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[ "What is the difference between an Annuity and IRA?", "What are the tax implications of an Annuity?" ]

[ "Both individual retirement accounts (IRAs) and annuities provide tax-advantaged ways to save for retirement, but there are distinct differences between the two. IRA is not in itself an asset. It's a vehicle for holding financial assets stocks, bonds, mutual funds. Annuities are assets specifically insurance products, designed to generate income.\n\n# IRA\nAn IRA can be thought of as an individual investment and savings account with tax benefits. You open an IRA for yourself (that's why it's called an individual retirement account). If you have a spouse, you'll have to open separate accounts (if one partner earns low or no wages, you can use the family income to open a spousal IRA, to benefit that spouse and double the family's retirement savings options).it is an account in which you keep investments such as stocks, bonds, and mutual funds. An IRA continues to accumulate contributions and interest until you reach retirement age, meaning you could have an IRA for decades before making any withdrawals.\n\nAn IRA usually may carry a small custodial fee, which is charged by the financial institution where your account is held. mutual funds within the IRA charge their own annual management fees, called expense ratios.\n\n# Annuity\nAnnuities are insurance products that provide a source of monthly, quarterly, annual, or lump-sum income during retirement. An annuity makes periodic payments for a certain amount of time, or until a specified event occurs (for example, the death of the person who receives the payments). Money invested in an annuity grows tax-deferred until it is withdrawn.\nUnlike an IRA, which typically can have only one owner, an annuity can be jointly owned. Annuities also do not have the annual contribution limits and income restrictions that IRAs have. There are a variety of annuities. You can fund an annuity all at once (known as a single premium) or you can pay into it over time.\nWith an immediate payment annuity (also called an income annuity), fixed payments begin as soon as the investment is made. If you invest in a deferred annuity, the principal you invest grows for a specific period of time until you begin taking withdrawals usually during retirement As with IRAs, you will be penalized if you try to withdraw funds from the deferred annuity early before the payout period begins.\n\n\nIRAs and annuities are two types of saving vehicles meant for retirement. But the two are inherently different. The main distinction between an IRA and an annuity is that an IRA is an investment account that is tax-advantaged (you place pre-tax money into the account and pay taxes when the amount is withdrawn at the legally allowed age). An annuity is an insurance product that makes fixed-income payments at a specified time.", "Annuity payments are subject to tax based on how the annuity was funded. If your annuity was funded with pre-tax dollars, typically seen in qualified plans, the entire amount of the withdrawals or payments you receive is taxable as income. if your annuity was purchased with post-tax dollars, as with nonqualified plans, you are only taxed on the earnings portion of the withdrawals.\nOne of the biggest benefits of annuities is their ability to grow on a tax-deferred basis. This includes dividends, interest and capital gains, all of which may be fully reinvested while they remain in the annuity. \nYour investment grows without being reduced by tax payments, but that doesn't mean annuities are a way to avoid taxes completely. Annuities are subject to taxation, and how they are taxed depends on various factors. \nThe tax treatment of an annuity is determined by the type of annuity, the source of funds meaning whether it is held in a qualified or non-qualified account and the purpose of the annuity.\n\n# Qualified vs. Non-Qualified Annuity Taxation\n\nAnnuities are classified as either qualified or non-qualified. \nQualified annuities are funded with pre-tax dollars, typically through an employer-sponsored retirement plan like a 401(k) or an IRA. Contributions to these annuities are tax-deferred, meaning taxes are paid when withdrawals are made. \nNon-qualified annuities, on the other hand, are funded with after-tax dollars. As such, they require tax payments only on the earnings portion at withdrawal." ]

[ "What is the difference between FRS 105, the Financial Reporting Standard applicable to the Micro-entities Regime and FRS 102, The Financial Reporting Standard applicable in the England and Ireland?", "You advise a client who is in the process of incorporating a fast growing UK-based technology company. The company has the choice of qualifying as a micro-entity and, as such, could apply either FRS 105 or FRS 102.\n\nWhich FRS should the company follow?" ]

[ "FRS 105, is a simplified version of FRS 102 that's specifically designed for micro-entities. These are the smallest businesses, with relatively low turnover and limited financial complexity. FRS 105 allows them to prepare their accounts in a less time-consuming and burdensome way while still meeting the basic legal requirements. FRS 105 requires fewer disclosures than FRS 102. FRS 105 does not permit property, plant and equipment, intangible assets, or investment properties to be held at fair value. \n\nAccounting policy choices allowed in FRS 102 have been removed in FRS 105. For instance, borrowing costs and development costs must be expensed. Profits reported under FRS 105 may be lower than if FRS 102 was applied.", "The company should apply FRS 102 as it is a fast growing company.\n\nIf competitors prepare financial statements in accordance with FRS 105 then it will be easier to compare and benchmark performance against them. If the company is expected to grow quickly, it might be easier to simply apply FRS 102 from the outset. That way, it will avoid the burden of transitioning from FRS 105 to FRS 102 later.\n\nFRS 105 will reduce the time and cost burden of producing financial statements. However, consideration should be given to whether the users of the financial statements will find this lack of disclosure a hindrance to making economic decisions. This is unlikely in the case of such a small company. FRS 105 will also have an impact on perception of the company's financial position, particularly if carrying amounts of assets are materially lower than other companies as a result." ]

[ "Kensho gave laptops to its new team members in Pakistan on August 1st 2023 at a cost of $10000 each. The average life of the laptop according to the company's policy is 5 years and then they can be sold for $500 in scrap.\n\nOn 31 July 2024, the team will have completed their one year. What would be the depreciation expense per laptop using the straight-line method for 2024 and 2025? What will be the depreciated value of a laptop in 2025?", "By how much will the depreciated value of a laptop differ in 2025 if the reducing balance method @ 35% is used instead?" ]

[ "# Straight line method\nValue of the laptops = $10000\nScrap value = $500\nNet = $10000 - $500 = $9500\nThe useful life of laptops = 5\n\nAnnual depreciation = $9500 / 5 = $1900\n\nThe annual depreciation of $1900 will remain the same for both years 2024 and 2025.\n\n| Year | Depreciation | Remaining Value |\n|--------|--------|--------|\n| 2024 | $1900 | $8100 | \n| 2025 | $1900 | $6200 |\n\nAfter depreciation, the value of a laptop will be $6,200 in 2025.", "# Reducing balance method\n\nIn the reducing balance method, a large amount of the value of the asset is depreciated in the first year due to reasons such as technological obsolescence as laptop technology is evolving rapidly. \n\nValue of the laptops = $10000\nAnnual depreciation for 2024 = $10000 * 35% = $3500\nThe remaining value of the laptops will be $10000 - $3500 = $6500\nAnnual depreciation for 2025 = $6500 * 35% = $2275\n\n\n| Year | Depreciation | Remaining Value |\n|--------|--------|--------|\n| 2024 | $3500 | $6500 | \n| 2025 | $2275 | $4225 |\n\n# The difference\n\nThe difference in the valuation will be that the laptops will have a higher value (by 6200 - $4225 = $1775 = $1975) on the balance sheet of the company if the straight-line method is used." ]

[ "Bob financed his home purchase with a $500,000 5/1 ARM mortgage with a 5/2/6 cap. The breakdown of his initial monthly mortgage costs is as follows:\n\n(P&I): $2,108.62\nInsurance: $250\nTaxes: $500\nAdjustable Rate Formula: SOFR + 3%\n\nBob's initial interest rate was 3%; at the time, SOFR was 2%. Today, Bob's interest rate adjusted for the first time. His new total mortgage payment is $3,638.95. Since purchasing his home, his taxes have increased to $550 a month, and his insurance premium has remained unchanged.\n\nWith this information, can we determine the current SOFR value?", "After one additional year, SOFR skyrockets to 9%. Keeping in mind that Bob has a 5/1 ARM with a 5/2/6 cap—and an Adjustable Rate formula of SOFR + 3%—what can he expect Bob's new interest rate to be?" ]

[ "Yes, this information is sufficient to determine the current SOFR value.\n\nThe first step is to determine the new P&I payment:\n$3,638.95 - $250 - $550 = $2,838.95\n\nThe next step would be to determine the current interest rate on the mortgage (I). While this can't easily be solved algebraically, we can plug various values for (I) into the formula below until we arrive at an answer that is at or near $2838.95: \n\nSolve for I: 2838.95 = [500,000 * I * (1 + I)^360] / [(1 + I)^360 - 1]\n\nThrough trial and error, we can determine that (I) is roughly 5.5%. Furthermore, we know that the mortgage rate is now determined by SOFR + 3%:\n\nSince we know that 5.5% = SOFR + 3%, we can say that SOFR is roughly 2.5%.", "If SOFR skyrockets to 9% after one additional year, the Adjustable Rate formula of SOFR + 3% would imply that Bob's new interest rate is 12%. However, because Bob has a 5/1 ARM with a 5/2/6 cap structure, his rate increase after the initial adjustment is limited to a maximum of 2% per year. Therefore, Bob's new interest rate will be approximately 7.5%, which is his previous interest rate plus the 2%." ]

[ "I purchased 1000 shares of Microsoft at the beginning of 2024 when their price was $180. I wanted to protect myself from a fall in the value of the shares, so I purchased a put contract for $5 with an exercise price of $200. Today the share price is $150.\n\nWhat is my potential profit from these shares?", "I also purchased 500 shares of Amazon at the beginning of 2024 when their price was $200. I also purchased a put contract for these shares at a cost of $5 with an exercise price of $210. Today the share price is $250.\n\nWhat is my total potential profit from both of these two sets of shares and options?" ]

[ "# Microsoft\n\nThe spot price today is $150 whereas the option contract allows an exercise price of $200. Therefore, the option contract is more valuable so it will be exercised.\n\nIncome from sale of shares = $200 * 1000 = $200,000\n\nPurchase price of share = $180 * 1000 = $180,000\n\nOption contract cost = $5 * 1000 = $5,000\n\nTotal Profit = $200,000 - $180,000 - $5,000 = $15,000", "# Amazon\n\nThe price of Amazon’s share is $250 today whereas the option contract allows selling the share at $210 per share. In this case, it is better to sell the shares in the market and not exercise the option.\n\nIncome from sale of shares = $250 * 500 = $125,000\n\nPurchase price of share = $200 * 500 = $100,000\n\nOption contract cost = $5 * 500 = $2,500\n\nTotal Profit = $125,000 - $100,000 - $2,500 = $22,500\n\n\n\nThe total profit will be $15,000 + $22,500 = $37,500" ]

[ "What is the expected return of a stock according to the CAPM model?", "Our company recently completed divesting some of the spare assets 2 months ago, which has caused in increase in the volatility of our returns from 30% to 40%; however, the correlation of our stock's returns with the market has risen from 0.5 to 0.6. The risk free rate in the country has remained unchanged at 4% in the last 6 months. The market return before the divesting occurred was 18%; however, this month's revised estimates show an increase of 1.75%. The standard deviation in the market has decreased to 13% this month from 15% two months ago. \n\nWill our investors expect a lower or higher return after the divestiture based on the difference in the expected return of our stock before and after the divestiture?" ]

[ "The expected return of a stock can be calculated using the CAPM formula, which is as follows:\n\nE(R) = rf + β (rm - rf)\n\n- rf is the risk-free return\n- rm is the market return\n- β is the beta which is the volatility in the return of a stock compared to the market.\n\nand \n\nBeta = Correlation (Ri - Rm) * σi / σm\n\nHere: \n\n- Correlation (Ri - Rm) is the correlation between the return of a stock and the market return.\n- σi is the standard deviation of the return of the stock.\n- σm is the standard deviation of the market returns.", "# Expected return before the divestiture\n\n- E(R) = rf + β (rm - rf)\n- rf is the risk-free return = 4%\n- rm is the market return = 18%\n- Beta = Correlation (Ri - Rm) * σi / σm = 0.5 * 0.30 / 0.15 = 1\n- E(R) = rf + β * (rm - rf) = 4% + 1 * (18% - 4%) = 18%\n\n# Expected return after the divestiture\n\n- E(R) = rf + β * (rm - rf)\n- rf is the risk-free return = 4%\n- rm is the market return = 19.75%\n- Beta = Correlation (Ri - Rm) * σi / σm = 0.6 * 0.40 / 0.13 = 1.8\n- E(R) = rf + β * (rm - rf) = 4% + 1.8 * (19.75% - 4%) = 32.39%\n\n# Result\n\nBased on the calculation the investors will demand a higher expected return." ]

[ "According to IFRS, how should a company record the value of its inventory for accounting purposes?", "One of the companies in my portfolio manufactures pharmaceutical products. The company had an inventory of vaccines of $1,000,000. On June 1, 2024, it was now estimated that this inventory could be sold for $1,200,000 in the market and the cost of selling this inventory was $400,000. On June 30, 2024, the valuation of this inventory increased to $1,500,000 and the cost of selling remained unchanged. \n\nHow will these changes relatively impact the company's EPS?" ]

[ "According to the IFRS standard for accounting for inventories IAS 2, the inventory should be recorded at the lower of cost and net realisable value where the net realisable value is the selling price minus selling costs.", "# Valuation on June 1, 2024\n\nInventory valuation (Carrying amount in the books) = $1000000\nNet realisable value = Market value - selling costs = $1200000 - $400000 = $800000\n\nThe inventory valuation was $1000000 whereas, the net realisable value was $800000 ($1200000 - $400000).\n\nThe net realisable value of the inventory is less than the carrying amount, so an impairment loss must have been recorded on June 1, 2024.\n\nImpairment = Carrying amount - Net realisable value\nImpairment = $1000000 - $800000 = $200000\n\nThis impairment will result in a decrease in the value of inventory in the balance sheet by $200000 and an accompanying entry will be recorded in the income statement by reducing the income by $200000. \n\nThis decrease in the income will mean that your EPS went down on June 1, 2024, when this impairment in the value happened.\n\n# Valuation on June 30, 2024\n\nAt the end of the year, the value of the inventory has increased by $1500000 which is higher than the current amount recorded in the books which is $800000.\n\nInventory valuation (Carrying amount in the books) = $800000\nNet realisable value = Market value - selling costs = $1500000 - $400000 = $1100000\n\nThe original cost of the inventory was $1000000 and now the net realisable value is $1100000. So the lower cost and net realisable value is now $1000000. \nTherefore, according to the IFRS, the inventory should be recorded at $10000000.\n\nThe current valuation in the books is $800000 and the revised valuation should be $1000000. This means that an increase in the valuation of $20000 should be recorded and a corresponding positive increase in the income.\n\nThe impact of this positive addition to the income statement is that your EPS will increase.\n\n# Overall Impact\n\nThe change in the value of the inventory on June 1, 2024, had a negative impact on the EPS whereas, the change in the value on June 30, 2024, had a positive impact on EPS." ]

