{after}-V_\text{before}}{V_\text{before}} ###
Interest rates are expected to be constant over the life of the loan.
Loans are interest-only and have a life of 30 years.
Mortgage loan payments are made every month in arrears and all interest rates are given as annualised percentage rates compounding per month.
(a) 0.055679
Question 179 bond pricing, capital raising
A firm wishes to raise $20 million now. They will issue 8% pa semi-annual coupon bonds that will mature in 5 years and have a face value of $100 each. Bond yields are 6% pa, given as an APR compounding every 6 months, and the yield curve is flat.
How many bonds should the firm issue?
(a) 140,202
(b) 184,280
(c) 184,460
(d) 186,881
(e) 200,000
Question 183 bond pricing
A five year bond has a face value of $100, a yield of 12% and a fixed coupon rate of 6%, paid semi-annually.
What is the bond's price?
(a) 36.2655
(b) 55.8395
(c) 59.3381
(d) 77.9197
(e) 87.3629
Question 193 bond pricing, premium par and discount bonds
Which one of the following bonds is trading at par?
(a) a ten-year bond with a $4000 face value whose yield to maturity is 6.0% and coupon rate is 6.5% paid semi-annually.
(b) a 6-year bond with a principal of $40,000 and a price of $45,000.
(c) a 15-year bond with a $10,000 face value whose yield to maturity is 8.0% and coupon rate is 10.0% paid semi-annually.
(d) a two-year bond with a $50,000 face value whose yield to maturity is 5.2% compounding semi-annually which has a price of $50,000.
(e) None of the above bonds are trading at par.
A firm wishes to raise $8 million now. They will issue 7% pa semi-annual coupon bonds that will mature in 10 years and have a face value of $100 each. Bond yields are 10% pa, given as an APR compounding every 6 months, and the yield curve is flat.
(b) 98,393
(c) 90,480
(d) 80,000
(e) 64,039
Which one of the following bonds is trading at a premium?
(a) a ten-year bond with a $4,000 face value whose yield to maturity is 6.0% and coupon rate is 5.9% paid semi-annually.
(b) a fifteen-year bond with a $10,000 face value whose yield to maturity is 8.0% and coupon rate is 7.8% paid semi-annually.
(c) a five-year bond with a $2,000 face value whose yield to maturity is 7.0% and coupon rate is 7.2% paid semi-annually.
(d) a two-year bond with a $50,000 face value whose yield to maturity is 5.2% and coupon rate is 5.2% paid semi-annually.
(e) None of the above bonds are premium bonds.
An investor bought two fixed-coupon bonds issued by the same company, a zero-coupon bond and a 7% pa semi-annual coupon bond. Both bonds have a face value of $1,000, mature in 10 years, and had a yield at the time of purchase of 8% pa.
A few years later, yields fell to 6% pa. Which of the following statements is correct? Note that a capital gain is an increase in price.
(a) The zero-coupon bond and the 7% semi-annual coupon bond were both discount bonds but now they are both premium bonds.
(b) The zero-coupon bond and the 7% semi-annual coupon bond were both premium bonds but now they are both discount bonds.
(c) When yields fell, the investor made a capital loss on both bonds.
(d) When yields fell, the investor made a capital gain on both bonds.
(e) When yields fell, the investor made a capital gain on the zero coupon bond but a loss on the 7% semi-annual coupon bond.
A firm wishes to raise $10 million now. They will issue 6% pa semi-annual coupon bonds that will mature in 8 years and have a face value of $1,000 each. Bond yields are 10% pa, given as an APR compounding every 6 months, and the yield curve is flat.
(a) 9,022.2 bonds
(b) 10,000.0 bonds
(c) 11,484.5 bonds
(d) 12,712.9 bonds
(e) 12,767.4 bonds
A 10 year bond has a face value of $100, a yield of 6% pa and a fixed coupon rate of 8% pa, paid semi-annually. What is its price?
(d) $126.628
Bonds X and Y are issued by the same US company. Both bonds yield 6% pa, and they have the same face value ($100), maturity, seniority, and payment frequency.
The only difference is that bond X pays coupons of 8% pa and bond Y pays coupons of 12% pa. Which of the following statements is true?
(a) Bonds X and Y are premium bonds.
(b) Bonds X and Y are discount bonds.
(c) Bond X is a discount bond but bond Y is a premium bond.
(d) Bond X is a premium bond but bond Y is a discount bond.
(e) Bonds X and Y are par bonds.
Below are some statements about loans and bonds. The first descriptive sentence is correct. But one of the second sentences about the loans' or bonds' prices is not correct. Which statement is NOT correct? Assume that interest rates are positive.
Note that coupons or interest payments are the periodic payments made throughout a bond or loan's life. The face or par value of a bond or loan is the amount paid at the end when the debt matures.
(a) A bullet loan has no interest payments but it does have a face value. Therefore it's a discount loan.
(b) A fully amortising loan has interest payments but does not have a face value. Therefore it's a premium loan.
(c) An interest only loan has interest payments and its price and face value are equal. Therefore it's a par loan.
(d) A zero coupon bond has no coupon payments but it does have a face value. Therefore it's a premium bond.
(e) A balloon loan has interest payments and its face value is more than its price. Therefore it's a discount loan.
Question 143 bond pricing, zero coupon bond, term structure of interest rates, forward interest rate
An Australian company just issued two bonds:
A 6-month zero coupon bond at a yield of 6% pa, and
A 12 month zero coupon bond at a yield of 7% pa.
What is the company's forward rate from 6 to 12 months? Give your answer as an APR compounding every 6 months, which is how the above bond yields are quoted.
(a) 0.0400
(b) 0.0500
(c) 0.0660
Question 35 bond pricing, zero coupon bond, term structure of interest rates, forward interest rate
A European company just issued two bonds, a
1 year zero coupon bond at a yield of 8% pa, and a
2 year zero coupon bond at a yield of 10% pa.
What is the company's forward rate over the second year (from t=1 to t=2)? Give your answer as an effective annual rate, which is how the above bond yields are quoted.
Question 620 bond pricing, income and capital returns
Let the 'income return' of a bond be the coupon at the end of the period divided by the market price now at the start of the period ##(C_1/P_0)##. The expected income return of a premium fixed coupon bond is:
(a) Less than its expected total return.
(b) Equal to its expected total return.
(c) More than its expected total return.
(d) More than its coupon rate.
(e) Equal to its coupon rate.
Question 254 time calculation, APR
Your main expense is fuel for your car which costs $100 per month. You just refueled, so you won't need any more fuel for another month (first payment at t=1 month).
You have $2,500 in a bank account which pays interest at a rate of 6% pa, payable monthly. Interest rates are not expected to change.
Assuming that you have no income, in how many months time will you not have enough money to fully refuel your car?
(a) In 23 months (t=23 months).
(b) In 24 months (t=24 months).
(c) In 25 months (t=25 months).
(d) In 26 months (t=26 months).
(e) In 27 months (t=27 months).
Question 548 equivalent annual cash flow, time calculation, no explanation
An Apple iPhone 6 smart phone can be bought now for $999. An Android Kogan Agora 4G+ smart phone can be bought now for $240.
If the Kogan phone lasts for one year, approximately how long must the Apple phone last for to have the same equivalent annual cost?
Assume that both phones have equivalent features besides their lifetimes, that both are worthless once they've outlasted their life, the discount rate is 10% pa given as an effective annual rate, and there are no extra costs or benefits from either phone.
(a) 11 years
(b) 9 years
(c) 7 years
(d) 5 years
(e) 3 years
Question 27 bill pricing, simple interest rate
A 180-day Bank Accepted Bill has a face value of $1,000,000. The interest rate is 8% pa and there are 365 days in the year. What is its price now?
(a) $15,400,000.00
(b) $8,371,559.63
(c) $962,757.81
(d) $962,045.33
Question 327 bill pricing, simple interest rate, no explanation
On 27/09/13, three month Swiss government bills traded at a yield of -0.2%, given as a simple annual yield. That is, interest rates were negative.
If the face value of one of these 90 day bills is CHF1,000,000 (CHF represents Swiss Francs, the Swiss currency), what is the price of one of these bills?
(a) CHF 999,507.09
(b) CHF 1,000,000.00
(c) CHF 1,000,493.39
(d) CHF 1,002,004.01
(e) CHF 1,002,498.39
Question 582 APR, effective rate, effective rate conversion
A credit card company advertises an interest rate of 18% pa, payable monthly. Which of the following statements about the interest rate is NOT correct? All rates are given to four decimal places.
(a) The APR compounding monthly is 18.0000% per annum.
(b) The effective monthly rate is 1.5000% per month.
(c) The effective annual rate is 19.5618% per annum.
(d) The effective quarterly rate is 4.5678% per quarter.
(e) The APR compounding quarterly is 13.7035% per annum.
Question 64 inflation, real and nominal returns and cash flows, APR, effective rate
In Germany, nominal yields on semi-annual coupon paying Government Bonds with 2 years until maturity are currently 0.04% pa.
The inflation rate is currently 1.4% pa, given as an APR compounding per quarter. The inflation rate is not expected to change over the next 2 years.
What is the real yield on these bonds, given as an APR compounding every 6 months?
(a) -1.3529627%
(b) -0.4977348%
(c) 0.4977348%
(d) 1.3529627%
(e) 1.3621776%
What is the company's forward rate over the third year (from t=2 to t=3)? Give your answer as an effective annual rate, which is how the above bond yields are quoted.
Question 267 term structure of interest rates
4 year zero coupon bond at a yield of 6.5% pa.
What is the company's forward rate over the fourth year (from t=3 to t=4)? Give your answer as an effective annual rate, which is how the above bond yields are quoted.
(d) 0.07
A 1 year zero coupon bond at a yield of 10% pa, and
A 2 year zero coupon bond at a yield of 8% pa.
What is the forward rate on the company's debt from years 1 to 2? Give your answer as an APR compounding every 6 months, which is how the above bond yields are quoted.
Question 572 bond pricing, zero coupon bond, term structure of interest rates, expectations hypothesis, forward interest rate, yield curve
In the below term structure of interest rates equation, all rates are effective annual yields and the numbers in subscript represent the years that the yields are measured over:
###(1+r_{0-3})^3 = (1+r_{0-1})(1+r_{1-2})(1+r_{2-3}) ###
(a) ##r_{0-3}## is the three year spot rate, given as an effective annual rate.
(b) ##r_{0-1}## is the one year forward rate, given as an effective annual rate.
(c) ##r_{1-2}## is the one year forward rate one year ahead, given as an effective annual rate.
(d) ##r_{2-3}## is the one year forward rate two years ahead, given as an effective annual rate.
(e) ##r_{1-3} = \left((1+r_{1-2})(1+r_{2-3})\right)^{1/2}-1## is the two year forward rate, one year ahead, given as an effective annual rate.
You deposit cash into your bank account. Have you or debt?
You deposit cash into your bank account. Does the deposit account represent a debt or to you?
You owe money. Are you a or a ?
You are owed money. Are you a or a ?
You own a debt asset. Are you a or a ?
You buy a house funded using a home loan. Have you or debt?
Which of the following statements is NOT correct? Bond investors:
(a) Buy debt.
(c) Have debt assets.
(e) Are lenders.
Calculate the price of a newly issued ten year bond with a face value of $100, a yield of 8% pa and a fixed coupon rate of 6% pa, paid semi-annually. So there are two coupons per year, paid in arrears every six months.
Question 11 bond pricing
For a price of $100, Vera will sell you a 2 year bond paying semi-annual coupons of 10% pa. The face value of the bond is $100. Other bonds with similar risk, maturity and coupon characteristics trade at a yield of 8% pa.
Would you like to her bond or politely ?
For a price of $95, Nicole will sell you a 10 year bond paying semi-annual coupons of 8% pa. The face value of the bond is $100. Other bonds with the same risk, maturity and coupon characteristics trade at a yield of 8% pa.
Would you like to the bond or politely ?
Question 23 bond pricing, premium par and discount bonds
Bonds X and Y are issued by the same US company. Both bonds yield 10% pa, and they have the same face value ($100), maturity, seniority, and payment frequency.
The only difference is that bond X and Y's coupon rates are 8 and 12% pa respectively. Which of the following statements is true?
Bonds A and B are issued by the same company. They have the same face value, maturity, seniority and coupon payment frequency. The only difference is that bond A has a 5% coupon rate, while bond B has a 10% coupon rate. The yield curve is flat, which means that yields are expected to stay the same.
Which bond would have the higher current price?
(a) Bond A will have a higher price.
(b) Bond B will have a higher price.
(c) Bonds A and B will have the same price.
(d) The higher priced bond can't be determined without knowing their yields.
(e) The higher priced bond can't be determined without knowing the inflation rate.
Question 48 IRR, NPV, bond pricing, premium par and discount bonds, market efficiency
The theory of fixed interest bond pricing is an application of the theory of Net Present Value (NPV). Also, a 'fairly priced' asset is not over- or under-priced. Buying or selling a fairly priced asset has an NPV of zero.
Considering this, which of the following statements is NOT correct?
(a) The internal rate of return (IRR) of buying a fairly priced bond is equal to the bond's yield.
(b) The Present Value of a fairly priced bond's coupons and face value is equal to its price.
(c) If a fairly priced bond's required return rises, its price will fall.
(d) Fairly priced premium bonds' yields are less than their coupon rates, prices are more than their face values, and the NPV of buying them is therefore positive.
(e) The NPV of buying a fairly priced bond is zero.
A two year Government bond has a face value of $100, a yield of 2.5% pa and a fixed coupon rate of 0.5% pa, paid semi-annually. What is its price?
(e) 103.9751
Question 56 income and capital returns, bond pricing, premium par and discount bonds
Which of the following statements about risk free government bonds is NOT correct?
(a) Premium bonds have a positive expected capital return.
(b) Discount bonds have a positive expected capital return.
(c) Par bonds have a zero expected capital return.
(d) Par bonds have a total expected yield equal to their coupon yield.
(e) Zero coupon bonds selling at par would have zero expected total, income and capital yields.
Hint: Total return can be broken into income and capital returns as follows:
###\begin{aligned} r_\text{total} &= \frac{c_1}{p_0} + \frac{p_1-p_0}{p_0} \\ &= r_\text{income} + r_\text{capital} \end{aligned} ###
The capital return is the growth rate of the price.
The income return is the periodic cash flow. For a bond this is the coupon payment.
Question 63 bond pricing, NPV, market efficiency
(a) The internal rate of return (IRR) of buying a bond is equal to the bond's yield.
(c) If the required return of a bond falls, its price will fall.
(d) Fairly priced discount bonds' yield is more than the coupon rate, price is less than face value, and the NPV of buying them is zero.
A bond maturing in 10 years has a coupon rate of 4% pa, paid semi-annually. The bond's yield is currently 6% pa. The face value of the bond is $100. What is its price?
Bonds A and B are issued by the same Australian company. Both bonds yield 7% pa, and they have the same face value ($100), maturity, seniority, and payment frequency.
The only difference is that bond A pays coupons of 10% pa and bond B pays coupons of 5% pa. Which of the following statements is true about the bonds' prices?
(a) The prices of bonds A and B will be more than $100.
(b) The prices of bonds A and B will be less than $100.
(c) Bond A will have a price more than $100, and bond B will have a price less than $100.
(d) Bond A will have a price less than $100, and bond B will have a price more than $100.
(e) Bonds A and B will both have a price of $100.
Bonds X and Y are issued by different companies, but they both pay a semi-annual coupon of 10% pa and they have the same face value ($100) and maturity (3 years).
The only difference is that bond X and Y's yields are 8 and 12% pa respectively. Which of the following statements is true?
(e) Bonds X and Y have the same price.
Bonds X and Y are issued by different companies, but they both pay a semi-annual coupon of 10% pa and they have the same face value ($100), maturity (3 years) and yield (10%) as each other.
A four year bond has a face value of $100, a yield of 6% and a fixed coupon rate of 12%, paid semi-annually. What is its price?
(d) 111.1513
Question 403 PE ratio, no explanation
Which of the following investable assets is the LEAST suitable for valuation using PE multiples techniques?
(a) Common equity in a small private company.
(b) Common equity in a listed public company.
(c) Commercial real estate.
(d) Ten year commercial real estate lease.
(e) Residential real estate.
Question 414 PE ratio, pay back period, no explanation
A mature firm has constant expected future earnings and dividends. Both amounts are equal. So earnings and dividends are expected to be equal and unchanging.
(a) This firm's expected capital return equals zero.
(b) This firm's expected total return and income return are equal.
(c) This firm's forward looking PE ratio will equal the inverse of the firm's expected income return.
(d) This firm's forward looking PE ratio will equal the inverse of the firm's expected capital return.
(e) This firm's forward looking PE ratio is equal to the expected payback period, which is the time it will take for the sum of the cash flows to equal the share price.
Question 474 PE ratio
The below screenshot of Commonwealth Bank of Australia's (CBA) details were taken from the Google Finance website on 7 Nov 2014. Some information has been deliberately blanked out.
What was CBA's backwards-looking price-earnings ratio?
(a)17.06
(b) 0.063
(c) 15.88
(e) 8.44
A firm has 1 million shares which trade at a price of $30 each. The firm is expected to announce earnings of $3 million at the end of the year and pay an annual dividend of $1.50 per share.
What is the firm's (forward looking) price/earnings (PE) ratio?
(a) 20
(b) 10
(c) 3
(d) 2
(e) 0.5
What was MSFT's backwards-looking price-earnings ratio?
(b) 21.01
(d) 18.75
(e) 18.75%
A firm has 2m shares and a market capitalisation of equity of $30m. The firm just announced earnings of $5m and paid an annual dividend of $0.75 per share.
What is the firm's (backward looking) price/earnings (PE) ratio?
(e) 20
Question 537 PE ratio, Multiples valuation, no explanation
Estimate the French bank Societe Generale's share price using a backward-looking price earnings (PE) multiples approach with the following assumptions and figures only. Note that EUR is the euro, the European monetary union's currency.
The 4 major European banks Credit Agricole (ACA), Deutsche Bank AG (DBK), UniCredit (UCG) and Banco Santander (SAN) are comparable companies to Societe Generale (GLE);
Societe Generale's (GLE's) historical earnings per share (EPS) is EUR 2.92;
ACA's backward-looking PE ratio is 16.29 and historical EPS is EUR 0.84;
DBK's backward-looking PE ratio is 25.01 and historical EPS is EUR 1.26;
SAN's backward-looking PE ratio is 14.71 and historical EPS is EUR 0.47;
UCG's backward-looking PE ratio is 15.78 and historical EPS is EUR 0.40;
(a) EUR 209.6268
(b) EUR 52.4067
(c) EUR 8.6724
(d) EUR 3.9327
(e) EUR 2.1681
Question 165 DDM, PE ratio, payout ratio
For certain shares, the forward-looking Price-Earnings Ratio (##P_0/EPS_1##) is equal to the inverse of the share's total expected return (##1/r_\text{total}##).
For what shares is this true?
Assume:
The general accounting definition of 'payout ratio' which is dividends per share (DPS) divided by earnings per share (EPS).
All cash flows, earnings and rates are real.
(a) Shares of companies with a 100% payout ratio and high expected growth in earnings and dividends.
(b) Shares of companies with a 100% payout ratio and negative expected growth in earnings and dividends.
(c) Shares of companies with a 100% payout ratio and no expected growth in earnings or dividends.
(d) Shares of companies with a 0% payout ratio and no expected growth in earnings or dividends.
(e) Shares of companies with a 0% payout ratio and negative expected growth in earnings and dividends.
Question 376 leverage, capital structure, no explanation
Interest expense on debt is tax-deductible, but dividend payments on equity are not. or ?
Question 377 leverage, capital structure
Issuing debt doesn't give away control of the firm because debt holders can't cast votes to determine the company's affairs, such as at the annual general meeting (AGM), and can't appoint directors to the board. or ?
Question 379 leverage, capital structure, payout policy
Companies must pay interest and principal payments to debt-holders. They're compulsory. But companies are not forced to pay dividends to share holders. or ?
Question 121 capital structure, leverage, financial distress, interest tax shield
Fill in the missing words in the following sentence:
All things remaining equal, as a firm's amount of debt funding falls, benefits of interest tax shields __________ and the costs of financial distress __________.
(a) Fall, fall.
(b) Fall, rises.
(c) Rise, fall.
(d) Rise, rise.
(e) Remain unchanged, remain unchanged.
Question 238 CFFA, leverage, interest tax shield
A company increases the proportion of debt funding it uses to finance its assets by issuing bonds and using the cash to repurchase stock, leaving assets unchanged.
Ignoring the costs of financial distress, which of the following statements is NOT correct:
(a) The company is increasing its debt-to-assets and debt-to-equity ratios. These are types of 'leverage' or 'gearing' ratios.
(b) The company will pay less tax to the government due to the benefit of interest tax shields.
(c) The company's net income, also known as earnings or net profit after tax, will fall.
(d) The company's expected levered firm free cash flow (FFCF or CFFA) will be higher due to tax shields.
(e) The company's expected levered equity free cash flow (EFCF) will not change.
Question 536 idiom, bond pricing, capital structure, leverage
The expression 'my word is my bond' is often used in everyday language to make a serious promise.
Why do you think this expression uses the metaphor of a bond rather than a share?
(a) Because bonds are higher risk investments than shares.
(b) Because issuers must pay bond holders or face bankruptcy, while payments on shares are discretionary.
(c) Because bonds are paid last in the event of bankruptcy, while shares are paid first.
(d) Because bonds always pay higher returns than shares.
(e) Because bonds are generally more liquid than shares.
Question 663 leverage, accounting ratio, no explanation
A firm has a debt-to-assets ratio of 20%. What is its debt-to-equity ratio?
(a) 20%
(b) 25%
(c) 60%
(d) 75%
(e) 80%
Question 507 leverage, accounting ratio
A firm has a debt-to-equity ratio of 60%. What is its debt-to-assets ratio?
(c) 37.5%
(e) 6.25%
Question 241 Miller and Modigliani, leverage, payout policy, diversification, NPV
One of Miller and Modigliani's (M&M's) important insights is that a firm's managers should not try to achieve a particular level of leverage or interest tax shields under certain assumptions. So the firm's capital structure is irrelevant. This is because investors can make their own personal leverage and interest tax shields, so there's no need for managers to try to make corporate leverage and interest tax shields. This is true under the assumptions of equal tax rates, interest rates and debt availability for the person and the corporation, no transaction costs and symmetric information.
