Question 251 NPV
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) and in one year (t=1) and have nothing left in the bank at the end (t=1).
How much can you consume at each time?
(a) $57,619.0476
(c) $53,809.5238
(d) $52,380.9524
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).
(b) $23,666.6667
(e) $16,666.6667
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 $90.91 from the bank and lend it to your neighbour now.
Question 502 NPV, IRR, mutually exclusive projects
An investor owns an empty block of land that has local government approval to be developed into a petrol station, car wash or car park. The council will only allow a single development so the projects are mutually exclusive.
All of the development projects have the same risk and the required return of each is 10% pa. Each project has an immediate cost and once construction is finished in one year the land and development will be sold. The table below shows the estimated costs payable now, expected sale prices in one year and the internal rates of returns (IRR's).
Mutually Exclusive Projects
now ($) 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.
(d) All of the above.
(e) Any of the above.
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 ($)
(a) -100
(b) 0
(c) 10
(d) 21
(e) 121
Question 126 IRR
What is the Internal Rate of Return (IRR) of the project detailed in the table below?
Assume that the cash flows shown in the table are paid all at once at the given point in time. All answers are given as effective annual rates.
(a) 0.21
(b) 0.105
(d) 0.1
(e) 0
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 60 pay back period
The required return of a project is 10%, given as an effective annual rate.
What is the payback period of the project in years?
Assume that the cash flows shown in the table are received smoothly over the year. So the $121 at time 2 is actually earned smoothly from t=1 to t=2.
Question 190 pay back period
A project has the following cash flows:
Normally cash flows are assumed to happen at the given time. But here, assume that the cash flows are received smoothly over the year. So the $500 at time 2 is actually earned smoothly from t=1 to t=2.
(a) -0.80
(b) 0.80
(c) 1.20
(d) 1.80
(e) 2.20
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.
Question 501 NPV, IRR, pay back period
Which of the following statements is NOT correct?
(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 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
How many years will it take for an asset's price to quadruple (be four times as big, say from $1 to $4) if the price grows by 15% pa?
(d) 9.919 years
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.
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 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 404 income and capital returns, real estate
One and a half years ago Frank bought a house for $600,000. Now it's worth only $500,000, based on recent similar sales in the area.
The expected total return on Frank's residential property is 7% pa.
He rents his house out for $1,600 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 $18,617.27.
The future value of 12 months of rental payments one year in the future is $19,920.48.
What is the expected annual rental yield of the property? Ignore the costs of renting such as maintenance, real estate agent fees and so on.
(e) 7%
Question 542 price gains and returns over time, IRR, NPV, income and capital returns, effective return
For an asset price to double every 10 years, what must be the expected future capital return, given as an effective annual rate?
(a) 0.2
(b) 0.116123
(c) 0.082037
(d) 0.071773
(e) 0.06054
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 353 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 6% 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) 3.9216%, 2.9412%, 0.9804%.
(b) 3.9216%, 0.9804%, 2.9412%.
(c) 3.9216%, 0.9804%, 0.9804%.
(d) 1.9804%, 1.0000%, 0.9804%.
(e) 1.9608%, 0.9804%, 0.9804%.
Question 407 income and capital returns, inflation, real and nominal returns and cash flows
A stock has a real expected total return of 7% pa and a real expected capital return of 2% pa.
What is the nominal expected total return, capital return and dividend yield? The answers below are given in the same order.
(a) 11.100%, 4.000%, 7.100%.
(b) 11.140%, 4.040%, 7.100%.
(c) 4.902%, 0.000%, 4.902%.
(d) 9.140%, 4.040%, 5.100%.
(e) 9.140%, 4.040%, 7.100%.
Question 525 income and capital returns, real and nominal returns and cash flows, inflation
Which of the following statements about cash in the form of notes and coins is NOT correct? Assume that inflation is positive.
Notes and coins:
(a) Pay no income cash flow.
(b) Have a nominal total return of zero.
(c) Have a nominal capital return of zero.
(d) Have a nominal income return of zero.
(e) Have a real total return of zero.
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?
(b) III only.
(c) IV only.
(d) I and IV only.
(e) II and III only.
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##
You expect a nominal payment of $100 in 5 years. The real discount rate is 10% pa and the inflation rate is 3% pa. Which of the following statements is NOT correct?
(a) The nominal cash flow of $100 in 5 years is equivalent to a real cash flow of $86.2609 in 5 years. This means that $86.2609 will buy the same amount of goods and services now as $100 will buy in 5 years.
(b) The real discount rate of 10% pa is equivalent to a nominal discount rate of 13.3333% pa.
(c) The nominal price of goods and services will increase by 3% every year.
(d) The real price of goods and services will increase by 3% every year.
(e) The present value of your payment will increase by the nominal discount rate every year.
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.
(b) $471.298
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
Question 221 credit risk
You're considering making an investment in a particular company. They have preference shares, ordinary shares, senior debt and junior debt.
Which is the safest investment? Which will give the highest returns?
(a) Junior debt is the safest. Preference shares will have the highest returns.
(b) Preference shares are the safest. Ordinary shares will have the highest returns.
(c) Senior debt is the safest. Ordinary shares will have the highest returns.
(d) Junior debt is the safest. Ordinary shares will have the highest returns.
(e) Senior debt is the safest. Junior debt will have the highest returns.
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.
(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 473 market capitalisation of equity
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 market capitalisation of equity?
(a) $431.18 billion
(b) $429 billion
(c) $134.07 billion
(d) $8.44 billion
(e) $3.21 billion
Question 444 investment decision, corporate financial decision theory
The investment 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 445 financing decision, corporate financial decision theory
The financing decision primarily affects 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.
Suppose you had $100 in a savings account and the interest rate was 2% per year.
After 5 years, how much do you think you would have in the account if you left the money to grow?
than $102, $102 or than $102?
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."
You're trying to save enough money for a deposit to buy a house. You want to buy a house worth $400,000 and the bank requires a 20% deposit ($80,000) before it will give you a loan for the other $320,000 that you need.
You currently have no savings, but you just started working and can save $2,000 per month, with the first payment in one month from now. Bank interest rates on savings accounts are 4.8% pa with interest paid monthly and interest rates are not expected to change.
How long will it take to save the $80,000 deposit? Round your answer up to the nearest month.
(a) 27 months (t=27 months).
(b) 38 months (t=38 months).
(c) 40 months (t=40 months).
(d) 43 months (t=43 months).
(e) 79 months (t=79 months).
Question 490 expected and historical returns, accounting ratio
Which of the following is NOT a synonym of 'required return'?
(a) total required yield
(b) cost of capital
(c) discount rate
(d) opportunity cost of capital
(e) accounting rate of return
Question 534 NPV, no explanation
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.
How much can you consume at time zero and one? The answer choices are given in the same order.
(a) $26,190.48, $52380.95
(b) $31,250, $62,500
(c) $33,333.33, $66,666.67
(d) $34,375, $68,750
(e) $35,483.87, $70,967.74
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##
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.
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.
(a) 5.8824%, 0.9804%, 4.902%.
Question 155 inflation, real and nominal returns and cash flows, Loan, effective rate conversion
You are a banker about to grant a 2 year loan to a customer. The loan's principal and interest will be repaid in a single payment at maturity, sometimes called a zero-coupon loan, discount loan or bullet loan.
You require a real return of 6% pa over the two years, given as an effective annual rate. Inflation is expected to be 2% this year and 4% next year, both given as effective annual rates.
You judge that the customer can afford to pay back $1,000,000 in 2 years, given as a nominal cash flow. How much should you lend to her right now?
(c) $841,754.97
(d) $889,996.44
(e) $944,108.22
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
(d) $393.95 billion
(e) $1.02935 trillion
Question 729 book and market values, balance sheet, no explanation
If a firm makes a profit and pays no dividends, which of the following accounts will increase?
(a) Asset revaluation reserve.
(b) Foreign currency translation reserve.
(c) Retained earnings, also known as retained profits.
(d) Contributed equity, also known as paid up capital.
(e) General reserve.
Question 446 working capital decision, corporate financial decision theory
The working capital decision primarily affects which part of a business?
Question 447 payout policy, corporate financial decision theory
Payout policy is most closely related to which part of a business?
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?
For an asset price to triple every 5 years, what must be the expected future capital return, given as an effective annual rate?
(e) 0.219755
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.
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.
(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.
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.
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.
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%.
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%.
Question 2 NPV, Annuity
Katya offers to pay you $10 at the end of every year for the next 5 years (t=1,2,3,4,5) if you pay her $50 now (t=0). You can borrow and lend from the bank at an interest rate of 10% pa, given as an effective annual rate.
Ignore credit risk.
Will you or Katya's deal?