[ "ABC Co purchased an item of property, plant, and equipment for $10 million on January 1st 2020. The useful economic life was estimated to be five years. \n\nOn December 31st 2020, the asset was revalued to $12 million. \n\nExplain, with suitable calculations, how the above transactions should be dealt with in the financial statements.", "Then, on December 31st 2021, the asset's value had fallen to $4 million. The downward revaluation was recorded in other comprehensive income.\n\nHow the above transactions should be dealt with in the financial statements for the year ending December 31st, 2021?" ]

[ "IAS 16 Property, Plant, and Equipment state that revaluation gains on property, plant, and equipment are recorded in other comprehensive income (OCI) and held in a revaluation reserve in equity (other components of equity). Revaluation losses are charged to OCI to the extent that a revaluation reserve exists for that specific asset. Any revaluation loss in excess of the balance on the revaluation reserve is charged to profit or loss.\n\nThere was a revaluation gain of $4 million the difference between the carrying amount of $8 million ($10m x 4/5) and the fair value of $12 million. This revaluation gain would have been recognized in other comprehensive income and held in a revaluation surplus in equity.", "On December 31st, 2021, the carrying amount of the asset before the revaluation was $9 million ($12 million × 3/4).\nThe revaluation loss is $5 million ($9m - $4m). Of this, $4 million should be charged to other comprehensive income because that is the balance in the revaluation reserve. The remaining loss of $1 million should be charged against profit or loss. The profits are currently overstated by $1 million." ]

[ "Let's say I sell a product for $100 on credit. Which will be impacted first, operating income or cash flow for operations?", "| Metric ($M) | 2022 | 2023 |\n|--------------------|--------|--------|\n| Retained Earnings | 185 | 210 |\n| Receivables | 48 | 59 |\n| Inventory | 67 | 75 |\n| Payables | 99 | 79 |\n\nDuring the year, the company paid dividends of $50 million in 2023 and the depreciation in the same year was $55 million.\n\nWhat is the company's cash flow from operations for 2023?" ]

[ "Cash flow from operations measures the cash generated by a company’s core business activities, while operating income measures the profit earned from those operations. For example, if you sell an item for $100, that sale can be recorded as revenue immediately. However, it won't affect actual cash flows until the payment is received. Therefore, selling a product for $100 will increase operating income right away, but it won't increase cash flow from operations until the cash is actually collected.", "Net income = Increase in the retained earnings - dividends paid = $210 - $185 + $50 = $75 million\n\nChange in receivables = $59 - $48 = $11 million (increase)\n\nChange in inventory = $75 - $67 = $8 million (increase)\n\nChange in payables = $79 - $99 = -$20 (decrease)\n\n1. The depreciation will have to be added to the net income as it is a non-cash expense. $75 + $55 = $130 million\n\n2. The increase in receivables will have to be subtracted from the receivables because it represents a decrease in cash. $130 - $11 = $119 million\n\n3. The increase in the inventory will also be subtracted because it represents a reduction in cash. $119 - $8 = $111 million\n\n4. The decrease in payables represents an outflow of cash so it will also need to be deducted from the net income. $111 million - $20 = $91 million\n\nThe cash flow from operations in the year 2023 is $91 million" ]

[ "Which IFRS standard deals with the recognition of assets acquired through the merging of two business? What is the standard for intangible assets?", "On 1 January 2023, Jay's Perfume LLC acquired 100% of Tims Co. Both companies operate in the perfume sector. Jay's Perfume LLC intends to merge the manufacture of Tims Co products into its facilities and close the Tims Co manufacturing unit. Tims Co brand name is well known in the sector, retailing at premium prices, and therefore, Jay's Perfume LLC will continue to sell products under the Tims Co name after its registration has been transferred and its manufacturing units have been integrated. The directors of Jay's Perfume LLC believe that most of the value of Tims Co was derived from the brand and there is no indication of the impairment of the brand on 31 December 2023.\n\nWill the Tims Co brand name be accounted as part of goodwill or separately as cash-generating unit after the integration of the manufacturing units?" ]

[ "IFRS 3 Business Combinations. This states that the acquirer must recognize identifiable intangible assets acquired in a business combination separately from goodwill. To be identifiable, the asset must be separable or arise from contractual or legal rights.", "The Tims Co is intangible because it has no physical substance. It meets the definition of an asset because it has the potential to generate future economic benefits by increasing sales volumes and the ability to charge premium prices. Brands are separable because they can be disposed of. As such, the brand is a separable intangible asset and must be recognized separately from goodwill." ]

[ "What is the requirement for impairment of an asset under GAAP?", "What are the differences in accounting for impaired Assets under IFRS and GAAP?" ]

[ "In accounting, impairment is a permanent reduction in the value of a company asset. It may be a fixed asset or an intangible asset. When testing an asset for impairment, the total profit, cash flow, or other benefits that can be generated by the asset is periodically compared with its current book value. If the book value of the asset exceeds the future cash flow or other benefits of the asset, the difference between the two is written off, and the value of the asset declines on the company's balance sheet.\n\nUnder generally accepted accounting principles (GAAP) assets are considered to be impaired when their fair value falls below their book value.\n\nAny write-off due to an impairment loss can have adverse effects on a company's balance sheet and its resulting financial ratios. It is important for a company to test its assets for impairment periodically. Certain assets such as intangible goodwill, must be tested for impairment on an annual basis in order to ensure that the value of assets is not inflated on the balance sheet.\n\nGAAP also recommends that companies take into consideration events and economic circumstances that occur between annual impairment tests in order to determine if it is \"more likely than not\" that the fair value of an asset has dropped below its carrying value. Specific situations in which an asset might become impaired and unrecoverable include when a significant change occurs to an asset's intended use when there is a decrease in consumer demand for the asset, damage to the asset, or adverse changes to legal factors that affect the asset.If these types of situations arise mid-year, it's important to test for impairment immediately.\n\nStandard GAAP practice is to test fixed assets for impairment at the lowest level where there are identifiable cash flows. For example an auto manufacturer should test for impairment for each of the machines in a manufacturing plant rather than for the high-level manufacturing plant itself. If there are no identifiable cash flows at this low level, it's allowable to test for impairment at the asset group or entity level.", "Under GAAP rules, the total dollar value of an impairment is the difference between the asset’s carrying value and its fair market value. Under International Financial Reporting Standards (IFRS), the total dollar value of an impairment is the difference between the asset's carrying value and the recoverable value of the item. The recoverable value can be either its fair market value if you were to sell it today or its value in use. The value in use is determined based on the potential value the asset can bring in for the remainder of its useful life.\n\nThe journal entry to record an impairment is a debit to a loss, or expense account and a credit to the related asset. A contra asset impairment account which holds a balance opposite to the associated asset account may be used for the credit in order to maintain the historical cost of the asset on a separate line item, the net of the asset, its accumulated depreciation, and the contra asset impairment account reflect the new carrying value.\n\nUpon recording the impairment, the asset has a reduced carrying value. In future periods the asset will be reported at its lower carrying value. Even if the impaired asset’s market value returns to the original level, GAAP states the impaired asset must remain recorded at the lower adjusted dollar amount. This is in compliance with conservative accounting principles. Any increase in value is recognized upon the sale of the asset. Under IFRS, impairment losses can be reversed in specific instances.\n\nIf an asset group experiences impairment, the adjustment is allocated among all assets within the group. This proration is based on the current carrying value of the assets.\nIFRS prefers fixed asset impairment at the individual asset level. If that is not possible then it can be impaired at the cash generating unit (CGU) level. The CGU level is the smallest identifiable level at which there are identifiable cash flows largely independent of cash flows from other assets or groups of assets." ]

[ "What is the main difference between how you handle impairment losses for patents under IFRS and US GAAP?", "Our company has several patents that are recorded as a cost of $250 million in the 2023 balance sheet, with an accumulated amortisation of $25 million. Moreover, their accumulated losses from impairment are $80 million. In addition, the accumulated impairment reversals are $25 million. \n\nWhat will be the exact difference in dollars in the net valuation of these patents under IFRS and USGAAP?" ]

[ "# IFRS\n\nUnder IFRS, the impairment losses previously recognised can be reversed, therefore, the value of the patents will get an increase equal to the reversals.\n\nValue of the patents = cost - accumulated amortisation - impairment losses + impairment reversals\n\n# US GAAP\n\nAccording to the US GAAP, the impairment losses once recognized can never be reversed, therefore, they will not increase the value of the patents.\n\nValue of the patents = cost - accumulated amortisation - impairment losses", "# IFRS\n\n- Value of the patents = cost - accumulated amortisation - impairment losses + impairment reversals\n\n- Value of the patents = $250 million - $25 million - $80 million + $25 million \n\n- Value of the patents = $170 million\n\n# US GAAP\n\n- Value of the patents = cost - accumulated amortisation - impairment losses\n\n- Value of the patents = $250 million - $25 million - $80 million \n\n- Value of the patents = $145 million\n\n\n\nThe difference in the net valuation is $170 million - $145 million = $25 million" ]

[ "An investor is considering investing $100,000 in bonds. One potential option is a 3 years fixed-rate bond paying semiannual coupon of 5%. The bond is available for purchase at $930 per $1000.\n\nWhat is the yield to maturity of this bond (on an annual basis)?", "There is another option on the market, a 3 years 5% fixed-rate bond which pays interest quarterly. The bond is available for purchase at a price $940 per $1000.\n\nWhich of these two options has a higher yield to maturity?" ]

[ "Yield to Maturity is the expected return on a bond if the bond is held till the time it matures. \nThe yield to maturity can be found using the following formula: \nPrice = Coupon (1+YTM) ^ -1 + Coupon (1+YTM) ^ -2 + .... + (coupon + face value) (1+YTM) ^-n\n\n\nThe yield to maturity of the fixed rate bond can be determined using the following formula:\n930 = 25 (1+YTM) ^ -1 + 25 (1+YTM) ^ -2 + 25 (1+YTM) ^-3 + 25 (1+YTM) ^-4 + 25 (1+YTM) ^-5 + 1025 (1+YTM) ^-6\nYTM = 3.828%\nTo convert this to annual yield, this YTM will be multiplied by 2.\nYTM annual = 3.828% * 2 = 7.656% \n\nTherefore, the yield to maturity of this bond is 7.656%", "The yield to maturity of the fixed rate bond can be determined using the following formula:\n960 = 12.5 (1+YTM) ^ -1 + 12.5 (1+YTM) ^ -2 + 12.5 (1+YTM) ^-3 + 12.5 (1+YTM) ^-4 + 12.5 (1+YTM) ^-5 + 12.5 (1+YTM) ^-6 + 12.5 (1+YTM) ^-7 + 12.5 (1+YTM) ^-8 + 12.5 (1+YTM) ^-9 + 12.5 (1+YTM) ^-10 + 12.5 (1+YTM) ^-11 + 1125 (1+YTM) ^-12\nQuarterly YTM = 1.625%\nTo convert this to annual yield, this YTM will be multiplied by 4\nYTM annual = 1.625% * 4 = 6.500%\n\nThe first bond has a YTM of 7.656% and the second bond has a YTM of 6.5% (on an annual basis). The first bond has a higher YTM." ]

[ "There are three options available in the market, one is call with an exercise price of $90. The second option is a put option with an exercise price of $100. The third option is a call option with an exercise price of $110. \n\nWhich of them will have the highest value if the underlying of these options has a value of $90?", "What if it had a value of $120?" ]

[ "# Option 1\n\nCall option with an exercise price of $90\nValue of the call option = Spot at expiration - Exercise price\nValue of the call option = $90 - $90 = 0\n\n# Option 2\n\nPut option with an exercise price of $100\nValue of put option = Exercise price - Spot price at expiration \nValue of put option = $100 - $90 = $10\n\n# Option 3\n\nA call option with an exercise price of $110\nValue of the call option = Spot at expiration - Exercise price\nValue of the call option = $90 - $110 = -$20\n\n# Result\n\nOption 2 has the highest value at expiration.", "# Option 1\n\nCall option with an exercise price of $90\nValue of the call option = Spot at expiration - Exercise price\nValue of the call option = $120 - $90 = $30\n\n# Option 2\n\nPut option with an exercise price of $100\nValue of put option = Exercise price - Spot price at expiration \nValue of put option = $100 - $120 = -$10\n\n# Option 3\n\nA call option with an exercise price of $110\nValue of the call option = Spot at expiration - Exercise price\nValue of the call option = $120 - $110 = $10\n\n# Result\n\nOption 1 has the highest value at expiration." ]

[ "What are the differences between: a Private Offering, a Best Effort Offering, Firm Committment Underwriting or All or None Underwriting.", "Let's say we want to go with a best effort offering. Last year, we issued 50,000 shares and our desired price was $150 but we ended up selling only 35,000 shares. We lowered the price to $120 to sell the additional ones, but 5000 remained. We had to sell these at $100.\n\nOur company is planning to issue 1,000,000 shares in the stock market. Our desired price is $250. \n\nIf we sell the same portions of shares at the same percentage discounts, what could we expect to raise?" ]