This principal of 'home-made' or 'do-it-yourself' leverage can also be applied to other topics. Read the following statements to decide which are true:
(I) Payout policy: a firm's managers should not try to achieve a particular pattern of equity payout.
(II) Agency costs: a firm's managers should not try to minimise agency costs.
(III) Diversification: a firm's managers should not try to diversify across industries.
(IV) Shareholder wealth: a firm's managers should not try to maximise shareholders' wealth.
Which of the above statement(s) are true?
(b) I and II only.
(c) I and III only.
(d) III only.
(e) All are true.
Question 301 leverage, capital structure, real estate
Your friend just bought a house for $1,000,000. He financed it using a $900,000 mortgage loan and a deposit of $100,000.
In the context of residential housing and mortgages, the 'equity' or 'net wealth' tied up in a house is the value of the house less the value of the mortgage loan. Assuming that your friend's only asset is his house, his net wealth is $100,000.
If house prices suddenly fall by 15%, what would be your friend's percentage change in net wealth?
No income (rent) was received from the house during the short time over which house prices fell.
Your friend will not declare bankruptcy, he will always pay off his debts.
(a) -1,000%
(b) -150%
(c) -100%
(d) -15%
(e) -10%
Question 337 capital structure, interest tax shield, leverage, real and nominal returns and cash flows, multi stage growth model
A fast-growing firm is suitable for valuation using a multi-stage growth model.
It's nominal unlevered cash flow from assets (##CFFA_U##) at the end of this year (t=1) is expected to be $1 million. After that it is expected to grow at a rate of:
12% pa for the next two years (from t=1 to 3),
5% over the fourth year (from t=3 to 4), and
-1% forever after that (from t=4 onwards). Note that this is a negative one percent growth rate.
The nominal WACC after tax is 9.5% pa and is not expected to change.
The nominal WACC before tax is 10% pa and is not expected to change.
The firm has a target debt-to-equity ratio that it plans to maintain.
The inflation rate is 3% pa.
All rates are given as nominal effective annual rates.
What is the levered value of this fast growing firm's assets?
(a) $13.19m
(b) $12.36m
(c) $11.77m
(d) $11.53m
(e) $11.20m
Question 480 NPV, real estate, DDM, no explanation
What type of present value equation is best suited to value a residential house investment property that is expected to pay constant rental payments forever? Note that 'constant' has the same meaning as 'level' in this context.
(a) The single cash flow equation.
(b) The level annuity equation.
(c) The annuity with growth equation.
(d) The level perpetuity equation.
(e) The perpetuity with growth equation.
Question 397 financial distress, leverage, capital structure, NPV
A levered firm has a market value of assets of $10m. Its debt is all comprised of zero-coupon bonds which mature in one year and have a combined face value of $9.9m.
Investors are risk-neutral and therefore all debt and equity holders demand the same required return of 10% pa.
Therefore the current market capitalisation of debt ##(D_0)## is $9m and equity ##(E_0)## is $1m.
A new project presents itself which requires an investment of $2m and will provide a:
$6.6m cash flow with probability 0.5 in the good state of the world, and a
-$4.4m (notice the negative sign) cash flow with probability 0.5 in the bad state of the world.
The project can be funded using the company's excess cash, no debt or equity raisings are required.
What would be the new market capitalisation of equity ##(E_\text{0, with project})## if shareholders vote to proceed with the project, and therefore should shareholders proceed with the project?
(a) $2.5m, so they should vote yes.
(b) $2.045455m, so they should vote yes.
(c) $0.9m, so they should vote no.
(d) $0, so they should vote no.
(e) -$0.9m, so they should vote no.
Question 406 leverage, WACC, margin loan, portfolio return
One year ago you bought $100,000 of shares partly funded using a margin loan. The margin loan size was $70,000 and the other $30,000 was your own wealth or 'equity' in the share assets.
The interest rate on the margin loan was 7.84% pa.
Over the year, the shares produced a dividend yield of 4% pa and a capital gain of 5% pa.
What was the total return on your wealth? Ignore taxes, assume that all cash flows (interest payments and dividends) were paid and received at the end of the year, and all rates above are effective annual rates.
(a) 1.0757%
(b) 2.7067%
(e) 11.7067%
Hint: Remember that wealth in this context is your equity (E) in the house asset (V = D+E) which is funded by the loan (D) and your deposit or equity (E).
Question 408 leverage, portfolio beta, portfolio risk, real estate, CAPM
You just bought a house worth $1,000,000. You financed it with an $800,000 mortgage loan and a deposit of $200,000.
You estimate that:
The house has a beta of 1;
The mortgage loan has a beta of 0.2.
What is the beta of the equity (the $200,000 deposit) that you have in your house?
Also, if the risk free rate is 5% pa and the market portfolio's return is 10% pa, what is the expected return on equity in your house? Ignore taxes, assume that all cash flows (interest payments and rent) were paid and received at the end of the year, and all rates are effective annual rates.
(a) The beta of equity is 5 and the expected return on equity is 30% pa.
(b) The beta of equity is 4.2 and the expected return on equity is 26% pa.
(c) The beta of equity is 0.86 and the expected return on equity is 9.3% pa.
(d) The beta of equity is 1 and the expected return on equity is 10% pa.
(e) The beta of equity is 0.6 and the expected return on equity is 8% pa.
Question 68 WACC, CFFA, capital budgeting
A manufacturing company is considering a new project in the more risky services industry. The cash flows from assets (CFFA) are estimated for the new project, with interest expense excluded from the calculations. To get the levered value of the project, what should these unlevered cash flows be discounted by?
Assume that the manufacturing firm has a target debt-to-assets ratio that it sticks to.
(a) The manufacturing firm's before-tax WACC.
(b) The manufacturing firm's after-tax WACC.
(c) A services firm's before-tax WACC, assuming that the services firm has the same debt-to-assets ratio as the manufacturing firm.
(d) A services firm's after-tax WACC, assuming that the services firm has the same debt-to-assets ratio as the manufacturing firm.
(e) The services firm's levered cost of equity.
Question 113 WACC, CFFA, capital budgeting
The US firm Google operates in the online advertising business. In 2011 Google bought Motorola Mobility which manufactures mobile phones.
Assume the following:
Google had a 10% after-tax weighted average cost of capital (WACC) before it bought Motorola.
Motorola had a 20% after-tax WACC before it merged with Google.
Google and Motorola have the same level of gearing.
Both companies operate in a classical tax system.
You are a manager at Motorola. You must value a project for making mobile phones. Which method(s) will give the correct valuation of the mobile phone manufacturing project? Select the most correct answer.
The mobile phone manufacturing project's:
(a) Unlevered CFFA should be discounted by Google's 10% WACC after tax.
(b) Unlevered CFFA should be discounted by Motorola's 20% WACC after tax.
(c) Levered CFFA should be discounted by Google's 10% WACC after tax.
(d) Levered CFFA should be discounted by Motorola's 20% WACC after tax.
(e) Unlevered CFFA by 15%, the average of Google and Motorola's WACC after tax.
Question 67 CFFA, interest tax shield
Here are the Net Income (NI) and Cash Flow From Assets (CFFA) equations:
###NI=(Rev-COGS-FC-Depr-IntExp).(1-t_c)###
###CFFA=NI+Depr-CapEx - \varDelta NWC+IntExp###
What is the formula for calculating annual interest expense (IntExp) which is used in the equations above?
Select one of the following answers. Note that D is the value of debt which is constant through time, and ##r_D## is the cost of debt.
(a) ##D(1+r_D)##
(b) ##D/(1+r_D) ##
(c) ##D.r_D ##
(d) ##D / r_D##
(e) ##NI.r_D##
Question 95 interest tax shield
The equations for Net Income (NI, also known as Earnings or Net Profit After Tax) and Cash Flow From Assets (CFFA, also known as Free Cash Flow to the Firm) per year are:
For a firm with debt, what is the formula for the present value of interest tax shields if the tax shields occur in perpetuity?
You may assume:
the value of debt (D) is constant through time,
The cost of debt and the yield on debt are equal and given by ##r_D##.
the appropriate rate to discount interest tax shields is ##r_D##.
##\text{IntExp}=D.r_D##
(a) ##D.t_c##
(b) ##D.r_D/t_c ##
(c) ##D.r_D.(1-t_c)##
(d) ##D.r_D/(1-t_c)##
(e) ##D.r_D.(t_c-1)##
Question 223 CFFA, interest tax shield
Which one of the following will increase the Cash Flow From Assets in this year for a tax-paying firm, all else remaining constant?
(a) An increase in net capital spending.
(b) A decrease in the cash flow to creditors.
(c) An increase in interest expense.
(d) An increase in net working capital.
(e) A decrease in dividends paid.
Which one of the following will decrease net income (NI) but increase cash flow from assets (CFFA) in this year for a tax-paying firm, all else remaining constant?
###NI=(Rev-COGS-FC-Depr-IntExp).(1-t_c )### ###CFFA=NI+Depr-CapEx - ΔNWC+IntExp###
(a) An increase in revenue (##Rev##).
(b) An decrease in revenue (##Rev##).
(c) An increase in rent expense (part of fixed costs, ##FC##).
(d) An increase in interest expense (##IntExp##).
(e) An increase in dividends.
Question 84 WACC, capital structure, capital budgeting
A firm is considering a new project of similar risk to the current risk of the firm. This project will expand its existing business. The cash flows of the project have been calculated assuming that there is no interest expense. In other words, the cash flows assume that the project is all-equity financed.
In fact the firm has a target debt-to-equity ratio of 1, so the project will be financed with 50% debt and 50% equity. To find the levered value of the firm's assets, what discount rate should be applied to the project's unlevered cash flows? Assume a classical tax system.
(a) The required return on equity, ##r_E##
(b) The required return on debt, ##r_D##
(c) The after-tax required return on debt, ##r_D.(1-t_c)##
(d) The after-tax WACC, ##\text{WACC after tax}=\frac{D}{V_L}.r_D.(1-t_c )+\frac{E_L}{V_L}.r_E##
(e) The pre-tax WACC, ##\text{WACC before tax}=\frac{D}{V_L}.r_D+\frac{E_L}{V_L}.r_E##
Question 492 capital budgeting, opportunity cost, sunk cost
A man has taken a day off from his casual painting job to relax.
It's the end of the day and he's thinking about the hours that he could have spent working (in the past) which are now:
(a) A sunk cost.
(b) An opportunity cost.
(c) A negative side effect.
(d) A capital expense.
(e) A depreciation expense.
There are many ways to calculate a firm's free cash flow (FFCF), also called cash flow from assets (CFFA). Some include the annual interest tax shield in the cash flow and some do not.
Which of the below FFCF formulas include the interest tax shield in the cash flow?
###(1) \quad FFCF=NI + Depr - CapEx -ΔNWC + IntExp### ###(2) \quad FFCF=NI + Depr - CapEx -ΔNWC + IntExp.(1-t_c)### ###(3) \quad FFCF=EBIT.(1-t_c )+ Depr- CapEx -ΔNWC+IntExp.t_c### ###(4) \quad FFCF=EBIT.(1-t_c) + Depr- CapEx -ΔNWC### ###(5) \quad FFCF=EBITDA.(1-t_c )+Depr.t_c- CapEx -ΔNWC+IntExp.t_c### ###(6) \quad FFCF=EBITDA.(1-t_c )+Depr.t_c- CapEx -ΔNWC### ###(7) \quad FFCF=EBIT-Tax + Depr - CapEx -ΔNWC### ###(8) \quad FFCF=EBIT-Tax + Depr - CapEx -ΔNWC-IntExp.t_c### ###(9) \quad FFCF=EBITDA-Tax - CapEx -ΔNWC### ###(10) \quad FFCF=EBITDA-Tax - CapEx -ΔNWC-IntExp.t_c###
The formulas for net income (NI also called earnings), EBIT and EBITDA are given below. Assume that depreciation and amortisation are both represented by 'Depr' and that 'FC' represents fixed costs such as rent.
###NI=(Rev - COGS - Depr - FC - IntExp).(1-t_c )### ###EBIT=Rev - COGS - FC-Depr### ###EBITDA=Rev - COGS - FC### ###Tax =(Rev - COGS - Depr - FC - IntExp).t_c= \dfrac{NI.t_c}{1-t_c}###
(a) 1, 3, 5, 7, 9.
(b) 2, 4, 6, 8, 10.
(c) 1, 4, 6, 8, 10.
(d) 2, 3, 5, 7, 9.
(e) 1, 3, 5, 8, 10.
Question 369 interest tax shield, CFFA
One formula for calculating a levered firm's free cash flow (FFCF, or CFFA) is to use earnings before interest and tax (EBIT).
###\begin{aligned} FFCF &= (EBIT)(1-t_c) + Depr - CapEx -\Delta NWC + IntExp.t_c \\ &= (Rev - COGS - Depr - FC)(1-t_c) + Depr - CapEx -\Delta NWC + IntExp.t_c \\ \end{aligned} \\###
Does this annual FFCF or the annual interest tax shield?
One method for calculating a firm's free cash flow (FFCF, or CFFA) is to ignore interest expense. That is, pretend that interest expense ##(IntExp)## is zero:
###\begin{aligned} FFCF &= (Rev - COGS - Depr - FC - IntExp)(1-t_c) + Depr - CapEx -\Delta NWC + IntExp \\ &= (Rev - COGS - Depr - FC - 0)(1-t_c) + Depr - CapEx -\Delta NWC - 0\\ \end{aligned}###
Does this annual FFCF with zero interest expense or the annual interest tax shield?
One formula for calculating a levered firm's free cash flow (FFCF, or CFFA) is to use net operating profit after tax (NOPAT).
###\begin{aligned} FFCF &= NOPAT + Depr - CapEx -\Delta NWC \\ &= (Rev - COGS - Depr - FC)(1-t_c) + Depr - CapEx -\Delta NWC \\ \end{aligned} \\###
Question 413 CFFA, interest tax shield, depreciation tax shield
There are many ways to calculate a firm's free cash flow (FFCF), also called cash flow from assets (CFFA).
One method is to use the following formulas to transform net income (NI) into FFCF including interest and depreciation tax shields:
###FFCF=NI + Depr - CapEx -ΔNWC + IntExp###
###NI=(Rev - COGS - Depr - FC - IntExp).(1-t_c )###
Another popular method is to use EBITDA rather than net income. EBITDA is defined as:
###EBITDA=Rev - COGS - FC###
One of the below formulas correctly calculates FFCF from EBITDA, including interest and depreciation tax shields, giving an identical answer to that above. Which formula is correct?
(a) ##FFCF=EBITDA+ Depr - CapEx -ΔNWC + IntExp##
(b) ##FFCF=EBITDA.(1-t_c )+Depr- CapEx -ΔNWC##
(c) ##FFCF=EBITDA.(1-t_c )+ Depr.t_c - CapEx -ΔNWC + IntExp.t_c##
(d) ##FFCF=EBITDA.(1-t_c )+Depr.(1-t_c )- CapEx -ΔNWC+IntExp.(1-t_c)##
(e) ##FFCF=EBITDA.(1-t_c )- CapEx -ΔNWC##
Question 97 WACC, no explanation
A company has:
10 million common shares outstanding, each trading at a price of $90.
1 million preferred shares which have a face (or par) value of $100 and pay a constant dividend of 9% of par. They currently trade at a price of $120 each.
Debentures that have a total face value of $60,000,000 and a yield to maturity of 6% per annum. They are publicly traded and their market price is equal to 90% of their face value.
The risk-free rate is 5% and the market return is 10%.
Market analysts estimate that the company's common stock has a beta of 1.2. The corporate tax rate is 30%.
What is the company's after-tax Weighted Average Cost of Capital (WACC)? Assume a classical tax system.
(a) 10.27%
(b) 10.39%
(c) 10.43%
(d) 11.47%
Question 78 WACC, capital structure
A company issues a large amount of bonds to raise money for new projects of similar risk to the company's existing projects. The net present value (NPV) of the new projects is positive but small. Assume a classical tax system. Which statement is NOT correct?
(a) The debt-to-assets (D/V) ratio will increase.
(b) The debt-to-equity ratio (D/E) will increase.
(c) Firm value is likely to have increased due to the higher amount of interest tax shields, assuming that there will not be any costs of financial distress.
(d) The company's after-tax WACC is likely to have decreased.
(e) The company's before-tax WACC is likely to have decreased.
A firm has a debt-to-assets ratio of 50%. The firm then issues a large amount of equity to raise money for new projects of similar systematic risk to the company's existing projects. Assume a classical tax system. Which statement is correct?
(d) The company's after-tax WACC is likely to stay the same.
(e) The company's before-tax WACC is likely to stay the same.
Question 99 capital structure, interest tax shield, Miller and Modigliani, trade off theory of capital structure
A firm changes its capital structure by issuing a large amount of debt and using the funds to repurchase shares. Its assets are unchanged.
The firm and individual investors can borrow at the same rate and have the same tax rates.
The firm's debt and shares are fairly priced and the shares are repurchased at the market price, not at a premium.
There are no market frictions relating to debt such as asymmetric information or transaction costs.
Shareholders wealth is measured in terms of utiliity. Shareholders are wealth-maximising and risk-averse. They have a preferred level of overall leverage. Before the firm's capital restructure all shareholders were optimally levered.
According to Miller and Modigliani's theory, which statement is correct?
(a) The firm's share price and shareholder wealth will both decrease. This is because the firm will have more debt and therefore more risk so the discount rate applied to its cash flows will be higher, decreasing the value of the firm and therefore the value of the firm's equity and share price.
(b) The firm's share price and shareholder wealth will both increase. This is because the firm will have more debt which will amplify the returns of equity investors. This will mean that returns on equity can be much higher and investors will pay a premium for this, leading to an increase in the stock price.
(c) The firm's share price and shareholder wealth will both increase since it has more debt and therefore more tax shields.
(d) The firm's share price will increase due to the higher value of tax shields. But shareholder wealth will remain unchanged because capital structure is irrelevant when investors can use home-made leverage to create tax-shields themselves.
(e) The firm's share price and shareholder wealth will both increase. This is because the cost of debt is cheaper than equity, leading to a lower (before and after tax) WACC. This lower WACC will lead to a higher value of the firm and a higher share price.
Question 370 capital budgeting, NPV, interest tax shield, WACC, CFFA
Project life 2 yrs
Initial investment in equipment $600k
Depreciation of equipment per year $250k
Expected sale price of equipment at end of project $200k
Revenue per job $12k
Variable cost per job $4k
Quantity of jobs per year 120
Fixed costs per year, paid at the end of each year $100k
Interest expense in first year (at t=1) $16.091k
Interest expense in second year (at t=2) $9.711k
Tax rate 30%
Government treasury bond yield 5%
Bank loan debt yield 6%
Levered cost of equity 12.5%
Market portfolio return 10%
Beta of assets 1.24
Beta of levered equity 1.5
Firm's and project's debt-to-equity ratio 25%
The project will require an immediate purchase of $50k of inventory, which will all be sold at cost when the project ends. Current liabilities are negligible so they can be ignored.
The debt-to-equity ratio will be kept constant throughout the life of the project. The amount of interest expense at the end of each period has been correctly calculated to maintain this constant debt-to-equity ratio. Note that interest expense is different in each year.
Thousands are represented by 'k' (kilo).
All cash flows occur at the start or end of the year as appropriate, not in the middle or throughout the year.
All rates and cash flows are nominal. The inflation rate is 2% pa.
All rates are given as effective annual rates.
The 50% capital gains tax discount is not available since the project is undertaken by a firm, not an individual.
(a) $684.222k
(b) $690.919k
(c) $697.616k
(d) $698.713k
(e) $710.601k
Question 273 CFFA, capital budgeting
Value the following business project to manufacture a new product.
Initial investment in equipment $6m
Depreciation of equipment per year $3m
Expected sale price of equipment at end of project $0.6m
Unit sales per year 4m
Sale price per unit $8
Variable cost per unit $5
Fixed costs per year, paid at the end of each year $1m
Interest expense per year 0
Weighted average cost of capital after tax per annum 10%
The firm's current assets and current liabilities are $3m and $2m respectively right now. This net working capital will not be used in this project, it will be used in other unrelated projects.
Due to the project, current assets (mostly inventory) will grow by $2m initially (at t = 0), and then by $0.2m at the end of the first year (t=1).
Current liabilities (mostly trade creditors) will increase by $0.1m at the end of the first year (t=1).
At the end of the project, the net working capital accumulated due to the project can be sold for the same price that it was bought.
The project cost $0.5m to research which was incurred one year ago.
All rates and cash flows are real. The inflation rate is 3% pa.
The business considering the project is run as a 'sole tradership' (run by an individual without a company) and is therefore eligible for a 50% capital gains tax discount when the equipment is sold, as permitted by the Australian Tax Office.
What is the expected net present value (NPV) of the project?
(a) $5.2m
(b) $8.481735m
(c) $8.743802m
(d) $8.991736m
(e) $9.719008m
For a firm with debt, what is the amount of the interest tax shield per year?
(a) ##IntExp.t_c##
(b) ##IntExp/t_c##
(c) ##IntExp.(1-t_c)##
(d) ##IntExp/(1-t_c)##
(e) ##IntExp.(t_c-1)##
A new company's Firm Free Cash Flow (FFCF, same as CFFA) is forecast in the graph below.
To value the firm's assets, the terminal value needs to be calculated using the perpetuity with growth formula:
###V_{\text{terminal, }t-1} = \dfrac{FFCF_{\text{terminal, }t}}{r-g}###
Which point corresponds to the best time to calculate the terminal value?
(a) Point A.
(b) Point B.
(c) Point C.
(d) Any of the points.
(e) None of the points.
Question 173 CFFA
Find Candys Corporation's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.
Candys Corp
Income Statement for
year ending 30th June 2013
COGS 50
Operating expense 10
Depreciation 20
Interest expense 10
Income before tax 110
Tax at 30% 33
Net income 77
as at 30th June 2013 2012
$m $m
Current assets 220 180
Cost 300 340
Accumul. depr. 60 40
Carrying amount 240 300
Total assets 460 480
Current liabilities 175 190
Non-current liabilities 135 130
Owners' equity
Retained earnings 50 60
Contributed equity 100 100
Total L and OE 460 480
Note: all figures are given in millions of dollars ($m).