Question 288 Annuity
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)##
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 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?
Your friend overheard that you need some cash and asks if you would like to borrow some money. She can lend you $5,000 now (t=0), and in return she wants you to pay her back $1,000 in two years (t=2) and every year after that for the next 5 years, so there will be 6 payments of $1,000 from t=2 to t=7 inclusive.
What is the net present value (NPV) of borrowing from your friend?
Assume that banks loan funds at interest rates of 10% pa, given as an effective annual rate.
(a) -$1,000
(d) $1,040.6721
(e) $1,400.611
Question 58 NPV, inflation, real and nominal returns and cash flows, Annuity
A project to build a toll bridge will take two years to complete, costing three payments of $100 million at the start of each year for the next three years, that is at t=0, 1 and 2.
After completion, the toll bridge will yield a constant $50 million at the end of each year for the next 10 years. So the first payment will be at t=3 and the last at t=12. After the last payment at t=12, the bridge will be given to the government.
The required return of the project is 21% pa given as an effective annual nominal rate.
All cash flows are real and the expected inflation rate is 10% pa given as an effective annual rate. Ignore taxes.
The Net Present Value is:
(a) -$112,496,484
(b) -$32,260,693
(c) -$19,645,987
(d) $5,222,533
(e) $200,000,000
Some countries' interest rates are so low that they're zero.
If interest rates are 0% pa and are expected to stay at that level for the foreseeable future, what is the most that you would be prepared to pay a bank now if it offered to pay you $10 at the end of every year for the next 5 years?
In other words, what is the present value of five $10 payments at time 1, 2, 3, 4 and 5 if interest rates are 0% pa?
(a) $0
(b) $10
(d) Positive infinity
(e) Priceless
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 3 DDM, income and capital returns
The following equation is called the Dividend Discount Model (DDM), Gordon Growth Model or the perpetuity with growth formula: ### P_0 = \frac{ C_1 }{ r - g } ###
What is ##g##? The value ##g## is the long term expected:
(a) Income return of the stock.
(b) Capital return of the stock.
(c) Total return of the stock.
(d) Dividend yield of the stock.
(e) Price-earnings ratio of the stock.
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 ?
Question 451 DDM
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}##
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 28 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 would you call the expression ## C_1/P_0 ##?
(a) The expected total return of the stock.
(b) The expected income return of the stock.
(c) The expected capital return of the stock.
(d) The expected growth rate of the dividend.
(e) The expected growth rate of the stock price.
(a) $1,006.25
Question 730 DDM, income and capital returns, no explanation
A stock's current price is $1. Its expected total return is 10% pa and its long term expected capital return is 4% pa. It pays an annual dividend and the next one will be paid in one year. All rates are given as effective annual rates. The dividend discount model is thought to be a suitable model for the stock. Ignore taxes. Which of the following statements about the stock is NOT correct?
(a) The expected dividend yield is 6% pa.
(b) The expected growth rate of the dividend is 4% pa.
(c) The dividend in one year is expected to be $0.06.
(d) The price is expected to be $1.06 in one year, just before the dividend is paid.
(e) The price is expected to be $1.04 in one year, just after the dividend is paid.
In the dividend discount model (DDM), share prices fall when dividends are paid. Let the high price before the fall be called the peak, and the low price after the fall be called the trough.
Which of the following statements about the DDM is NOT correct?
(a) In between dividends, the stock price is expected to grow by the total return 'r'.
(b) From trough to trough, the stock price is expected to grow by the capital return 'g'.
(c) From peak to peak, the stock price is expected to grow by the capital return 'g'.
(d) Dividends are expected to grow by the total return 'r'.
(e) If the stock's dividends are re-invested by using the cash to buy more stocks, then the growth rate of the shareholder's wealth will be the total return 'r'.
Question 497 income and capital returns, DDM, ex dividend date
A stock will pay you a dividend of $10 tonight if you buy it today. Thereafter the annual dividend is expected to grow by 5% pa, so the next dividend after the $10 one tonight will be $10.50 in one year, then in two years it will be $11.025 and so on. The stock's required return is 10% pa.
What is the stock price today and what do you expect the stock price to be tomorrow, approximately?
(a) $200 today and $210 tomorrow.
(b) $210 today and $220 tomorrow.
(c) $220 today and $230 tomorrow.
(d) $210 today and $200 tomorrow.
(e) $220 today and $210 tomorrow.
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).
### p_0 = \frac{d_1}{r - g} ###
Which expression is NOT equal to the expected dividend yield?
(a) ## r-g ##
(b) ## \dfrac{d_1}{p_0} ##
(c) ## \dfrac{d_5}{p_4} ##
(d) ## \dfrac{d_5(1+g)^2}{p_6} ##
(e) ## \dfrac{d_3}{p_0(1+r)^2} ##
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) $53.2353
(b) $53.1831
(c) $53.0995
(e) $2.7849
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
(d) $28.25
Question 180 equivalent annual cash flow, inflation, real and nominal returns and cash flows
Details of two different types of light bulbs are given below:
Low-energy light bulbs cost $3.50, have a life of nine years, and use about $1.60 of electricity a year, paid at the end of each year.
Conventional light bulbs cost only $0.50, but last only about a year and use about $6.60 of energy a year, paid at the end of each year.
The real discount rate is 5%, given as an effective annual rate. Assume that all cash flows are real. The inflation rate is 3% given as an effective annual rate.
Find the Equivalent Annual Cost (EAC) of the low-energy and conventional light bulbs. The below choices are listed in that order.
(a) 1.4873, 6.7857
(b) 1.6525, 6.7857
(c) 2.1415, 7.1250
(d) 14.8725, 6.7857
(e) 2.0924, 7.1250
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
Question 732 real and nominal returns and cash flows, inflation, income and capital returns
An investor bought a bond for $100 (at t=0) and one year later it paid its annual coupon of $1 (at t=1). Just after the coupon was paid, the bond price was $100.50 (at t=1). Inflation over the past year (from t=0 to t=1) was 3% pa, given as an effective annual rate.
Which of the following statements is NOT correct? The bond investment produced a:
(a) Nominal income return of 1% pa ##\left( =\dfrac{1}{100} \right)##.
(b) Nominal capital return of 0.5% pa ##\left( =\dfrac{100.5-100}{100} \right)##.
(c) Nominal total return of 1.5% pa ##\left( =\dfrac{100.5-100+1}{100} \right)##.
(d) Real income return of 0.9708738% pa##\left( =\dfrac{ 1/(1+0.03)^1}{100} \right)##.
(e) Real capital return of 0.4854369% pa ##\left( =\dfrac{ (100.5-100)/(1+0.03)^1}{100} \right) ##.
Question 734 real and nominal returns and cash flows, inflation, DDM, no explanation
An equities analyst is using the dividend discount model to price a company's shares. The company operates domestically and has no plans to expand overseas. It is part of a mature industry with stable positive growth prospects.
The analyst has estimated the real required return (r) of the stock and the value of the dividend that the stock just paid a moment before ##(C_\text{0 before})##.
What is the highest perpetual real growth rate of dividends (g) that can be justified? Select the most correct statement from the following choices. The highest perpetual real expected growth rate of dividends that can be justified is the country's expected:
(a) Inflation rate.
(b) Nominal GDP growth rate.
(c) Real GDP growth rate.
(d) Nominal total return on the share market index.
(e) Real total return on the share market index.
A low-quality second-hand car can be bought now for $1,000 and will last for 1 year before it will be scrapped for nothing.
A high-quality second-hand car can be bought now for $4,900 and it will last for 5 years before it will be scrapped for nothing.
What is the equivalent annual cost of each car? Assume a discount rate of 10% pa, given as an effective annual rate.
The answer choices are given as the equivalent annual cost of the low-quality car and then the high quality car.
(a) $100, $490
(b) $909.09, $608.5
(c) $1,000, $980
(d) $1,000, $1578.3
(e) $1,100, $1,292.61
You just bought a nice dress which you plan to wear once per month on nights out. You bought it a moment ago for $600 (at t=0). In your experience, dresses used once per month last for 6 years.
Your younger sister is a student with no money and wants to borrow your dress once a month when she hits the town. With the increased use, your dress will only last for another 3 years rather than 6.
What is the present value of the cost of letting your sister use your current dress for the next 3 years?
Assume: that bank interest rates are 10% pa, given as an effective annual rate; you will buy a new dress when your current one wears out; your sister will only use the current dress, not the next one that you will buy; and the price of a new dress never changes.
(a) 300
(b) 283.1403
(c) 282.2849
(d) 257.4003
(e) 225.3944
Question 215 equivalent annual cash flow, effective rate conversion
You're about to buy a car. These are the cash flows of the two different cars that you can buy:
You can buy an old car for $5,000 now, for which you will have to buy $90 of fuel at the end of each week from the date of purchase. The old car will last for 3 years, at which point you will sell the old car for $500.