[ "There are different types of offerings in which investment banks assist including private offering, best effort offering, firm commitment and all or none. The following is the expected amount of capital that can be generated in each of the cases.\n\n# Private Offering\n\nIn the private offering, the shares are sold only to a selected list of investors that the investment banks identify. The market is not brought into the transaction due to which there is no volatility in the share price. However, it can be the case the investors might not agree to the offered price and they would negotiate for a lower price.\n# Best effort offering\n\nIn this offering, the underwriter commits in good faith to sell as much of the issue at the agreed price as possible, there is no financial or legal responsibility imposed on the underwriter for any unsold shares or deal performance.\n\nIn the best-effort offering, you can expect to raise capital based on the price established through the supply and demand in the market.\n\n# Firm commitment\n\nIn the case of a firm commitment, the underwriter agrees to buy the entire issue at a certain price. If the underwriter fails to sell the entire issue, the underwriter must take full financial responsibility for any unsold shares.\n\nIn the firm commitment offering, the investment bank will guarantee that the shares will be sold at the agreed price. If they are unable to sell, they will buy them themselves. So you can be sure that all the shares will be sold at the desired price\n\n# All or none\n\nWith an all or none underwriting, the issuer determines it must receive the proceeds from the sale of all of the securities. Investors’ funds are held in escrow until all of the securities are sold. If all of the securities are sold, the proceeds are released to the issuer. If all of the securities are not sold, the issue is cancelled and the investors’ funds are returned to them.", "Based on your previous experience, you can expect the following amount of capital offering calculated using the expected value\n\nLast time you were able to generate the following \n35000 shares (70%) at $150 (full price)\n10000 shares (20%) at $120 (20% discount)\n5000 shares (10%) at $100 (33% discount)\n\nWe can use these values to establish an expected value for the current offering\n\n70% shares at full price\nshares: 70% of 1000000 = 700000 \nprice: $250 \ntotal = 700000 * $250 = $175000000\n\n20% shares at 20% discount\nshares: 20% of 1000000 = 200000\nprice: $250 - 20% ($50) = $ 200\ntotal: 200000 * $200 = $ 40000000\n\n10% shares at a 33% discount \nshares: 10% of 1000000 = 100000\nprice: $250 - 33% ($83.33) = $ 166.66\ntotal: $100000 * $166.66 = $ 16660000\n\nTotal capital raised = $175000000 + $ 40000000 + $ 6660000 = $221.66 Million\n\nTherefore, you could expect to raise around $220 Million." ]

[ "Imagine two bonds. One is a 3.50% annual coupon bond which is currently trading at 102.55 in the market with a maturity of three years. The other bond is a 7.25% annual coupon bond which is currently trading at 122.4 and has a maturity of 5 years. What is the YTM of these bonds?", "Our investment banking firm is in the process of underwriting a corporate bond which will be issued for four years at an annual coupon of 4.5%. We are trying to price the bond according to the market. Since this is a new issue, there is no straightforward way to price this bond. \n\nHowever, those two bounds are very similar and were underwritten by our investment bank earlier. They are actively traded on the market and have similar credit risk and features as the one being underwritten.\n\nI want you to use these two bonds to provide a good estimate of the price at which we should underwrite our client's bond." ]

[ "YTM of a bond can be calculated using the following formula\n\nP = C/(1+r)^-1 + C/(1+r)^-2 + ... + (C+F)/(1+r)^-n\nwhere p is the price at which the bond is currently trading, C is the coupon payment on the bond, F is the future value at which the bond will be redeemed at maturity, n is the number of periods from issue of the bond to its redemption. r is the YTM which we will find out.\n\nBond 1\n102.55 = 3.5/(1+r)^-1 + 3.5/(1+r)^-2 + 103.5/(1+r)^-3\nr = 2.605%\n\nBond 2\n-122.4 = 7.25(1+r)^-1 +7.25(1+r)^-2 +7.25(1+r)^-3 +7.25(1+r)^-4 +107.25(1+r)^-5\nr = 2.437%\n\nThe first bond has a yield to maturity of 2.605% and the second bond has a yield to maturity of 2.437%.", "This can be achieved using Matrix pricing as we have access to the two comparable bonds. Matrix pricing involves using prices of comparable, actively traded bonds with similar structure, coupon rates, credit rating, and similar maturities to estimate the price of a new bond with no market (CFI, 2024).\n\nThe problem is that we do not have exactly similar bond but we do have comparable bonds with maturities of 3 and 5 years so we can value the new bond (maturity of 4 years) by taking the average of the YTMs of these two bonds. \n\nEstimating the YTM using the two bonds:\n\nr = (2.605% + 2.437%) / 2 = 2.521%\n\nEstimating the Bond Price at which the bond should be underwritten\n\nValue of bond = 4.5(1+0.02521)^-1 + 4.5(1+0.02521)^-2 + 4.5(1+0.02521)^-3 + 104.5(1+0.02521)^\n\nValue of bond = $107.44\n\nBased on the comparable bonds in the market, the matrix pricing suggests that the new bond should be underwritten at $107.44." ]

[ "My company purchased some bonds worth $69,000 that pay a 10% coupon semi-annually on January 1 2024. At the end of six months on June 30 2024, I checked the market and realized that interest rates have fallen and the value of these bonds has increased. The bonds that I purchased are now trading at $100,000. I have also received a semi-annual payment of interest of $3450. \n\nWhat are the main ways this can show up on my company's income statement according to the following applicable IFRS standards: Cost or Amortized Value, Fair Value Through Other Comprehensive Income, and Measured at Fair Value through Profit and loss", "What about on the balance sheet?" ]

[ "# The Available Treatments According to IFRS\n\nAccording to IFRS, there are three ways in which the financial instruments can be recorded in the financial statements.\n\nThe three treatments are as follows:\n\n## Method 1. Cost or amortized value\n\nThis treatment is followed in the following conditions:\na. debt securities are to be held throughout their tenor.\nb. debt securities that are loans and notes receivables\nc. equity instruments that do not have reliable estimates of their fair value\n\n## Method 2. Fair value through other comprehensive income\nThis treatment is followed in the following cases\na. debt securities which are held with the intent of collecting interest and principal as well as selling it.\nb. equity instruments which are elected at purchase to be treated this way.\n\n## Method 3. Measured at fair value through Profit and loss\nThis treatment is followed in the following cases\na. if none of the other two methods is assigned\nb. financial instruments which are elected at purchase to be treated this way.\n\n# Impact on the income statement as of June 30 2024\n\n## Method 1. Cost or amortized value\n\nInterest income in the income statement = $3450\n\nThe appreciation of the value of $31000 will not impact the income statement under this method.\n\n## Method 2. Fair value through other comprehensive income\nInterest income in the income statement = $3450\n\nUnrealized gains (the rise in the value of the asset) = $31000 ($100000 - $69000) will appear in the other comprehensive income and not the income statement.\n\n## Method 3. Measured at fair value through Profit and loss\n\nInterest income in the income statement = $3450\nUnrealized gains (the rise in the value of the asset) = $31000 ($100000 - $69000) will appear in the income statement.", "# Impact on the balance sheet\n\n## Method 1. Cost or amortized value\n\nThe bonds will initially be recognized at the cost which was $69000 as assets in the balance sheet on June 1 2024\n\nIn the equity section of the balance sheet, the interest of $3450 will be added to the retained earnings on June 30 2024.\n\n## Method 2. Fair value through other comprehensive income\n\nThe bonds will initially be recognized at the cost which was $69000 as assets in the balance sheet on June 1 2024\n\nThe unrealized gains of $31000 will be added to the value of the bonds which will make the new value of the bonds $100000 on June 30 2024.\n\nIn the equity section of the balance sheet, the interest of $3450 will be added to the retained earnings on June 30 2024.\n\nThe unrealized gains of $31000 will be recorded in the Other Comprehensive Income section of the Equity on June 30 2024.\n\n## Method 3. Measured at fair value through Profit and loss\n\nThe bonds will initially be recognized at the cost which was $69000 as assets in the balance sheet on June 1 2024\n\nThe unrealized gains of $31000 will be added to the value of the bonds which will make the new value of the bonds $100000 on June 30 2024.\n\nIn the equity section of the balance sheet, the interest of $3450 plus the gain in value of $31000 will be added to the retained earnings on June 30 2024." ]

[ "My hedge fund had capital of $500 million at the start of the January 2024. During the year, I borrowed $200 million from William capital management LLC at 12%, and $100 million from James Capital LLC at 8%. I charge a 10% management fee based on the year-end assets under management after accounting for trading costs. In addition to this, the tax rate in our country is 18% on profits. The fund generated a gross return of 35% before deducting the 2% in trading costs of the total assets under management at August 31 2024. \n\nWhat is my net return?", "I have three clients: Salman (35% share), Zaneeq (35%) and Blake (30%). What will each of them recieve?" ]

[ "Capital of investors at 1 Jan 2024 $500,000,000\nBorrowed from William $200,000,000\nWilliam interest rate 12%\nBorrowed from James $100,000,000\nJames' interest rate 8%\nTrading costs (2% of AUM) 2%\nGross return 35%\nManagement fee 10%\nTaxation 18%\n \nStep 1 - Assets under management at period end \nAssets under management (August 2024) = Total capital * (1+gross return) $1,080,000,000\n \nStep 2 - Trading costs \nTrading costs = assets at period end * 2% $21,600,000\n \nStep 3 - Management Fee \nManagement fee = AUM after trading costs * management fee $108,000,000\n \nStep 4 - Borrowing costs \nInterest costs on borrowing from William (Borrowing * interest rate) = $24,000,000\nInterest costs on borrowing from James (Borrowing * interest rate) = $8,000,000\n \nTotal borrowing costs: $32,000,000\n \nStep 5 Net Return after deducting all costs \nTotal return (35%) $280,000,000\nLess: Trading costs $21,600,000\nLess: management costs $108,000,000\nLess: Borrowing costs $32,000,000\n \nNet return: $118,400,000", "Each client will receive a share of the net return in proportion to their holdings.\n\nSalman's share: $118,400,00 * 0.35 = $41,440,000\nZaneeq's share $118,400,00 * 0.35 = $41,440,000\nBlake's share: $118,400,00 * 0.30 = $35,520,000" ]

[ "What is the formula for NPV?", "I have two investment opportunities to invest my $950. My required rate of return is 5%. The first opportunity returns $370.5 for the next three years whereas the second opportunity provides $427.5 in the first year, $370.5 in the second year and $304.0125 in the third year. \n\nWhich opportunity is better?" ]

[ "NPV = (C1 / (1 + r)^1) + (C2 / (1 + r)^2) + ... + (Cn / (1 + r)^n) - C0\n\nC1, C2, C3 ... Cn = the cash flows in each of the years.\n\nC0 = the initial cash flow \n\nr = the required rate of return.", "These investment opportunities can be evaluated by comparing their present values.\n\n# Opportunity 1\n\nNPV = (C1 / (1 + r)^1) + (C2 / (1 + r)^2) + ... + (Cn / (1 + r)^n) - C0\nNPV = 370.5 / (1.05)^1 + 370.5 / (1.05)^2 + 370.5 / (1.05)^3 - 950\nNPV = $58.96\n\n# Opportunity 2\n\nNPV = (C1 / (1 + r)^1) + (C2 / (1 + r)^2) + ... + (Cn / (1 + r)^n) - C0\nNPV = 427.5 / (1.05)^1 + 370.5 / (1.05)^2 + 304.0152 / (1.05)^3 -950 \nNPV = $55.82\n\n# Result\nOppurtunity 1 has a slightly higher NPV, therefore it is the better oppurtunity." ]

[ "Our startup company W&J Global purchased networking equipment at the beginning of 2024 for $6,690,055. We use a 10% depreciation method for our fixed assets; however, the taxation authority in our country requires the depreciation of network equipment at 14.9% per year. The taxation rate in our country is 39%. \n\nWhat will be the ending carrying amount of this asset in 2026?", "The taxation authority in our country requires the depreciation of network equipment at 14.9% per year. The taxation rate in our country is 39%. \n\nWhat will the deferred tax liability be in 2026, if any?" ]

[ "The yearly depreciation for accounting purposes will be 10% of $6,690,055.00, or $669,005.50.\n\nEnding Carrying Amount = Opening carrying amount - Depreciation\n\n| Accounting | | | |\n|---------------------------|--------------|--------------|------------------------|\n| Year | Opening Carrying amount | Depreciation | Ending carrying amount |\n| 2024 | $6,690,055.00 | $669,005.50 | $6,021,049.50 |\n| 2025 | $6,021,049.50 | $669,005.50 | $5,352,044.00 |\n| 2026 | $5,352,044.00 | $669,005.50 | $4,683,038.50 |\n\nThe ending carrying amount in 2026 is $4,683,038.50.", "Different rates of depreciation will cause the book value and the tax value of an asset to differ. This difference will show up on the balance sheet as a deferred tax liability. To find the value of this liability, we need to first find the book value, then find the tax value, compute their difference and apply the tax rate.\n\nThe yearly depreciation for tax purposes will be 14% of $6,690,055.00, or $996,818.20.\n\n| Tax Purposes | | | |\n|---------------------------|--------------|--------------|------------------------|\n| Year | Opening Carrying amount | Depreciation | Ending carrying amount |\n| 2024 | $6,690,055.00 | $996,818.20 | $5,693,236.81 |\n| 2025 | $5,693,236.81 | $996,818.20 | $4,696,418.61 |\n| 2026 | $4,696,418.61 | $996,818.20 | $3,699,600.42 |\n\n# Temporary differences and Deferred Tax Liability\n\nWe can compute the,\n\nTemporary Difference = Carrying Amount - Tax Base\nDeferred Tax Liability = Temporary Difference * Tax Rate (39%)\n\n$4,683,038.50 - $3,699,600.42 = $983,438.09 \n$983,438.09 * 0.39 = $383,540.85 \n\n# Result\n\nThe impact of the purchase in 2026 will be a deferred tax liability of $383,540.85" ]

[ "How is the cash conversion cycle calculated? What does it measure?", "| | 2023 | 2022 |\n|----------------|-------------|-------------|\n| Sales | $450,354.00 | $850,105.00 |\n| Cost of Sales | $315,247.80 | $595,073.50 |\n| Receivables | $22,517.70 | $42,505.25 |\n| Inventory | $27,021.24 | $51,006.30 |\n| Payables | $13,510.62 | $25,503.15 |\n\nWhat is the cash conversion cycle in the year 2023?" ]