(b) 182
(c) 112
Why is Capital Expenditure (CapEx) subtracted in the Cash Flow From Assets (CFFA) formula?
###CFFA=NI+Depr-CapEx - \Delta NWC+IntExp###
(a) CapEx is added in the Net Income (NI) equation so it needs subtracting in the CFFA equation.
(b) CapEx is a financing cash flow that needs to be ignored. Therefore it should be subtracted.
(c) CapEx is not a cash flow, it's a non-cash expense made up by accountants that needs to be subtracted.
(d) CapEx is subtracted to account for the net cash spent on capital assets.
(e) CapEx is subtracted because it's too hard to predict, therefore we exclude it.
Find Trademark Corporation's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.
Trademark Corp
Operating expense 5
Income before tax 30
Tax at 30% 9
Current assets 120 80
Carrying amount 90 100
Current liabilities 75 65
Non-current liabilities 75 55
Contributed equity 50 50
(a) -19
Find UniBar Corp's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.
UniBar Corp
Sales 80
Interest expense 5
Net income 7
Current liabilities 110 60
(c) -8
(d) -18
Find Piano Bar's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.
COGS 185
Find World Bar's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.
World Bar
Taxable income 50
Retained earnings 100 100
Note: all figures above and below are given in millions of dollars ($m).
(e) -20
Cash Flow From Assets (CFFA) can be defined as:
(a) Cash available to distribute to creditors and stockholders.
(b) Cash flow to creditors minus cash flow to stockholders.
(c) Net income (or earnings) plus depreciation plus interest expense.
(d) Net income minus the increase in net working capital.
(e) Net income minus net capital spending minus the increase in net working capital.
A firm has forecast its Cash Flow From Assets (CFFA) for this year and management is worried that it is too low. Which one of the following actions will lead to a higher CFFA for this year (t=0 to 1)? Only consider cash flows this year. Do not consider cash flows after one year, or the change in the NPV of the firm. Consider each action in isolation.
(a) Buy less land, buildings and trucks than what was planned. Assume that this has no impact on revenue.
(b) Pay less cash to creditors by refinancing the firm's existing coupon bonds with zero-coupon bonds that require no interest payments. Assume that there are no transaction costs and that both types of bonds have the same yield to maturity.
(c) Change the depreciation method used for tax purposes from diminishing value to straight line, so less depreciation occurs this year and more occurs in later years. Assume that the government's tax department allow this.
(d) Buying more inventory than was planned, so there is an increase in net working capital. Assume that there is no increase in sales.
(e) Raising new equity through a rights issue. Assume that all of the money raised is spent on new capital assets such as land and trucks, but they will be fitted out and delivered in one year so no new cash will be earned from them.
Find Scubar Corporation's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.
Scubar Corp
Rent expense 11
Taxes at 30% 27
Inventory 60 50
Trade debtors 19 6
Rent paid in advance 3 2
PPE 420 400
Trade creditors 10 8
Bond liabilities 200 190
Retained profits 162 130
The cash flow from assets was:
(a) $40m
(b) $41m
(c) $54m
(d) $60m
(e) $74m
Question 349 CFFA, depreciation tax shield
###NI = (Rev-COGS-FC-Depr-IntExp).(1-t_c )### ###CFFA=NI+Depr-CapEx - \Delta NWC+IntExp###
(a) An increase in revenue (Rev).
(b) An increase in rent expense (part of fixed costs, FC).
(c) An increase in depreciation expense (Depr).
(d) An decrease in net working capital (ΔNWC).
Find Sidebar Corporation's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.
Sidebar Corp
Taxable Income 210
Net income 147
Trade debtors 11 16
Trade creditors 11 19
(a) $138m
(b) $142m
(c) $143m
(d) $172m
(e) $176m
Over the next year, the management of an unlevered company plans to:
Achieve firm free cash flow (FFCF or CFFA) of $1m.
Pay dividends of $1.8m
Complete a $1.3m share buy-back.
Spend $0.8m on new buildings without buying or selling any other fixed assets. This capital expenditure is included in the CFFA figure quoted above.
All amounts are received and paid at the end of the year so you can ignore the time value of money.
The firm has sufficient retained profits to pay the dividend and complete the buy back.
The firm plans to run a very tight ship, with no excess cash above operating requirements currently or over the next year.
How much new equity financing will the company need? In other words, what is the value of new shares that will need to be issued?
(b) $1.3m
(c) $0.8m
(d) $0.3m
(e) No new shares need to be issued, the firm will be sufficiently financed.
Which one of the following will have no effect on net income (NI) but decrease cash flow from assets (CFFA or FFCF) in this year for a tax-paying firm, all else remaining constant?
(b) An increase in rent expense (a type of recurring fixed cost, FC).
(d) An increase in inventories (a current asset).
(e) An decrease in interest expense (IntExp).
Find Ching-A-Lings Corporation's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.
Ching-A-Lings Corp
Taxes at 30% 9
Trade creditors 4 10
(e) $1m
Make $5m in sales, $1.9m in net income and $2m in equity free cash flow (EFCF).
Pay dividends of $1m.
The firm has sufficient retained profits to legally pay the dividend and complete the buy back.
(a) $2m
(b) $1m
Read the following financial statements and calculate the firm's free cash flow over the 2014 financial year.
UBar Corp
Gas expense 8
EBIT 60
Taxes 18
Cash 30 29
Accounts receivable 5 7
Pre-paid rent expense 1 0
Trade payables 20 18
Accrued gas expense 3 2
Non-current liabilities 0 0
Asset revaluation reserve 5 0
The firm's free cash flow over the 2014 financial year was:
(b) $52
(c) $58
(d) $61
(e) $62
Question 366 opportunity cost, NPV, CFFA, needs refinement
Your friend is trying to find the net present value of a project. The project is expected to last for just one year with:
a negative cash flow of -$1 million initially (t=0), and
a positive cash flow of $1.1 million in one year (t=1).
The project has a total required return of 10% pa due to its moderate level of undiversifiable risk.
Your friend is aware of the importance of opportunity costs and the time value of money, but he is unsure of how to find the NPV of the project.
He knows that the opportunity cost of investing the $1m in the project is the expected gain from investing the money in shares instead. Like the project, shares also have an expected return of 10% since they have moderate undiversifiable risk. This opportunity cost is $0.1m ##(=1m \times 10\%)## which occurs in one year (t=1).
He knows that the time value of money should be accounted for, and this can be done by finding the present value of the cash flows in one year.
Your friend has listed a few different ways to find the NPV which are written down below.
(I) ##-1m + \dfrac{1.1m}{(1+0.1)^1} ##
(II) ##-1m + \dfrac{1.1m}{(1+0.1)^1} - \dfrac{1m}{(1+0.1)^1} \times 0.1 ##
(III) ##-1m + \dfrac{1.1m}{(1+0.1)^1} - \dfrac{1.1m}{(1+0.1)^1} \times 0.1 ##
(IV) ##-1m + 1.1m - \dfrac{1.1m}{(1+0.1)^1} \times 0.1 ##
(V) ##-1m + 1.1m - 1.1m \times 0.1 ##
Which of the above calculations give the correct NPV? Select the most correct answer.
(b) II only.
(c) III only.
(e) II and V only.
Question 300 NPV, opportunity cost
What is the net present value (NPV) of undertaking a full-time Australian undergraduate business degree as an Australian citizen? Only include the cash flows over the duration of the degree, ignore any benefits or costs of the degree after it's completed.
The degree takes 3 years to complete and all students pass all subjects.
There are 2 semesters per year and 4 subjects per semester.
University fees per subject per semester are $1,277, paid at the start of each semester. Fees are expected to stay constant for the next 3 years.
There are 52 weeks per year.
The first semester is just about to start (t=0). The first semester lasts for 19 weeks (t=0 to 19).
The second semester starts immediately afterwards (t=19) and lasts for another 19 weeks (t=19 to 38).
The summer holidays begin after the second semester ends and last for 14 weeks (t=38 to 52). Then the first semester begins the next year, and so on.
Working full time at the grocery store instead of studying full-time pays $20/hr and you can work 35 hours per week. Wages are paid at the end of each week.
Full-time students can work full-time during the summer holiday at the grocery store for the same rate of $20/hr for 35 hours per week. Wages are paid at the end of each week.
The discount rate is 9.8% pa. All rates and cash flows are real. Inflation is expected to be 3% pa. All rates are effective annual.
The NPV of costs from undertaking the university degree is:
(c) $75,130.29
(d) $54,018.93
Question 511 capital budgeting, CFFA
Find the cash flow from assets (CFFA) of the following project.
One Year Mining Project Data
Project life 1 year
Initial investment in building mine and equipment $9m
Depreciation of mine and equipment over the year $8m
Kilograms of gold mined at end of year 1,000
Sale price per kilogram $0.05m
Variable cost per kilogram $0.03m
Before-tax cost of closing mine at end of year $4m
Note 1: Due to the project, the firm also anticipates finding some rare diamonds which will give before-tax revenues of $1m at the end of the year.
Note 2: The land that will be mined actually has thermal springs and a family of koalas that could be sold to an eco-tourist resort for an after-tax amount of $3m right now. However, if the mine goes ahead then this natural beauty will be destroyed.
Note 3: The mining equipment will have a book value of $1m at the end of the year for tax purposes. However, the equipment is expected to fetch $2.5m when it is sold.
Find the project's CFFA at time zero and one. Answers are given in millions of dollars ($m), with the first cash flow at time zero, and the second at time one.
(a) -9, 15.65
(b) -9, 14.3
(c) -12, 16.8
(d) -12, 16.35
(e) -12, 14.3
Project life 2 years
Depreciation of equipment per year for tax purposes $1m
Fixed costs per year, paid at the end of each year $1.5m
Note 1: The equipment will have a book value of $4m at the end of the project for tax purposes. However, the equipment is expected to fetch $0.9 million when it is sold at t=2.
Note 2: Due to the project, the firm will have to purchase $0.8m of inventory initially, which it will sell at t=1. The firm will buy another $0.8m at t=1 and sell it all again at t=2 with zero inventory left. The project will have no effect on the firm's current liabilities.
Find the project's CFFA at time zero, one and two. Answers are given in millions of dollars ($m).
(a) -6, 12.25, 16.68
(b) -6.8, 13.25, 14.05
(c) -6.8, 13.25, 15.88
(d) -6.8, 13.25, 18.51
(e) -6.8, 13.25, 17.71
The hardest and most important aspect of business project valuation is the estimation of the:
(a) Diversifiable standard deviation of asset returns.
(b) Systematic standard deviation of asset returns.
(c) Proportion of debt and equity used to fund the assets.
(d) Cash flows from assets.
(e) Risk free rate.
Question 409 NPV, capital structure, capital budgeting
A pharmaceutical firm has just discovered a valuable new drug. So far the news has been kept a secret.
The net present value of making and commercialising the drug is $200 million, but $600 million of bonds will need to be issued to fund the project and buy the necessary plant and equipment.
The firm will release the news of the discovery and bond raising to shareholders simultaneously in the same announcement. The bonds will be issued shortly after.
Once the announcement is made and the bonds are issued, what is the expected increase in the value of the firm's assets (ΔV), market capitalisation of debt (ΔD) and market cap of equity (ΔE)?
The triangle symbol is the Greek letter capital delta which means change or increase in mathematics.
Ignore the benefit of interest tax shields from having more debt.
Remember: ##ΔV = ΔD+ΔE##
(a) ##ΔV=800m, ΔD = 600m, ΔE=200m##
(b) ##ΔV=200m, ΔD = 600m, ΔE= 0##
(c) ##ΔV=200m, ΔD =0m, \quad ΔE=200m##
(d) ##ΔV=400m, ΔD = 600m, ΔE=-200m##
(e) ##ΔV=800m, ΔD = 800m, ΔE= 0##
Question 410 CAPM, capital budgeting
The CAPM can be used to find a business's expected opportunity cost of capital:
###r_i=r_f+β_i (r_m-r_f)###
What should be used as the risk free rate ##r_f##?
(a) The current central bank policy rate (RBA overnight money market rate).
(b) The current 30 day federal government treasury bill rate.
(c) The average historical 30 day federal government treasury bill rate over the last 20 years.
(d) The current 30 year federal government treasury bond rate.
(e) The average historical 30 year federal government treasury bond rate over the last 20 years.
Question 458 capital budgeting, no explanation
Which of the following is NOT a valid method to estimate future revenues or costs in a pro-forma income statement when trying to value a company?
(a) Extrapolation of past trends to estimate future revenues or costs.
(b) Using a constant or trending 'percent of sales' method to forecast future costs.
(c) Use futures (derivative) prices, if available, to forecast prices which helps calculate revenues.
(d) Use forecast GDP growth rates published by the statistics bureau to estimate future revenue growth.
(e) Assume that markets are efficient and use the random walk hypothesis to substitute a random value for revenue.
A young lady is trying to decide if she should attend university or begin working straight away in her home town.
The young lady's grandma says that she should not go to university because she is less likely to marry the local village boy whom she likes because she will spend less time with him if she attends university.
What's the correct way to classify this item from a capital budgeting perspective when trying to decide whether to attend university?
The cost of not marrying the local village boy should be classified as:
(c) A non-pecuniary cost that should be disregarded.
(d) A positive side effect.
The 'time value of money' is most closely related to which of the following concepts?
(a) Competition: Firms in competitive markets earn zero economic profit.
(b) Opportunity cost: The cost of the next best alternative foregone should be subtracted.
(c) Separation of the investment and financing decisions.
(d) Diversification: Risks can often be reduced by pooling them together.
(e) Sunk costs: Costs that cannot be recouped should be ignored.
Unit sales per year 10m
Note 1: Due to the project, the firm will have to purchase $40m of inventory initially (at t=0). Half of this inventory will be sold at t=1 and the other half at t=2.
Note 2: The equipment will have a book value of $2m at the end of the project for tax purposes. However, the equipment is expected to fetch $1m when it is sold. Assume that the full capital loss is tax-deductible and taxed at the full corporate tax rate.
Note 3: The project will be fully funded by equity which investors will expect to pay dividends totaling $10m at the end of each year.
(a) -48, 54.5, 55.8
(b) -48, 54.5, 74.5
(c) -48, 74.5, 35.8
(d) -48, 74.5, 75.8
(e) -8, 74.5, 75.8
To value a business's assets, the free cash flow of the firm (FCFF, also called CFFA) needs to be calculated. This requires figures from the firm's income statement and balance sheet. For what figures is the balance sheet needed? Note that the balance sheet is sometimes also called the statement of financial position.
(a) Net income, depreciation and interest expense.
(b) Depreciation and capital expenditure.
(c) Current assets, current liabilities and cost of goods sold (COGS).
(d) Current assets, current liabilities and capital expenditure.
(e) Current assets, current liabilities and depreciation expense.
Question 658 CFFA, income statement, balance sheet, no explanation
To value a business's assets, the free cash flow of the firm (FCFF, also called CFFA) needs to be calculated. This requires figures from the firm's income statement and balance sheet. For what figures is the income statement needed? Note that the income statement is sometimes also called the profit and loss, P&L, or statement of financial performance.
Question 104 CAPM, payout policy, capital structure, Miller and Modigliani, risk
Assume that there exists a perfect world with no transaction costs, no asymmetric information, no taxes, no agency costs, equal borrowing rates for corporations and individual investors, the ability to short the risk free asset, semi-strong form efficient markets, the CAPM holds, investors are rational and risk-averse and there are no other market frictions.
For a firm operating in this perfect world, which statement(s) are correct?
(i) When a firm changes its capital structure and/or payout policy, share holders' wealth is unaffected.
(ii) When the idiosyncratic risk of a firm's assets increases, share holders do not expect higher returns.
(iii) When the systematic risk of a firm's assets increases, share holders do not expect higher returns.
Select the most correct response:
(a) Only (i) is true.
(b) Only (ii) is true.
(c) Only (iii) is true.
(d) Only (i) and (ii) are true.
(e) All statements (i), (ii) and (iii) are true.
Question 114 WACC, capital structure, risk
A firm's WACC before tax would decrease due to:
(a) the firm's industry becoming more systematically risky, for example if it was a mining company and commodities prices varied more strongly and were more positively correlated with the market portfolio.
(b) the firm's industry becoming less systematically risky, for example if it was a child care centre and the government announced permanently higher subsidies for parents' child care expenses.
(c) the firm issuing more debt and using the proceeds to repurchase stock.
(d) the firm issuing more equity and using the proceeds to pay off debt holders.
(e) none of the above.
Question 116 capital structure, CAPM
A firm changes its capital structure by issuing a large amount of equity and using the funds to repay debt. Its assets are unchanged. Ignore interest tax shields.
According to the Capital Asset Pricing Model (CAPM), which statement is correct?
(a) The beta of the firm's assets will increase.
(b) The beta of the firm's assets will decrease.
(c) The beta of the firm's equity will increase.
(d) The beta of the firm's equity will decrease.
(e) The beta of the firm's equity will be unchanged.
Question 418 capital budgeting, NPV, interest tax shield, WACC, CFFA, CAPM
Expected sale price of equipment at end of project 0
Sale price per unit $10
Interest expense in first year (at t=1) $0.562m
Corporate tax rate 30%
Covariance of levered equity returns with market 0.32
Variance of market portfolio returns 0.16
Due to the project, current assets will increase by $6m now (t=0) and fall by $6m at the end (t=1). Current liabilities will not be affected.
The debt-to-equity ratio will be kept constant throughout the life of the project. The amount of interest expense at the end of each period has been correctly calculated to maintain this constant debt-to-equity ratio.
Millions are represented by 'm'.
All rates and cash flows are real. The inflation rate is 2% pa. All rates are given as effective annual rates.
The project is undertaken by a firm, not an individual.
(a) $5.772m
(b) $4.979m
(c) $4.959m
(d) $4.733m
(e) $4.584m
Question 419 capital budgeting, NPV, interest tax shield, WACC, CFFA, CAPM, no explanation
Interest expense in first year (at t=1) $0.53m
Firm's and project's debt-to-assets ratio 50%
The debt-to-assets ratio will be kept constant throughout the life of the project. The amount of interest expense at the end of each period has been correctly calculated to maintain this constant debt-to-equity ratio.
(a) $7.33k
(b) $7.299k
(c) $6.946k
(d) $6.729k
(e) $6.667k
Question 205 depreciation tax shield, CFFA
There are a number of ways that assets can be depreciated. Generally the government's tax office stipulates a certain method.
But if it didn't, what would be the ideal way to depreciate an asset from the perspective of a businesses owner?
(a) 'Straight line' or 'prime cost' depreciation, which allocates equal depreciation expenses over each year of the asset's life.
(b) 'Diminishing value' or 'reducing balance' depreciation, which allocates more depreciation expense at the start of the asset's life and less towards the end.
(c) No depreciation at all, so the asset is always kept on the books as being the same value that it was bought for. The asset will cause no depreciation expense in any year.
(d) Allocating all of the depreciation expense to the final year of the asset's life.
(e) Allocating all of the depreciation expense to the first year of the asset's life. Accountants would call this 'expensing' the asset, rather than 'capitalising' it and depreciating it slowly.
Question 303 WACC, CAPM, CFFA
There are many different ways to value a firm's assets. Which of the following will NOT give the correct market value of a levered firm's assets ##(V_L)##? Assume that:
The firm is financed by listed common stock and vanilla annual fixed coupon bonds, which are both traded in a liquid market.
The bonds' yield is equal to the coupon rate, so the bonds are issued at par. The yield curve is flat and yields are not expected to change. When bonds mature they will be rolled over by issuing the same number of new bonds with the same expected yield and coupon rate, and so on forever.
Tax rates on the dividends and capital gains received by investors are equal, and capital gains tax is paid every year, even on unrealised gains regardless of when the asset is sold.
There is no re-investment of the firm's cash back into the business. All of the firm's excess cash flow is paid out as dividends so real growth is zero.
The firm operates in a mature industry with zero real growth.
All cash flows and rates in the below equations are real (not nominal) and are expected to be stable forever. Therefore the perpetuity equation with no growth is suitable for valuation.
(a) ##V_L = n_\text{shares}.P_\text{share} + n_\text{bonds}.P_\text{bond}##
(b) ##V_L = n_\text{shares}.\dfrac{\text{Dividend per share}}{r_f + \beta_{EL}(r_m - r_f)} + n_\text{bonds}.\dfrac{\text{Coupon per bond}}{r_f + \beta_D(r_m - r_f)}##
(c) ##V_L = \dfrac{\text{CFFA}_{L}}{r_\text{WACC before tax}}##
(d) ##V_L = \dfrac{\text{CFFA}_{U}}{r_\text{WACC after tax}}##
(e) ##V_L = \dfrac{\text{CFFA}_{L}}{r_\text{WACC after tax}}##
###r_\text{WACC before tax} = r_D.\frac{D}{V_L} + r_{EL}.\frac{E_L}{V_L} = \text{Weighted average cost of capital before tax}### ###r_\text{WACC after tax} = r_D.(1-t_c).\frac{D}{V_L} + r_{EL}.\frac{E_L}{V_L} = \text{Weighted average cost of capital after tax}### ###NI_L=(Rev-COGS-FC-Depr-\mathbf{IntExp}).(1-t_c) = \text{Net Income Levered}### ###CFFA_L=NI_L+Depr-CapEx - \varDelta NWC+\mathbf{IntExp} = \text{Cash Flow From Assets Levered}### ###NI_U=(Rev-COGS-FC-Depr).(1-t_c) = \text{Net Income Unlevered}### ###CFFA_U=NI_U+Depr-CapEx - \varDelta NWC= \text{Cash Flow From Assets Unlevered}###
Question 240 negative gearing, interest tax shield
Unrestricted negative gearing is allowed in Australia, New Zealand and Japan. Negative gearing laws allow income losses on investment properties to be deducted from a tax-payer's pre-tax personal income. Negatively geared investors benefit from this tax advantage. They also hope to benefit from capital gains which exceed the income losses.
For example, a property investor buys an apartment funded by an interest only mortgage loan. Interest expense is $2,000 per month. The rental payments received from the tenant living on the property are $1,500 per month. The investor can deduct this income loss of $500 per month from his pre-tax personal income. If his personal marginal tax rate is 46.5%, this saves $232.5 per month in personal income tax.