Or you can buy a new car for $14,000 now for which you will have to buy $50 of fuel at the end of each week from the date of purchase. The new car will last for 4 years, at which point you will sell the new car for $1,000.
Bank interest rates are 10% pa, given as an effective annual rate. Assume that there are exactly 52 weeks in a year. Ignore taxes and environmental and pollution factors.
Should you buy the or the ?
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 290 APR, effective rate, debt terminology
Which of the below statements about effective rates and annualised percentage rates (APR's) is NOT correct?
(a) An effective annual rate could be called: "a yearly rate compounding per year".
(b) An APR compounding monthly could be called: "a yearly rate compounding per month".
(c) An effective monthly rate could be called: "a yearly rate compounding per month".
(d) An APR compounding daily could be called: "a yearly rate compounding per day".
(e) An effective 2-year rate could be called: "a 2-year rate compounding every 2 years".
Question 16 credit card, APR, effective rate
A credit card offers an interest rate of 18% pa, compounding monthly.
Find the effective monthly rate, effective annual rate and the 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) 0.0072, 0.09, 0.0002.
(b) 0.0139, 0.18, 0.0005.
(d) 0.015, 0.1956, 0.0005.
(e) 0.015, 0.1956, 0.006.
Question 19 fully amortising loan, APR
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 a fully amortising 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 loan payments are paid in arrears (at the end of the month).
(b) 2,700
(c) 2,722.1
(d) 2,843.71
(e) 34,424.99
Question 328 bond pricing, APR
A 10 year Australian government bond was just issued at par with a yield of 3.9% pa. The fixed coupon payments are semi-annual. The bond has a face value of $1,000.
Six months later, just after the first coupon is paid, the yield of the bond decreases to 3.65% pa. What is the bond's new price?
(a) $1,000
(b) $1,019.9181
(c) $1,033.8330
(e) $1,060.5226
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".
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 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 581 APR, effective rate, effective rate conversion
A home loan company advertises an interest rate of 6% 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 6.0000% per annum.
(b) The effective monthly rate is 0.5000% per month.
(c) The effective annual rate is 6.1678% per annum.
(d) The effective 6 month rate is 3.0000% per six months.
(e) The APR compounding semi-annually is 6.0755% per annum.
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.
(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.
A semi-annual coupon bond has a yield of 3% pa. Which of the following statements about the yield is NOT correct? All rates are given to four decimal places.
(a) The APR compounding semi-annually is 3.0000% per annum.
(b) The effective 6 month rate is 1.5000% per six months.
(d) The effective monthly rate is 0.2500% per month.
(e) The APR compounding monthly is 2.9814% per annum.
Question 660 fully amortising loan, interest only loan, APR
How much more can you borrow using an interest-only loan compared to a 25-year fully amortising loan if interest rates are 6% pa compounding per month and are not expected to change? If it makes it easier, assume that you can afford to pay $2,000 per month on either loan. Express your answer as a proportional increase using the following formula:
###\text{Proportional Increase} = \dfrac{V_\text{0,interest only}}{V_\text{0,fully amortising}} - 1###
(a) 77.6034%
(b) 30.3779%
(c) 28.8603%
(d) 22.3966%
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
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 just signed up for a 30 year fully amortising mortgage loan with monthly payments of $2,000 per month. The interest rate is 9% pa which is not expected to change.
How much did you borrow? After 5 years, how much will be owing on the mortgage? The interest rate is still 9% and is not expected to change.
(a) 246,567.70, 93,351.63
(b) 246,567.70, 235,741.91
(c) 248,563.73, 96,346.75
(d) 248,563.73, 238,323.24
(e) 256,580.38, 245,314.97
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.
(b) 166,791.61, 90,073.45
(c) 166,791.61, 139,580.77
(d) 165,177.97, 88,321.04
(a) 184,925.77, 164,313.82
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).
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).
(a) $495,533.92, $349,640.96
(b) $500,374.84, $355,510.54
(c) $500,374.84, $250,187.42
(d) $600,000.00, $600,000.00
(e) $600,000.00, $300,000.00
You just borrowed $400,000 in the form of a 25 year interest-only mortgage with monthly payments of $3,000 per month. The interest rate is 9% pa which is not expected to change.
You actually plan to pay more than the required interest payment. You plan to pay $3,300 in mortgage payments every month, which your mortgage lender allows. These extra payments will reduce the principal and the minimum interest payment required each month.
At the maturity of the mortgage, what will be the principal? That is, after the last (300th) interest payment of $3,300 in 25 years, how much will be owing on the mortgage?
(a) $6,766.6469
(e) Nothing, the mortgage will be fully paid off prior to maturity.
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
Question 239 income and capital returns, inflation, real and nominal returns and cash flows, interest only loan
A bank grants a borrower an interest-only residential mortgage loan with a very large 50% deposit and a nominal interest rate of 6% that is not expected to change. Assume that inflation is expected to be a constant 2% pa over the life of the loan. Ignore credit risk.
From the bank's point of view, what is the long term expected nominal capital return of the loan asset?
(a) Approximately 6%.
(b) Approximately 4%.
(c) Approximately 2%.
(d) Approximately 0%.
(e) Approximately -2%.
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}} ###
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 (APR's) compounding per month.
(a) 0.095
Question 15 bond pricing
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 ?
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 ?
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.
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 annually. So there's only one coupon per year, paid in arrears every year.
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?
(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.
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.
A two year Government bond has a face value of $100, a yield of 0.5% and a fixed coupon rate of 0.5%, paid semi-annually. What is its price?
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?
(a) 90.6421
(c) 95.2055
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.
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?
(e) $85.12
Question 138 bond pricing, premium par and discount bonds
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.
A three year bond has a fixed coupon rate of 12% pa, paid semi-annually. The bond's yield is currently 6% pa. The face value is $100. What is its 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.
Which of the following statements is true?
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?
Which one of the following bonds is trading at a discount?
(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% and coupon rate is 5.2% paid semi-annually.
(e) None of the above bonds are discount bonds.
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?
Which one of the following bonds is trading at par?
(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.
Question 194 bond pricing, capital raising
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.
How many bonds should the firm issue?
(a) 107,441
(b) 98,393
(c) 90,480
(d) 80,000
(e) 64,039
Question 213 income and capital returns, bond pricing, premium par and discount bonds
The coupon rate of a fixed annual-coupon bond is constant (always the same).
What can you say about the income return (##r_\text{income}##) of a fixed annual coupon bond? Remember that:
###r_\text{total} = r_\text{income} + r_\text{capital}###
###r_\text{total, 0 to 1} = \frac{c_1}{p_0} + \frac{p_1-p_0}{p_0}###
Assume that there is no change in the bond's total annual yield to maturity from when it is issued to when it matures.
Select the most correct statement.
From its date of issue until maturity, the income return of a fixed annual coupon:
(a) Premium bond will increase.
(b) Premium bond will decrease.
(c) Premium bond will remain constant.
(d) Par bond will increase.
(e) Par bond will decrease.
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 94 leverage, capital structure, real estate
Your friend just bought a house for $400,000. He financed it using a $320,000 mortgage loan and a deposit of $80,000.
In the context of residential housing and mortgages, the 'equity' tied up in the value of a person's house is the value of the house less the value of the mortgage. So the initial equity your friend has in his house is $80,000. Let this amount be E, let the value of the mortgage be D and the value of the house be V. So ##V=D+E##.
If house prices suddenly fall by 10%, what would be your friend's percentage change in equity (E)? Assume that the value of the mortgage is unchanged and that no income (rent) was received from the house during the short time over which house prices fell.
### r_{0\rightarrow1}=\frac{p_1-p_0+c_1}{p_0} ###
where ##r_{0-1}## is the return (percentage change) of an asset with price ##p_0## initially, ##p_1## one period later, and paying a cash flow of ##c_1## at time ##t=1##.
(a) -100%
(b) -50%
(c) -12.5%
(d) -10%
(e) -8%
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%
(e) -10%
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 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 89 WACC, CFFA, interest tax shield
A retail furniture company buys furniture wholesale and distributes it through its retail stores. The owner believes that she has some good ideas for making stylish new furniture. She is considering a project to buy a factory and employ workers to manufacture the new furniture she's designed. Furniture manufacturing has more systematic risk than furniture retailing.
Her furniture retailing firm's after-tax WACC is 20%. Furniture manufacturing firms have an after-tax WACC of 30%. Both firms are optimally geared. Assume a classical tax system.
Which method(s) will give the correct valuation of the new furniture-making project? Select the most correct answer.