[ "The cash conversion cycle (CCC) also called the net operating cycle or cash cycle, is a metric that expresses, in days, how long it takes a company to convert the cash spent on inventory back into cash from selling its product or service. The shorter the cash cycle the better, as it indicates less time that cash is bound in accounts receivable or inventory. The cash conversion cycle encompasses three key stages of a company’s sales activity:\n• Selling current inventory\n• Collecting cash from current sales\n• Paying vendors for goods and services purchased\nFormula for CCC = DIO + DSO – DPO\n\nWhere:\nDIO = Days Inventory Outstanding (average inventory/cost of goods sold x number of days)\nDSO = Days Sales Outstanding (accounts receivable x number of days/total credit sales)\nDPO = Days Payable Outstanding (accounts payable x number of days/cost of goods sold)\n\nThe cash conversion cycle attempts to measure how long each net input dollar is tied up in the production and sales process before it gets converted into cash received.\nThis metric considers how much time the company needs to sell its inventory, how much time it takes to collect receivables, and how much time it has to pay its bills.\n• The cash conversion cycle (CCC) is a metric that expresses the length of time (in days) that it takes for a company to convert its investments in inventory and other resources into cash flows from sales.\n• This metric takes into account the time needed for the company to sell its inventory, the time required for the company to collect receivables, and the time that the company is allowed to pay its bills without incurring any penalties.\n• CCC will differ by industry sector based on the nature of business operations.\nCCC is one of several quantitative measures that help evaluate the efficiency of a company’s operations and management. A trend of decreasing or steady CCC values over multiple periods is a good sign while rising ones should lead to more investigation and analysis based on other factors.\n\nThe cash conversion cycle (CCC) is a measure of management effectiveness. It measures how fast a company can convert cash on hand into even more cash on hand. The CCC does this by following the cash, or the capital investment as it is first converted into inventory and accounts payable through sales and accounts receivable and then back into cash. The lower the number for the CCC, the better it is for the company.", "The Cash Conversion Cycle is defined as: \n\nCCC = Days Inventory in Hand + Days Receivables Outstanding - Days Payables Outstanding)\n\nWhere:\nReceivables Turnover = Sales / Average Receivables\nInventory Turnover = Cost of Sales / Average Inventory\nDays Inventory in Hand = 365 / Inventory Turnover\nDays Receivables Outstanding = 365 / Receivables Turnover\nPayables Turnover = Purchases / Average Payables\nDays Payables Outstanding = 365 / Payables Turnover\n\nLet's walk through each of these calculations step-by-step. First, lets create a table with some averages.\n\n| | 2023 | 2022 | Average |\n|-----------------------------------------------------------|-------------|-------------|-------------|\n| Sales | $450,354.00 | $850,105.00 | |\n| Cost of Sales | $315,247.80 | $595,073.50 | |\n| Receivables | $22,517.70 | $42,505.25 | $32,511.48 |\n| Inventory | $27,021.24 | $51,006.30 | $39,013.77 |\n| Payables | $13,510.62 | $25,503.15 | $19,506.89 |\n\n1. Purchases in 2023\n\nPurchases in 2023 = (Cost of Sales in 2023 - Opening Inventory in 2023 + Closing Inventory in 2023)\n\nPurchases in 2023 = ($315,247.80 - $51,006.30 + $27,021.24) = $291262.74\n\n2. Inventory Turnover (Cost of Sales / Average Inventory)\n\nInventory turnover = $315.247.80 / $39,013.77 = 8.08\n\n3. Days Inventory in Hand (365 / Inventory Turnover)\n\nDays inventory on hand = 365 / 8.08 = 45.17 days\n\n3. Receivables Turnover (Sales / Average Receivables)\n\nReceivables turnover = $450,354 / $32,511.48 = 13.85\n\n4. Days Receivables Outstanding (365 / Receivables Turnover)\n\nDays receivables outstanding = 365 / 13.85 = 26.35 days \n\n5. Payables Turnover (Purchases / Average Payables)\n\nPayables turnover = $291262.74 / $19,506.89 = 14.93\n\n6. Days Payables Outstanding (365 / Payables Turnover)\n\nDays payables outstanding = 365 / 15.55 = 24.45 days\n\n7. Cash Conversion Cycle (Days Inventory in Hand + Days Receivables Outstanding - Days Payables Outstanding)\n\nCash conversion cycle = 45.17 days + 26.35 days - 24.45 days = 47.08 days\n\nThe Cash Conversion Cycle in 2023 is 47.08 days." ]

[ "Salman currently owns a single share of Amazon (which does not pay any dividend), and which is currently trading at $194 as of July 12, 2024. He has entered into a contract to sell these shares forward to a broker at a price of $220 on January 12 2024, six months from now. \n\nWhat will be the value of this contract for both parties if the price falls by 10% at the end of the sixth months.", "What if it rises by 10%?" ]

[ "At the beginning of the contract, the value of the contract will be zero. So, on July 12 2024:\nValue of the forward contract for Salman = 0 \nValue of the forward contract for broker = 0 \n\n\nThe value of a forward contract at maturity is calculated using the following formulas:\n\n# Selling party \nValue of the contract = Forward price agreed - Spot price on settlement date \n\n# Buying Party \nValue of the contract = Spot Price on settlement date - Forward price agreed \n\n\nIf the price falls by 10%, the new price will be 194 * 0.9 = 174.6 \n \n# Selling Party (Salman) \nValue of the contract = Forward price agreed - Spot price on settlement date \nValue of the contract = $220 - $174.6 = $45.4 \n\nThe value of the contract for Salman will be $45.4 because Salman will have an already fixed price of $220 while the stock will be trading at 10% less price. Therefore, Salman will gain from this forward contract. \n\n \n# Buying Party (Broker)\nValue of the contract = Spot Price on settlement date - Forward price agreed \nValue of the contract = $174.6 - $220 = - $45.4 \n\nThe value of the contract for Broker will be - $45.4 because the broker will have to buy the shares at a price that will be higher than the one already prevailing in the market which will result in a loss for them.", "If price rises by 10%, the new price will be $194 * 1.1 = $213.4 \n \n# Selling Party (Salman) \nValue of the contract = Forward price agreed - Spot price on settlement date \nValue of the contract = $213.4 - $220 = - $6.6 \n\nThe value of the contract for Salman in this case will be negative because Salman will have to sell the shares at a price that is less than the one that he will be able to sell for in the market. \n\n\n# Buying Party (Broker) \n\nValue of the contract = Spot Price on settlement date - Forward price agreed \nValue of the contract = $220 - $213.4 = $ 6.6 \n\nThe broker will gain from the contract because he will be able to buy the shares at a price lower than the one that he would otherwise be able to sell for in the market." ]

[ "How do IFRS 9 and FRS 102 differ in their treatment of impairments for debt instruments?", "HCB purchased a debt instrument in the current reporting period that is measured at amortized cost. By the reporting date, no actual defaults had occurred. However, due to a general economic decline, the directors of HCB concluded that credit risk associated with the remaining loan period had increased significantly.\n\nThe following credit losses have been calculated:\n12-month expected credit losses: $0.3 million\nLifetime expected credit losses: $1.0 million\n\nWhat are the differences in how the above should be dealt with under International Financial Reporting Standards (IFRS) and FRS 102?" ]

[ "IFRS 9 Financial Instruments applies to debt instruments at amortized cost or fair value through other comprehensive income (FVTOCI), lease receivables, contract assets, and certain written loan commitments and financial guarantee contracts. The impairment model focuses on assessing credit risk and recognizing expected credit losses over the life of the financial instrument. Under FRS 102, impairment is also based on expected credit losses. Similar to IFRS 9, FRS 102 applies to debt instruments at amortized cost or FVTOCI.\n\nUnder IFRS 9 Financial Instruments, a loss allowance should be recognized at an amount equal to lifetime expected credit losses if credit risk has increased significantly since inception.\n\nUnder FRS 102, financial asset impairments are calculated if there is objective evidence that impairment has occurred.", "Under IFRS 9, 1 million will be charged to the income statement. Whereas, under FRS 102, no loss will be recognized in the income statement.\n\n\nIn accordance with IFRS 9 Financial Instruments, a loss allowance should be recognized at an amount equal to lifetime expected credit losses if credit risk has increased significantly since inception. As such an allowance for $1 million and a corresponding charge to profit or loss, should be recognized.\n\nIn accordance with FRS 102, financial asset impairments are calculated if there is objective evidence that impairment has occurred. No objective evidence exists about the particular borrower involved, and no default of payments has occurred. Therefore no impairment loss is recognised." ]

[ "What is the relationship between Receivable Days and Receivable Turnover? What do they measure?", "Our company currently has an average days of receivables of 29 days, whereas the industry average is 25 days. We currently have sales of $400 million and in the next year, we expect the sales to increase by 10%.\n\nHow much will the receivables need to change get our receivables days to match that of the industry?" ]

[ "# Formulas\n\nThere are two key formulas:\n\nReceivables Turnover = Sales / Receivables \n\nand \n\nReceivables Days = 365 / Receivables turnover\n\nBoth metrics are trying to measure the rate at which companies collect payments for their goods and services. Receivable Days is a direct approximation of the number of days it takes to collect payment. Receivables Turnover is the number of times per year a company is collecting on customers who paid in credit.", "# Receivables before the change in policy\n\nTo find the current receivables, we can use the Receivables Days formula.\n \nReceivables Days = 365 / Receivables turnover\nReceivable days / 365 = Sales / Receivables \nReceivables = Sales / 365 * Receivable days\n\nSince sales were $400 million and they had a receivable days of 29,\n\nReceivables = $400 million / 365 * 29 = 31.78 million\n\n# Receivables after the change in policy\n\nAfter the change in policy, our sales are going to increase to 400 * 1.1 = 440 million dollars. To get our receivable days to 25, our receivables must be,\nReceivables = $400 million * 110% / 365 * 25 = 30.14 \n\n# Change in Receivables\n\nWe can then say that,\n\nChange in receivables = Receivables after the policy change - Receivables before the policy change \nChange = 30.14 million - 31.78 million = -1.64 million\n\nTherefore, the receivables will need to decrease by 1.64 million in order for the days of receivables to match the industry average." ]

[ "Amazon had sales of $1,389,900 million with cost of sales of 75% in 2023. Moreover, its inventory in 2023 was $253,999 million and $234,975 million in 2022. What is Amazon's inventory turnover?", "Walmart had sales of $2,859,485 million with the cost of sales of 65% in 2023. Moreover, its inventory in 2023 was $34,999 million and in 2022 it was $40,838 million. \n\nBased on these numbers, is it more likely that Walmart or Amazon has a higher relative investment in inventories?" ]

[ "Inventory turnover = Cost of sales / average inventory in the year\n\n# Amazon\n\nInventory turnover = Cost of sales / average inventory in the year\n\nCost of sales = 75% of 1,389,900 = 1,042,425\n\nAverage inventory = 1/2 *($253,999 + $234,975) = 244487\n\nInventory turnover = $1042425 / $244487 = 4.26\n\nAmazon's inventory turnover is 4.26", "The inventory turnover ratio can be used to find out which one of them has the highest relative investment in inventories as it will help find out how often the company uses its inventory to generate sales.\n\n# Walmart\n\nInventory turnover = Cost of sales / average inventory in the year\n\nCost of sales = 65% of 2,859,485 = 1,858,665.25\n\nAverage inventory = 1/2 *($40838 + $34999) = 37918.5\n\nInventory turnover = $1858665.25 / $37918.5 = 49.02\n\n\n\nWalmart has a higher inventory turnover, which means that it utilizes its inventory more frequently and therefore has lower relative investment compared to Amazon" ]

[ "What is the difference between a defined benefit plan and a defined contribution plan?", "Matt has a defined contribution pension scheme. However, during the year, he introduced a new post-employment plan (the Fund) for its employees as a way of enhancing the benefits they will receive when they retire. Matt makes monthly contributions into the Fund that are equal to a set percentage of the salary cost. Upon retirement, employees will receive annual payments from the Fund based on their number of years of service and their final salary. The Fund is voluntary, and Matt can cancel it at any point.\n\nMatt has a history of paying employees benefits that are substantially above the national average, with annual increases more than inflation. Matt has won many accolades as a 'top employer' and received positive coverage from the national press when the Fund was announced.\n\nAdvise Matt on whether the above fund is a defined benefit plan or a defined contribution plan." ]

[ "A defined benefit plan and a defined contribution plan are two types of retirement plans with distinct differences:\n\n# Defined Benefit Plan:\n- Employer promises a specific benefit amount to employees based on a formula, typically considering salary and service years.\n- Employer bears investment risks and guarantees benefits.\n- Funding is typically employer driven.\n\n# Defined Contribution Plan:\n- Employer contributes a fixed amount to each employee's retirement account, without promising a specific benefit amount.\n- Employee bears investment risks and benefits may vary.\n- Funding is typically shared between employer and employee.\n\nDefined benefit plans promise a specific benefit, while defined contribution plans promise a specific contribution. The employer's role, investment risks, and benefit certainty differ significantly between the two. It is possible that there will be insufficient assets in the Fund to pay the benefits due to retired employees, particularly if final salaries or life expectancy rise substantially. Matt therefore bears actuarial and investment risk because if he continues with the Fund, he will need to make up for any shortfall.", "The Fund should be accounted for as a defined benefit plan.\n\nAlthough the Fund is voluntary and can be cancelled, Matt has a history of remunerating its employees above the national average as well as a strong reputation as a good and honest employer. Matt therefore has a constructive obligation to continue with the Fund and to ensure that its level of assets is sufficient. As a result of the above, the Fund should be accounted for as a defined benefit plan." ]

[ "How do you compute the value of a bond based on its:\n\nC = coupon payment per period\nr = market interest rate\nn = Number of Coupon Payments in A Year\nt = Number of Years until Maturity\nF = the face value of the bond", "William is a portfolio manager whose investment strategy is primarily in bonds in an emerging market. He is trying to find underpriced bonds to invest $500 million of spare cash to generate stable cash flows for clients over the next 5 years. He has the following options in the market. \n\n| Bond | Payment Frequency | Coupon Rate | Trading Price |\n|--------|--------------------|--------------|---------------|\n| Bond 1 | Semiannual | 3.0% | $1010 |\n| Bond 2 | Annual | 3.5% | $1079 |\n| Bond 3 | Quarterly | 3.6% | $1080 |\n| Bond 4 | Semiannual | 2.8% | $990 |\n| Bond 5 | Quarterly | 2.4% | $1005 |\n\n\nAll the bonds have a par value of $1000 and a time to maturity of five years. The benchmark yield in the bond market is 2%. Which, if any, of these bonds are underpriced according to these assumptions?" ]

[ "Using the variables you provided, you can compute intrinsic value of a bond using the following formula:\n\nBond Price = C * [1-(1+r/n)^-n*t] / r/n + (F / (1 + r/n)^n*t", "Using this formula, following are the intrinsic values of the bonds.\n\nBond 1. $1047 (under-priced)\nBond 2. $1070 (over-priced)\nBond 3. $1075 (over-priced)\nBond 4. $1028 (under-priced)\nBond 5. $1018 (under-priced)\n\nBonds 1, 4 and 5 meet the objectives of William as they are underpriced in the market." ]

[ "How do you compute the standard deviation of a portfolio with two stocks?", "James has a portfolio of two companies, Kensho and Bloomberg. He has invested $60,000 in Kensho and $40,000 in Bloomberg. Based on past performance Kensho has had a standard deviation of 19% in its returns whereas the standard deviation in the returns of Bloomberg is 15%. Moreover, the correlation between these two stocks is 0.30. James is trying to figure out what is the standard deviation of his portfolio so that he can decide whether he should change the composition of his portfolio or not. Based on his risk tolerance, he prefers to hold a portfolio with a standard deviation of at most 14%. Should James alter his portfolio?" ]