The advantage of negative gearing is an example of the benefits of:
(a) Diversification.
(b) The time value of money.
(c) Interest tax shields.
(d) Depreciation tax shields.
(e) A 'buy and hold' investment strategy.
A mining firm has just discovered a new mine. So far the news has been kept a secret.
The net present value of digging the mine and selling the minerals is $250 million, but $500 million of new equity and $300 million of new bonds will need to be issued to fund the project and buy the necessary plant and equipment.
The firm will release the news of the discovery and equity and bond raising to shareholders simultaneously in the same announcement. The shares and bonds will be issued shortly after.
Once the announcement is made and the new shares and bonds are issued, what is the expected increase in the value of the firm's assets ##(\Delta V)##, market capitalisation of debt ##(\Delta D)## and market cap of equity ##(\Delta E)##? Assume that markets are semi-strong form efficient.
The triangle symbol ##\Delta## is the Greek letter capital delta which means change or increase in mathematics.
Remember: ##\Delta V = \Delta D+ \Delta E##
(a) ##\Delta V = 250m##, ##ΔD = 300m##, ##ΔE= 250##
(b) ##\Delta V = 250m##, ##ΔD = 300m##, ##ΔE= 750##
(c) ##\Delta V = 400m##, ##ΔD = 300m##, ##ΔE= -250##
(d) ##\Delta V = 1,050m##, ##ΔD = 300m##, ##ΔE= 750##
(e) ##\Delta V = 1,050m##, ##ΔD = 300m##, ##ΔE= 250##
Question 74 WACC, capital structure, CAPM
A firm's weighted average cost of capital before tax (##r_\text{WACC before tax}##) would increase due to:
(a) The firm issuing more debt and using the proceeds to repurchase stock.
(b) The firm issuing more equity and using the proceeds to pay off debt holders.
(c) The firm's industry becoming more systematically risky, for example if it was a mining company whose performance became more sensitive to countries' GDP growth, so the correlation of the firm's returns with the market was higher.
(d) The firm's industry becoming less systematically risky, for example if it was a child care centre and the government announced higher subsidies for parents using child care centres, so the correlation of the firm's returns with the market was lower.
Question 98 capital structure, CAPM
A firm changes its capital structure by issuing a large amount of debt and using the funds to repurchase shares. Its assets are unchanged. Ignore interest tax shields.
Question 524 risk, expected and historical returns, bankruptcy or insolvency, capital structure, corporate financial decision theory, limited liability
(a) Stocks are higher risk investments than debt.
(b) Stocks have higher expected returns than debt.
(c) Firms' past realised stock returns are always higher than their past realised debt returns.
(d) In the event of bankruptcy, stock holders are paid after debt holders are fully paid.
(e) Stock holders have a residual claim on the firm's assets.
Question 566 capital structure, capital raising, rights issue, on market repurchase, dividend, stock split, bonus issue
A company's share price fell by 20% and its number of shares rose by 25%. Assume that there are no taxes, no signalling effects and no transaction costs.
Which one of the following corporate events may have happened?
(a) $1 cash dividend when the pre-announcement stock price was $5.
(b) On-market buy-back of 20% of the company's outstanding stock.
(c) 5 for 4 stock split.
(d) 1 for 5 bonus issue.
(e) 1 for 4 rights issue at a subscription price of $3 when the pre-announcement stock price was $5.
Question 567 stock split, capital structure
A company conducts a 4 for 3 stock split. What is the percentage change in the stock price and the number of shares outstanding? The answers are given in the same order.
(a) -33.33%, 50%
(b) -25%, 33.33%
(c) -25%, 25%
(d) -20%, 25%
(e) 33.33%, -25%
Question 568 rights issue, capital raising, capital structure
A company conducts a 1 for 5 rights issue at a subscription price of $7 when the pre-announcement stock price was $10. What is the percentage change in the stock price and the number of shares outstanding? The answers are given in the same order. Ignore all taxes, transaction costs and signalling effects.
(b) -5%, 20%
(c) 0%, 20%
(d) 7.14%, 20%
(e) 11.67%, 0%
Question 75 WACC, CAPM
50 million shares outstanding.
The market price of one share is currently $6.
Market analysts believe that the company's ordinary shares have a beta of 2.
The company has 1 million preferred stock which have a face (or par) value of $100 and pay a constant dividend of 10% of par. They currently trade for $80 each.
The company's debentures are publicly traded and their market price is equal to 90% of their face value.
The debentures have a total face value of $60,000,000 and the current yield to maturity of corporate debentures is 10% per annum. The corporate tax rate is 30%.
140 million shares outstanding.
The company's debentures are publicly traded and their market price is equal to 93% of the face value.
The debentures have a total face value of $50,000,000 and the current yield to maturity of corporate debentures is 12% per annum.
The risk-free rate is 8.50% and the market return is 13.7%.
Market analysts estimated that the company's stock has a beta of 0.90.
The corporate tax rate is 30%.
What is the company's after-tax weighted average cost of capital (WACC) in a classical tax system?
A firm can issue 3 year annual coupon bonds at a yield of 10% pa and a coupon rate of 8% pa.
The beta of its levered equity is 2. The market's expected return is 10% pa and 3 year government bonds yield 6% pa with a coupon rate of 4% pa.
The market value of equity is $1 million and the market value of debt is $1 million. The corporate tax rate is 30%.
What is the firm's after-tax WACC? Assume a classical tax system.
(a) 8.40%
Question 117 WACC
A firm can issue 5 year annual coupon bonds at a yield of 8% pa and a coupon rate of 12% pa.
The beta of its levered equity is 1. Five year government bonds yield 5% pa with a coupon rate of 6% pa. The market's expected dividend return is 4% pa and its expected capital return is 6% pa.
The firm's debt-to-equity ratio is 2:1. The corporate tax rate is 30%.
(b) 8.93%
(c) 8.53%
(d) 7.80%
100 million ordinary shares outstanding which are trading at a price of $5 each. Market analysts estimated that the company's ordinary stock has a beta of 1.5. The risk-free rate is 5% and the market return is 10%.
1 million preferred shares which have a face (or par) value of $100 and pay a constant annual dividend of 9% of par. The next dividend will be paid in one year. Assume that all preference dividends will be paid when promised. They currently trade at a price of $90 each.
Debentures that have a total face value of $200 million and a yield to maturity of 6% per annum. They are publicly traded and their market price is equal to 110% of their face value.
The corporate tax rate is 30%. All returns and yields are given as effective annual rates.
Question 92 CAPM, SML, CML
Which statement(s) are correct?
(i) All stocks that plot on the Security Market Line (SML) are fairly priced.
(ii) All stocks that plot above the Security Market Line (SML) are overpriced.
(iii) All fairly priced stocks that plot on the Capital Market Line (CML) have zero idiosyncratic risk.
(d) All statements (i), (ii) and (iii) are true.
(e) Only statements (i) and (iii) are true.
Question 80 CAPM, risk, diversification
Diversification is achieved by investing in a large amount of stocks. What type of risk is reduced by diversification?
(a) Idiosyncratic risk.
(b) Systematic risk.
(c) Both idiosyncratic and systematic risk.
(d) Market risk.
(e) Beta risk.
Question 81 risk, correlation, diversification
Stock A and B's returns have a correlation of 0.3. Which statement is NOT correct?
(a) If stock A's return increases, stock B's return is also expected to increase.
(b) If stock A's return decreases, stock B's return is also expected to decrease.
(c) If stock A and B were combined in a portfolio, there would be no diversification at all since they are positively correlated.
(d) Stock A and B's returns have positive covariance.
(e) a and b.
Question 236 diversification, correlation, risk
Diversification in a portfolio of two assets works best when the correlation between their returns is:
(a) -1
(b) -0.5
(d) 0.5
(e) 1
Question 66 CAPM, SML
Government bonds currently have a return of 5% pa. A stock has an expected return of 6% pa and the market return is 7% pa. What is the beta of the stock?
(a) -0.5
(c) 0.5
Question 72 CAPM, portfolio beta, portfolio risk
Stock Expected
return Standard
deviation Correlation Beta Dollars
A 0.2 0.4 0.12 0.5 40
B 0.3 0.8 1.5 80
What is the beta of the above portfolio?
(a) 0.75
(b) 0.833333333
(d) 1.166666667
Question 71 CAPM, risk
Stock A has a beta of 0.5 and stock B has a beta of 1. Which statement is NOT correct?
(a) Stock A has less systematic risk than stock B, so stock A's return should be less than stock B's.
(b) Stock B has the same systematic risk as the market, so its return should be the same as the market's.
(c) Stock B has the same beta as the market, so it also has the same total risk as the market.
(d) If stock A and B were combined in a portfolio with weights of 50% each, the beta of the portfolio would be 0.75.
(e) Stocks A and B have more systematic risk than the risk free security (government bonds) so their return should be greater than the risk free rate.
Which statement is the most correct?
(a) The risk free rate has zero systematic risk and zero idiosyncratic risk.
(b) The market portfolio has zero idiosyncratic risk.
(c) The market portfolio has zero systematic risk.
(d) a and b are true.
(e) a and c are true.
Question 93 correlation, CAPM, systematic risk
A stock's correlation with the market portfolio increases while its total risk is unchanged. What will happen to the stock's expected return and systematic risk?
(a) The stock will have a higher return and higher systematic risk.
(b) The stock will have a lower return and higher systematic risk.
(c) The stock will have a higher return and lower systematic risk.
(d) The stock will have a lower return and lower systematic risk.
(e) The stock's return and systematic risk will be unchanged.
Question 106 CAPM
A fairly priced stock has an expected return of 15% pa. Treasury bonds yield 5% pa and the market portfolio's expected return is 10% pa. What is the beta of the stock?
(a) 0
(b) 0.5
Question 86 CAPM
Treasury bonds currently have a return of 5% pa. A stock has a beta of 0.5 and the market return is 10% pa. What is the expected return of the stock?
(a) 5% pa
(b) 7.5% pa
(c) 10% pa
(d) 12.5% pa
(e) 20% pa
According to the theory of the Capital Asset Pricing Model (CAPM), total variance can be broken into two components, systematic variance and idiosyncratic variance. Which of the following events would be considered the most diversifiable according to the theory of the CAPM?
(a) Global economic recession.
(b) A major terrorist attack, grounding all commercial aircraft in the US and Europe.
(c) An increase in corporate tax rates.
(d) The outbreak of world war.
(e) A company's poor earnings announcement.
Question 112 CAPM, risk
According to the theory of the Capital Asset Pricing Model (CAPM), total risk can be broken into two components, systematic risk and idiosyncratic risk. Which of the following events would be considered a systematic, undiversifiable event according to the theory of the CAPM?
(a) A decrease in house prices in one city.
(b) An increase in mining industry tax rates.
(d) A case of fraud at a major retailer.
(e) A poor earnings announcement from a major firm.
Question 110 CAPM, SML, NPV
The security market line (SML) shows the relationship between beta and expected return.
Investment projects that plot above the SML would have:
(a) A positive NPV.
(b) A zero NPV.
(c) A negative NPV.
(d) A large amount of diversifiable risk.
(e) Zero diversifiable risk.
A fairly priced stock has a beta that is the same as the market portfolio's beta. Treasury bonds yield 5% pa and the market portfolio's expected return is 10% pa. What is the expected return of the stock?
(a) 5%
(b) 7.5%
Question 232 CAPM, DDM
A stock has a beta of 0.5. Its next dividend is expected to be $3, paid one year from now. Dividends are expected to be paid annually and grow by 2% pa forever. Treasury bonds yield 5% pa and the market portfolio's expected return is 10% pa. All returns are effective annual rates.
What is the price of the stock now?
(e) $37.5
Question 617 systematic and idiosyncratic risk, risk, CAPM
A stock's required total return will increase when its:
(a) Systematic risk increases.
(b) Idiosyncratic risk increases.
(c) Total risk increases.
(d) Systematic risk decreases.
(e) Idiosyncratic risk decreases.
A fairly priced stock has an expected return equal to the market's. Treasury bonds yield 5% pa and the market portfolio's expected return is 10% pa. What is the stock's beta?
Question 627 CAPM, SML, NPV, Jensens alpha
Assets A, B, M and ##r_f## are shown on the graphs above. Asset M is the market portfolio and ##r_f## is the risk free yield on government bonds. Which of the below statements is NOT correct?
(a) Asset A has a Jensen's alpha of 4.5% pa.
(b) Asset A is under-priced.
(c) The NPV of buying asset A is zero.
(d) Asset B has a Jensen's alpha of zero.
(e) Asset B is fairly priced.
Question 235 SML, NPV, CAPM, risk
Investment projects that plot on the SML would have:
(a) A positive NPV and should be accepted.
(c) A negative NPV and should be rejected.
Question 628 CAPM, SML, risk, no explanation
Assets A, B, M and ##r_f## are shown on the graphs above. Asset M is the market portfolio and ##r_f## is the risk free yield on government bonds. Assume that investors can borrow and lend at the risk free rate. Which of the below statements is NOT correct?
(a) Asset A has the same systematic risk as asset B.
(b) Asset A has more total variance than asset B.
(c) Asset B has zero idiosyncratic risk. Asset B must be a portfolio of half the market portfolio and half government bonds.
(d) If risk-averse investors were forced to invest all of their wealth in a single risky asset, so they could not diversify, every investor would logically choose asset A over the other three assets.
(e) Assets M and B have the highest Sharpe ratios, which is defined as the gradient of the capital allocation line (CAL) from the government bonds through the asset on the graph of expected return versus total standard deviation.
Government bonds currently have a return of 5%. A stock has a beta of 2 and the market return is 7%. What is the expected return of the stock?
(c) 9%
Question 244 CAPM, SML, NPV, risk
Examine the following graph which shows stocks' betas ##(\beta)## and expected returns ##(\mu)##:
Assume that the CAPM holds and that future expectations of stocks' returns and betas are correctly measured. Which statement is NOT correct?
(a) Asset A is underpriced.
(b) Asset B has a negative alpha (a negative excess return or abnormal return).
(c) Buying asset C would be a positive NPV investment.
(d) Asset D has less systematic variance than the market portfolio (M).
(e) Asset E is fairly priced.
Question 82 portfolio return
deviation Correlation Dollars
A 0.1 0.4 0.5 60
B 0.2 0.6 140
What is the expected return of the above portfolio?
(b) 0.17
Question 556 portfolio risk, portfolio return, standard deviation
An investor wants to make a portfolio of two stocks A and B with a target expected portfolio return of 12% pa.
Stock A has an expected return of 10% pa and a standard deviation of 20% pa.
Stock B has an expected return of 15% pa and a standard deviation of 30% pa.
The correlation coefficient between stock A and B's expected returns is 70%.
What will be the annual standard deviation of the portfolio with this 12% pa target return?
(a) 24.28168% pa
(b) 24% pa
(c) 22.126907% pa
(d) 19.697716% pa
(e) 16.970563% pa
Question 557 portfolio weights, portfolio return
An investor wants to make a portfolio of two stocks A and B with a target expected portfolio return of 6% pa.
Stock A has an expected return of 5% pa.
Stock B has an expected return of 10% pa.
What portfolio weights should the investor have in stocks A and B respectively?
(a) 80%, 20%
(b) 60%, 40%
(c) 40%, 60%
(d) 20%, 80%
(e) 20%, 20%
Question 558 portfolio weights, portfolio return, short selling
(a) 200%, -100%
(b) 200%, 100%
(c) -100%, 200%
(d) 100%, 200%
(e) -100%, 100%
Question 73 portfolio risk, standard deviation
deviation Covariance ##(\sigma_{A,B})## Beta Dollars
What is the standard deviation (not variance) of the above portfolio? Note that the stocks' covariance is given, not correlation.
deviation Correlation ##(\rho_{A,B})## Dollars
What is the standard deviation (not variance) of the above portfolio?
Question 111 portfolio risk, correlation
All things remaining equal, the variance of a portfolio of two positively-weighted stocks rises as:
(a) The correlation between the stocks' returns rise.
(b) The correlation between the stocks' returns decline.
(c) The portfolio standard deviation declines.
(d) Both stocks' individual variances decline.
(e) Both stocks' individual standard deviations decline.
Question 285 covariance, portfolio risk
Two risky stocks A and B comprise an equal-weighted portfolio. The correlation between the stocks' returns is 70%.
If the variance of stock A increases but the:
Prices and expected returns of each stock stays the same,
Variance of stock B's returns stays the same,
Correlation of returns between the stocks stays the same.
(a) The variance of the portfolio will increase.
(b) The standard deviation of the portfolio will increase.
(c) The covariance of returns between stocks A and B will stay the same.
(d) The portfolio return will stay the same.
(e) The portfolio value will stay the same.
Question 294 short selling, portfolio weights
Which of the following statements about short-selling is NOT true?
(a) Short sellers benefit from price falls.
(b) To short sell, you must borrow the asset from person A and sell it to person B, then later on buy an identical asset from person C and return it to person A.
(c) Short selling only works for assets that are 'fungible' which means that there are many that are identical and substitutable, such as shares and bonds and unlike real estate.
(d) An investor who short-sells an asset has a negative weight in that asset.
(e) An investor who short-sells an asset is said to be 'long' that asset.
Question 305 option, short selling, speculation
You believe that the price of a share will fall significantly very soon, but the rest of the market does not. The market thinks that the share price will remain the same. Assuming that your prediction will soon be true, which of the following trades is a bad idea? In other words, which trade will NOT make money or prevent losses?
(a) Sell all existing stock that you own.
(b) Short sell the stock.
(c) Buy put options on the stock.
(d) Sell put options on the stock.
(e) Sell call options on the stock.
Question 591 short selling, future, option
After doing extensive fundamental analysis of a company, you believe that their shares are overpriced and will soon fall significantly. The market believes that there will be no such fall.
Which of the following strategies is NOT a good idea, assuming that your prediction is true?
(a) Sell any of the firm's shares that you already own.
(b) Short-sell the firm's shares.
(c) Sell futures written on the shares.
(d) Buy put options written on the shares.
(e) Buy call options written on the shares.
Question 589 future, contango, market efficiency
In general, stock prices tend to rise. What does this mean for futures on equity?
(a) Equity futures prices tend to be higher than spot prices. This is called contango.
(b) Equity futures prices tend to be equal to spot prices.
(c) Equity futures are generally under-priced.
(d) Equity futures are generally over-priced.
(e) Long equity futures traders tend to make more money than short equity futures traders.
Question 307 risk, variance
Let the variance of returns for a share per month be ##\sigma_\text{monthly}^2##.
What is the formula for the variance of the share's returns per year ##(\sigma_\text{yearly}^2)##?
Assume that returns are independently and identically distributed (iid) so they have zero auto correlation, meaning that if the return was higher than average today, it does not indicate that the return tomorrow will be higher or lower than average.
(a) ##\sigma_\text{yearly}^2 = \sigma_\text{monthly}^2##
(b) ##\sigma_\text{yearly}^2 = \sigma_\text{monthly}^2 \times 12##
(c) ##\sigma_\text{yearly}^2 = \sigma_\text{monthly}^2 \times 12^2##
(d) ##\sigma_\text{yearly}^2 = \sigma_\text{monthly}^2 \times \sqrt{12}##
(e) ##\sigma_\text{yearly}^2 = \sigma_\text{monthly}^2 \times {12}^{1/3}##
Question 308 risk, standard deviation, variance, no explanation
A stock's standard deviation of returns is expected to be:
0.09 per month for the first 5 months;
0.14 per month for the next 7 months.
What is the expected standard deviation of the stock per year ##(\sigma_\text{annual})##?
Assume that returns are independently and identically distributed (iid) and therefore have zero auto-correlation.
(a) ##\sigma_\text{annual} = 0.09 \times 5 + 0.14 \times 7##
(b) ##\sigma_\text{annual} = (0.09 \times 5 + 0.14 \times 7)^{1/2}##
(c) ##\sigma_\text{annual} = (0.09^2 \times 5 + 0.14^2 \times 7)^{1/2}##
(d) ##\sigma_\text{annual} = (1+0.09)^5\times (1+0.14)^7 - 1##
(e) ##\sigma_\text{annual} = \left( \dfrac{0.09^2 \times 5 + 0.14^2 \times 7}{12} \right)^{1/2}##
Question 559 variance, standard deviation, covariance, correlation
Which of the following statements about standard statistical mathematics notation is NOT correct?
(a) The arithmetic average of variable X is represented by ##\bar{X}##.
(b) The standard deviation of variable X is represented by ##\sigma_X##.
(c) The variance of variable X is represented by ##\sigma_X^2##.
(d) The covariance between variables X and Y is represented by ##\sigma_{X,Y}^2##.
(e) The correlation between variables X and Y is represented by ##\rho_{X,Y}##.
Question 560 standard deviation, variance
The standard deviation and variance of a stock's annual returns are calculated over a number of years. The units of the returns are percent per annum ##(\% pa)##.
What are the units of the standard deviation ##(\sigma)## and variance ##(\sigma^2)## of returns respectively?
(a) Percentage points per annum ##(\text{pp pa})## and percentage points per annum ##(\text{pp pa})##.
(b) Percentage points per annum ##(\text{pp pa})## and percentage points per annum all squared ##\left( (\text{pp pa})^2 \right)##.
(c) Percentage points per annum all squared ##\left( (\text{pp pa})^2 \right)## and percentage points per annum ##(\text{pp pa})##.
(d) Percentage points per annum all squared ##\left( (\text{pp pa})^2 \right)## and percentage points per annum all squared ##\left( (\text{pp pa})^2 \right)##.
(e) Percent per annum ##(\% pa)## and percent per annum ##(\% pa)##.
Hint: Visit Wikipedia to understand the difference between percentage points ##(\text{pp})## and percent ##(\%)##.
Question 669 beta, CAPM, risk
Which of the following is NOT a valid method for estimating the beta of a company's stock? Assume that markets are efficient, a long history of past data is available, the stock possesses idiosyncratic and market risk. The variances and standard deviations below denote total risks.