(a) Discount the project's unlevered CFFA by the furniture manufacturing firms' 30% WACC after tax.
(b) Discount the project's unlevered CFFA by the company's 20% WACC after tax.
(c) Discount the project's levered CFFA by the company's 20% WACC after tax.
(d) Discount the project's levered CFFA by the furniture manufacturing firms' 30% WACC after tax.
(e) The methods outlined in answers (a) and (c) will give the same valuations, both are correct.
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 368 interest tax shield, CFFA
A method commonly seen in textbooks for calculating a levered firm's free cash flow (FFCF, or CFFA) is the following:
###\begin{aligned} FFCF &= (Rev - COGS - Depr - FC - IntExp)(1-t_c) + \\ &\space\space\space+ Depr - CapEx -\Delta NWC + IntExp(1-t_c) \\ \end{aligned}###
Does this annual FFCF or the annual interest tax shield?
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} \\###
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##
Value the following business project to manufacture a new product.
Project life 2 yrs
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
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.
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
Question 486 capital budgeting, opportunity cost, sunk cost
A young lady is trying to decide if she should attend university. Her friends say that she should go to university because she is more likely to meet a clever young man than if she begins full time work straight away.
What's the correct way to classify this item from a capital budgeting perspective when trying to find the Net Present Value of going to university rather than working?
The opportunity to meet a desirable future spouse should be classified as:
(a) A sunk cost.
(b) An opportunity cost.
(c) A negative side effect.
(d) A positive side effect.
(e) A depreciation expense.
A man is thinking about taking a day off from his casual painting job to relax.
He just woke up early in the morning and he's about to call his boss to say that he won't be coming in to work.
But he's thinking about the hours that he could work today (in the future) which are:
(d) A capital expense.
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:
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).
(e) 52
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.
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.
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).
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 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
Question 370 capital budgeting, NPV, interest tax shield, WACC, CFFA
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
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 rates and cash flows are nominal. The inflation rate is 2% pa.
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 411 WACC, capital structure
A firm plans to issue equity and use the cash raised to pay off its debt. No assets will be bought or sold. Ignore the costs of financial distress.
Which of the following statements is NOT correct, all things remaining equal?
(a) The firm's WACC before tax will rise.
(b) The firm's WACC after tax will rise.
(c) The firm's required return on equity will be lower.
(d) The firm's net income will be higher.
(e) The firm's free cash flow will be lower.
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 91 WACC, capital structure
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?
(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 stay the same.
(e) The company's before-tax WACC is likely to stay the same.
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?
(d) The company's after-tax WACC is likely to have decreased.
(e) The company's before-tax WACC is likely to have decreased.
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 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.
You deposit money into a bank. Which of the following statements is NOT correct? You:
(a) Are a lender.
(b) Issued debt.
(c) Bought debt.
(d) Are a debt holder.
(e) Own a debt asset.
You bought a house, primarily funded using a home loan from a bank. Which of the following statements is NOT correct?
(a) The home loan is a debt liability to the bank.
(b) The bank invested in your debt.
(c) You are indebted to the bank.
(d) You owe the bank principal and interest payments.
(e) You sold your promise to the bank to pay the principal and interest.
Question 738 financial statement, balance sheet, income statement
Where can a private firm's market value of equity be found? It can be sourced from the company's:
(a) Income statement
(b) Balance sheet
(c) Cash flow statement
(d) Stock exchange data.
(e) It's not published, it can only be estimated using multiples or discounted cash flow methods.
Question 739 real and nominal returns and cash flows, inflation
There are a number of different formulas involving real and nominal returns and cash flows. Which one of the following formulas is NOT correct? All returns are effective annual rates. Note that the symbol ##\approx## means 'approximately equal to'.
(a) ##r_\text{real} \approx r_\text{nominal} - r_\text{inflation}##
(b) ##(1+r_\text{real})^t = \left( \dfrac{1+r_\text{nominal}}{1+r_\text{inflation}} \right)^t ##
(c) ##V_\text{t,real} = V_\text{t,nominal}.(1+r_\text{inflation})^t##
(d) ##V_\text{0} = \dfrac{V_\text{t,nominal}}{(1+r_\text{nominal})^t}##
(e) ##V_\text{0} = \dfrac{V_\text{t,real}}{(1+r_\text{real})^t}##
Question 741 APR, effective rate
A home loan company advertises an interest rate of 4.5% pa, payable monthly. Which of the following statements about the interest rate is NOT correct?
(a) The APR compounding monthly is 4.5% pa.
(b) The effective monthly rate is 0.3675% pa.
(c) The effective annual rate is 4.594% pa.
(d) The effective 6 month rate is 2.2712% pa.
(e) The APR compounding semi-annually is 4.5424% pa.
Question 742 price gains and returns over time, no explanation
For an asset's price to quintuple every 5 years, what must be its effective annual capital return? Note that a stock's price quintuples when it increases from say $1 to $5.
(a) 20% pa.
(b) 37.973% pa.
(c) 43.0969% pa.
(d) 56.9031% pa.
(e) 80% pa.
How many years will it take for an asset's price to triple (increase from say $1 to $3) if it grows by 5% pa?
(a) 17.7643 years
(b) 22.5171 years
(c) 29.2722 years
(d) 40 years
(e) 60 years
If someone says "my shares rose by 10% last year", what do you assume that they mean?
(a) The historical nominal effective annual total return was 10%.
(b) The historical real effective annual total return was 10%.
(c) The expected nominal effective annual total return was 10%.
(d) The historical nominal effective annual capital return was 10%.
(e) The expected real effective annual dividend return was 10%.
A stock will pay you a dividend of $2 tonight if you buy it today.
Thereafter the annual dividend is expected to grow by 3% pa, so the next dividend after the $2 one tonight will be $2.06 in one year, then in two years it will be $2.1218 and so on. The stock's required return is 8% pa.
(a) $40 tonight and $38 tomorrow.
(b) $41.2 tonight and $39.2 tomorrow.
(c) $41.2 tonight and $43.2 tomorrow.
(d) $43.2 tonight and $41.2 tomorrow.
(e) $45.2 tonight and $43.2 tomorrow.
Itau Unibanco is a major listed bank in Brazil with a market capitalisation of equity equal to BRL 85.744 billion, EPS of BRL 3.96 and 2.97 billion shares on issue.
Banco Bradesco is another major bank with total earnings of BRL 8.77 billion and 2.52 billion shares on issue.
Estimate Banco Bradesco's current share price using a price-earnings multiples approach assuming that Itau Unibanco is a comparable firm.
Note that BRL is the Brazilian Real, their currency. Figures sourced from Google Finance on the market close of the BVMF on 24/7/15.
(a) BRL 28.87
(b) BRL 25.372
(c) BRL 22.1
(d) BRL 21.653
(e) BRL 21.528
Telsa Motors advertises that its Model S electric car saves $570 per month in fuel costs. Assume that Tesla cars last for 10 years, fuel and electricity costs remain the same, and savings are made at the end of each month with the first saving of $570 in one month from now.
The effective annual interest rate is 15.8%, and the effective monthly interest rate is 1.23%. What is the present value of the savings?
Question 752 IRR, NPV
All other things remaining equal, a project is worse if its:
(a) IRR is lower.
(b) Discount rate is lower.
(c) NPV is higher.
(d) Positive cash flows occur sooner.
(e) Negative cash flows occur later.
Question 753 NPV, perpetuity, DDM, no explanation
A perpetuity of yearly payments of $30, with the first payment in 5 years (first payment at t=5, which continues every year after that forever).
One payment of $100 in 6 years and 3 months (t=6.25).
(a) $260.022324
(b) $213.660269
(c) $178.949525
(d) $151.628987
(e) $140.71319
Question 754 fully amortising loan, interest only loan
Question 755 bond pricing, capital raising, no explanation
A firm wishes to raise $50 million now. They will issue 7% pa semi-annual coupon bonds that will mature in 6 years and have a face value of $100 each. Bond yields are 5% pa, given as an APR compounding every 6 months, and the yield curve is flat.
(b) 453,483
(c) 500,000
(d) 527,541
(e) 666,873
A firm wishes to raise $50 million now. They will issue 5% pa semi-annual coupon bonds that will mature in 10 years and have a face value of $100 each. Bond yields are 5% pa, given as an APR compounding every 6 months, and the yield curve is flat.
Question 763 multi stage growth model, DDM
A stock is expected to pay its first dividend of $20 in 3 years (t=3), which it will continue to pay for the next nine years, so there will be ten $20 payments altogether with the last payment in year 12 (t=12).
From the thirteenth year onward, the dividend is expected to be 4% more than the previous year, forever. So the dividend in the thirteenth year (t=13) will be $20.80, then $21.632 in year 14, and so on forever. The required return of the stock is 10% pa. All rates are effective annual rates. Calculate the current (t=0) stock price.