[ "# Formula\n\nThe standard deviation of a portfolio can be found by calculating the variance of a portfolio and squaring it. The formula of variance of a portfolio is as follows:\n\nPortfolio variance σp² = w1²σ1² + w2²σ2² + 2w1w2 Covariance(R1,R2)\n\n- σp² = the variance of the portfolio \n- w1 = the weight of the first stock in the portfolio\n- σ1 = the standard deviation of the first stock\n- w2 = the weight of the second stock in the portfolio\n- σ2 = the standard deviation of the second stock in the portfolio \n- Covariance(R1, R2) = This is the covariance between the two stocks", "# Calculations\n\nFormula: Portfolio variance σp² = w1²σ1² + w2²σ2² + 2w1w2 Covariance(R1,R2)\n\n1. w1 = the weight of the first stock (Kensho) = ($40,000) / ($40,000 + $60,000) = 40% = 0.4\n\n2. σ1 = the standard deviation of the first stock = 19% = 0.19\n\n3. w2 = the weight of the second stock (Bloomberg) = ($60,000) / ($40,000 + $60,000) = 60% = 0.6\n\n4. σ2 = the weight of the second stock = 15% = 0.15\n\n5. Covariance(R1, R2) = This is the covariance between two stocks which can be found using the formula of correlation. \n\nThe correlation between two stocks is given as follows:\nCorrelation (R1, R2) = Covariance (R1, R2) / (σ1 * σ2)\n\nFrom this, the Covariance (R1, R2) = Correlation (R1, R2) * (σ1 * σ2)\n\nCovariance (R1, R2) = 0.30 * (0.19 * 0.15) = 0.00855\n\nThese values can be inserted in the formula now \n\nFormula: Portfolio variance σp² = w1²σ1² + w2²σ2² + 2w1w2 Covariance(R1,R2)\n\nPortfolio variance σp² = w1²σ1² + w2²σ2² + 2w1w2 Covariance(R1,R2)\n\nPortfolio variance σp² = (0.4)²(0.19)² + (0.6)²(0.15)² + 2(0.4)(0.6)(0.00855)\n\nPortfolio variance σp² = 0.005776 + 0.0081 + 0.004104\n\nPortfolio variance σp² = 0.01798\n\nStandard deviation σp can be found by taking the square root of the variance\n\nStandard deviation σp = ( 0.01798)^½ = 0.1341 = 13.41%\n\nThe standard deviation of James’ current portfolio is 13.41% which is below his preference of 14%. Therefore, James should not change the composition of his current portfolio" ]

[ "How do you determine if convertible bonds are dilutive?", "The profit after interest and tax of PK in the year 2023 was $300 million (its tax rate was 40%). Moreover, it had common shares outstanding at the beginning of 2023 of 40 million. During the year 2023, it issued 10 million shares in May, 2 million in July and 5 million shares in August. At the end of the year, it has $200 million in convertible bonds which are convertible into 500,000 common shares. Their interest rate is 20%. \n\nAre the convertible bonds dilutive?" ]

[ "To determine whether convertible bonds are dilutive, the Basic EPS and diluted EPS need to be compared. If the diluted EPS is greater than the basic EPS, it means that the convertible does not have a diluting effect on the earnings. You can compute the Basic and Diluted EPS as follows:\n\n# Basic EPS: \n\nBasic EPS = Net income / weighted average number of shares\n\n# Diluted EPS\n\nDiluted EPS = (Net income + savings of interest) / (Weighted average number of shares + new shares that would be issued if the convertible bonds are converted to common shares)", "To determine whether the convertible bonds are dilutive, the Basic EPS and diluted EPS need to be compared. If the diluted EPS is greater than the basic EPS, it means that the convertible does not have a diluting effect on the earnings.\n\n# Basic EPS: \n\nBasic EPS = Net income / weighted average number of shares.\n\nNet income = $300 million\n\nWeighted average number of shares = 40 million + (10 million * 8/12) + (2 million * 6/12) + (5 million * 5/12) = 40+6.67+1+2.08 million = $49.75\n\nBasic EPS = $300 million / $49.75 = $6.03 \n\n# Diluted EPS\n\nDiluted EPS = (Net income + savings of interest) / (Weighted average number of shares + new shares that would be issued if the convertible bonds are converted to common shares)\n\nNet income = $300 million\nAfter tax cost of convertible bonds = $200 million * 20% * (1-40%) = $24 million\n\nWeighted average number of shares = 40 million + (10 million * 8/12) + (2 million * 6/12) + (5 million * 5/12) = 40+6.67+1+2.08 million = 49.75 million shares\n\nNew shares upon conversion = 0.5 million shares\n\nDiluted EPS = ($300 million + $24 million) / (49.75 million + 0.5 million) = $6.45\n\n# Result\n\nSince the diluted EPS is greater than the basic EPS, it means that the convertible does not have a diluting effect on the earnings. EPS is diluted only if the diluted EPS is greater than the basic EPS which is not the case here." ]

[ "William is the sole owner of Catco. On its balance sheet, Catco has the following assets:\n\nCash: $30,000 \nAccount Receivable: $20,000\nOffice Building: $100,000\nWarehouse Building: $30,000\n5 Trucks($4,000 each): $20,000\nOffice Equipment: $30,000\nWarehouse Equipment: $20,000\nInventory: $50,000\n\nCatco also owes the following liabilities:\n\nBank loan: $50,000\nAccounts Payable: $50,000\nCredit card balance: $20,000\n\nWhat's Catco total owner's Equity?", "Assume Catco will be launching new product line for which it needs $5 million investment. Due to circumstance, Catco wants to increase its tax deduction as much as possible. Given this information, what would be the preferred way of raising this investment?" ]

[ "$300,000 (assets) - $120,000 (liabilities) = $180,000\n\nThis $180,000 represents William's stake in Catco. That is, his financial interest in the business.", "Debt financing involves out loans or issuing bonds to raise capital. Importantly, businesses can deduct the interest paid on these obligations from their taxes, lowering their tax liability.\n\nEquity financing, on the other hand, does not provide this tax benefit when shares are sold to investors. Since interest payments are not made with equity financing, there is no tax deduction associated with it.\n\nHence, Catco's preferred way of raising $5 million investment is to get external financing through debt." ]

[ "What is the loan-to-value (LTV) ratio for Class A of the following structured finance securities? Assume a loan amount of $407 million and an as-is appraised value of the underlying securities of $550,750,000. Also, keep in mind that the total required credit risk retention percentage (RR interest) for this transaction is 5.00%.\n\nCLASS PRELIMINARY AMOUNT ($)\nA 183,160,000\nB 59,185,000\nC 43,890,000\nD 58,178,000\nE 42,237,000\nRR interest 20,350,000", "If the RR interest balance of $20,350,000 is instead allocated to Class E, how does this affect the loan-to-value (LTV) ratio for Class A?" ]

[ "1.) The total loan amount is $407 million.\n2.) The as-is appraised value of the underlying collateral is $550,744,248.99.\n3.) The required RR interest (credit risk retention) is 5.00% of the total loan amount, or 20,350,000. \n\nThe RR interest represents the portion of the loan that the sponsor retains in order to share the risk. This amount is subtracted from the appraised value since it's not part of the bondholder allocation.\n\n$550,744,248 - $20,350,000 = $530,394,248.99 \n\nNext, divide the Class A balance by $530,394,248.99: \n$183,160,000 / $530,394,248.99 = 0.3453\n\nThe LTV of Class A is approximately 34.53%, or 35% when rounded to the nearest percent.", "In this scenario, the new balance of Class E is the original Class E balance of $42,237,000 plus the previous RR balance of $20,350,000, or $62,587,000.\n\nSince the RR class is no longer a factor, the Appraisal value is $550,750,000. Therefore, the Class A LTV is simply the Class A balance divided by the Appraisal value, or 183,160,000 / $550,750,000 = ~33.24%, or 33% if rounded to the nearest percent. \n​" ]

[ "A portfolio has exactly three stocks (one share each) in it. Amazon's stock was priced at $153 at the start of 2023 and $190 at the end of the year. During the year it paid a dividend of $0.75. Walmart's stock was priced at $562 at the start of 2023 and $590 at the end of the year. During the year it paid a dividend of $1. Meta's stock was priced at $125 at the start of 2023 and $124 at the end of the year. During the year it paid a dividend of $3. \n\nWhat is the price return of this portfolio?", "Is the total return of this portfolio higher than the price return?" ]

[ "Price return = (VP1 - VP0) / VP0\n\nwhere:\n- VP1 = end price\n- VP0 = initial price\n\n## Amazon\n\nIndividual price return = ($190 - $153)/$153 = 24.18%\n\nWeight in the portfolio = 1/3\n\nContribution to the portfolio price return = 24.18% * 1/3 = 8.6%\n\n## Walmart\n\nIndividual price return = ($590 - $562) / $562 = 4.98%\n\nWeight in the portfolio = 1/3\n\nContribution to the portfolio price return = 4.98% * 1/3 = 1.66%\n\n## Meta\n\nIndividual price return = ($124 - $125) / $125 = -0.80%\n\nWeight in the portfolio = 1/3\n\nContribution to the portfolio price return = -0.80% * 1/3 = -0.27%\n\n## Portfolio Price Return\n\n 8.06% + 1.66% + (-0.27%) = 9.46%\n\nThe price return was 9.46%.", "# Total Return\n\nTotal return = (year-end value + dividends - Beginning value) / Beginning value \n\n## Amazon\n\nIndividual - total return = (190 + 0.75 - 153) / 153 = 24.67%\n\nWeight in the portfolio = 1/3\n\nContribution to the portfolio price return = 24.67% * 1/3 = 8.22%\n\n## Walmart\n\nIndividual - total return = ( 590 + 1 - 562) / 562 = 5.16%\n\nWeight in the portfolio = 1/3\n\nContribution to the portfolio price return = 5.16% * 1/3 = 1.72%\n\n## Meta\n\nIndividual - total return = ( 124 + 3 - 125) / 125 = 1.60%\n\nWeight in the portfolio = 1/3\n\nContribution to the portfolio price return = 1.6% * 1/3 = 0.53%\n\n## Portfolio Total Return\n\n8.22% + 1.72% + 0.53% = 10.48%\n\n# Results\n\nThe total return was 10.48%, which is higher than the price return of 9.46%." ]

[ "What is a two-stage discount model for valuation?", "I am trying to value a stock in my portfolio. The stock paid a dividend of $5 recently. Based on the most recent earnings call, I expect the dividend will keep on growing for the next 5 years at a rate of 10% per year and then have a constant growth rate of 2% from that point on. My required rate of return in this portfolio is 12%. \n\nWhat will be the value of this stock using the two stage dividend discount model?" ]

[ "A two-stage discount model is a method used in finance and economics to value a company or project by applying different discount rates to different phases or stages of its cash flows. \n\nIn the initial stage, the company or project is expected to experience high growth. This phase might reflect early development, rapid market penetration, or significant expansion. Cash flows during this stage are often uncertain but are expected to grow rapidly.\n\nAfter the high-growth phase, the company or project is expected to reach a more stable growth rate. Cash flows in this stage are typically more predictable and grow at a more moderate rate.\n\n# Formula\n\nStock Value = Stock Value for the first first short period + Stock value onwards for the period of indefinite growth \n\nStock Value for the first shorter period = D (1+g1)^1 / (1+r)^ 1+ D (1+g1)^2 / (1+r)^ 2+ D (1+g1)^3 / (1+r)^ 3+ ... + D(1+r)^n/(1+r)^n + [Dn(1+g2) / (r-g2) ] / (1+r) ^ n \n\nWhere:\nD = The current dividend \ng1 = The growth rate for the first part. \nr = the required rate of return \nN = number of periods \n\nStock Value for the period of indefinite growth = D (1+g1)^n (1+g2) / (r-g2)(1+r)^n", "## Step 1\n\nStock Value = Stock Value for the first 5 years + Stock value onwards \n\nStock Value for the first 5 years = [5 (1+0.1)^1 / (1+0.12)^ 1] + [5 (1+.1)^2 / (1+.12)^ 2] + [5 (1+.1)^3 / (1+.12)^ 3] + [5 (1+.1)^4 / (1+.12)^ 4] + [5 (1+.1)^5 / (1+.12)^ 5] \n\n= 4.91 + 4.82 + 4.74 + 4.65 + 4.57 \n\n= 23.68 \n\n## Step 2\n\nStock Value for the period of indefinite growth = D (1+g1)^n (1+g2) / (r-g2)(1+r)^n\n\n= 5(1+ 0.1)^5 (1 + 0.02) / (0.12 - 0.2) (1 + 0.12)^5\n\n= 46.60 \n\n## Step 3: Total Value\n\nStock Value = Stock Value for the first first short period + Stock value onwards for the period of indefinite growth \n\nStock Value = 23.68 + 46.60 = 70.28 \n\n\nThe value of this stock using the two stage dividend discount model is $70.28." ]

[ "Assume we have a commercial mortgage loan with the following terms:\n\nLoan amount: $400 million.\nLoan type: Floating Rate\nLoan term: 2 years, with 3 1-year extension options\nInterest rate: SOFR +3.25%.\nInitial SOFR Cap (Strike): 8.00%\nExtension period terms: If the borrower extends the loan after the initial two years, the interest rate can't go higher than either:\n the greater of the strike rate at closing \nand the rate, that when added to the spread, yields a debt service coverage of 1.20x\n\nAfter the initial 2-year period, the borrower decides to exercise an extension option. \n\nThe borrower now has an NCF of $58,800,000. SOFR is now at 9%. What is the maximum Strike value that could be implemented?", "Assume the company finds a lender offering loan terms that are expected to be more favorable in the long term and decides not to exercise its extension option. However, the loan will result in a DSCR of 0.97x. Explain how the company can meet its mortgage payment obligations despite having a DSCR below 1.00x. Assume that the company's NCF will not increase in the foreseeable future." ]