(a) ##Β_E=\dfrac{cov(r_E,r_M )}{var(r_M)}##
(b) ##Β_E=\dfrac{correl(r_E,r_M ).sd(r_E)}{sd(r_M)} ##
(c) ##Β_E=\dfrac{sd(r_E)}{sd(r_M)}##, since ##var(r_E)=β_E^2.var(r_M)##
(d) ##Β_E=\dfrac{r_E-r_f}{r_M-r_f }##, since ##r_E=r_f+Β_E. (r_M-r_f )##
(e) ##Β_E= \left(B_V - \dfrac{D}{V}.Β_D \right).\dfrac{V}{E}##, since ##B_V=\dfrac{E}{V}.Β_E+\dfrac{D}{V}.Β_D ##
Question 274 derivative terminology, option
The 'option price' in an option contract is paid at the start when the option contract is agreed to. or ?
The 'option strike price' in an option contract, also known as the exercise price, is paid at the start when the option contract is agreed to. or ?
Question 277 derivative terminology, future
The 'initial margin', also known as the performance bond in a futures contract, is paid at the start when the futures contract is agreed to. or ?
Question 563 correlation
What is the correlation of a variable X with itself?
The corr(X, X) or ##\rho_{X,X}## equals:
(a) var(X) or ##\sigma_X^2##
(b) sd(X) or ##\sigma_X##
(e) Mathematically undefined
The following is the Dividend Discount Model used to price stocks:
### p_0=\frac{d_1}{r-g} ###
Which of the following statements about the Dividend Discount Model is NOT correct?
(a) The dividend yield is equal to ##(r-g)##.
(b) The dividend yield is equal to ##\left( \dfrac{d_1}{p_0} \right)##.
(c) The total return of the stock is equal to ##(r)##.
(d) The total return of the stock is equal to ##\left( \dfrac{d_1+p_0.g}{p_0} \right)##.
(e) The total return of the stock is equal to ##(r+g)##.
Question 293 covariance, correlation, portfolio risk
All things remaining equal, the higher the correlation of returns between two stocks:
(a) The more diversification is possible when those stocks are combined in a portfolio.
(b) The lower the variance of returns of an equally-weighted portfolio of those stocks.
(c) The lower the volatility of returns of an equal-weighted portfolio of those stocks.
(d) The higher the covariance between those stocks' returns.
(e) The more likely that when one stock has a positive return, the other has a negative return.
Question 292 standard deviation, risk
Find the sample standard deviation of returns using the data in the table:
Stock Returns
Year Return pa
2010 -0.2
The returns above and standard deviations below are given in decimal form.
Question 471 risk, accounting ratio
High risk firms in danger of bankruptcy tend to have:
(a) Low debt to assets ratios.
(b) High quick ratios.
(c) Low interest coverage ratios.
(d) Positive amounts of net working capital.
(e) High net profit margins.
Question 495 risk, accounting ratio, no explanation
(b) Low quick ratios.
(c) High interest coverage ratios.
Question 622 expected and historical returns, risk
An economy has only two investable assets: stocks and cash.
Stocks had a historical nominal average total return of negative two percent per annum (-2% pa) over the last 20 years. Stocks are liquid and actively traded. Stock returns are variable, they have risk.
Cash is riskless and has a nominal constant return of zero percent per annum (0% pa), which it had in the past and will have in the future. Cash can be kept safely at zero cost. Cash can be converted into shares and vice versa at zero cost.
The nominal total return of the shares over the next year is expected to be:
(a) Less than or equal to negative two percent per annum ##(r_\text{shares} \leq -0.02)##.
(b) Exactly negative two percent per annum ##(r_\text{shares} = -0.02)##.
(c) More than or equal to negative two percent per annum ##(r_\text{shares} \geq -0.02)##.
(d) Less than or equal to zero percent per annum ##(r_\text{shares} \leq 0)##.
(e) More than or equal to zero percent per annum ##(r_\text{shares} \geq 0)##.
Question 283 portfolio risk, correlation, needs refinement
Three important classes of investable risky assets are:
Corporate debt which has low total risk,
Real estate which has medium total risk,
Equity which has high total risk.
Assume that the correlation between total returns on:
Corporate debt and real estate is 0.1,
Corporate debt and equity is 0.1,
Real estate and equity is 0.5.
You are considering investing all of your wealth in one or more of these asset classes. Which portfolio will give the lowest total risk? You are restricted from shorting any of these assets. Disregard returns and the risk-return trade-off, pretend that you are only concerned with minimising risk.
(a) Most money in corporate debt, with some money in equity and real estate.
(b) Most money in equity, with some money in corporate debt and real estate.
(c) Most money in real estate, with some money in corporate debt and equity.
(d) Most money in corporate debt, with some money in real estate and none in equity.
(e) All money in corporate debt.
Question 561 covariance, correlation
The covariance and correlation of two stocks X and Y's annual returns are calculated over a number of years. The units of the returns are in percent per annum ##(\% pa)##.
What are the units of the covariance ##(\sigma_{X,Y})## and correlation ##(\rho_{X,Y})## of returns respectively?
(e) Percentage points per annum all squared ##\left( (\text{pp pa})^2 \right)## and a pure number with no units.
The following table shows a sample of historical total returns of shares in two different companies A and B.
Total effective annual returns
Year ##r_A## ##r_B##
2007 0.2 0.4
2008 0.04 -0.2
2009 -0.1 -0.3
What is the historical sample covariance (##\hat{\sigma}_{A,B}##) and correlation (##\rho_{A,B}##) of stock A and B's total effective annual returns?
(a) 0.05696, 0.702247
(b) 0.05696, 0.238663
(c) 0.053333, 0.936329
(d) 0.040889, 0.930519
(e) 0.04, 0.930519
Question 105 NPV, risk, market efficiency
A person is thinking about borrowing $100 from the bank at 7% pa and investing it in shares with an expected return of 10% pa. One year later the person will sell the shares and pay back the loan in full. Both the loan and the shares are fairly priced.
What is the Net Present Value (NPV) of this one year investment? Note that you are asked to find the present value (##V_0##), not the value in one year (##V_1##).
(b) $3
(c) $2.8037
(d) $2.7273
(e) $0
Question 248 CAPM, DDM, income and capital returns
The total return of any asset can be broken down in different ways. One possible way is to use the dividend discount model (or Gordon growth model):
###p_0 = \frac{c_1}{r_\text{total}-r_\text{capital}}###
Which, since ##c_1/p_0## is the income return (##r_\text{income}##), can be expressed as:
###r_\text{total}=r_\text{income}+r_\text{capital}###
So the total return of an asset is the income component plus the capital or price growth component.
Another way to break up total return is to use the Capital Asset Pricing Model:
###r_\text{total}=r_\text{f}+β(r_\text{m}- r_\text{f})###
###r_\text{total}=r_\text{time value}+r_\text{risk premium}###
So the risk free rate is the time value of money and the term ##β(r_\text{m}- r_\text{f})## is the compensation for taking on systematic risk.
Using the above theory and your general knowledge, which of the below equations, if any, are correct?
(I) ##r_\text{income}=r_\text{time value}##
(II) ##r_\text{income}=r_\text{risk premium}##
(III) ##r_\text{capital}=r_\text{time value}##
(IV) ##r_\text{capital}=r_\text{risk premium}##
(V) ##r_\text{income}+r_\text{capital}=r_\text{time value}+r_\text{risk premium}##
Which of the equations are correct?
(a) I, IV and V only.
(b) II, III and V only.
(c) V only.
(d) All are true.
(e) None are true.
Question 695 utility, risk aversion, utility function
Mr Blue, Miss Red and Mrs Green are people with different utility functions. Which of the statements about the 3 utility functions is NOT correct?
(a) All rational people prefer more wealth to less.
(b) Mr Blue is risk averse.
(c) Miss Red is risk neutral.
(d) Mrs Green is risk averse.
(e) Mrs Green may enjoy gambling.
Mr Blue, Miss Red and Mrs Green are people with different utility functions.
(a) Mr Blue is as happy with zero wealth as he is with $1,000. Similarly for Miss Red and Mrs Green.
(b) All of the people would appear irrational to an economist. Though Mr Blue appears to be rational when he has more than $192 in wealth.
(c) Mr Blue is risk averse. Miss Red is risk neutral. Mrs Green is risk loving.
(d) Miss Red is totally indifferent to how much wealth she has. She doesn't care about gaining or losing money.
(e) Mr Blue prefers more to less up to a wealth of around $192. At about $192 he is the happiest he can be. This is his bliss point. With more than $192 he becomes less happy.
(a) Mr Blue prefers more wealth to less. Mrs Green enjoys losing wealth.
(b) Miss Red has the same utility no matter how much wealth she has.
(c) Mr Blue is risk averse.
(d) Miss Red is risk averse.
(e) Mrs Green is risk loving.
(a) Neither Miss Red nor Mrs Green would appear rational to an economist.
(b) Mrs Green is satiated when she has $25 of wealth. That is her bliss point.
(c) Mrs Green is risk loving when she has between zero and $25 of wealth, same as Mr Blue.
(d) Mrs Green is risk averse when she has between $25 and $50 of wealth.
(e) Mrs Green is risk loving when she has between $50 and $100 of wealth, same as Mr Blue.
Question 665 stock split
A company conducts a 10 for 3 stock split. What is the percentage increase in the stock price and the number of shares outstanding? The answers are given in the same order.
(a) -76.92%, 333.33%
(b) -70%, 333.33%
(c) -70%, 233.33%
(d) -57.14%, 233.33%
(e) 233.33%, -70%
Question 469 franking credit, personal tax on dividends, imputation tax system, no explanation
A firm pays a fully franked cash dividend of $70 to one of its Australian shareholders who has a personal marginal tax rate of 45%. The corporate tax rate is 30%.
What will be the shareholder's personal tax payable due to the dividend payment?
Question 448 franking credit, personal tax on dividends, imputation tax system
A small private company has a single shareholder. This year the firm earned a $100 profit before tax. All of the firm's after tax profits will be paid out as dividends to the owner.
The corporate tax rate is 30% and the sole shareholder's personal marginal tax rate is 45%.
The Australian imputation tax system applies because the company generates all of its income in Australia and pays corporate tax to the Australian Tax Office. Therefore all of the company's dividends are fully franked. The sole shareholder is an Australian for tax purposes and can therefore use the franking credits to offset his personal income tax liability.
What will be the personal tax payable by the shareholder and the corporate tax payable by the company?
(a) Personal tax of $6.43 and corporate tax of $45.
(b) Personal tax of $15 and corporate tax of $30.
(c) Personal tax of $16.5 and corporate tax of $45.
(d) Personal tax of $31.5 and corporate tax of $30.
(e) Personal tax of $45 and corporate tax of $0.
Question 625 dividend re-investment plan, capital raising
Which of the following statements about dividend re-investment plans (DRP's) is NOT correct?
(a) DRP's are voluntary, shareholders only participate if they choose.
(b) DRP's increase the number of shares.
(c) The number of shares issued to a shareholder participating in a DRP is usually calculated as their total dividends owed, divided by the allocation share price which is usually close to the current market share price.
(d) DRP's do not incur brokerage costs for the shareholder. This is unlike the case where the shareholder uses the cash dividend to buy more shares herself.
(e) If all shareholders participated in a company's DRP, the company would not pay any dividends and the firm's share price would not fall due to the cash dividend or the DRP.
Question 70 payout policy
Due to floods overseas, there is a cut in the supply of the mineral iron ore and its price increases dramatically. An Australian iron ore mining company therefore expects a large but temporary increase in its profit and cash flows. The mining company does not have any positive NPV projects to begin, so what should it do? Select the most correct answer.
(a) Pay out the excess cash by increasing the regular dividend, and cutting it later.
(b) Pay out a special dividend.
(c) Conduct an on or off-market share repurchase.
(d) Conduct a share dividend (also called a 'bonus issue').
(e) Either b or c.
Question 550 fully amortising loan, interest only loan, APR, no explanation
Many Australian home loans that are interest-only actually require payments to be made on a fully amortising basis after a number of years.
You decide to borrow $600,000 from the bank at an interest rate of 4.25% pa for 25 years. The payments will be interest-only for the first 10 years (t=0 to 10 years), then they will have to be paid on a fully amortising basis for the last 15 years (t=10 to 25 years).
Assuming that interest rates will remain constant, what will be your monthly payments over the first 10 years from now, and then the next 15 years after that? The answer options are given in the same order.
(a) $3,250.43, $4,513.67
(b) $3,250.43, $1,530.28
(c) $2,125, $4,513.67
(d) $2,125, $3,250.43
(e) $1,530.28, $3,250.43
Question 459 interest only loan, inflation
In Australia in the 1980's, inflation was around 8% pa, and residential mortgage loan interest rates were around 14%.
In 2013, inflation was around 2.5% pa, and residential mortgage loan interest rates were around 4.5%.
If a person can afford constant mortgage loan payments of $2,000 per month, how much more can they borrow when interest rates are 4.5% pa compared with 14.0% pa?
Give your answer as a proportional increase over the amount you could borrow when interest rates were high ##(V_\text{high rates})##, so:
###\text{Proportional increase} = \dfrac{V_\text{low rates}-V_\text{high rates}}{V_\text{high rates}} ###
Mortgage loan payments are made every month in arrears and all interest rates are given as annualised percentage rates (APR's) compounding per month.
(a) 0.095
Question 242 technical analysis, market efficiency
Select the most correct statement from the following.
'Chartists', also known as 'technical traders', believe that:
(a) Markets are weak-form efficient.
(b) Markets are semi-strong-form efficient.
(c) Past prices cannot be used to predict future prices.
(d) Past returns can be used to predict future returns.
(e) Stock prices reflect all publically available information.
Question 668 buy and hold, market efficiency, idiom
A quote from the famous investor Warren Buffet: "Much success can be attributed to inactivity. Most investors cannot resist the temptation to constantly buy and sell."
Buffet is referring to the buy-and-hold strategy which is to buy and never sell shares. Which of the following is a disadvantage of a buy-and-hold strategy? Assume that share markets are semi-strong form efficient. Which of the following is NOT an advantage of the strict buy-and-hold strategy? A disadvantage of the buy-and-hold strategy is that it reduces:
(a) Capital gains tax.
(b) Explicit transaction costs such as brokerage fees.
(c) Implicit transaction costs such as bid-ask spreads.
(d) Portfolio rebalancing to maintain maximum diversification.
(e) Time wasted on researching whether it's better to buy or sell.
Question 623 market efficiency, no explanation
The efficient markets hypothesis (EMH) and no-arbitrage pricing theory is most closely related to which of the following concepts?
(a) Competition.
(b) Opportunity costs.
(d) Diversification.
(e) The stand-alone principle, incremental cash flows and sunk costs.
Question 630 mispriced asset, NPV, DDM, market efficiency
A company advertises an investment costing $1,000 which they say is underpriced. They say that it has an expected total return of 15% pa, but a required return of only 10% pa. Of the 15% pa total expected return, the dividend yield is expected to always be 7% pa and rest is the capital yield.
Assuming that the company's statements are correct, what is the NPV of buying the investment if the 15% total return lasts for the next 100 years (t=0 to 100), then reverts to 10% after that time? Also, what is the NPV of the investment if the 15% return lasts forever?
In both cases, assume that the required return of 10% remains constant, the dividends can only be re-invested at 10% pa and all returns are given as effective annual rates.
The answer choices below are given in the same order (15% for 100 years, and 15% forever):
(a) 84,214.90, Infinite
(b) 2,521.12, 3,000
(c) 2,100.93, 2,500
(d) 1,249.38, 1,333.33
(e) 0, 0
Question 339 bond pricing, inflation, market efficiency, income and capital returns
Economic statistics released this morning were a surprise: they show a strong chance of consumer price inflation (CPI) reaching 5% pa over the next 2 years.
This is much higher than the previous forecast of 3% pa.
A vanilla fixed-coupon 2-year risk-free government bond was issued at par this morning, just before the economic news was released.
What is the expected change in bond price after the economic news this morning, and in the next 2 years? Assume that:
Inflation remains at 5% over the next 2 years.
Investors demand a constant real bond yield.
The bond price falls by the (after-tax) value of the coupon the night before the ex-coupon date, as in real life.
(a) Today the price would have increased significantly.
Over the next 2 years, the bond price is expected to increase, measured on each ex-coupon date.
(b) Today the price would have increased significantly.
Over the next 2 years, the bond price is expected to be unchanged, measured on each ex-coupon date.
(c) Today the price would have been unchanged.
(d) Today the price would have decreased significantly.
(e) Today the price would have decreased significantly.
Question 119 market efficiency, fundamental analysis, joint hypothesis problem
Your friend claims that by reading 'The Economist' magazine's economic news articles, she can identify shares that will have positive abnormal expected returns over the next 2 years. Assuming that her claim is true, which statement(s) are correct?
(i) Weak form market efficiency is broken.
(ii) Semi-strong form market efficiency is broken.
(iii) Strong form market efficiency is broken.
(iv) The asset pricing model used to measure the abnormal returns (such as the CAPM) is either wrong (mis-specification error) or is measured using the wrong inputs (data errors) so the returns may not be abnormal but rather fair for the level of risk.
(a) Only (iii) is true.
(b) Only (ii) and (iii) are true.
(c) Only (i), (ii) and (iii) are true.
(d) Either (ii) and (iii) are true, or (iv) is true, or (ii), (iii) and (iv) are true.
(e) Either (i), (ii) and (iii) are true, or (iv) is true, or all are true.
Question 544 bond pricing, capital raising, no explanation
Question 449 personal tax on dividends, classical tax system
The United States' classical tax system applies because the company generates all of its income in the US and pays corporate tax to the Internal Revenue Service. The shareholder is also an American for tax purposes.
Question 569 personal tax
The average weekly earnings of an Australian adult worker before tax was $1,542.40 per week in November 2014 according to the Australian Bureau of Statistics. Therefore average annual earnings before tax were $80,204.80 assuming 52 weeks per year. Personal income tax rates published by the Australian Tax Office are reproduced for the 2014-2015 financial year in the table below:
Tax on this income
0 – $18,200 Nil
$18,201 – $37,000 19c for each $1 over $18,200
$37,001 – $80,000 $3,572 plus 32.5c for each $1 over $37,000
$80,001 – $180,000 $17,547 plus 37c for each $1 over $80,000
$180,001 and over $54,547 plus 45c for each $1 over $180,000
The above rates do not include the Medicare levy of 2%. Exclude the Medicare levy from your calculations
How much personal income tax would you have to pay per year if you earned $80,204.80 per annum before-tax?
In 2014 the median starting salaries of male and female Australian bachelor degree accounting graduates aged less than 25 years in their first full-time industry job was $50,000 before tax, according to Graduate Careers Australia. See page 9 of this report. Personal income tax rates published by the Australian Tax Office are reproduced for the 2014-2015 financial year in the table below.
How much personal income tax would you have to pay per year if you earned $50,000 per annum before-tax?
(b) $7,797
(d) $18,500
(e) $22,500
Question 309 stock pricing, ex dividend date
A company announces that it will pay a dividend, as the market expected. The company's shares trade on the stock exchange which is open from 10am in the morning to 4pm in the afternoon each weekday. When would the share price be expected to fall by the amount of the dividend? Ignore taxes.
The share price is expected to fall during the:
(a) Day of the payment date, between the payment date's morning opening price and afternoon closing price.
(b) Night before the payment date, between the previous day's afternoon closing price and the payment date's morning opening price.
(c) Day of the ex-dividend date, between the ex-dividend date's morning opening price and afternoon closing price.
(d) Night before the ex-dividend date, between the last with-dividend date's afternoon closing price and the ex-dividend date's morning opening price.
(e) Day of the last with-dividend date, between the with-dividend date's morning opening price and afternoon closing price.
Question 202 DDM, payout policy
Currently, a mining company has a share price of $6 and pays constant annual dividends of $0.50. The next dividend will be paid in 1 year. Suddenly and unexpectedly the mining company announces that due to higher than expected profits, all of these windfall profits will be paid as a special dividend of $0.30 in 1 year.
If investors believe that the windfall profits and dividend is a one-off event, what will be the new share price? If investors believe that the additional dividend is actually permanent and will continue to be paid, what will be the new share price? Assume that the required return on equity is unchanged. Choose from the following, where the first share price includes the one-off increase in earnings and dividends for the first year only ##(P_\text{0 one-off})## , and the second assumes that the increase is permanent ##(P_\text{0 permanent})##:
(a) ##P_\text{0 one-off} = 9.6000, \space \space P_\text{0 permanent} = 6.2766##
(b) ##P_\text{0 one-off} = 6.3000, \space \space P_\text{0 permanent} = 6.2769##
(c) ##P_\text{0 one-off} = 9.6000, \space \space P_\text{0 permanent} = 6.3000##
(d) ##P_\text{0 one-off} = 6.2769, \space \space P_\text{0 permanent} = 9.6000##
(e) ##P_\text{0 one-off} = 6.3000, \space \space P_\text{0 permanent} = 9.6000##
Note: When a firm makes excess profits they sometimes pay them out as special dividends. Special dividends are just like ordinary dividends but they are one-off and investors do not expect them to continue, unlike ordinary dividends which are expected to persist.
Question 475 payout ratio, dividend, no explanation
What was CBA's approximate payout ratio over the 2014 financial year?
Note that the firm's interim and final dividends were $1.83 and $2.18 respectively over the 2014 financial year.
(d) 129.93%
(e) 247.53%
Question 214 rights issue
In late 2003 the listed bank ANZ announced a 2-for-11 rights issue to fund the takeover of New Zealand bank NBNZ. Below is the chronology of events:
23/10/2003. Share price closes at $18.30.
24/10/2003. 2-for-11 rights issue announced at a subscription price of $13. The proceeds of the rights issue will be used to acquire New Zealand bank NBNZ. Trading halt announced in morning before market opens.
28/10/2003. Trading halt lifted. Last (and only) day that shares trade cum-rights. Share price opens at $18.00 and closes at $18.14.
29/10/2003. Shares trade ex-rights.
All things remaining equal, what would you expect ANZ's stock price to open at on the first day that it trades ex-rights (29/10/2003)? Ignore the time value of money since time is negligibly short. Also ignore taxes.
Question 345 capital budgeting, break even, NPV
Project life 10 yrs
Initial investment in factory $10m
Depreciation of factory per year $1m
Expected scrap value of factory at end of project $0
Cost of capital per annum 10%
The firm's current liabilities are forecast to stay at $0.5m. The firm's current assets (mostly inventory) is currently $1m, but is forecast to grow by $0.1m at the end of each year due to the project.