(e) $469.558
Question 764 bond pricing, no explanation
A 4.5% fixed coupon Australian Government bond was issued at par in mid-April 2009. Coupons are paid semi-annually in arrears in mid-April and mid-October each year. The face value is $1,000. The bond will mature in mid-April 2020, so the bond had an original tenor of 11 years.
Today is mid-September 2015 and similar bonds now yield 1.9% pa.
What is the bond's new price? Note: there are 10 semi-annual coupon payments remaining from now (mid-September 2015) until maturity (mid-April 2020); both yields are given as APR's compounding semi-annually; assume that the yield curve was flat before the change in yields, and remained flat afterwards as well.
(a) $1,108.390216
(b) $1,114.640575
(c) $1,123.457853
(d) $1,127.892613
(e) $1,132.344879
An investor bought a 5 year government bond with a 2% pa coupon rate at par. Coupons are paid semi-annually. The face value is $100.
Calculate the bond's new price 8 months later after yields have increased to 3% pa. Note that both yields are given as APR's compounding semi-annually. Assume that the yield curve was flat before the change in yields, and remained flat afterwards as well.
(a) $95.345378
(b) $95.819741
(c) $96.138082
(d) $96.296464
(e) $96.775559
Question 766 CFFA, WACC, interest tax shield, DDM
Use the below information to value a levered company with constant annual perpetual cash flows from assets. The next cash flow will be generated in one year from now, so a perpetuity can be used to value this firm. Both the cash flow from assets including and excluding interest tax shields are constant (but not equal to each other).
Data on a Levered Firm with Perpetual Cash Flows
Item abbreviation Value Item full name
##\text{CFFA}_\text{U}## $100m Cash flow from assets excluding interest tax shields (unlevered)
##\text{CFFA}_\text{L}## $112m Cash flow from assets including interest tax shields (levered)
##g## 0% pa Growth rate of cash flow from assets, levered and unlevered
##\text{WACC}_\text{BeforeTax}## 7% pa Weighted average cost of capital before tax
##\text{WACC}_\text{AfterTax}## 6.25% pa Weighted average cost of capital after tax
##r_\text{D}## 5% pa Cost of debt
##r_\text{EL}## 9% pa Cost of levered equity
##D/V_L## 50% pa Debt to assets ratio, where the asset value includes tax shields
##t_c## 30% Corporate tax rate
What is the value of the levered firm including interest tax shields?
(a) $431.111m
(b) $444.444m
(c) $485m
(d) $515.464m
(e) $1600m
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.
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 30 year Japanese government bond was just issued at par with a yield of 1.7% pa. The fixed coupon payments are semi-annual. The bond has a face value of $100.
Six months later, just after the first coupon is paid, the yield of the bond increases to 2% pa. What is the bond's new price?
Bonds X and Y are issued by the same 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 pays coupons of 6% pa and bond Y pays coupons of 8% pa. Which of the following statements is true?
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.
(e) None of the above bonds are premium bonds.
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
(c) 10.517092% pa
(d) 10.468982% pa
(e) 9.531018% pa
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})##
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
(c) 12% pa
Question 712 effective rate conversion
An effective monthly return of 1% ##(r_\text{eff monthly})## is equivalent to an effective annual return ##(r_\text{eff annual})## of:
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 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 ?
Question 718 arithmetic and geometric averages
The symbol ##\text{GDR}_{0\rightarrow 1}## represents a stock's gross discrete return per annum over the first year. ##\text{GDR}_{0\rightarrow 1} = P_1/P_0##. The subscript indicates the time period that the return is mentioned over. So for example, ##\text{AAGDR}_{1 \rightarrow 3}## is the arithmetic average GDR measured over the two year period from years 1 to 3, but it is expressed as a per annum rate.
Which of the below statements about the arithmetic and geometric average GDR is NOT correct?
(a) Arithmetic average gross discrete return is ##\text{AAGDR}_{0\rightarrow T} = \dfrac{\text{GDR}_{0 \rightarrow 1}+\text{GDR}_{1\rightarrow 2}+...+\text{GDR}_{T-1 \rightarrow T}}{T}##
(b) Geometric average gross discrete return is ##\text{GAGDR}_{0\rightarrow T} = \dfrac{\text{GDR}_{0 \rightarrow 1} . \text{GDR}_{1\rightarrow 2} ... \text{GDR}_{T-1 \rightarrow T}}{T}##
(c) The geometric average gross discrete return can be quickly found using the first ##(P_0)## and last ##(P_T)## prices. ##\text{GAGDR}_{0\rightarrow T} = \left( \dfrac{P_T}{P_0} \right)^{1/T}##
(d) The arithmetic average is always bigger than or equal to the geometric average, ##\text{AAGDR} \ge \text{GAGDR}##.
(e) The arithmetic and geometric averages of returns will be equal if the variance of the stock's returns is zero.
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 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?
(c) $110
(e) $108
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?
(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.
Convert a 10% effective annual rate ##(r_\text{eff annual})## into a continuously compounded annual rate ##(r_\text{cc annual})##. The equivalent continuously compounded annual rate is:
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
(e) 10% pa
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
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.
Fred owns some BHP shares. He has calculated BHP's monthly returns for each month in the past 30 years using this formula:
He then took the arithmetic average and found it to be 0.8% per month using this formula:
###\bar{r}_\text{monthly}= \dfrac{ \displaystyle\sum\limits_{t=1}^T{\left( r_\text{t monthly} \right)} }{T} =0.008=0.8\% \text{ per month}###
He also found the standard deviation of these monthly returns which was 15% 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} =0.15=15\%\text{ per month}###
Assume that the past historical average return is the true population average of future expected returns and the stock's returns calculated above ##(r_\text{t monthly})## are normally distributed. Which of the below statements about Fred's BHP shares is NOT correct?
(a) The returns ##r_\text{t monthly}## are continuously compounded monthly returns.
(b) The mean, median and mode of the continuously compounded annual return is expected to equal 0.8% per month.
(c) The annualised average continuously compounded return is ##\bar{r}_\text{cc annual}=12×0.008=0.096=9.6\%\text{ pa}##. The annualised standard deviation is ##\sigma_\text{annual} = \sqrt{12}×0.15=0.519615242 = 52\%\text{ pa}##.
(d) If the current price of the BHP shares is $20, they're expected to have a median value of $52.2339 ##(= 20×e^{0.008×12×10})## in 10 years.
(e) If the current price of the BHP shares is $20, they're expected to have a mean value of $13.5411 ##(= 20×e^{(0.008 - 0.15^2/2)×12×10})## in 10 years.
Question 633 personal 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.
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 $50,000 per annum before-tax?
(b) $7,797
(c) $9,614
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##
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##
A young lady is trying to decide if she should attend university or not.
The young lady's parents say that she must attend university because otherwise all of her hard work studying and attending school during her childhood was a waste.
What's the correct way to classify this item from a capital budgeting perspective when trying to decide whether to attend university?
The hard work studying at school in her childhood should be classified as:
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.
Question 513 stock split, reverse stock split, stock dividend, bonus issue, rights issue
(a) A 3 for 2 stock split means that for every 2 existing shares, all shareholders will receive 1 extra share.
(b) A 3 for 10 bonus issue means that for every 10 existing shares, all shareholders will receive 3 extra shares.
(c) A 20% stock dividend means that for every 10 existing shares, all shareholders will receive 2 extra shares.
(d) A 1 for 10 reverse stock split means that for every 10 existing shares, all shareholders will lose 9 shares, so they will only be left with 1 share.
(e) A 3 for 10 rights issue at a subscription price of $8 means that for every 10 existing shares, all shareholders can sell 3 of their shares back to the company at a price of $8 each, so shareholders receive money.
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 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 212 rights issue
In mid 2009 the listed mining company Rio Tinto announced a 21-for-40 renounceable rights issue. Below is the chronology of events:
04/06/2009. Share price opens at $69.00 and closes at $66.90.
05/06/2009. 21-for-40 rights issue announced at a subscription price of $28.29.
16/06/2009. Last day that shares trade cum-rights. Share price opens at $76.40 and closes at $75.50.
17/06/2009. Shares trade ex-rights. Rights trading commences.
All things remaining equal, what would you expect Rio Tinto's stock price to open at on the first day that it trades ex-rights (17/6/2009)? Ignore the time value of money since time is negligibly short. Also ignore taxes.
Question 455 income and capital returns, payout policy, DDM, market efficiency
A fairly priced unlevered firm plans to pay a dividend of $1 next year (t=1) which is expected to grow by 3% pa every year after that. The firm's required return on equity is 8% pa.