[ "To answer this question, we need to take the \"Extension period terms\" into consideration.\n\nGiven that SOFR is now at 9%, the borrower's current interest rate is:\n8% (Cap) + 3.25% = 11.25%\n\nThis rate would result in an annual debt service of:$400,000,000 * 11.25% = $45,000,000 \n\nThis debt service would result in debt service coverage of:\n$58,800,000 / $45,000,000 = 1.31x. With the original cap in effect, the DSCR is still above 1.20x, which means the SOFR Cap can potentially be increased beyond the initial 8.00%.\n\nTo determine the maximum SOFR Cap allowed, we must first determine the Maximum Annual Debt Service:\nNCF / 1.20 = Maximum Annual Debt Service $58,800,000 / 1.2 = $49,000,000\n\nWith can then determine what interest rate would result in the Maximum Annual Debt Service:\n Maximum Annual Debt Service / Loan Amount = Interest Rate\n$49,000,000 / $400,000,000 = 12.25%\n\nSince we know that Spread is 3.25%, we can then determine the Maximum Cap:\nMaximum Rate - Spread = Maximum Cap\n\n12.25% - 3.25% = 9.00%\n\nThe SOFR Cap can potentially be raised as high as 9.0%", "While a DSCR below 1 means the company’s net cash flow will fall short of fully covering its debt service, it’s still possible for the company to meet its mortgage payments. One option is to use cash reserves to supplement its NCF and cover the relatively small gap in debt service. Alternatively, the company could rely on a line of credit to bridge the shortfall." ]

[ "What is the difference between an operating lease and a financial lease?", "Rafay is a lessor and is drawing up a lease agreement for a building.\nThe building has a remaining useful life of 50 years. The lease term, which would commence on 1 January 2020, is for 30 years.\nRafay will receive 40% of the asset's value upfront from the lessee, and at the end of each of the 30 years, Rafay will receive 6% of the asset's fair value as of 1 January 2020.\nThe Legal title at the end of the lease remains with Rafay, but the lessee can continue to lease the asset indefinitely at a rental that is substantially below its market value. If the lessee cancels the lease, it must make a payment to Rafay to recover its remaining investment.\n\nIn above scenario should the lease be classified as an operating lease or a finance lease?" ]

[ "Operating Lease:\n- The lessee uses the asset for a specific period, usually less than the asset's economic life.\n- The lessor retains ownership and risks.\n- Lease payments are expensed as operating expenses.\n- No asset or liability is recorded on the lessee's balance sheet.\n\nFinance Lease:\n- The lessee uses the asset for a significant part of its economic life.\n- The lessee bears the risks and rewards of ownership.\n- Lease payments are split into interest and principal, like loan repayments.\n- The asset and corresponding liability are recorded on the lessee's balance sheet.", "This is a financial lease.\n\nIn general, operating leases are for shorter periods and more like rentals, while finance leases are longer-term and more like financing agreements. IFRS 16 has introduced new criteria to classify leases as finance or operating leases, which may affect the accounting treatment.\n\nA finance lease, as defined by IFRS 16, is a lease where the risks and rewards of ownership transfer from the lessor to the lessee. As mentioned above in Indicators of a finance lease and as described in scenario, despite some indications of an operating lease, factors like lessee's ability to continue the lease at a low cost, inability to cancel without penalty, and substantial lease payments suggest that the lease is a finance lease." ]

[ "What is the formula for a continuously compounded return?", "The stock price of Microsoft went from $109.86 to $138.78 in 2024. Amazon’s stock jumped from $88 to $129 and Meta’s stock increased from $152 per share to $177. Which stock had the highest continuously compounded return?" ]

[ "# Formula\n\nContinuously compounded return can be calculated using the following formula\n\nContinuously compounded return = rt,t+1 = ln[P1 / P0]\n\n- rt,t+1 is the continuously compounded return.\n- P1 is the price at the end of the period.\n- P0 is the price at the beginning of the period.", "# Microsoft\n\nP1 = $138.78\nP0 = $109.86\n\nrt,t+1 = ln[P1 / P0]\nrt,t+1 = ln[$138.78 / $109.86]\nrt,t+1 = ln[1.2632]\nrt,t+1 = 0.2336 = 23.36%\n\n# Amazon\n\nP1 = $129\nP0 = $88\n\nrt,t+1 = ln[P1 / P0]\nrt,t+1 = ln[$129 / $88]\nrt,t+1 = ln[1.4659]\nrt,t+1 = 0.3825 = 38.25%\n\n\n# Meta\n\nP1 = $177\nP0 = $152\n\nrt,t+1 = ln[P1 / P0]\nrt,t+1 = ln[$177 / $152]\nrt,t+1 = ln[1.1645]\nrt,t+1 = 0.1523 = 15.23%\n\n# Result\n\nAmazon had the highest continuously compounded return last year." ]

[ "Assume ABC Pvt. Ltd. sold 2,000,000 goods, each having the selling price of $50 and cost of $20. ABC pvt. ltd. recorded its receivables of $50,000 and payables of $30,000. The company went into some legal dispute, due to which it had to pay an additional fee of $40,000 to settle the dispute. The company recorded its PPE of $1,000,000 last year. However, it bought 4 buildings for office use on rent, paying $20,000 per building. The net book value of the PPE for the year end was $900,000. There are 100 employees working in the company, each of which get paid $60,000 on annual basis. The company launched a new brand, and spent $30,000 on its advertisement. Net utility expense of the company was recorded as $20,000 for the year ended. The company earned interest income of $800,000. The company took loan of $5,000,000 and paid 20% of the principal amount as interest. The maintenance of the building costed $10,000. The Income Tax Expense was calculated as 12% of Profit Before Tax.\n\nWhat is the Operating Profit of ABC Pvt. Ltd?", "What is its net profit?" ]

[ "The Operating Profit of ABC Pvt. Ltd. is calculated as follows:\n\n Calculation\nSales 2,000,000 x $50 = 100,000,000\nCost of Goods Sold 2,000,000 x $20 = (40,000,000)\nGross Profit 100,000,000 - 40,000,000 = 60,000,00\n\nOperating Expenses:\n\nDepreciation $1,000,000 - $900,000 = (100,000)\nLegal Fee (40,000)\nRental Expense $20,000 x 4 = (80,000)\nWages $60,000 x 100 = (6,000,000)\nMarketing Expense (30,000)\nUtility Expense (20,000)\nMaintenance Expense (10,000)\nOther Income (Interest) 800,000\nTotal 800,000 - (100,000 + 40,000 + 80,000 + 6,000,000 + 30,000 + 20,000 + 10,000) = (5,480,000)\n\nOperating Profit (EBIT) = Gross Profit - Operating Expenses = 60,000,000 - 5,480,000 = 54,520,000 \n\nThe operating profit was $54,520,000.", "Interest Expense $5,000,000 x 20% = (1,000,000)\n\nProfit (Loss) Before Tax 54,520,000 - 1,000,000 = 53,520,000\nIncome Tax $53,520,000 x 12% = (6,422,400)\n\nNet Profit (Loss) After Tax 53,520,000 - 6,422,400 = 47,097,600\n\nThe Net Profit for ABC Pvt. Ltd. is $47,097,600 for the year ended." ]

[ "What is the IFRS 16 treatment of short term or low value leased assets? What are the restrictions?", "On April 1st 2023, Abigail acquired telephones for her salesforce under a two-year lease agreement. The terms of the lease require an initial payment of $3,000, followed by a payment of $9,000 on March 31st 2024 and an additional $9,000 on March 31st 2025. \n\nShow the impact of this lease arrangement on Abigail's financial statements for the year ended 31 December 2023 under IFRS 16?" ]

[ "IFRS 16 Leases permit a simplified treatment for assets with a lease period of 12 months or less, or of low value. Although the standard does not give a numerical definition of 'low value' it does give examples of the types of assets that may be included, and this includes telephones. The simplified treatment allows the lease payments to be charged as an expense over the lease period, applying the accruals concept.\n\nIFRS 16 Leases does not specify a particular monetary amount below which an asset would be considered 'low value', although the basis for conclusion indicates a value of $5,000 as a guide. The standard also gives the following examples of low-value assets:\n- tablets\n- small personal computers\n- telephones\n- small items of furniture.\nThe assessment of whether an asset qualifies as having a 'low value' must be made based on its value when new. Therefore, a car would not qualify as a low-value asset, even if it was very old at the commencement of the lease.", "Annual lease rental expense = Total rentals payable/Total lease period\n= $3,000 + $9,000 + $9,000 / 2 years\n= $10,500 per annum\nExpense to 31 December 2023 = $10,500 × 9/12\n= $7,875\nThe expense in this period of $7,875 is not the same as the payment of $3,000 so we need to accrue an additional expense of $4,875." ]

[ "Compare and contrast the cost, equity and consolidation method of reporting ownership interest between companies.", "What are the requirements for accounting of consolidated financial statements?" ]

[ "There are primarily three ways to report ownership interest between companies. The first way is to create consolidated subsidiary financial statements. The cost and equity methods are two additional ways companies may account for ownership interests in their financial reporting. Ownership is usually based on the total amount of equity owned. If a company owns less than 20% of another company's stock, it will usually use the cost method of financial reporting. If a company owns more than 20% but less than 50%, it will usually use the equity method.\n\nEquity Method:\nThe equity method is an accounting technique used by a company to record the profits earned through its investment in another company. With the equity method of accounting, the investor company reports the revenue earned by the other company on its income statement. This amount is proportional to the percentage of its equity investment in the other company.\nThe equity method is the standard technique used when one company, the investor, has a significant influence over another company, the investee. When a company holds approximately 20% or more of a company's stock, it is considered to have significant influence.The significant influence means that the investor company can impact the value of the investee company, which in turn benefits the investor.the change in value of that investment must be reported on the investor's income statement.Companies with less than 20% interest in another company may also hold significant influence, in which case they also need to use the equity method. Significant influence is defined as an ability to exert power over another company. This power includes representation on the board of directors, involvement in policy development, and the interchanging of managerial personnel.\n\nCost method:\nthe cost method is used when making a passive, long-term investment that doesn't result in influence over the company. The cost method should be used when the investment results in an ownership stake of less than 20%, but this isn't a set-in-stone rule, as the influence is the more important factor.\nUnder the cost method, the stock purchased is recorded on a balance sheet as a non-current asset at the historical purchase price, and is not modified unless shares are sold, or additional shares are purchased. Any dividends received are recorded as income, and can be taxed as such.\nFor example, if your company buys a 5% stake in another company for $1 million, that is how the shares are valued on your balance sheet -- regardless of their current price. If your investment pays $10,000 in quarterly dividends, that amount is added to your company's income.\n\nWhen an investor company exercises full control, generally over 50% ownership, over the investee company, it must record its investment in the subsidiary using a consolidation method. All revenue, expenses, assets, and liabilities of the subsidiary would be included in the parent company's financial statements. The consolidation method works by reporting the subsidiary’s balances in a combined statement along with the parent company’s balances, hence “consolidated”. Under the consolidation method, a parent company combines its own revenue with 100% of the revenue of the subsidiary.\n\n\nThe consolidation method records 100% of the subsidiary’s assets and liabilities on the parent company’s balance sheet, even though the parent may not own 100% of the subsidiary’s equity. The parent income statement will also include 100% of the subsidiary’s revenue and expenses. If the parent does not own 100% of the subsidiary, then the parent will allocate to the noncontrolling interest the percentage of the subsidiary’s net income that the parent does NOT own. When the companies are consolidated, an elimination entry must be made to eliminate these amounts to ensure there is no overstatement.\nThe elimination adjustment is made with the intent of offsetting the intercompany transaction and the shareholders’ equity, such that the values are not double counted at the consolidated level.", "IFRS requires to combine like items of assets, liabilities, equity, income, expenses and cash flows of the parent with those of its subsidiaries offset (eliminate) the carrying amount of the parent's investment in each subsidiary and the parent's portion of equity of each subsidiary (IFRS 3 Business Combinations explains how to account for any related goodwill) eliminate in full intra group assets and liabilities, equity, income, expenses and cash flows relating to transactions between entities of the group (profits or losses resulting from intragroup transactions that are recognized in assets, such as inventory and fixed assets, are eliminated in full).\nA reporting entity includes the income and expenses of a subsidiary in the consolidated financial statements from the date it gains control until the date when the reporting entity ceases to control the subsidiary. Income and expenses of the subsidiary are based on the amounts of the assets and liabilities recognised in the consolidated financial statements at the acquisition date. \nThe parent and subsidiaries are required to have the same reporting dates, or consolidation based on additional financial information prepared by subsidiary, unless impracticable. Where impracticable, the most recent financial statements of the subsidiary are used, adjusted for the effects of significant transactions or events between the reporting dates of the subsidiary and consolidated financial statements. The difference between the date of the subsidiary's financial statements and that of the consolidated financial statements shall be no more than three months." ]

[ "What is the relationship between Net Present Value (NPV) and Internal Rate of Return (IRR) in capital budgeting?", "Let's say I have an investment opportunity that will cost $100, but will generate $20 at the end of the first year and will grow 10% per year in perpetuity onwards. What is the IRR of this opportunity?" ]

[ "Capital budgeting also known as investment appraisal is a process that businesses to evaluate major projects. The process involves analyzing company's cash inflows and outflows to check whether expected return meets the benchmark. Two major techniques used for this are Net Present Value (NPV) and Internal Rate of Return (IRR). \n\nNPV is used to calculate current value of expected future cash flows of project. It calculates difference between net cash inflows and net cash outflows over a time period. A positive NPV indicates that a project or investment is profitable when discounting the cash flows by a certain discount rate, whereas, a negative NPV indicates that a project or investment is unprofitable. NPV is calculated as:\nNPV = [ Cash Flow / (1+r)^t ] - initial investment (for 1 cash flow from project)\nwhere \nr = discount rate\nt = time period \n\nIRR is a discount rate that makes value of NPV of all cash flows equal to zero. It is in general an annual rate of growth that an investment is expected to generate. Once the IRR is determined it is compared with company's cost of capital and if it is greater than that the project is considered to be a lucrative investment. IRR can be calculated in multiple ways. \n\nThe most common method is to find the discount rate that sets NPV to 0. This is done by taking the formula for an opportunities present value, setting it equal to 0 and then solving for the discount rate.\n\nAnother method is interpolation:\nIRR = R1 + { [NPV1 x (R2-R1)] / [(NPV1 - NPV2)] }\nwhere\nR1 & R2 = randomly selected discount rates \nNPV1 = higher NPV\nNPV2 = lower NPV\n\n\nBoth of the methods can be calculated with the single formula, when we have a predefined discount rate we calculate NPV and when NPV is set to 0 we can get IRR.", "To find the IRR, we need to find an interest rate r such that the cost of this opportunity equals the present value of its future cash flows. We can treat this opportunity as an annuity with constant growth. The present value of such an annuity is defined as:\n\nPV = C / (r - g)\n\nwhere:\nPV = present value\nC = initial return\ng = growth rate\nr = interest rate\n\nFilling these variables in and setting it equal to the initial cost gives us:\n\n100 = 20 / (r - 0.10)\n\nSolving for r gives us r = 0.3 or r = 30%. Therefore, the IRR of this opportunity is 30%." ]