At the end of the project, the current assets accumulated due to the project can be sold for the same price that they were bought.
A marketing survey was used to forecast sales. It cost $1.4m which was just paid. The cost has been capitalised by the accountants and is tax-deductible over the life of the project, regardless of whether the project goes ahead or not. This amortisation expense is not included in the depreciation expense listed in the table above.
Find the break even unit production (Q) per year to achieve a zero Net Income (NI) and Net Present Value (NPV), respectively. The answers below are listed in the same order.
(a) 750,000 and 750,000.
(b) 750,000 and 951,682.
(c) 750,000 and 987,396.
(d) 750,000 and 1,009,805.
(e) 750,000 and 1,024,807.
Question 594 future, continuously compounding rate
The current gold price is $700, gold storage costs are 2% pa and the risk free rate is 10% pa, both with continuous compounding.
What should be the 3 year gold futures price?
Question 634 continuously compounding rate
A $100 stock has a continuously compounded expected total return of 10% pa. Its dividend yield is 2% pa with continuous compounding. What do you expect its price to be in one year?
(a) $112.749685
(b) $110.517092
(d) $108.328707
A $100 stock has a continuously compounded expected total return of 10% pa. Its dividend yield is 2% pa with continuous compounding. What do you expect its price to be in 2.5 years?
(c) $126.905871
(e) $121.215844
Question 691 continuously compounding rate, effective rate, continuously compounding rate conversion, no explanation
A bank quotes an interest rate of 6% pa with quarterly compounding. Note that another way of stating this rate is that it is an annual percentage rate (APR) compounding discretely every 3 months.
Which of the following statements about this rate is NOT correct? All percentages are given to 6 decimal places. The equivalent:
(a) Continuously compounded rate is 5.955445% per annum. Note that this rate is the annual rate with continuous compounding.
(b) Continuously compounded rate is 1.500000% per quarter. Note that this rate is the quarterly rate with continuous compounding.
(c) Effective quarterly rate is 1.500000% per quarter. Note that this rate is the quarterly rate with discrete quarterly compounding.
(d) Effective annual rate is 6.136355% per annum. Note that this rate is the annual rate with discrete annual compounding.
(e) $1,000,000 invested in this bank account for one year will give $1,061,363.551 at the end of the year.
Question 329 DDM, expected and historical returns
### P_0= \frac{d_1}{r-g} ###
The pronumeral ##g## is supposed to be the:
(a) Expected future growth rate of the dividend.
(b) Actual historical growth rate of the dividend.
(c) Expected future growth rate of the total required return on equity r.
(d) Actual historical growth rate of the market share price.
(e) Actual historical growth rate of the return on equity (ROE) defined as (Net Income / Owners Equity).
Question 579 price gains and returns over time, time calculation, effective rate
How many years will it take for an asset's price to double if the price grows by 10% pa?
(a) 1.8182 years
(b) 3.3219 years
(c) 7.2725 years
(d) 11.5267 years
(e) 13.7504 years
Question 282 expected and historical returns, income and capital returns
You're the boss of an investment bank's equities research team. Your five analysts are each trying to find the expected total return over the next year of shares in a mining company. The mining firm:
Is regarded as a mature company since it's quite stable in size and was floated around 30 years ago. It is not a high-growth company;
Share price is very sensitive to changes in the price of the market portfolio, economic growth, the exchange rate and commodities prices. Due to this, its standard deviation of total returns is much higher than that of the market index;
Experienced tough times in the last 10 years due to unexpected falls in commodity prices.
Shares are traded in an active liquid market.
Your team of analysts present their findings, and everyone has different views. While there's no definitive true answer, who's calculation of the expected total return is the most plausible?
The analysts' source data is correct and true, but their inferences might be wrong;
All returns and yields are given as effective annual nominal rates.
(a) Alice says 5% pa since she calculated that this was the average total yield on government bonds over the last 10 years. She says that this is also the expected total yield implied by current prices on one year government bonds.
(b) Bob says 4% pa since he calculated that this was the average total return on the mining stock over the last 10 years.
(c) Cate says 3% pa since she calculated that this was the average growth rate of the share price over the last 10 years.
(d) Dave says 6% pa since he calculated that this was the average growth rate of the share market price index (not the accumulation index) over the last 10 years.
(e) Eve says 15% pa since she calculated that this was the discount rate implied by the dividend discount model using the current share price, forecast dividend in one year and a 3% growth rate in dividends thereafter, which is the expected long term inflation rate.
Question 659 APR, effective rate, effective rate conversion, no explanation
A home loan company advertises an interest rate of 9% pa, payable monthly. Which of the following statements about the interest rate is NOT correct? All rates are given with an accuracy of 4 decimal places.
(a) The APR compounding monthly is 9.000% pa.
(b) The effective monthly rate is 0.7500% pa.
(c) The effective annual rate is 9.3807% pa.
(d) The effective 6 month rate is 4.5000% pa.
(e) The APR compounding semi-annually is 9.1704% pa.
Question 551 fully amortising loan, time calculation, APR
You just entered into a fully amortising home loan with a principal of $600,000, a variable interest rate of 4.25% pa and a term of 25 years.
Immediately after settling the loan, the variable interest rate suddenly falls to 4% pa! You can't believe your luck. Despite this, you plan to continue paying the same home loan payments as you did before. How long will it now take to pay off your home loan?
Assume that the lower interest rate was granted immediately and that rates were and are now again expected to remain constant. Round your answer up to the nearest whole month.
(a) 301 months
(b) 288 months
(c) 271 months
(d) 270 months
(e) 75 months
Question 540 APR, effective rate, no explanation
Which one of the below statements about effective rates and annualised percentage rates (APR's) is NOT correct?
(a) An effective semi-annual rate could be called: "a six month rate compounding per six months".
(b) An APR compounding semi-annually could be called: "a yearly rate compounding per six months".
(c) An effective monthly rate could be called: "a monthly rate compounding every month".
(d) An APR compounding monthly could be called: "a monthly rate compounding per year".
(e) An effective daily rate could be called: "a daily rate compounding every day".
A 2 year corporate bond yields 3% pa with a coupon rate of 5% pa, paid semi-annually.
Find the effective monthly rate, effective six month rate, and effective annual rate.
##r_\text{eff monthly}##, ##r_\text{eff 6 month}##, ##r_\text{eff annual}##.
(a) 0.002466, 0.014889, 0.03.
(b) 0.002485, 0.015, 0.030225.
(c) 0.004074, 0.024695, 0.05.
(d) 0.004124, 0.025, 0.050625.
(e) 0.004167, 0.025, 0.05.
Question 253 NPV, APR
You just started work at your new job which pays $48,000 per year.
The human resources department have given you the option of being paid at the end of every week or every month.
Assume that there are 4 weeks per month, 12 months per year and 48 weeks per year.
Bank interest rates are 12% pa given as an APR compounding per month.
What is the dollar gain over one year, as a net present value, of being paid every week rather than every month?
Harvey Norman the large retailer often runs sales advertising 2 years interest free when you purchase its products. This offer can be seen as a free personal loan from Harvey Norman to its customers.
Assume that banks charge an interest rate on personal loans of 12% pa given as an APR compounding per month. This is the interest rate that Harvey Norman deserves on the 2 year loan it extends to its customers. Therefore Harvey Norman must implicitly include the cost of this loan in the advertised sale price of its goods.
If you were a customer buying from Harvey Norman, and you were paying immediately, not in 2 years, what is the minimum percentage discount to the advertised sale price that you would insist on? (Hint: if it makes it easier, assume that you're buying a product with an advertised price of $100).
A three year corporate bond yields 12% pa with a coupon rate of 10% pa, paid semi-annually.
Find the effective six month yield, effective annual yield and the effective daily yield. Assume that each month has 30 days and that there are 360 days in a year.
##r_\text{eff semi-annual}##, ##r_\text{eff yearly}##, ##r_\text{eff daily}##.
(a) 0.06, 0.1236, 0.000324.
(b) 0.058301, 0.12, 0.000315.
(c) 0.05, 0.1025, 0.000271.
(d) 0.05, 0.1, 0.000278.
(e) 0.048809, 0.1, 0.000265.
Question 145 NPV, APR, annuity due
A student just won the lottery. She won $1 million in cash after tax. She is trying to calculate how much she can spend per month for the rest of her life. She assumes that she will live for another 60 years. She wants to withdraw equal amounts at the beginning of every month, starting right now.
All of the cash is currently sitting in a bank account which pays interest at a rate of 6% pa, given as an APR compounding per month. On her last withdrawal, she intends to have nothing left in her bank account. How much can she withdraw at the beginning of each month?
(a) $1,388.89
Question 135 credit card, APR, no explanation
Your credit card shows a $600 debt liability. The interest rate is 24% pa, payable monthly. You can't pay any of the debt off, except in 6 months when it's your birthday and you'll receive $50 which you'll use to pay off the credit card. If that is your only repayment, how much will the credit card debt liability be one year from now?
Question 20 NPV, APR, Annuity
Your friend wants to borrow $1,000 and offers to pay you back $100 in 6 months, with more $100 payments at the end of every month for another 11 months. So there will be twelve $100 payments in total. She says that 12 payments of $100 equals $1,200 so she's being generous.
If interest rates are 12% pa, given as an APR compounding monthly, what is the Net Present Value (NPV) of your friend's deal?
(a) -648.51
(d) 125.51
Question 700 utility, risk aversion, utility function, gamble
Each person has $50 of initial wealth. A coin toss game is offered to each person at a casino where the player can win or lose $50. Each player can flip a coin and if they flip heads, they receive $50. If they flip tails then they will lose $50. Which of the following statements is NOT correct?
(a) Mr Blue's expected utility of wealth from gambling is 7.5 while refusing is 8.54. So the gamble makes him less happy.
(b) Miss Red's expected utility of wealth from gambling is 5 and refusing is also 5. So the gamble doesn't affect her happiness at all.
(c) Mr Blue's certainty equivalent of the risky gamble is $25. This is less than his current wealth which is why he would refuse.
(d) Miss Red's certainty equivalent of the risky gamble is any wealth. She's indifferent since she always has the same level of happiness.
(e) Mrs Green's certainty equivalent of the risky gamble is $25. This is less than her current wealth which is why she would refuse.
(a) Mr Blue's expected utility of wealth from gambling is 7.5 while refusing is 6.25. So the gamble makes him more happy.
(b) Miss Red's expected utility of wealth from gambling is 7.5 and refusing is also 7.5. This is why she is indifferent.
(c) Mr Blue's certainty equivalent of the risky gamble is $70.71. So he would pay to take part in the gamble.
(d) Miss Red's certainty equivalent of the risky gamble is $50.
(e) Mrs Green's certainty equivalent of the risky gamble is $70.71. She would enjoy taking part in the gamble.
(a) Mr Blue would enjoy the gamble.
(b) Miss Red would be indifferent to gambling or not.
(c) Mrs Green would dislike the gamble.
(d) Mr Blue's certainty equivalent of the risky gamble is $70.71. This is more than his current wealth which is why he would like to gamble.
(e) Miss Red's certainty equivalent of the risky gamble is $50. This is the same as her current wealth which is why she is indifferent to gambling or not.
Each person has $500 of initial wealth. A coin toss game is offered to each person at a casino where the player can win or lose $500. Each player can flip a coin and if they flip heads, they receive $500. If they flip tails then they will lose $500. Which of the following statements is NOT correct?
(a) All people prefer more rather than less wealth which is rational.
(b) Mr Blue is risk averse, Miss Red is risk neutral and Mrs Green is risk loving.
(c) Mr Blue's certainty equivalent of the gamble is $225. This is less than his current $500 which is why he would dislike the gamble.
(d) Miss Red's certainty equivalent of the gamble is $500. This is the same as her current $500 which is why she would be indifferent to gambling.
(e) Mrs Green's certainty equivalent of the gamble is $793.70. This is more than her current $500 which is why she would like the gamble.
(a) All people would appear rational to an economist since they prefer more wealth to less.
(b) Mrs Green and Miss Red would appear unusual to an economist since they are not risk averse.
(c) Mr Blue's certainty equivalent of the gamble is $64. This is less than his current wealth of $256 which is why he would refuse the gamble.
(d) Miss Red's certainty equivalent of the gamble is $256. This is the same as her current wealth of $256 which is why she would be indifferent to playing or not.
(e) Mrs Green's certainty equivalent of the gamble is $512. This is more than her current wealth of $256 which is why she would love to play.
Question 54 NPV, DDM
After year 4, the annual dividend will grow in perpetuity at -5% pa. Note that this is a negative growth rate, so the dividend will actually shrink. So,
the dividend at t=5 will be ##$1(1-0.05) = $0.95##,
the dividend at t=6 will be ##$1(1-0.05)^2 = $0.9025##, and so on.
What is the current price of the stock?
(a) $7.2968
(b) $7.5018
What will be the price of the stock in four and a half years (t = 4.5)?
Question 166 DDM, no explanation
A stock pays annual dividends. It just paid a dividend of $3. The growth rate in the dividend is 4% pa. You estimate that the stock's required return is 10% pa. Both the discount rate and growth rate are given as effective annual rates. Using the dividend discount model, what will be the share price?
(c) 31.2
A stock pays annual dividends. It just paid a dividend of $5. The growth rate in the dividend is 1% pa. You estimate that the stock's required return is 8% pa. Both the discount rate and growth rate are given as effective annual rates.
A share pays annual dividends. It just paid a dividend of $2. The growth rate in the dividend is 3% pa. You estimate that the stock's required return is 8% pa. Both the discount rate and growth rate are given as effective annual rates.
Using the dividend discount model, what is the share price?
(e) 41.2
A share just paid its semi-annual dividend of $5. The dividend is expected to grow at 1% every 6 months forever. This 1% growth rate is an effective 6 month rate.
Therefore the next dividend will be $5.05 in six months. The required return of the stock 8% pa, given as an effective annual rate.
Question 355 DDM, stock pricing
Stocks in the United States usually pay quarterly dividends. For example, the retailer Wal-Mart Stores paid a $0.47 dividend every quarter over the 2013 calendar year and plans to pay a $0.48 dividend every quarter over the 2014 calendar year.
Using the dividend discount model and net present value techniques, calculate the stock price of Wal-Mart Stores assuming that:
The time now is the beginning of January 2014. The next dividend of $0.48 will be received in 3 months (end of March 2014), with another 3 quarterly payments of $0.48 after this (end of June, September and December 2014).
The quarterly dividend will increase by 2% every year, but each quarterly dividend over the year will be equal. So each quarterly dividend paid in 2015 will be $0.4896 (##=0.48×(1+0.02)^1##), with the first at the end of March 2015 and the last at the end of December 2015. In 2016 each quarterly dividend will be $0.499392 (##=0.48×(1+0.02)^2##), with the first at the end of March 2016 and the last at the end of December 2016, and so on forever.
The total required return on equity is 6% pa.
The required return and growth rate are given as effective annual rates.
All cash flows and rates are nominal. Inflation is 3% pa.
Dividend payment dates and ex-dividend dates are at the same time.
Remember that there are 4 quarters in a year and 3 months in a quarter.
What is the current stock price?
Stocks in the United States usually pay quarterly dividends. For example, the software giant Microsoft paid a $0.23 dividend every quarter over the 2013 financial year and plans to pay a $0.28 dividend every quarter over the 2014 financial year.
Using the dividend discount model and net present value techniques, calculate the stock price of Microsoft assuming that:
The time now is the beginning of July 2014. The next dividend of $0.28 will be received in 3 months (end of September 2014), with another 3 quarterly payments of $0.28 after this (end of December 2014, March 2015 and June 2015).
The quarterly dividend will increase by 2.5% every year, but each quarterly dividend over the year will be equal. So each quarterly dividend paid in the financial year beginning in September 2015 will be $ 0.287 ##(=0.28×(1+0.025)^1)##, with the last at the end of June 2016. In the next financial year beginning in September 2016 each quarterly dividend will be $0.294175 ##(=0.28×(1+0.025)^2)##, with the last at the end of June 2017, and so on forever.
(a) $32.71126
(d) $30.859679
Question 503 DDM, NPV, stock pricing
A share currently worth $100 is expected to pay a constant dividend of $4 for the next 5 years with the first dividend in one year (t=1) and the last in 5 years (t=5).
The total required return is 10% pa.
What do you expected the share price to be in 5 years, just after the dividend at that time has been paid?
(a) $100
Question 520 NPV, DDM, no explanation
Constant perpetual yearly payments of $70, with the first payment in 2.5 years from now (first payment at t=2.5).
A single payment of $600 in 3 years and 9 months (t=3.75) from now.
(d) $1,026.438978
(e) $1,119.690058
Question 529 DDM, real and nominal returns and cash flows, inflation, real estate, no explanation
If housing rents are constrained from growing more than the maximum target inflation rate, and houses can be priced as a perpetuity of growing net rental cash flows, then what is the implication for house prices, all things remaining equal? Select the most correct answer.
(a) Real house prices must grow by more than the maximum target inflation rate in perpetuity.
(b) Real house prices must grow by less than or equal to the maximum target inflation rate in perpetuity.
(c) Nominal house prices must grow by more than the maximum target inflation rate in perpetuity.
(d) Nominal house prices must grow by less than or equal to the maximum target inflation rate in perpetuity.
(e) Real house prices must grow by more than nominal house prices in perpetuity.
Background: Since 1990, many central banks across the world have become 'inflation targeters'. They have adopted a policy of trying to keep inflation in a predictable narrow range, with the hope of encouraging long-term lending to fund more investment and maintain higher GDP growth.
Australia's central bank, the Reserve Bank of Australia (RBA), has specifically stated their inflation target range is between 2 and 3% pa.
Some Australian residential property market commentators suggest that because rental costs comprise a large part of the Australian consumer price index (CPI), rent costs across the nation cannot significantly exceed the maximum inflation target range of 3% pa without the prices of other goods growing by less than the target range for long periods, which is unlikely.
Question 9 DDM, NPV
For a price of $129, Joanne will sell you a share which is expected to pay a $30 dividend in one year, and a $10 dividend every year after that forever. So the stock's dividends will be $30 at t=1, $10 at t=2, $10 at t=3, and $10 forever onwards.
Question 46 NPV, annuity due
The phone company Telstra have 2 mobile service plans on offer which both have the same amount of phone call, text message and internet data credit. Both plans have a contract length of 24 months and the monthly cost is payable in advance. The only difference between the two plans is that one is a:
'Bring Your Own' (BYO) mobile service plan, costing $50 per month. There is no phone included in this plan. The other plan is a:
'Bundled' mobile service plan that comes with the latest smart phone, costing $71 per month. This plan includes the latest smart phone.
Neither plan has any additional payments at the start or end.
The only difference between the plans is the phone, so what is the implied cost of the phone as a present value?
Assume that the discount rate is 2% per month given as an effective monthly rate, the same high interest rate on credit cards.
In Australia, domestic university students are allowed to buy concession tickets for the bus, train and ferry which sell at a discount of 50% to full-price tickets.
The Australian Government do not allow international university students to buy concession tickets, they have to pay the full price.
Some international students see this as unfair and they are willing to pay for fake university identification cards which have the concession sticker.
What is the most that an international student would be willing to pay for a fake identification card?
Assume that international students:
consider buying their fake card on the morning of the first day of university from their neighbour, just before they leave to take the train into university.
buy their weekly train tickets on the morning of the first day of each week.
ride the train to university and back home again every day seven days per week until summer holidays 40 weeks from now. The concession card only lasts for those 40 weeks. Assume that there are 52 weeks in the year for the purpose of interest rate conversion.
a single full-priced one-way train ride costs $5.
have a discount rate of 11% pa, given as an effective annual rate.
Approach this question from a purely financial view point, ignoring the illegality, embarrassment and the morality of committing fraud.
Question 140 IRR, NPV, profitability index
A project has an internal rate of return (IRR) which is greater than its required return. Select the most correct statement.
(a) The NPV will be negative and the profitability index will be less than 1.
(b) The NPV will be positive and the profitability index will be more than 1.
(c) The payback period will be positive and the Accounting Rate of Return will be more than the target return.
(d) The NPV will be positive and the profitability index will be negative.
(e) The NPV will be negative and the profitability index will be positive.
Question 144 NPV
A text book publisher is thinking of asking some teachers to write a new textbook at a cost of $100,000, payable now. The book would be written, printed and ready to sell to students in 2 years. It will be ready just before semester begins.
A cash flow of $100 would be made from each book sold, after all costs such as printing and delivery. There are 600 students per semester. Assume that every student buys a new text book. Remember that there are 2 semesters per year and students buy text books at the beginning of the semester.
Assume that text book publishers will sell the books at the same price forever and that the number of students is constant.
If the discount rate is 8% pa, given as an effective annual rate, what is the NPV of the project?
(a) $543,004
(b) $594,444
(c) $1,211,234
(d) $1,262,674
(e) $1,489,423
A project's net present value (NPV) is negative. Select the most correct statement.
(a) The project should be accepted.
(b) The project's IRR is less than its required return.
(c) The project's IRR is more than its required return.
(e) The project is under-priced.
Dividend ($) 8 8 8 20 8 ...
After year 4, the dividend will grow in perpetuity at 4% pa. The required return on the stock is 10% pa. Both the growth rate and required return are given as effective annual rates.
(a) 170.24
(b) 141.09
(c) 137.09
What will be the price of the stock in 5 years (t = 5), just after the dividend at that time has been paid?
Question 184 NPV, DDM
Question 191 NPV, IRR, profitability index, pay back period
A project's Profitability Index (PI) is less than 1. Select the most correct statement:
(c) The project's payback period will be less than 3 years.
(e) The project's NPV is greater than 1.
Dividend ($) 0 6 12 18 20 ...
After year 4, the dividend will grow in perpetuity at 5% pa. The required return of the stock is 10% pa. Both the growth rate and required return are given as effective annual rates.
Question 200 NPV, no explanation
If all of the dividends since time period zero were deposited into a bank account yielding 8% pa as an effective annual rate, how much money will be in the bank account in 2.5 years (in other words, at t=2.5)?
(a) 14.85
(e) 21.82
Question 218 NPV, IRR, profitability index, average accounting return
(a) If a project has a positive NPV, its Profitability Index (PI) will be more than 1.