The firm is thinking about reducing its future dividend payments by 10% so that it can use the extra cash to invest in more projects which are expected to return 8% pa, and have the same risk as the existing projects. Therefore, next year's dividend will be $0.90. No new equity or debt will be issued to fund the new projects, they'll all be funded by the cut in dividends.
What will be the stock's new annual capital return (proportional increase in price per year) if the change in payout policy goes ahead?
Assume that payout policy is irrelevant to firm value (so there's no signalling effects) and that all rates are effective annual rates.
(a) 2.7% pa.
(b) 3.0% pa.
(c) 3.5% pa.
(d) 3.3% pa.
(e) 3.8% pa.
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.
Project life 2 years
Depreciation of equipment per year for tax purposes $3m
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 $10m at the end of each year.
Find the project's CFFA at time zero, one and two. Answers are given in millions of dollars ($m).
(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
Question 706 utility, risk aversion, utility function
Mr Blue, Miss Red and Mrs Green are people with different utility functions.
Note that a fair gamble is a bet that has an expected value of zero, such as paying $0.50 to win $1 in a coin flip with heads or nothing if it lands tails. Fairly priced insurance is when the expected present value of the insurance premiums is equal to the expected loss from the disaster that the insurance protects against, such as the cost of rebuilding a home after a catastrophic fire.
(a) Mr Blue, Miss Red and Mrs Green all prefer more wealth to less. This is rational from an economist's point of view.
(b) Mr Blue is risk averse. He will not enjoy a fair gamble and would like to buy fairly priced insurance.
(c) Miss Red is risk-neutral. She will not enjoy a fair gamble but wouldn't oppose it either. Similarly with fairly priced insurance.
(d) Mrs Green is risk-loving. She would enjoy a fair gamble and would dislike fairly priced insurance.
(e) Mr Blue would like to buy insurance, but only if it is fairly or under priced.
(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.
Question 703 utility, risk aversion, utility function, gamble
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.
Question 694 utility
Which of the below statements about utility is NOT generally accepted by economists? Most people are thought to:
(a) Prefer more to less, meaning that they will always like to have more wealth.
(b) Be risk averse, meaning that they dislike risk as measured by the standard deviation of wealth.
(c) Have a positively sloped utility function, so the gradient or first derivative of the utility function is always positive.
(d) Have a utility function that increases at a diminishing rate. So the shape is concave down like a frown, or the second derivative is always negative.
(e) Have a utility function that rises until it reaches the satiation point, then it falls because too much wealth causes problems.
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.
(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) Mr Blue and Miss Red prefer more wealth to less.
(b) Mrs Green enjoys losing wealth.
(d) Miss Red is risk neutral.
(e) Mrs Green is risk averse.
(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.
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 5 while refusing is 7.07. So the gamble makes him less happy.
(b) Mrs Green's expected utility of wealth from gambling is 7.07 while refusing is 5. So the gamble makes her more happy.
(c) Mr Blue's certainty equivalent of the risky gamble is $25. This is less than his current wealth of $50 which is why he would refuse.
(d) Miss Red's certainty equivalent of the risky gamble is $50. This is equal to her current wealth of $50 which is why she is indifferent to gambling or not.
(e) Mrs Green's certainty equivalent of the risky gamble is $70.71. This is more than her current wealth of $50 which is why she would accept.
(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.
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.
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%
Question 767 idiom, corporate financial decision theory, no explanation
The sayings "Don't cry over spilt milk", "Don't regret the things that you can't change" and "What's done is done" are most closely related to which financial concept?
(a) Competition.
(b) Opportunity costs.
(d) Diversification.
(e) Sunk costs.
Question 768 accounting terminology, book and market values, no explanation
Accountants and finance professionals have lots of names for the same things which can be quite confusing.
Which of the following groups of items are NOT synonyms?
(a) Revenue, sales, turn over.
(b) Paid up capital, contributed equity.
(c) Shares, stock, equity.
(d) Net income, earnings, net profit after tax, the bottom line.
(e) Market capitalisation of equity, book value of equity.
Question 769 short selling, idiom, no explanation
"Buy low, sell high" is a well-known saying. It suggests that investors should buy low then sell high, in that order.
How would you re-phrase that saying to describe short selling?
(a) Buy high, then sell low.
(b) Buy low, then sell high.
(c) Sell high, then buy low.
(d) Sell low, then buy high.
(e) Sell high, then buy high.
Question 770 expected and historical returns, income and capital returns, coupon rate, bond pricing, no explanation
Which of the following statements is NOT correct? Assume that all things remain equal. So for example, don't assume that just because a company's dividends and profit rise that its required return will also rise, assume the required return stays the same.
(a) If a company's dividend (and profit and free cash flow to equity) rises, its share price will rise.
(b) If a fixed coupon bond's yield to maturity rises, its price will rise.
(c) If a residential property's rent revenue rises, its price will rise.
(d) If a patent's royalty revenue rises, its price will also rise.
(e) If a software asset's licensing revenue rises, its price will also rise.
Question 771 debt terminology, interest expense, interest tax shield, credit risk, no explanation
You deposit money into a bank account. Which of the following statements about this deposit is NOT correct?
(a) You have a debt asset.
(b) The bank sold you its promise to pay back interest and principal payments.
(c) The bank is exposed to your credit risk, it's afraid that you'll default on your debt.
(d) The interest income you're paid is taxable income for you.
(e) The interest expense that the bank pays is tax-deductible for the bank.
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.
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
Question 772 interest tax shield, capital structure, leverage
A firm issues debt and uses the funds to buy back equity. Assume that there are no costs of financial distress or transactions costs. Which of the following statements about interest tax shields is NOT correct?
(a) Higher debt leads to higher interest expense.
(b) Higher interest expense leads to lower profit before tax, following on from above.
(c) Lower profit before tax leads to lower tax payments, following on from above.
(d) Lower tax payments lead to higher cash flow from assets, following on from above.
(e) Lower profit after tax leads to a lower share price, following on from above.
Question 775 utility, utility function
Below is a graph of 3 peoples' utility functions, Mr Blue (U=W^(1/2) ), Miss Red (U=W/10) and Mrs Green (U=W^2/1000). Assume that each of them currently have $50 of wealth.
Which of the following statements about them is NOT correct?
(a) Mr Blue would prefer to invest his wealth in a well diversified portfolio of stocks rather than a single stock, assuming that all stocks had the same total risk and return.
(b) Mrs Green would prefer to invest her wealth in a single stock rather than a well diversified portfolio of stocks, assuming that all stocks had the same total risk and return.
(c) The popularity of insurance only makes sense if people are similar to Mr Blue.
(d) CAPM theory only makes sense if people are similar to Miss Red.
(e) The popularity of casino gambling and lottery tickets only make sense if people are similar to Mrs Green.
Question 340 market efficiency, opportunity cost
A managed fund charges fees based on the amount of money that you keep with them. The fee is 2% of the start-of-year amount, but it is paid at the end of every year.
This fee is charged regardless of whether the fund makes gains or losses on your money.
The fund offers to invest your money in shares which have an expected return of 10% pa before fees.
You are thinking of investing $100,000 in the fund and keeping it there for 40 years when you plan to retire.
What is the Net Present Value (NPV) of investing your money in the fund? Note that the question is not asking how much money you will have in 40 years, it is asking: what is the NPV of investing in the fund? Assume that:
The fund has no private information.
Markets are weak and semi-strong form efficient.
The fund's transaction costs are negligible.
The cost and trouble of investing your money in shares by yourself, without the managed fund, is negligible.
(b) -$20,000.00
(c) -$48,000.17
(d) -$51,999.83
(e) -$80,000.00
Question 416 real estate, market efficiency, income and capital returns, DDM, CAPM
A residential real estate investor believes that house prices will grow at a rate of 5% pa and that rents will grow by 2% pa forever.
All rates are given as nominal effective annual returns. Assume that:
His forecast is true.
Real estate is and always will be fairly priced and the capital asset pricing model (CAPM) is true.
Ignore all costs such as taxes, agent fees, maintenance and so on.
All rental income cash flow is paid out to the owner, so there is no re-investment and therefore no additions or improvements made to the property.
The non-monetary benefits of owning real estate and renting remain constant.
Which one of the following statements is NOT correct? Over time:
(a) The rental yield will fall and approach zero.
(b) The total return will fall and approach the capital return (5% pa).
(c) One or all of the following must fall: the systematic risk of real estate, the risk free rate or the market risk premium.
(d) If the country's nominal wealth growth rate is 4% pa and the nominal real estate growth rate is 5% pa then real estate will approach 100% of the country's wealth over time.