[ "At the end of the year 2022, Party A sells $1,000,000 worth of corporate bonds to Party B with an agreement to repurchase them later. The agreed repurchase price is $1,020,000 after one year.\n\nParty A receives $1,000,000 in cash from Party B in exchange for the corporate bonds. Party A pays interest to Party B for the use of funds.\n\nIn December 2023, a year after that, Party A repurchases the corporate bonds from Party B for $1,020,000. Party B returns the corporate bonds to Party A.\n\nWhat is the impact of these transactions in income statements and balance sheets of both Party A in 2022 and 2023?", "What about Party B?" ]

[ "# Party A’s Financial Statements for the year 2022:\n\n1. Impact on Income Statement: \n\nThe selling of corporate bonds would have no impact on the Income Statement of Party A as it would not generate any revenue from sales of goods or services. It is just a transaction of financial instruments. \n\n2. Impact on Balance Sheet: \n\nDue to selling corporate bonds of worth $1,000,000, Party A would record an increase of $1,000,000 in its Assets. This increase would be reflected in Cash and Cash Equivalents. A corresponding repurchase agreement liability of $1000000 will need to be recognized. \n\n# Party A’s Financial Statements for the year 2023:\n\n1. Impact on Income Statement: \n\nThe interest expense of $20,000 would be recorded in the Income Statement of Party A under the heading of Finance Cost or Interest Expense. This increase in Interest Expense would ultimately result in decrease of Net Profit of Party A for the year. \n\n2. Impact on Balance Sheet: \n\nDue to repurchasing corporate bonds of worth $1,020,000, Party A would record a decrease of $1,020,000 in its Cash and Cash Equivalents. Also, the decrease of $20,000 in Net Profit figure would also be reflected in Retained Earnings in the Equity section of balance sheet i.e. Retained Earnings would decrease by $20,000. As the cash has been repaid, the repurchase liability will have to be unrecognized. This will result in a decrease in the liabilities of $1000000.", "# Party B’s Financial Statements for the year 2022:\n\n1. Impact on Income Statement: \n\nThe buying of corporate bonds would have no impact on the Income Statement of Party B as it would not generate any revenue from sales of goods or services or any expenses from purchasing those bonds. \n\n2. Impact on Balance Sheet: \n\nDue to the purchase of corporate bonds of worth $1,000,000, Party B would record a decrease of $1,000,000 in its Cash and Cash Equivalents and an increase of similar amount in Short-Term Investment. \n\n# Party B’s Financial Statements for the year 2023:\n\n1. Impact on Income Statement: \n\nThe interest income of $20,000 would be recorded in the Income Statement of Party B under the heading of Finance Income or Interest Income. This increase in Interest Expense would ultimately result in increase of Net Profit of Party B for the year. \n\n2. Impact on Balance Sheet: \n\nDue to reselling corporate bonds, Party B would record a decrease of $1,000,000 in its Short-Term Investment balance and an increase of $1,020,000 in Cash and Cash Equivalents. Also, the increase of $20,000 in Net Profit figure would also be reflected in Retained Earnings in the Equity section of balance sheet i.e. Retained Earnings would increase by $20,000." ]

[ "What is the difference between a bond's duration and convexity? How do you use these values to estimate the price change from a change in yields?", "James is a bond portfolio manager at Kentech. He is worried about the impact of changes in the yields on the prices of his bonds. \n\nOne of his bonds was issued by a company in Boston and has a modified duration of 31.11 and its convexity is 300.90. \nMoreover, his second bond is in an emerging market in Asia. Its modified duration is 59.21 and its convexity is 350.26.\nThe third bond in his portfolio is also in the U.S., however it is a high-risk bond. Its modified duration is 60.23 and its convexity is 360.9.\n\nIn the next six months, the expected change in the U.S. is 26 basis points. Whereas, the expected change in yields in the emerging market in Asia is 53 basis points due to high volatility in the market. \n\nWhich bond is the riskiest based on the expected changes in price in the next 6 months?" ]

[ "# Definitions\n\n## Modified Duration\n\nA mathematical formula that measures how much a bond's value changes in response to a 1% change in interest rates\n\n## Convexity\n\nConvexity is the curvature in the relationship between bond prices and interest rates.\n\n## Difference\n\nBond-modified duration and convexity measure the sensitivity of a bond's price to the change in yields. The difference is that modified duration measures the linear relationship and convexity measures the degree of curve in the relationship between bond prices and change in yields. \n\nAlthough modified duration can provide a good measure, measuring convexity can enhance the accuracy of the change in price as a result of a change in yield.\n\n# Formula \nThe change in the price of the bonds can be found using the following \n\nPercentage change in price = -(Annual Modified Duration * Change in yield) + [1/2 * Annual Convexity * (Change in yield)^2]", "Bond 1: \n\nPercentage change in price = -(Annual Modified Duration * Change in yield) + [1/2 * Annual Convexity * (Change in yield)^2]\nPercentage change in price = - (31.11 * -0.0026) + [1/2 * 300.90 * (0.0026)^2]\nPercentage change in price = 0.1826 \nPercentage change in price = 18.26 %\n\nBond 2: \n\nPercentage change in price = -(Annual Modified Duration * Change in yeild) + [1/2 * Annual Convexity * (Change in yeild)^2]\nPercentage change in price = -(59.21 * -0.0053) + [1/2 * 350.26 * (0.0053)^2]\nPercentage change in price = 0.3187\nPercentage change in price = 31.87%\n\nBond 3: \n\nPercentage change in price = -(Annual Modified Duration * Change in yield) + [1/2 * Annual Convexity * (Change in yield)^2]\nPercentage change in price = -(60.23 * -0.0026) + [1/2 * 360.9 * (0.0026)^2]\nPercentage change in price = .01578\nPercentage change in price = 15.78%\n\n# Result\n\nThe expected changes in the prices of the bonds are 18.26% for bond 1, 31.87% for bond 2 and 15.78% for bond 3. \n\nBond 2 has the highest expected change in price for the expected change in yields.\n\nThis is because bond 2 is in an emerging market with volatile interest rates which has been confirmed by the calculations." ]

[ "How do you compute the present value of an annuity with a fixed number of periods?", "I am considering purchasing a home on a 20 year mortgage. The house currently costs $1,500,000 but I can only contribute $200,000 right now. Three financing companies have provided me with their financing plans. I want to choose the most affordable financial plan and secure the lowest possible payment per month. \n\nChase Bank has provided with the option to fund the remaining payment at 5%. \n\nBank of America has offered me $1,000,000 at 5% and $300,000 at 4% \n\nPNC Bank has a plan of financing my shortfall through the market rate of 4% and it's plan includes increasing the interest rate 0.5% after every $400,000. This means that the first $400,000 will be provided at 4%, the next $400,000 will increase to 4.5%, and so on. \n\nWhich should I choose?" ]

[ "The following formula can be used to value these annuities:\n\nPV = p x ((1 – (1 + r) ^{-n}) / r)\n\nwhere:\np = payment per period\nr = interest/discount rate\nn = number of periods remaining", "Since the payments will be made every month, they will be accounted for as annuities. Instead of computing PV, we can solve for p instead. After doing some algebra, we get:\n\np = (r x PV) / [1 - (1+r) ^ -n ]\n\nComputing p will then tell us the estimate montly payment.\n\n1. Chase Bank: \n\nFinancing = $1,300,000 \nAnnual Rate = 5% \n\nSince the payment is going to be monthly, the rate needs to be converted to monthly rate \n\nMonthly rate = 5% / 12 = 0.42% \nNumber of periods = 20 years \n\nSince the payments will be made monthly, the number of periods = 20*12 = 240 \n\nAnnuity = (r x PV) / [1 - (1+r) ^ -n ] \nAnnuity = (0.42% * $1,300,000) / [1 - (1+0.42 %) ^ - 240 \nAnnuity = $8608 \n\n2. Bank of America\n\nFinancing = $1,300,000 \nAnnual Rate = 5% for 1,000,000 and 4% for $300,000. \n\nA weighted average rate needs to be calculated as there are two different rates \nWeighted average rate = (5% * 1,000,000 / (1300,000) + (4% * 300,000 / (1300,000) \nWeighted average rate = 4.76%. \n\nSince the payment is going to be monthly, the rate needs to be converted to montly rate \nMonthly rate = 4.76% / 12 = 0.40% \nNumber of periods = 20 years \n\nSince the payments will be made monthly, the number of periods = 20*12 = 240 \n\nAnnuity = (r x PV) / [1 - (1+r) ^ -n ] \nAnnuity = (0.40% * $1,300,000) / [1 - (1+0.40 %) ^ - 240 \nAnnuity = $8436 \n\n3. PNC Bank\n\nFinancing = $1,300,000 \n\nAnnual Rate = 4% for 400,000, 4.5% for the next 400,000, 5% for the next 400,000 and 5.5% for the remaining 100,000 \n\nA weighted average rate needs to be calculated as there are different rates involved \n\nWeighted average rate = (4% x 400,000 / (1300000) + (4.5% x 400,000 / (1300000) + (5% x 400,000 / (1300000) + (5.5% x 100,000 / (1300000) \n\nWeighted average rate = 4.58%. \n\nSince the payment is going to be monthly, the rate needs to be converted to monthly rate \nMonthly rate = 4.58% / 12 = 0.38% \nNumber of periods = 20 years \n\nSince the payments will be made monthly, the number of periods = 20*12 = 240 \n\nAnnuity = (r x PV) / [1 - (1+r) ^ -n ] \nAnnuity = (0.38% * $1,300,000) / [1 - (1+0.38%) ^ - 240 \nAnnuity = $8266 \n\n\n\nThe monthly payments in each of the plans will be as follows:\n \nChase Bank: $8608 \nBank of America: $8436 \nPNC: $8266 \n\nPNC offers the lowest payment per month plan which suits your needs." ]

[ "As Per IAS 12, when can a deferred tax asset be recognized?", "The directors of Swirl wish to recognize a material deferred tax asset in relation to $250 million of unused trading losses that have accumulated as of 31 December 2022. Swirl has budgeted profits for $80 million for the year ended 31 December 2023. The directors have forecast that profits will grow by 20% each year for the next four years. The market is currently depressed and sales orders are at a lower level for the first quarter of 2023 than they were for the same period in any of the previous five years. Swirl operates under a tax jurisdiction which allows for trading losses to be only carried forward for a maximum of two years.\n\nExplain whether a deferred tax asset can be recognized in the financial statements of Swirl in the year ended 31 December 2022." ]

[ "IAS 12 Income Taxes says that a deferred tax asset shall be recognized for the carry forward of unused tax losses and unused tax credits to the extent that it is probable that future taxable profit will be available against which the unused tax losses and unused tax credits can be utilized.", "Deferred tax asset can not be recognized in the financial statements of Swirl in the year ended 31 December 2022.\n\nBecause swirl operates under a tax jurisdiction that only allows losses to be carried forward for two years. The maximum total losses that can be utilized are therefore equal to total unused losses for 2021 and 2022. Losses incurred before 2021 can no longer be carried forward so no deferred tax asset should be recognized in respect of them.\n\nThe directors of Swirl should base their forecast of future profitability on reasonable and supportable assumptions. There appears to be evidence that this is not the case. Swirl has a recent history of trading losses and there is little evidence that there will be an improvement in trading results within the next couple of years.\nThe market is depressed and sales orders for the first quarter of 2023 are below levels in any of the previous five years. It is also likely that Swirl will incur various costs in relation to the restructuring which would increase losses into 2023 and possibly 2024. Only directly attributable expenses such as redundancies should be included within a provision and expensed in 2022 which would increase the current year's loss. Ongoing expenses may be incurred such as retraining and relocating costs but these should only be expensed from 2023. The forecast profitability for 2023 and subsequent growth rate therefore appear to be unrealistically optimistic.\n\nThe existence of unused tax losses is strong evidence that future taxable profit may not be available. Therefore, when an entity has a history of recent losses, the entity recognizes a deferred tax asset arising from unused tax losses or tax credits only to the extent that the entity has sufficient taxable temporary differences or there is convincing other evidence that sufficient taxable profit will be available against which the unused tax losses or unused tax credits can be utilized by the entity." ]

[ "The following numbers are pulled from the filings of a manufacturing company. All numbers are in millions of dollars.\n\n| Year | Debt | Equity | \n|------|------|--------|\n| 2021 | 3.5 | 10 |\n| 2022 | 3.8 | 9 |\n| 2023 | 4 | 8 |\n\n\nBased solely on debt-to-equity, how has the solvency of the company increased or decreased in the past three years?", "Below are the EBIT and Interest Expense values for the same company. Do these metrics indicate a similar trend in the company’s solvency over the years? All numbers are in millions of dollars.\n\n| Year | EBIT | Interest Expense | \n|------|------|--------|\n| 2021 | 2.0 | 0.25 |\n| 2022 | 1.8 | 0.30 |\n| 2023 | 1.6 | 0.35 |" ]

[ "The solvency of a company can be approximated by calculating the ratio of debt to equity.\n\n# 2023\n \nDebt to equity = $4,000,000 / $8,000,000 = 0.5\n\n# 2022\n\nDebt to equity = $3,800,000 / $9,000,000 = 0.42\n\n# 2021\n\nDebt to equity = $3,500,000 / $10,000,000 = 0.35\n\n\n\nThe debt to equity of the company has increased in the past three years which means that it is using more debt compared to equity. This shows that it has become less solvent.", "Below are the Interest Coverage Ratios for 2021-2023:\n\n#2023\nInterest Coverage = $1,600,000 / $350,000 = 4.57\n\n#2022\nInterest Coverage = $1,800,000 / $300,000 = 6.0\n\n#2021\nInterest Coverage = $2,000,000 / $250,000 = 8.0\n\nThe interest coverage ratio has decreased steadily over the past three years. Similar to the trend in the debt-to-equity ratio, this indicates that the company’s solvency has weakened" ]