(b) If a project has a negative NPV and the discount rate is zero, then the payback period will be infinite so the project will never pay back its costs.
(c) If a project's NPV is zero, then the PI must be 1.
(d) If a project has a negative NPV, its IRR will be negative.
(e) If a project has a positive NPV, its Average Accounting Return (AAR) is not necessarily positive, it could be positive, negative or zero.
Question 250 NPV, Loan, arbitrage table
Your neighbour asks you for a loan of $100 and offers to pay you back $120 in one year.
You don't actually have any money right now, but you can borrow and lend from the bank at a rate of 10% pa. Rates are given as effective annual rates.
Assume that your neighbour will definitely pay you back. Ignore interest tax shields and transaction costs.
The Net Present Value (NPV) of lending to your neighbour is $9.09. Describe what you would do to actually receive a $9.09 cash flow right now with zero net cash flows in the future.
(a) Borrow $109.09 from the bank and lend $100 of it to your neighbour now.
(b) Borrow $100 from the bank and lend it to your neighbour now.
(c) Borrow $209.09 from the bank and lend $100 to your neighbour now.
(d) Borrow $120 from the bank and lend $100 of it to your neighbour now.
(e) Borrow $90.91 from the bank and lend it to your neighbour now.
You have $100,000 in the bank. The bank pays interest at 10% pa, given as an effective annual rate.
You wish to consume an equal amount now (t=0), in one year (t=1) and in two years (t=2), and still have $50,000 in the bank after that (t=2).
How much can you consume at each time?
(a) $36,555.8912
(b) $23,666.6667
(c) $21,450.1511
(d) $18,277.9456
(e) $16,666.6667
Question 346 NPV, annuity due
Your poor friend asks to borrow some money from you. He would like $1,000 now (t=0) and every year for the next 5 years, so there will be 6 payments of $1,000 from t=0 to t=5 inclusive. In return he will pay you $10,000 in seven years from now (t=7).
What is the net present value (NPV) of lending to your friend?
Assume that your friend will definitely pay you back so the loan is risk-free, and that the yield on risk-free government debt is 10% pa, given as an effective annual rate.
(a) $1,340.7944
A firm is considering a business project which costs $10m now and is expected to pay a single cash flow of $12.1m in two years.
(a) The NPV is zero.
(b) The IRR is 10% pa, equal to the 10% cost of capital.
(c) The payback period is two years assuming that the whole $12.1m cash flow occurs at t=2, or 1.826 years if the $12.1m cash flow is paid smoothly over the second year.
(d) The project could be accepted or rejected, the owners would be indifferent.
(e) If the project is accepted then the market value of the firm's assets will increase by $2.1m more than it would otherwise if the project was rejected.
Question 502 NPV, IRR, mutually exclusive projects
An investor owns an empty block of land that has local government approval to be developed into a petrol station, car wash or car park. The council will only allow a single development so the projects are mutually exclusive.
All of the development projects have the same risk and the required return of each is 10% pa. Each project has an immediate cost and once construction is finished in one year the land and development will be sold. The table below shows the estimated costs payable now, expected sale prices in one year and the internal rates of returns (IRR's).
Mutually Exclusive Projects
now ($) Sale price in
one year ($) IRR
(% pa)
Petrol station 9,000,000 11,000,000 22.22
Car wash 800,000 1,100,000 37.50
Car park 70,000 110,000 57.14
Which project should the investor accept?
(a) Petrol station.
(b) Car wash.
(c) Car park.
(d) None of the projects.
(e) All of the projects.
Question 532 mutually exclusive projects, NPV, IRR
An investor owns a whole level of an old office building which is currently worth $1 million. There are three mutually exclusive projects that can be started by the investor. The office building level can be:
Rented out to a tenant for one year at $0.1m paid immediately, and then sold for $0.99m in one year.
Refurbished into more modern commercial office rooms at a cost of $1m now, and then sold for $2.4m when the refurbishment is finished in one year.
Converted into residential apartments at a cost of $2m now, and then sold for $3.4m when the conversion is finished in one year.
All of the development projects have the same risk so the required return of each is 10% pa. The table below shows the estimated cash flows and internal rates of returns (IRR's).
Project Cash flow
now ($) Cash flow in
Rent then sell as is -900,000 990,000 10
Refurbishment into modern offices -2,000,000 2,400,000 20
Conversion into residential apartments -3,000,000 3,400,000 13.33
(a) Rent then sell as is.
(b) Refurbishment into modern offices.
(c) Conversion into residential apartments.
(e) Any of the above.
You wish to consume twice as much now (t=0) as in one year (t=1) and have nothing left in the bank at the end.
How much can you consume at time zero and one? The answer choices are given in the same order.
(a) $52,380.95, $52,380.95
(b) $62,500, $31,250
(c) $66,666.67, $33,333.33
(d) $68,750, $34,375
(e) $70,967.74, $35,483.87
You wish to consume half as much now (t=0) as in one year (t=1) and have nothing left in the bank at the end.
(a) $26,190.48, $52380.95
Question 210 real estate, inflation, real and nominal returns and cash flows, income and capital returns
Assume that the Gordon Growth Model (same as the dividend discount model or perpetuity with growth formula) is an appropriate method to value real estate.
The rule of thumb in the real estate industry is that properties should yield a 5% pa rental return. Many investors also regard property to be as risky as the stock market, therefore property is thought to have a required total return of 9% pa which is the average total return on the stock market including dividends.
Assume that all returns are effective annual rates and they are nominal (not reduced by inflation). Inflation is expected to be 2% pa.
You're considering purchasing an investment property which has a rental yield of 5% pa and you expect it to have the same risk as the stock market. Select the most correct statement about this property.
(a) The nominal property price is expected to grow by approximately 9% pa.
(b) The nominal property price is expected to grow by approximately 5% pa.
(c) The nominal property price is expected to grow by approximately 4% pa.
(d) The real property price is expected to grow by approximately 7% pa.
(e) The real property price is expected to grow by approximately 6% pa.
Question 522 income and capital returns, real and nominal returns and cash flows, inflation, real estate
A residential investment property has an expected nominal total return of 6% pa and nominal capital return of 2.5% pa. Inflation is expected to be 2.5% pa.
All of the above are effective nominal rates and investors believe that they will stay the same in perpetuity.
What are the property's expected real total, capital and income returns?
The answer choices below are given in the same order.
(a) 3.4146%, 3.4146%, 0%.
(c) 3.4146%, 0%, 3.4146%.
(d) 0.9878%, 0.5%, 0.4878%.
Question 523 income and capital returns, real and nominal returns and cash flows, inflation
A low-growth mature stock has an expected nominal total return of 6% pa and nominal capital return of 2% pa. Inflation is expected to be 3% pa.
What are the stock's expected real total, capital and income returns?
(a) 2.9126%, 3.8835%, -0.9709%.
(b) 2.9126%, -0.9709%, 3.8835%.
(c) 2.9126%, -0.9709%, 0.9709%.
(d) -0.0291%, -1%, 0.9709%.
(e) 0%, -0.9709%, 0.9709%.
What is the present value of real payments of $100 every year forever, with the first payment in one year? The nominal discount rate is 7% pa and the inflation rate is 4% pa.
(c) $3,205.1282
For a price of $100, Carol will sell you a 5 year bond paying semi-annual coupons of 16% pa. The face value of the bond is $100. Other bonds with similar risk, maturity and coupon characteristics trade at a yield of 12% pa.
For a price of $100, Rad will sell you a 5 year bond paying semi-annual coupons of 16% pa. The face value of the bond is $100. Other bonds with the same risk, maturity and coupon characteristics trade at a yield of 6% pa.
For a price of $100, Andrea will sell you a 2 year bond paying annual coupons of 10% pa. The face value of the bond is $100. Other bonds with the same risk, maturity and coupon characteristics trade at a yield of 6% pa.
A three year bond has a face value of $100, a yield of 10% and a fixed coupon rate of 5%, paid semi-annually. What is its price?
Question 538 bond pricing, income and capital returns, no explanation
Risk-free government bonds that have coupon rates greater than their yields:
(a) Are discount bonds.
(b) Have positive expected capital returns.
(c) Have higher expected income returns than total returns.
(d) Have prices less than their face values.
(e) Have significant credit risk.
Question 539 debt terminology, fully amortising loan, bond pricing
A 'fully amortising' loan can also be called a:
(a) Discount loan
(b) Par loan
(c) Premium loan
(d) Deferred repayment loan
(e) Interest only loan
An investor bought a 10 year 2.5% pa fixed coupon government bond priced at par. The face value is $100. Coupons are paid semi-annually and the next one is in 6 months.
Six months later, just after the coupon at that time was paid, yields suddenly and unexpectedly fell to 2% pa. Note that all yields above are given as APR's compounding semi-annually.
What was the bond investors' historical total return over that first 6 month period, given as an effective semi-annual rate?
On 22-Mar-2013 the Australian Government issued series TB139 treasury bonds with a combined face value $23.4m, listed on the ASX with ticker code GSBG25.
The bonds mature on 21-Apr-2025, the fixed coupon rate is 3.25% pa and coupons are paid semi-annually on the 21st of April and October of each year. Each bond's face value is $1,000.
At market close on Friday 11-Sep-2015 the bonds' yield was 2.736% pa.
At market close on Monday 14-Sep-2015 the bonds' yield was 2.701% pa. Both yields are given as annualised percentage rates (APR's) compounding every 6 months. For convenience, assume 183 days in 6 months and 366 days in a year.
What was the historical total return over those 3 calendar days between Friday 11-Sep-2015 and Monday 14-Sep-2015?
There are 183 calendar days from market close on the last coupon 21-Apr-2015 to the market close of the next coupon date on 21-Oct-2015.
Between the market close times from 21-Apr-2015 to 11-Sep-2015 there are 143 calendar days. From 21-Apr-2015 to 14-Sep-2015 there are 146 calendar days.
From 14-Sep-2015 there were 20 coupons remaining to be paid including the next one on 21-Oct-2015.
All of the below answers are given as effective 3 day rates.
(a) -0.035%
(c) 0.035%
Question 708 continuously compounding rate, continuously compounding rate conversion
Convert a 10% continuously compounded annual rate ##(r_\text{cc annual})## into an effective annual rate ##(r_\text{eff annual})##. The equivalent effective annual rate is:
(a) 230.258509% pa
(b) 10.536052% pa
(e) 9.531018% pa
A continuously compounded monthly return of 1% ##(r_\text{cc monthly})## is equivalent to a continuously compounded annual return ##(r_\text{cc annual})## of:
(a) 12.682503% pa
Question 714 return distribution, no explanation
Which of the following quantities is commonly assumed to be normally distributed?
(a) Prices, ##P_1##.
(b) Gross discrete returns per annum, ##r_{\text{gdr 0 }\rightarrow \text{ 1}} = \dfrac{P_1}{P_0} ##.
(c) Effective annual returns per annum also known as net discrete returns, ##r_{\text{eff 0 }\rightarrow \text{ 1}} = \dfrac{P_1 - P_0}{P_0} = \dfrac{P_1}{P_0}-1##.
(d) Continuously compounded returns per annum, ##r_{\text{cc 0 }\rightarrow \text{ 1}} = \ln \left( \dfrac{P_1}{P_0} \right)##.
(e) Annualised percentage rates compounding per month, ##r_{\text{apr comp monthly 0 }\rightarrow \text{ 1 mth}} = \left( \dfrac{P_1 - P_0}{P_0} \right) \times 12##.
Question 716 return distribution
The below three graphs show probability density functions (PDF) of three different random variables Red, Green and Blue.
Which of the below statements is NOT correct?
(a)##-1 < \text{Red} < \infty## if Red is log-normally distributed.
(b) ##-2 < \text{Green} < 2## if Green is normally distributed.
(c) ##0 < \text{Blue} < \infty## if Blue is log-normally distributed.
(d) If the Green distribution is normal, then the mode = median = mean.
(e) If the Red and Blue distributions are log-normal, then the mode < median < mean.
Question 725 return distribution, mean and median returns
If a stock's future expected effective annual returns are log-normally distributed, what will be bigger, the stock's or effective annual return? Or would you expect them to be ?
If a stock's future expected continuously compounded annual returns are normally distributed, what will be bigger, the stock's or continuously compounded annual return? Or would you expect them to be ?
If a stock's expected future prices are log-normally distributed, what will be bigger, the stock's or future price? Or would you expect them to be ?
Question 709 continuously compounding rate, APR
Which of the following interest rate quotes is NOT equivalent to a 10% effective annual rate of return? Assume that each year has 12 months, each month has 30 days, each day has 24 hours, each hour has 60 minutes and each minute has 60 seconds. APR stands for Annualised Percentage Rate.
(a) 9.7617696% is the APR compounding semi-annually ##(r_\text{apr comp 6mth})##
(b) 9.5689685% is the APR compounding monthly ##(r_\text{apr comp monthly})##
(c) 9.6454756% is the APR compounding daily ##(r_\text{apr comp daily})##
(d) 9.5310182% is the APR compounding per second ##(r_\text{apr comp per second})##
(e) 9.5310180% is the continuously compounded rate per annum ##(r_\text{cc annual})##
Question 721 mean and median returns, return distribution, arithmetic and geometric averages, continuously compounding rate
Fred owns some Commonwealth Bank (CBA) shares. He has calculated CBA's monthly returns for each month in the past 20 years using this formula:
###r_\text{t monthly}=\ln \left( \dfrac{P_t}{P_{t-1}} \right)###
He then took the arithmetic average and found it to be 1% per month using this formula:
###\bar{r}_\text{monthly}= \dfrac{ \displaystyle\sum\limits_{t=1}^T{\left( r_\text{t monthly} \right)} }{T} =0.01=1\% \text{ per month}###
He also found the standard deviation of these monthly returns which was 5% per month:
###\sigma_\text{monthly} = \dfrac{ \displaystyle\sum\limits_{t=1}^T{\left( \left( r_\text{t monthly} - \bar{r}_\text{monthly} \right)^2 \right)} }{T} =0.05=5\%\text{ per month}###
Which of the below statements about Fred's CBA shares is NOT correct? Assume that the past historical average return is the true population average of future expected returns.
(a) The returns ##r_\text{t monthly}## are continuously compounded monthly returns and are likely to be normally distributed, so the mean, median and mode of these continuously compounded returns are all equal to 1% per month.
(b) The annualised average continuously compounded return is ##\bar{r}_\text{cc annual}=12×0.01=0.1=12\%\text{ pa}##. The annualised standard deviation is ##\sigma_\text{annual} = \sqrt{12}×0.05=0.173205081=17.32\%\text{ pa}##.
(c) Over the next 10 years the mean, median and mode continuously compounded 10 year returns will all equal ##0.01 \times 12 \times 10 = 120\%##.
(d) Over the next 10 years the expected mean gross discrete 10 year return is ##e^{(0.01 - 0.05^2/2)×12×10} = 2.857651118## and the median gross discrete 10 year return is ##e^{(0.01 + 0.05^2/2)×12×10}=3.857425531##.
(e) If the current price of the CBA shares is $75, then in 10 years they're expected to have a mean value of ##75×e^{(0.01 + 0.05^2/2)×12×10} = 289.3069148## and a median value of ##75×e^{0.01×12×10}=249.0087692##.
Here is a table of stock prices and returns. Which of the statements below the table is NOT correct?
Price and Return Population Statistics
Time Prices LGDR GDR NDR
1 50 -0.6931 0.5 -0.5
2 100 0.6931 2 1
Arithmetic average 0 1.25 0.25
Arithmetic standard deviation -0.6931 0.75 0.75
(a) The geometric average of the gross discrete returns (GAGDR) equals 1 which is 100%.
(b) ##\text{GAGDR} = \exp \left( \text{AALGDR} \right)##. The GAGDR is equal to the natural exponent of the arithmetic average of the logarithms of the gross discrete returns (AALGDR).
(c) ##\text{GAGDR} = \left( P_T/P_0 \right)^{1/T}##. The GAGDR equals the ratio of the last and first prices raised to the power of the inverse of the number of time periods between them.
(d) ##\text{LGAGDR} = \text{AALGDR}##. This is always true, regardless of the distribution of the prices or returns and the number of return observations. The logarithm of the geometric average of the gross discrete returns (LGAGDR) is always equal to the arithmetic average of the logarithms of the gross discrete returns (AALGDR).
(e) ##\text{LAAGDR} = \text{AALGDR} + \text{SDLGDR}^2/2##. This is always true, regardless of the distribution of the prices or returns and the number of return observations. The logarithm of the arithmetic average of the gross discrete returns (LAAGDR) equals the arithmetic average of the logarithms of the gross discrete returns (AALGDR) plus half the variance of the LGDR's.
Question 18 DDM, income and capital returns
The following equation is the Dividend Discount Model, also known as the 'Gordon Growth Model' or the 'Perpetuity with growth' equation.
### p_{0} = \frac{c_1}{r_{\text{eff}} - g_{\text{eff}}} ###
What is the discount rate '## r_\text{eff} ##' in this equation?
(a) The expected total return of the stock.
(b) The expected capital return of the stock.
(c) The expected dividend return of the stock.
(d) The expected income return of the stock.
(e) The expected growth rate of the stock price.
Question 30 income and capital returns
A share was bought for $20 (at t=0) and paid its annual dividend of $3 one year later (at t=1). Just after the dividend was paid, the share price was $16 (at t=1). What was the total return, capital return and income return? Calculate your answers as effective annual rates.
(a) -0.2, -0.35, 0.15.
(b) -0.05, -0.2, 0.15.
(c) -0.05, 0.15, -0.2.
(d) 0.05, 0.2, -0.15.
(e) 0.15, -0.05, -0.2.
Question 672 CAPM, beta
A stock has a beta of 1.5. The market's expected total return is 10% pa and the risk free rate is 5% pa, both given as effective annual rates.
What do you think will be the stock's expected return over the next year, given as an effective annual rate?
(b) Own debt.
(d) Write debt.
(e) Have debt assets.
Question 666 rights issue, capital raising
A company conducts a 2 for 3 rights issue at a subscription price of $8 when the pre-announcement stock price was $9. Assume that all investors use their rights to buy those extra shares.
What is the percentage increase in the stock price and the number of shares outstanding? The answers are given in the same order.
(a) -60%, 150%
(b) -42.22%, 150%
(c) -40%, 66.67%
(d) -22.22%, 66.67%
(e) -4.44%, 66.67%
1 99 -0.010050 0.990000 -0.010000
2 180.40 0.600057 1.822222 0.822222
Arithmetic average 0.0399 1.1457 0.1457
Arithmetic standard deviation 0.4384 0.5011 0.5011
(a) The geometric average of the gross discrete returns (GAGDR) equals 1.04075 which is 104.075%.
(b) ##\exp \left( \text{GAGDR} \right) = \text{AALGDR}##. The natural exponent of the GAGDR equals the arithmetic average of the logarithms of the gross discrete returns (AALGDR).
(c) ##\text{GAGDR}^T = \left( P_T/P_0 \right)##. The GAGDR raised to the power of the number of time period that it's measured over equals the ratio of the first and last prices.
(d) ##\text{GAGDR} = \exp \left( \text{AALGDR} \right)##. This is always true, regardless of the distribution of the prices or returns. The logarithm of the geometric average of the gross discrete returns (LGAGDR) is always equal to the arithmetic average of the logarithm of the gross discrete returns (AALGDR).
(e) ##\text{AAGDR} \approx \exp \left( \text{AALGDR} + \text{SDLGDR}^2/2 \right)##. This is only approximately true and depends on the distribution of the prices and returns. It's asymptotically true as the time period that the returns are measured over reaches infinity.
A continuously compounded semi-annual return of 5% ##(r_\text{cc 6mth})## is equivalent to a continuously compounded annual return ##(r_\text{cc annual})## of:
(a) 30% pa
(d) 10.25% pa
If a variable, say X, is normally distributed with mean ##\mu## and variance ##\sigma^2## then mathematicians write ##X \sim \mathcal{N}(\mu, \sigma^2)##.
If a variable, say Y, is log-normally distributed and the underlying normal distribution has mean ##\mu## and variance ##\sigma^2## then mathematicians write ## Y \sim \mathbf{ln} \mathcal{N}(\mu, \sigma^2)##.
Select the most correct statement:
(a)##Red \sim \mathcal{N}(\mu, \sigma^2)##, ##Green \sim \mathcal{N}(\mu, \sigma^2)## and ##Blue \sim \mathcal{N}(\mu, \sigma^2)##
(b) ##Red \sim \mathcal{N}(\mu, \sigma^2)##, ##Green \sim \mathcal{N}(\mu, \sigma^2)## and ##Blue \sim \mathbf{ln} \mathcal{N}(\mu, \sigma^2)##
(c) ##Red \sim \mathcal{N}(\mu, \sigma^2)##, ##Green \sim \mathbf{ln} \mathcal{N}(\mu, \sigma^2)## and ##Blue \sim \mathbf{ln} \mathcal{N}(\mu, \sigma^2)##
(d) ##Red \sim \mathbf{ln} \mathcal{N}(\mu, \sigma^2)##, ##Green \sim \mathcal{N}(\mu, \sigma^2)## and ##Blue \sim \mathbf{ln} \mathcal{N}(\mu, \sigma^2)##
(e) ##Red \sim \mathbf{ln} \mathcal{N}(\mu, \sigma^2)##, ##Green \sim \mathbf{ln} \mathcal{N}(\mu, \sigma^2)## and ##Blue \sim \mathbf{ln} \mathcal{N}(\mu, \sigma^2)##
A stock has an arithmetic average continuously compounded return (AALGDR) of 10% pa, a standard deviation of continuously compounded returns (SDLGDR) of 80% pa and current stock price of $1. Assume that stock prices are log-normally distributed.
In one year, what do you expect the mean and median prices to be? The answer options are given in the same order.
(a) $1.521962, $1.105171
(b) $1.42, $1.1
(c) $1.105171, $1.521962
(d) $1.105171, $0.802519
(e) $1.1, $1.42
In 5 years, what do you expect the mean and median prices to be? The answer options are given in the same order.
(b) $1.648721, $8.16617
(c) $1.648721, $1.61051
(d) $5.773534, $1.61051
(e) $8.16617, $1.648721
A share was bought for $4 and paid an dividend of $0.50 one year later (at t=1 year).