(e) If the country's nominal gross domestic production (GDP) growth rate is 4% pa and the nominal real estate rent growth rate is 2% pa then real estate rent will approach 100% of the country's GDP over time.
##\text{CFFA}_\text{U}## $48.5m Cash flow from assets excluding interest tax shields (unlevered)
##\text{CFFA}_\text{L}## $50m Cash flow from assets including interest tax shields (levered)
##\text{WACC}_\text{BeforeTax}## 10% pa Weighted average cost of capital before tax
##\text{WACC}_\text{AfterTax}## 9.7% pa Weighted average cost of capital after tax
##r_\text{EL}## 11.25% pa Cost of levered equity
(b) $500m
(e) $431.111m
Question 774 leverage, WACC, real estate
One year ago you bought a $1,000,000 house partly funded using a mortgage loan. The loan size was $800,000 and the other $200,000 was your wealth or 'equity' in the house asset.
The interest rate on the home loan was 4% pa.
Over the year, the house produced a net rental yield of 2% pa and a capital gain of 2.5% pa.
Assuming that all cash flows (interest payments and net rental payments) were paid and received at the end of the year, and all rates are given as effective annual rates, what was the total return on your wealth over the past year?
(a) 0.4808% pa
(b) 2% pa
(c) 4.5% pa
(d) 6.5% pa
(e) 8.5% pa
Question 777 CAPM, beta
The market's expected total return is 10% pa and the risk free rate is 5% pa, both given as effective annual rates.
A stock has a beta of 0.5.
In the last 5 minutes, the federal government unexpectedly raised taxes. Over this time the share market fell by 3%. The risk free rate was unchanged.
What do you think was the stock's historical return over the last 5 minutes, given as an effective 5 minute rate?
(a) -1%
(b) -1.5%
(c) -2.5%
(d) -3%
(e) -7.5%
Question 673 CAPM, beta, expected and historical returns
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.
In the last 5 minutes, bad economic news was released showing a higher chance of recession. Over this time the share market fell by 1%. The risk free rate was unchanged.
(a) -12.5%
(b) -4%
(e) 12.5%
Over the last year, bad economic news was released showing a higher chance of recession. Over this time the share market fell by 1%. The risk free rate was unchanged.
What do you think was the stock's historical return over the last year, given as an effective annual rate?
(a) -12.5% pa
(b) -4% pa
(c) -1.5% pa
(d) -1% pa
(e) 12.5% pa
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 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 302 WACC, CAPM
Which of the following statements about the weighted average cost of capital (WACC) is NOT correct?
(a) WACC before tax ##= r_D.\dfrac{D}{V_L} + r_{EL}.\dfrac{E_L}{V_L}##
(b) WACC before tax ##= r_f + \beta_{VL}.(r_m - r_f)##
(c) WACC after tax ##= r_D.(1-t_c).\dfrac{D}{V_L} + r_{EL}.\dfrac{E_L}{V_L}##
(d) WACC after tax ##= r_f + \beta_{VL}.(r_m - r_f) - \dfrac{r_D.D.t_c}{V_L}##
(e) WACC after tax ##= r_f + \beta_{VL}.(r_m - r_f)##
Question 418 capital budgeting, NPV, interest tax shield, WACC, CFFA, CAPM
Expected sale price of equipment at end of project 0
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 778 CML, systematic and idiosyncratic risk, portfolio risk, CAPM, no explanation
The capital market line (CML) is shown in the graph below. The total standard deviation is denoted by σ and the expected return is μ. Assume that markets are efficient so all assets are fairly priced.
Which of the below statements is NOT correct?
(a) The risk free security has zero systematic variance and zero idiosyncratic variance.
(b) The market portfolio has zero idiosyncratic variance.
(c) Any portfolio comprised of the market portfolio and risk free security has zero idiosyncratic variance.
(d) Portfolios that plot on the CML must only be comprised of the risk free security and the market portfolio.
(e) Portfolios that plot on the CML have some idiosyncratic variance and some systematic variance.
Question 780 mispriced asset, NPV, DDM, market efficiency, no explanation
A company advertises an investment costing $1,000 which they say is under priced. 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 be 4% pa and the capital yield 11% pa. Assume 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) $7,359.46, Infinite
(b) $4,887.57, $10,000
(c) $1,786.35, -$5,000 (Note the negative sign)
(d) $1,471.89, $830.28
(e) $830.28, $3,000
Question 657 systematic and idiosyncratic risk, CAPM, no explanation
A stock's required total return will decrease when its:
(a) Systematic risk increases.
(b) Idiosyncratic risk increases.
(c) Total risk increases.
(d) Systematic risk decreases.
(e) Idiosyncratic risk decreases.
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 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.
(c) The effective annual rate is 9.3807% pa.
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%
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.
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 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 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 617 systematic and idiosyncratic risk, risk, CAPM
A stock's required total return will increase when its:
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 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 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?
(e) The stand-alone principle, incremental cash flows and sunk costs.
Question 624 franking credit, personal tax on dividends, imputation tax system, no explanation
Which of the following statements about Australian franking credits is NOT correct? Franking credits:
(a) Refund the corporate tax paid by companies to their individual shareholders. Therefore they prevent the double-taxation of dividends at the corporate and personal level.
(b) Are distributed to shareholders together with cash dividends.
(c) Are also called imputation credits.
(d) Are worthless to individuals who earn less than the tax-free threshold because they have a zero marginal personal tax rate.
(e) Are worthless to individual shareholders who are foreigners for tax purposes.
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 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 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.
Question 629 yield curve, forward interest rate
Which of the following statements about yield curves is NOT correct?
(a) A yield curve graph shows bonds' spot yields at different maturities. The y-axis shows spot yields and the x-axis shows the bonds' times to maturity.
(b) A yield curve is a graph of forward rates.
(c) Normal yield curves slope upwards, they have a positive gradient.
(d) A yield curve is 'as at' a certain date, it's a snapshot in time.
(e) Every point on the yield curve corresponds to a different bond with a different maturity.
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
You deposit cash into your bank account. Does the deposit account represent a debt or to you?
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} ##
Question 50 DDM, stock pricing, inflation, real and nominal returns and cash flows
Most listed Australian companies pay dividends twice per year, the 'interim' and 'final' dividends, which are roughly 6 months apart.
You are an equities analyst trying to value the company BHP. You decide to use the Dividend Discount Model (DDM) as a starting point, so you study BHP's dividend history and you find that BHP tends to pay the same interim and final dividend each year, and that both grow by the same rate.
You expect BHP will pay a $0.55 interim dividend in six months and a $0.55 final dividend in one year. You expect each to grow by 4% next year and forever, so the interim and final dividends next year will be $0.572 each, and so on in perpetuity.
Assume BHP's cost of equity is 8% pa. All rates are quoted as nominal effective rates. The dividends are nominal cash flows and the inflation rate is 2.5% pa.
What is the current price of a BHP share?
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%.
Question 790 mean and median returns, return distribution, arithmetic and geometric averages, continuously compounding rate, log-normal distribution, VaR, confidence interval
A risk manager has identified that their hedge fund's continuously compounded portfolio returns are normally distributed with a mean of 10% pa and a standard deviation of 30% pa. The hedge fund's portfolio is currently valued at $100 million. Assume that there is no estimation error in these figures and that the normal cumulative density function at 1.644853627 is 95%.
Which of the following statements is NOT correct? All answers are rounded to the nearest dollar.
(a) Future portfolio values have a log-normal distribution. The mean (expected or arithmetic average) portfolio value in one year is $115,603,957.
(b) The median (50th percentile) portfolio value in one year is $115,603,957.
(c) The 90% confidence interval of continuously compounded portfolio returns over the next year ##(r_{0 \rightarrow 1})## is ##-39.3456088\% < r_{0 \rightarrow 1} < 59.3456088\%##.
(d) The 90% confidence interval of portfolio values in one year ##(V_1)## is ##\$67,472,095 < V_1 < \$181,023,395##.
(e) The annual 95% relative VaR is $48,131,863 and the absolute VaR is $32,527,905.
Question 811 log-normal distribution, mean and median returns, return distribution, arithmetic and geometric averages
Which of the following statements about probability distributions is NOT correct?
(a) A normally distributed variable's mean, median and mode are all expected to be equal.
(b) A log-normally distributed variable's mean, median and mode are all expected to be different. Mean > median > mode.
(c) Future stock prices ##(P_t )## are often assumed to be log-normally distributed.
(d) Stocks' annual net discrete returns ##(P_t/P_0-1)## must be normally distributed when stock prices ##(P_t)## are log-normally distributed.
(e) The total area under a probability density function (pdf) is always one.
Question 808 Markowitz portfolio theory, portfolio return
A graph of assets' expected returns ##(\mu)## versus standard deviations ##(\sigma)## is given in the below diagram.