Just after the dividend was paid, the share price fell to $3.50 (at t=1 year). What were the total return, capital return and income returns given as effective annual rates? The answer choices are given in the same order:
##r_\text{total}##, ##r_\text{capital}##, ## r_\text{income}##
(a) -0.125, -0.25, 0.
(b) 0, -0.125, 0.125
(c) 0, 0.125, -0.125
(d) 0, 0.125, 0.125
(e) 0.125, 0, -0.125
Three years ago Frederika bought a house for $400,000.
Frederika's residential property has an expected total return of 7% pa.
She rents her house out for $2,500 per month, paid in advance. Every 12 months she plans to increase the rental payments.
What is the expected annual capital yield of the property?
(b) -0.2724%
(d) 2%
Question 405 DDM, income and capital returns, no explanation
The perpetuity with growth formula is:
###P_0= \dfrac{C_1}{r-g}###
Which of the following is NOT equal to the total required return (r)?
(a) ## \dfrac{C_1}{P_0} +g ##
(b) ## \dfrac{C_1}{P_0} + \dfrac{P_1}{P_0} -1 ##
(c) ## \dfrac{C_1+P_1 - 1}{P_0} ##
(d) ## \dfrac{C_1}{P_0} + \dfrac{P_1-P_0}{P_0} ##
(e) ## \dfrac{C_1+P_0.g}{P_0} ##
The perpetuity with growth equation is:
Which of the following is NOT equal to the expected capital return as an effective annual rate?
(a) ##g##
(b) ##r+\dfrac{C_1}{P_0}##
(c) ##\dfrac{C_2}{C_1} -1##
(d) ##\dfrac{C_3-C_2}{C_2} ##
(e) ##\left( \dfrac{P_5}{P_3} \right)^{1/2}-1##
Question 102 option, hedging
A company runs a number of slaughterhouses which supply hamburger meat to McDonalds. The company is afraid that live cattle prices will increase over the next year, even though there is widespread belief in the market that they will be stable. What can the company do to hedge against the risk of increasing live cattle prices? Which statement(s) are correct?
(i) buy call options on live cattle.
(ii) buy put options on live cattle.
(iii) sell call options on live cattle.
(d) Only (i) and (ii) is true.
Question 103 option
Below are 4 option graphs. Note that the y-axis is payoff at maturity (T). What options do they depict? List them in the order that they are numbered.
(a) 1: short call, 2: long call, 3: short put, 4: long put.
(b) 1: long call, 2: long put, 3: short call, 4: short put.
(c) 1: short put, 2: long put, 3: short call, 4: long call.
(d) 1: long put, 2: short put, 3: long call, 4: short call.
(e) 1: long put, 2: short call, 3: short put, 4: long call.
Below are 4 option graphs. Note that the y-axis is payoff at maturity (T). What options do they depict? List them in the order that they are numbered
(e) 1: short call, 2: long put, 3: long call, 4: short put.
Question 636 option, option payoff at maturity, no explanation
Which of the below formulas gives the payoff ##(f)## at maturity ##(T)## from being long a call option? Let the underlying asset price at maturity be ##S_T## and the exercise price be ##X_T##.
(a) ##f_{LC,T}=max(S_T-X_T,0)##
(b) ##f_{LC,T}=max(X_T-S_T,0)##
(c) ##f_{LC,T}=-max(S_T-X_T,0)##
(d) ##f_{LC,T}=-max(X_T-S_T,0)##
(e) ##f_{LC,T}=min(X_T-S_T,0)##
Which of the below formulas gives the payoff ##(f)## at maturity ##(T)## from being short a call option? Let the underlying asset price at maturity be ##S_T## and the exercise price be ##X_T##.
(a) ##f_{SC,T}=max(S_T-X_T,0)##
(b) ##f_{SC,T}=max(X_T-S_T,0)##
(c) ##f_{SC,T}=-max(S_T-X_T,0)##
(d) ##f_{SC,T}=-max(X_T-S_T,0)##
(e) ##f_{SC,T}=min(X_T-S_T,0)##
Which of the below formulas gives the payoff ##(f)## at maturity ##(T)## from being long a put option? Let the underlying asset price at maturity be ##S_T## and the exercise price be ##X_T##.
(a) ##f_{LP,T}=max(S_T-X_T,0)##
(b) ##f_{LP,T}=max(X_T-S_T,0)##
(c) ##f_{LP,T}=-max(S_T-X_T,0)##
(d) ##f_{LP,T}=-max(X_T-S_T,0)##
(e) ##f_{LP,T}=min(X_T-S_T,0)##
Which of the below formulas gives the payoff ##(f)## at maturity ##(T)## from being short a put option? Let the underlying asset price at maturity be ##S_T## and the exercise price be ##X_T##.
(a) ##f_{SP,T}=max(S_T-X_T,0)##
(b) ##f_{SP,T}=max(X_T-S_T,0)##
(c) ##f_{SP,T}=-max(S_T-X_T,0)##
(d) ##f_{SP,T}=-max(X_T-S_T,0)##
(e) ##f_{SP,T}=min(X_T-S_T,0)##
Question 640 option, future, no explanation
Which one of the below option and futures contracts gives the possibility of potentially unlimited gains?
(a) Long call contracts.
(b) Short call contracts.
(c) Long put contracts.
(d) Short put contracts.
(e) Short future contracts.
Question 641 future, no explanation
Which of the below formulas gives the payoff at maturity ##(f_T)## from being long a future? Let the underlying asset price at maturity be ##S_T## and the locked-in futures price be ##K_T##.
(a) ##f_{LF,T}=S_T+K_T##
(b) ##f_{LF,T}=-S_T-K_T##
(c) ##f_{LF,T}=S_T-K_T##
(d) ##f_{LF,T}=K_T-S_T##
(e) ##f_{LF,T}=S_T##
Which of the below formulas gives the payoff at maturity ##(f_T)## from being short a future? Let the underlying asset price at maturity be ##S_T## and the locked-in futures price be ##K_T##.
(a) ##f_{SF,T}=S_T+K_T##
(b) ##f_{SF,T}=-S_T-K_T##
(c) ##f_{SF,T}=S_T-K_T##
(d) ##f_{SF,T}=K_T-S_T##
(e) ##f_{SF,T}=S_T##
A trader buys one crude oil futures contract on the CME expiring in one year with a locked-in futures price of $38.94 per barrel. If the trader doesn't close out her contract before expiry then in one year she will have the:
(a) Obligation to buy the underlying oil at $38.94 per barrel.
(b) Obligation to sell the underlying oil at $38.94 per barrel.
(c) Right to buy the underlying oil at $38.94 per barrel if she wants.
(d) Right to sell the underlying oil at $38.94 per barrel if she wants.
(e) Obligation to buy the underlying oil $38.94 per barrel if her counter party chooses to sell it.
A trader sells one crude oil futures contract on the CME expiring in one year with a locked-in futures price of $38.94 per barrel. The crude oil spot price is $40.33. If the trader doesn't close out her contract before expiry then in one year she will have the:
(e) Obligation to buy the underlying oil $38.94 per barrel if the counter party chooses to sell it.
Question 645 option, no explanation
A trader buys one crude oil European style call option contract on the CME expiring in one year with an exercise price of $44 per barrel for a price of $6.64. The crude oil spot price is $40.33. If the trader doesn't close out her contract before maturity, then at maturity she will have the:
(a) Obligation to buy the underlying oil at $44 per barrel.
(b) Obligation to sell the underlying oil at $44 per barrel.
(c) Right to buy the underlying oil at $44 per barrel if she wants.
(d) Right to sell the underlying oil at $44 per barrel if she wants.
(e) Obligation to buy the underlying oil at $44 per barrel if her counter party chooses to sell it.
Question 646 open interest, trade volume, future
Alice, Bob, Chris and Delta are traders in the futures market. The following trades occur over a single day in a newly-opened equity index future that matures in one year which the exchange just made available.
1. Alice buys a future from Bob.
2. Chris buys a future from Delta.
3. Delta buys a future from Alice.
These were the only trades made in this equity index future. What was the trading volume and what is the open interest?
(a) Daily trading volume is 3 contracts, open interest is 3 contracts.
(b) Daily trading volume is 3 contracts, open interest is 2 contracts.
(c) Daily trading volume is 3 contracts, open interest is 1 contract.
(d) Daily trading volume is 2 contracts, open interest is 3 contracts.
(e) Daily trading volume is 2 contracts, open interest is 2 contracts.
Question 648 margin call, future
A trader buys a one year futures contract on crude oil. The contract is for the delivery of 1,000 barrels. The current futures price is $38.94 per barrel. The initial margin is $3,410 per contract, and the maintenance margin is $3,100 per contract.
What is the smallest price change that would lead to a margin call for the buyer?
(a) A price fall of $0.087571 per barrel.
(b) A price fall of $0.31 per barrel.
(c) A price fall of $3.41 per barrel.
(d) A price fall of $3.54 per barrel.
(e) A price fall of $3.894 per barrel.
A trader sells a one year futures contract on crude oil. The contract is for the delivery of 1,000 barrels. The current futures price is $38.94 per barrel. The initial margin is $3,410 per contract, and the maintenance margin is $3,100 per contract.
What is the smallest price change that would lead to a margin call for the seller?
(a) A price rise of $0.087571 per barrel.
(b) A price rise of $0.31 per barrel.
(c) A price rise of $3.41 per barrel.
(d) A price rise of $3.54 per barrel.
(e) A price rise of $3.894 per barrel.
Question 650 future, closing out future contract
In February a company sold one December 40,000 pound (about 18 metric tons) lean hog futures contract. It closed out its position in May.
The spot price was $0.68 per pound in February. The December futures price was $0.70 per pound when the trader entered into the contract in February, $0.60 when he closed out his position in May, and $0.55 when the contract matured in December.
What was the total profit?
(d) $5,200
(e) $6,000
Question 651 future
Which of the following statements about futures is NOT correct?
(a) Futures quotes displayed on the exchange change continuously.
(b) Futures prices written in existing futures contracts are fixed, they do not change since they're written in the legal contract.
(c) One year futures quotes equal the market's expectation of the underlying asset price in one year. For this reason futures markets are a good predictor of the underlying asset prices.
(d) Futures prices can be calculated based on the spot price of the underlying asset compounded forward at the total opportunity cost of capital, less any storage costs and plus any income yields such as dividends.
(e) The futures price quote and the underlying asset's spot price will converge over time. At the future's expiry they'll be equal.
An equity index is currently at 5,200 points. The 6 month futures price is 5,300 points and the total required return is 6% pa with continuous compounding. Each index point is worth $25.
What is the implied dividend yield as a continuously compounded rate per annum?
(a) 5.7145% pa
(b) 4.0952% pa
(c) 3.8096% pa
(d) 2.1904% pa
(e) 1.9048% pa
An equity index is currently at 4,800 points. The 1.5 year futures price is 5,100 points and the total required return is 6% pa with continuous compounding. Each index point is worth $25.
(a) -0.0625% pa
Question 654 future, forward
Which of the following statements about futures and forward contracts is NOT correct?
(a) Forward contracts are traded over-the-counter (OTC).
(b) Futures contracts are exchange traded.
(c) Futures contracts are highly standardised in their contract sizes and expiry dates.
(d) Forward contracts expose the winner to credit risk at maturity.
(e) Forward contracts are novated.
Question 592 future, margin call
A trader buys one December futures contract on orange juice. Each contract is for the delivery of 10,000 pounds. The current futures price is $1.20 per pound. The initial margin is $5,000 per contract, and the maintenance margin is $4,000 per contract.
What is the smallest price change would that would lead to a margin call for the buyer?
(a) A price fall of $0.76 per pound.
(b) A price fall of $0.10 per pound.
(c) A price fall of $0.04 per pound.
(d) A price rise of $0.04 per pound.
(e) A price rise of $0.10 per pound.
Question 593 future, arbitrage table
The price of gold is currently $700 per ounce. The forward price for delivery in 1 year is $800. An arbitrageur can borrow money at 10% per annum given as an effective discrete annual rate. Assume that gold is fairly priced and the cost of storing gold is zero.
What is the best way to conduct an arbitrage in this situation? The best arbitrage strategy requires zero capital, has zero risk and makes money straight away. An arbitrageur should sell 1 forward on gold and:
(a) Borrow $636.3636 and use it to buy 0.9091 ounces of gold right now (t=0). Then pay back the loan with $700 at the end (t=1).
(b) Borrow $700 and use it to buy 1 ounce of gold right now (t=0). Then pay back the loan with $770 at the end (t=1).
(c) Borrow $727.2727 and use it to buy 1 ounce of gold right now (t=0). Then pay back the loan with $800 at the end (t=1).
(d) Borrow $800 and use it to buy 1.1039 ounces of gold right now (t=0). Then pay back the loan with $880 at the end (t=1).
(e) Borrow $880 and use it to buy 1 ounce of gold right now (t=0). Then pay back the loan with $800 at the end (t=1).
A 2-year futures contract on a stock paying a continuous dividend yield of 3% pa was bought when the underlying stock price was $10 and the risk free rate was 10% per annum with continuous compounding. Assume that investors are risk-neutral, so the stock's total required return is the risk free rate.
Find the forward price ##(F_2)## and value of the contract ##(V_0)## initially. Also find the value of the contract in 6 months ##(V_{0.5})## if the stock price rose to $12.
(a) ##F_2=11.5027, V_0=0, V_{0.5}=1.5715##
(b) ##F_2=11.5027, V_0=0, V_{0.5}=1.8258##
(c) ##F_2=12.9693, V_0=0, V_{0.5}=1.3218##
(d) ##F_2=12.9693, V_0=0, V_{0.5}=1.3896##
(e) ##F_2=12.9693, V_0=0, V_{0.5}=1.6144##
Question 671 future, forward, hedging
It's possible for both parties in a futures or forward contract to be hedging, so neither are speculating. or ?
3. Bob buys a future from Chris.
3. Alice buys a future from Chris.
Question 310 foreign exchange rate
Is it possible for all countries' exchange rates to appreciate by 5% in the same year? or ?
When someone says that they're "buying American dollars" (USD), what type of asset are they probably buying? They're probably buying:
(a) Short term debt denominated in USD, for example lending to a US bank as a USD deposit.
(b) Long term debt denominated in USD, for example lending to a US company by buying their USD bonds.
(c) Shares denominated in USD, for example buying shares in Coca-Cola which is listed on the NYSE.
(d) Real estate denominated in USD, for example buying an apartment in Chicago.
(e) Commodities with USD, for example buying gold, wheat, or coal.
Question 312 foreign exchange rate, American and European terms
If the current AUD exchange rate is USD 0.9686 = AUD 1, what is the American terms quote of the AUD against the USD?
(a) 0.9686 USD per AUD
(b) 0.9686 AUD per USD
(c) 1.0324 USD per AUD
(d) 1.0324 AUD per USD
(e) 1.0324 AUD per 2 USD
If the AUD appreciates against the USD, the American terms quote of the AUD will or ?
If the USD appreciates against the AUD, the American terms quote of the AUD will or ?
If the current AUD exchange rate is USD 0.9686 = AUD 1, what is the European terms quote of the AUD against the USD?
(e) 1.0324 AUD per EUR
If the AUD appreciates against the USD, the European terms quote of the AUD will or ?
If the USD appreciates against the AUD, the European terms quote of the AUD will or ?
How is the AUD normally quoted in Australia? Using or terms?
Question 319 foreign exchange rate, monetary policy, American and European terms
Investors expect the Reserve Bank of Australia (RBA) to keep the policy rate steady at their next meeting.
Then unexpectedly, the RBA announce that they will increase the policy rate by 25 basis points due to fears that the economy is growing too fast and that inflation will be above their target rate of 2 to 3 per cent.
What do you expect to happen to Australia's exchange rate in the short term? The Australian dollar is likely to:
(a) Appreciate against the USD, so the 'European terms' quote of the AUD (AUD per USD) will increase.
(b) Depreciate against the USD, so the 'European terms' quote of the AUD (AUD per USD) will decrease.
(c) Appreciate against the USD, so the 'European terms' quote of the AUD (AUD per USD) will decrease.
(d) Depreciate against the USD, so the 'European terms' quote of the AUD (AUD per USD) will increase.
(e) Appreciate against the USD, so the 'American terms' quote of the AUD (USD per AUD) will decrease.
Question 109 credit rating, credit risk
Bonds with lower (worse) credit ratings tend to have:
(a) Lower yields to maturity.
(b) Higher probabilities of default.
(c) Lower coupon rates when priced at par.
(d) Lower total risk.
(e) Lower credit risk.
Question 427 takeover
In a takeover deal where the offer is 100% cash, the merged firm's number of shares will be equal to the acquirer firm's original number of shares. or ?
In a takeover deal where the offer is 100% scrip (shares), the merged firm's number of shares will be equal to the acquirer firm's original number of shares. or ?
In a takeover deal where the offer is 100% scrip (shares), the merged firm's number of shares will be equal to the sum of the acquirer and target firms' original number of shares. or ?
Question 381 Merton model of corporate debt, option, real option
In the Merton model of corporate debt, buying a levered company's debt is equivalent to buying risk free government bonds and:
(a) Selling the company's assets.
(b) Buying a call option on the company's assets.
(c) Buying a put option on the company's assets.
(d) Selling a call option on the company's assets.
(e) Selling a put option on the company's assets.
Question 382 Merton model of corporate debt, real option, option
In the Merton model of corporate debt, buying a levered company's shares is equivalent to:
(a) Buying the company's assets.
(d) Buying the company's assets and buying a call option on those assets.
(e) Buying the company's assets and buying a put option on those assets.
In the Merton model of corporate debt, buying a levered company's debt is equivalent to buying the company's assets and:
(a) Selling government bonds.
Question 384 option, real option
Which of the following is the least useful method or model to calculate the value of a real option in a project?
(a) Project value with the option less project value without the option.
(b) No-arbitrage binomial option pricing model.
(c) Risk-neutral binomial option pricing model.
(d) Gordon growth model.
(e) Black-Sholes option pricing model.
Question 245 foreign exchange rate, monetary policy, foreign exchange rate direct quote, no explanation
Investors expect Australia's central bank, the RBA, to leave the policy rate unchanged at their next meeting.
Then unexpectedly, the policy rate is reduced due to fears that Australia's GDP growth is slowing.
What do you expect to happen to Australia's exchange rate? Direct and indirect quotes are given from the perspective of an Australian.
The Australian dollar will:
(a) Appreciate against the USD, so the 'direct quote' of the AUD (AUD per USD) will increase.
(b) Depreciate against the USD, so the 'direct quote' of the AUD (AUD per USD) will decrease.
(c) Appreciate against the USD, so the 'direct quote' of the AUD (AUD per USD) will decrease.
(d) Depreciate against the USD, so the 'direct quote' of the AUD (AUD per USD) will increase.
(e) Depreciate against the USD, so the 'indirect quote' of the AUD (USD per AUD) will increase.
Investors expect the Reserve Bank of Australia (RBA) to decrease the overnight cash rate at their next meeting.
Then unexpectedly, the RBA announce that they will keep the policy rate unchanged.
(e) Be unaffected by the change in the policy rate, so the exchange rate will remain the same.
The market expects the Reserve Bank of Australia (RBA) to increase the policy rate by 25 basis points at their next meeting.
Then unexpectedly, the RBA announce that they will increase the policy rate by 50 basis points due to high future GDP and inflation forecasts.
What do you expect to happen to Australia's exchange rate in the short term? The Australian dollar will:
(a) Appreciate against the USD, so the 'American terms' quote of the AUD (USD per AUD) will increase.
(b) Depreciate against the USD, so the 'American terms' quote of the AUD (USD per AUD) will decrease.
(c) Appreciate against the USD, so the 'American terms' quote of the AUD (USD per AUD) will decrease.
(d) Depreciate against the USD, so the 'American terms' quote of the AUD (USD per AUD) will increase.
Question 246 foreign exchange rate, forward foreign exchange rate, cross currency interest rate parity
Suppose the Australian cash rate is expected to be 8.15% pa and the US federal funds rate is expected to be 3.00% pa over the next 2 years, both given as nominal effective annual rates. The current exchange rate is at parity, so 1 USD = 1 AUD.
What is the implied 2 year forward foreign exchange rate?
(a) 1 USD = 1.1025 AUD
(b) 1.1025 USD = 1 AUD
(c) 1 USD = 1.05 AUD
(d) 1 USD = 1.1 AUD
(e) 1.1 USD = 1 AUD
The market expects the Reserve Bank of Australia (RBA) to decrease the policy rate by 25 basis points at their next meeting.
Then unexpectedly, the RBA announce that they will decrease the policy rate by 50 basis points due to fears of a recession and deflation.
What do you expect to happen to Australia's exchange rate? The Australian dollar will:
Australians usually quote the Australian dollar in USD per 1 AUD. For example, in October 2015 the Australian dollar was quoted as 0.72 USD per AUD. Is this an or terms quote?
Chinese people usually quote the Chinese Yuan or Renminbi in RMB per 1 USD. For example, in October 2015 the Chinese Renminbi was 6.35 RMB per USD. Is this an or terms quote?
As expected, the RBA increases the policy rate by 25 basis points.
Vietnamese people usually quote the Vietnamese Dong in VND per 1 USD. For example, in October 2015 the Vietnamese Dong was 22,300 VND per USD. Is this an or terms quote?
The Australian dollar's value was:
1.4875 USD per AUD on 31 August 1974.
0.4890 USD per AUD on 31 March 2001.
Did the Australian dollar or against the US dollar between these dates?
Question 387 real option, option
One of the reasons why firms may not begin projects with relatively small positive net present values (NPV's) is because they wish to maximise the value of their:
(a) Expansion option.
(b) Abandonment option.
(c) Timing (or delaying) option.
(d) Production (or switching) option.
(e) Underlying asset.
You're thinking of starting a new cafe business, but you're not sure if it will be profitable.
You have to decide what type of cups, mugs and glasses you wish to buy. You can pay to have your cafe's name printed on them, or just buy the plain un-marked ones. For marketing reasons it's better to have the cafe name printed. But the plain un-marked cups, mugs and glasses maximise your:
An expansion option is best modeled as a or option?
An abandonment option is best modeled as a or option?
Copyright © 2014 Keith Woodward

redpajama_set_name: RedPajamaCommonCrawl