Each letter corresponds to a separate coloured area. The portfolios at the boundary of the areas, on the black lines, are excluded from each area. Assume that all assets represented in this graph are fairly priced, and that all risky assets can be short-sold.
Which of the following statements about this graph and Markowitz portfolio theory is NOT correct?
(a) Area A contains ideal portfolios but unfortunately these portfolios are unattainable.
(b) Area B portfolios are only attainable if investors can borrow at the risk free rate, meaning that they can risklessly short sell government bonds and only pay the risk free rate to do so.
(c) Area C contains all individual risky assets and portfolios of those risky assets.
(d) Area D portfolios are only attainable if investors can borrow at the risk free rate, meaning that they can risklessly short sell government bonds and only pay the risk free rate to do so, similarly to Area B.
(e) Area E contains unattainable portfolios.
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 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
(d) 1
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?
(a) 5%
(c) 9%
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.
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 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.
An effective semi-annual return of 5% ##(r_\text{eff 6mth})## is equivalent to an effective annual return ##(r_\text{eff annual})## of:
Question 715 return distribution
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)##.
The below three graphs show probability density functions (PDF) of three different random variables Red, Green and Blue.
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)##
The below three graphs show probability density functions (PDF) of three different random variables Red, Green and Blue. Let ##P_1## be the unknown price of a stock in one year. ##P_1## is a random variable. Let ##P_0 = 1##, so the share price now is $1. This one dollar is a constant, it is not a variable.
Which of the below statements is NOT correct? Financial practitioners commonly assume that the shape of the PDF represented in the colour:
(a) Green is a stock's continuously compounded rate of return, also called the log gross discrete return. ##r_\text{cc} = \ln(P_1/P_0)##
(b) Blue is a stock's future price, ##P_1##
(c) Blue is a stock's gross discrete return. ##\text{GDR} = P_1/P_0##
(d) Blue is a stock's effective rate of return. ##r_\text{eff} = (P_1-P_0)/P_0##
(e) Red is a stock's net discrete return. ##\text{NDR} = \text{GDR}-1##
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 ?
Use the below information to value a levered company with annual perpetual cash flows from assets that grow. The next cash flow will be generated in one year from now, so a perpetuity can be used to value this firm. Note that 'k' means kilo or 1,000. So the $30k is $30,000.
##\text{CFFA}_\text{U}## $30k Cash flow from assets excluding interest tax shields (unlevered)
##g## 1.5% pa Growth rate of cash flow from assets, levered and unlevered
##r_\text{EL}## 16.3% pa Cost of levered equity
(a) The WACC before tax is 6.46% pa.
(b) The WACC after tax is 5.55% pa.
(c) The current value of the firm's levered assets including tax shields is $603.839k.
(d) The current value of debt is $600k.
(e) The benefit from interest tax shields in the first year is $7.2k.
Question 812 rights issue, no explanation
A firm is about to conduct a 2-for-7 rights issue with a subscription price of $10 per share. They haven't announced the capital raising to the market yet and the share price is currently $13 per share. Assume that every shareholder will exercise their rights, the cash raised will simply be put in the bank, and the rights issue is completed so quickly that the time value of money can be ignored. Disregard signalling, taxes and agency-related effects.
Which of the following statements about the rights issue is NOT correct? After the rights issue is completed:
(a) The number of shares will rise by 2/7 or around 28.57%.
(b) The share price will fall by 2/7 or around 28.57%.
(c) The firm's market capitalisation of equity will rise by 26/70 or around 37.14%.
(d) The market share price is expected to be $10.67.
(e) The company will have more cash.
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 877 arithmetic and geometric averages, utility, utility function
Gross discrete returns in different states of the world are presented in the table below. A gross discrete return is defined as ##P_1/P_0##, where ##P_0## is the price now and ##P_1## is the expected price in the future. An investor can purchase only a single asset, A, B, C or D. Assume that a portfolio of assets is not possible.
Gross Discrete Returns
In Different States of the World
Investment World states (probability)
asset Good (50%) Bad (50%)
A 2 0.5
B 1.1 0.9
C 1.1 0.95
D 1.01 1.01
Which of the following statements about the different assets is NOT correct? Asset:
(a) A's Arithmetic Average Gross Discrete Return (AAGDR) is the highest.
(b) B's Geometric Average Gross Discrete Return (GAGDR) is the lowest.
(c) C's GAGDR is higher than its AAGDR.
(d) D's AAGDR and GAGDR are equal since it's volatility is zero.
(e) C's expected utility of wealth would be the highest for an investor with a log utility function.
Question 876 foreign exchange rate, forward foreign exchange rate, cross currency interest rate parity
Suppose the yield curve in the USA and Germany is flat and the:
USD federal funds rate at the Federal Reserve is 1% pa;
EUR deposit facility at the European Central Bank is -0.4% pa (note the negative sign);
Spot EUR exchange rate is 1 USD per EUR;
One year forward EUR exchange rate is 1.011 USD per EUR.
You suspect that there's an arbitrage opportunity. Which one of the following statements about the potential arbitrage opportunity is NOT correct?
(a) Right now, borrow USD in America, convert it into EUR at the spot, lend it in Germany and lock in to buy USD and sell EUR forward one year. One year later, withdraw the EUR, convert it into USD and pay back the USD loan.
(b) American debt may be under-priced, buy it.
(c) German debt may be over-priced, sell it.
(d) The spot EUR may be over-priced compared to the USD, sell the EUR now.
(e) The forward EUR may be under-priced compared to the USD, lock in to buy the EUR in one year.
Question 871 duration, Macaulay duration, modified duration, portfolio duration
Which of the following statements about Macaulay duration is NOT correct? The Macaulay duration:
(a) Is the weighted average time that an asset's cash flows are received, usually measured in years.
(b) Divided by (1+y) equals the modified duration, where y is the yield to maturity given as an effective annual rate and duration is measured in years.
(c) Of a zero-coupon bond is equal to the bond's maturity.
(d) Of a fixed-coupon-paying bond will be less than the bond's maturity.
(e) Of a portfolio is an arithmetic average of the Macaulay durations of the assets in the portfolio, weighted by their face values.
A fixed coupon bond's modified duration is 20 years, and yields are currently 10% pa compounded annually. Which of the following statements about the bond is NOT correct?
(a) The Macaulay duration of the bond is 22 years.
(b) If yields-to-maturity suddenly fell by 1 percentage point then bond prices would suddenly rise by 20% or more.
(c) If yields-to-maturity suddenly rose by 2 percentage points then bond prices would suddenly fall by 40% or less.
(d) If the bond is a zero-coupon bond then its maturity is 20 years.
(e) The modified-duration-price-change formula assumes parallel shifts in the yield curve.
Question 873 Sharpe ratio, Treynor ratio, Jensens alpha, SML, CAPM
Which of the following statements is NOT correct? Fairly-priced assets should:
(a) Have Sharpe ratios equal to the market's.
(b) Have Treynor ratios equal to the market's.
(c) Have Jensen's alphas that are zero.
(d) Not necessarily be bought or sold since there's no gain either way.
(e) Plot on the Security Market Line (SML).
Question 875 omitted variable bias, systematic and idiosyncratic risk, CAPM, single factor model, two factor model
The Capital Asset Pricing Model (CAPM) and the Single Index Model (SIM) are single factor models whose only risk factor is the market portfolio's return. Say a Solar electricity generator company and a Beach bathing chair renting company are influenced by two factors, the market portfolio return and cloud cover in the sky. When it's sunny and not cloudy, both the Solar and Beach companies' stock prices do well. When there's dense cloud cover and no sun, both do poorly. Assume that cloud coverage risk is a systematic risk that cannot be diversified and that cloud cover has zero correlation with the market portfolio's returns.
Which of the following statements about these two stocks is NOT correct?
The CAPM and SIM:
(a) Betas of the Solar and Beach companies will only measure the companies' sensitivity to the market portfolio risk factor, not the cloud coverage factor.
(b) Will under-estimate the Solar and Beach stocks' systematic variance.
(c) Will under-estimate the Solar and Beach stocks' diversifiable variance.
(d) Models will show positive correlations between the Solar and Beach stock's residual (also called idiosyncratic or diversifiable) returns.
Question 874 utility, return distribution, log-normal distribution, arithmetic and geometric averages
Who was the first theorist to endorse the maximisiation of the geometric average gross discrete return for investors (not gamblers) since it gave a "...portfolio that has a greater probability of being as valuable or more valuable than any other significantly different portfolio at the end of n years, n being large"?
(a) Daniel Bernoulli.
(b) John Larry Kelly Jr.
(c) Henry Allen Latane.
(d) Ole Peters.
(e) Paul Anthony Samuelson.