[ "What is the Pecking Order Theory for capital structure?", "Alex is a manager in LMN Limited's finance department. LMN is expanding its operations into a new city, and Alex is responsible for raising $10 million in order to execute this project. The company has taken loans in the past and has a good credit history, with an effective interest rate of 8%. The company's Beta is 1 with a risk free rate in market of 5% and a market risk premium of 12%, while their corporate tax rate is 25%. How should Alex finance the company's expansion project?\n\nNote: The company has $2.5 million in retained earnings." ]

[ "Pecking Order Theory states that managers follow a hierarchy when selecting the sourcing of funding. Managers first consider internal retained earnings to fund investment opportunities followed by debt and then equity in the last. \n\nEquity financing involves the raising of funds through sale of company's shares. Selling of shares means to provide ownership to investors in exchange of funds. Companies undergo Initial Public Offering (IPO) when they go public and offer to sell shares for the first time. Investors earn dividend payments for their shares when companies declare them.\n\nDebt financing on the other hand involves raising capital by selling debt instruments to investors. In exchange for borrowing the money the companies pay fixed payments (principal + interest) to lenders/investors. \n\nWhen a company considers external source of funding they frequently prefer debt over equity due to the lower overall cost. The issuance of debt often signals an undervalued stock and confidence that the board believes the investment is profitable. On the other hand, the issuance of equity sends a negative signal that the stock is overvalued and that the management is looking to generate financing by diluting shares in the company. Debt is often \"cheaper\" than Equity because interest paid on debt is tax-deductible, and lenders’ expected returns are lower than those of equity investors (shareholders).", "Alex needs to raise an additional $7.5 million since the company already has $2.5 million in retained earnings. The retained earnings will exhaust first and then based on information provided can estimate the cost of debt and equity here as follows,\n\nCost of debt = effective interest rate * (1 - tax rate)\n = 0.08 * (1 - 0.25) \n = 0.06 0r 6%\n\nCost of equity = Risk free rate + Beta (Market risk premium - risk free rate)\n = 0.05 + 1(0.12 - 0.05)\n = 0.12 or 12%\n\n\nWith this in mind, Alex should opt to fund the remaining $7.5 million with debt rather than equity." ]

[ "A client of mine purchased a home in LA. They purchased the property for $1,000,000 with a down payment of $200,000. Their current mortgage rate is 8% with a 30-year fixed term, and the remaining principal balance is $790,000. What is their current monthly payment?", "Since purchasing the home last year, mortgage rates have dropped significantly, and they’ve been offered a refinance rate of 5.625%. However, the refinancing fees would be 5.5% of the remaining principal balance. If my client decides to refinance and keep a 30-year fixed term, how long would it take them to recoup the refinancing costs through the savings on their monthly mortgage payment? Assume that the savings on principal and interest are the only factor to consider, and ignore other costs or benefits (such as tax implications or changes in property taxes)." ]

[ "Current Mortgage Payment:\nPurchase Price — $1,000,000\nDown Payment — $200,000\nAmount Financed — $800,000\nRate — 8.00%\nTerm — 360 months\n\nUsing M = P × (r(1 + r)^n) / ((1 + r)^n - 1), we can determine that the current P&I payment is $5,870.12.", "To answer this question, we must determine:\n\n1.) The current mortgage payment (answered in last question)\n2.) The refinanced mortgage payment\n3.) The dollar amount of the refinance costs\n\nRefinanced Mortgage Payment:\nAmount Financed — $790,000\nRate — 5.625%\nTerm — 360 months\n\nUsing the same formula as above, we can determine that the new P&I payment would be $4,547.69.\n\nThis new payment is $1,322.43 less than the current payment. With refinance costs of (790,000 × 5.5%) = $43,450, it would take (43,450 / 1,322.43) ≈ 33 months to break even." ]

[ "What are the formulas for Sharpe ratio, Treynor's ratio and Jensen's alpha?", "Nick and Harry are two portfolio managers who have diversified portfolios. Their portfolios performed as follows: \n\nNicks' portfolio returned an 18% annualized return in 2023 with a standard deviation of 16% and a beta of 0.8. \nHarry's portfolio had an annualised return of 15% with a standard deviation of 14% and a beta of 1.1. \nThe current risk free rate in the market is 3% and the current market return is 10% with a standard deviation of 20%. \n\nWho performed better according to each of those metrics?" ]

[ "The formulas of the ratios are as follows: \n\nSharpe Ratio = (Rp - Rf) / σp \nRp = Return of the portfolio \nRf = Risk free return \nσp = Standard deviation of the portfolio \n\nTreynor’s Ratio = (Rp − Rf) / βp \nRp = Return of the portfolio \nRf = Risk free return \nβp = Portfolio Beta \n\nJensen's Alpha = Rp - [Rf + βp ( Rm - Rf)] \nRp = Return of the portfolio \nRf = Risk free return \nRm = market return \nβp = Portfolio Beta", "1. Sharpe Ratio\nSharpe Ratio = (Rp - Rf) / σp \nNick's Portfolio = (Rp - Rf) / σp = (0.18 - 0.03) / 0.16 = 0.9375\nHarry's Portfolio = (Rp - Rf) / σp = (0.15 - 0.03) / 0.14 = 0.8571 \n\nBased on Sharpe ratio, Nick's portfolio performed better because it generated higher return relative to the risk of the portfolio.\n\n2. Treynor's Ratio\nTreynor’s Ratio = (Rp − Rf) / βp \nNick's Portfolio = (Rp − Rf) / βp = (0.18 - 0.03) / 0.8 = 0.1875 \nHarry's Portfolio = (Rp − Rf) / βp = (0.15 - 0.03) / 1.1 = 0.1091 \n\nBased on the Treynor's ratio, Nick's portfolio had better performance because it generated a higher return per unit of portfolio beta. \n\n3. Jensen's Alpha\nJensen's Alpha = Rp - [Rf + βp ( Rm - Rf)] \nNick's Portfolio = Rp - [Rf + βp ( Rm - Rf)] = 0.18 - [0.03 + 0.8 (0.1 - 0.03)] = 6.25% \nHarry's Portfolio = Rp - [Rf + βp ( Rm - Rf)] = 0.15 - [0.03 + 1.1 (0.1 - 0.03)] = 4.3% \n\nBased on Jensen's Alpha ratio, Nick has a higher excess return over the market return which implies that his portfolio has performed better. \n\n\nNick outperformed Harry in all three ratios." ]

[ "How are payback periods used in capital budgeting?", "We are considering investing in a facility with an initial outflow of 500,000. The project is expected to generate cash flows of 100,000 in the first year, with an annual growth rate of 7% for the next 5 years. Assuming a discount rate of 3%, how long will it take to recover the initial investment based on the payback period, considering the time value of money and the projected increase in cash flows?" ]

[ "The payback period is the expected amount of time for an investment to generate returns that exceed its costs. A payback investment rule will normally define a timeframe that a payback period must meet. For example, a firm could decide to only invest in projects that will break even after four years.", "The initial investment is 500,000. The cash flow in the first year is 100,000, with a 7% increase each year for the next 5 years. Using a 3% discount rate, here’s how to calculate the payback period:\n\n*Year 1 cash flow = 100,000, discounted to 97,087.38\n*Year 2 cash flow = 107,000, discounted to 100,710.68\n*Year 3 cash flow = 114,490, discounted to 104,924.45\n*Year 4 cash flow = 122,104.3, discounted to 108,870.16\n*Year 5 cash flow = 130,050.6, discounted to 112,577.92\n\nThe cumulative discounted cash flow after each year is:\n\n*End of Year 1: 97,087.38\n*End of Year 2: 197,798.06\n*End of Year 3: 302,722.51\n*End of Year 4: 411,592.67\n*End of Year 5: 524,170.59\n\nBy the end of year 5, the cumulative cash flow is forecasted to exceed 500,000, and the initial investment should be recouped." ]

[ "Assume that a CMBS securitization consists of 5 loans:\nLoan 1: $300,000,000 (35% out of trust)\nLoan 2: $250,000,000\nLoan 3: $100,000,000\nLoan 4: $75,000,000\nLoan 5: $50,000,000\n\nThe loans mature in 300 months, 240 months, 240 months, 300 months, and 120 months, respectively. What is the WAM, rounded to the nearest month?", "Before closing, the issuer decides to securitize additional assets with the goal of achieving a Weighted Average Maturity (WAM) of 275 months.\n\nThe issuer has a large number of loans available with 300-month maturities. What is the approximate balance of 300-month loans that would need to be added to the original pool to bring the overall WAM to 275 months?" ]

[ "To calculate the weighted average maturity (WAM), we need to determine the maturity of each loan by its size relative to the entire pool.\n\nSince loan 1 is 35% out of trust, we only consider 65% of the $300,000,000 loan amount.\n\nWAM = (195000000 / 670000000 * 300) + (250000000 / 670000000 * 240) + (100000000 / 670000000 * 240) + (75000000 / 670000000 * 300) + (50000000 / 670000000 * 120)\nWAM = ~255.22 or 255 when rounded to the nearest month", "To determine the balance of 300-month maturity loans the issuer needs to add to the existing pool to achieve a WAM of 275 months, we can use the following formula:\n\n275 = ((670,000,000 × 255) + (X × 300)) / (670,000,000 + X)\n\nX represents the balance of the new 300-month loans to be added.\n\nSolving for X gives a value of 536,000,000.\n\nTherefore, if the issuer wants the WAM of the new pool to be 275 months, they should add 536,000,000 in new loans with 300-month maturities to the original pool." ]

[ "What are the key differences between IFRS 15 and FRS 102?", "On June 30 2022, Poly entered a contract to manufacture bespoke machinery for a local customer. The customer instructed Poly on the machinery specification, as Poly's standard machines were unsuitable. The customer paid an upfront deposit, which is refundable if Poly fails to complete the construction of the machinery. The remaining balance on the contract is due when the machinery is delivered to the customer's site and Poly is responsible for arranging delivery. If the customer defaults on the contract before the completion of the machines, Poly only has the right to retain the deposit.\n\nWhich reporting standard should the company follow, FRS 102 or IFRS 15?" ]

[ "IFRS 15 and FRS 102 are both accounting standards that deal with revenue recognition, but they have key differences in complexity and approach:\n- FRS 102: Based on IAS 18 Revenue, it offers a principle-based approach, requiring judgment to identify when revenue can be recognized.\n- IFRS 15: Introduces a more comprehensive and prescriptive five-step model for revenue recognition. This step-by-step approach aims to be more consistent and easier to apply.", "FRS 102 will still likely be a simpler standard with less detailed disclosure requirements. \n\nAs per IFRS 15 Revenue providing the bespoke machinery is a single performance obligation. Poly needs to assess whether the performance obligation is satisfied over a period or at a point, to determine when and how the revenue should be recognized. As the machinery being produced is bespoke, an asset is created that has no alternative use to Poly.\n\nHowever, Poly only has an enforceable right to the deposit received and therefore does not have the right to payment for work completed to date. This means Poly should account for the sale as a performance obligation satisfied at a point in time, rather than over time. Revenue will most likely be recognized when the machinery is delivered to the customer, assuming control of the asset has been transferred to the customer. The deposit should be recognized as a contract liability.\n\nAs per FRS 102, revenue from goods should be recognized when the risks and rewards of ownership transfer from the buyer to the seller. Poly has responsibility for the delivery of the machinery and therefore is exposed to the potential risks of ownership of the asset until delivery has been completed. Poly therefore cannot recognize any revenue until this point. The deposit received in advance should be recorded in deferred income." ]

[ "During the past two years 2022 and 2023, a semiconductor distributor made the following purchases and sales:\n\nIn 2022, it purchased an inventory of 121,500 wafers at a cost of $10.67 per wafer and sold 112,650 units at a price of $13.99 per wafer. In 2023, it bought 284,800 units at a cost of $8.23 per wafer and sold 274,580 units for $11.59 per wafer.\n\nWhat would be the inventory turnover ratio in 2023 using the FIFO and LIFO methods?", "Would the using the Weighted Average method lead to a higher or lower inventory turnover ratio compared to the FIFO method?" ]

[ "First, let's recap the data given in the question.\n\n| Year | Purchases | | Sales | |\n|-----------|---------------|-------------|------------|----------|\n| | Units | Cost | Units | Price |\n| 2022 | 121,500.00 | 10.67 | 121,500.00 | 13.99 |\n| 2023 | 284,800.00 | 8.23 | 274,580.00 | 11.59 |\n\nWe need to find the inventory valuation method used in order to recieve an inventory turnover valuation of 12.66. Inventory Turnover is defined as the Cost of Goods Sold / Year-End Inventory Balance.\n\nAt the end of 2022, we have 121,500.00 - 121,500.00 = 8,850 units left over. In 2023, we add 284,800 more units, bringing the total up to 284,800 + 8,850 = 293,650. We then sold 274,580 of those units to reduce inventory to 19,070. \n\n# First in first out (FIFO)\n\nUsing the FIFO method, we would value the 274,580 units sold in 2023 as 8,850 of the units from 2022 at $10.97 and then 274,580 - 8,850 = 265,730 at 8.23. The cost of goods sold would then be,\n\n265,730 * 8.23 + 8,850 * 10.67 = 2,281,387.40\n\nThe remaining 19,070 would be valued at 8.23, meaning our remaining inventory balance would be\n\n19,070 * 8.23 = 156,946.10\n\nThis would give us an inventory turnover of\n\n2,281,387.40 / 156,946.10 = 14.54\n\n# Last in first out (LIFO)\n\nUsing the FIFO method, we would value the 274,580 units sold in 2023 as being from 2023. Of the 19,070 left over, 8,850 of those would be valued using the value from 2022 and 19,070 - 8,850 = 10,220. The cost of goods sold would then be,\n\n274,580 * 8.23 = 2,259,793.40\n\nThe ending inventory balance would then be\n\n10,220 * 8.23 + 8,850 * 10.67 = 178,540.10 \n\nThis would give us an inventory turnover of,\n\n2,259,793.40 / 178,540.1 = 12.66", "# Weighted average\n\nUsing the weighted average method, we would evaluate each unit as having the weighted average cost across the entire inventory. Since we had 8,850 at 10.67 and 284,800 at 8.23, this value would be\n\n10.67 * 8,850 / (8,850 + 284,800) + 8.23 * 284,800 / (8,850 + 284,800) = 8.30\n\nThe cost of goods sold would then be,\n\n274,580 * 8.30 = 2,279,014\n\nThe ending inventory balance would then be\n\n19,070 * 8.30 = 158281\n\nThis would give us an inventory turnover of,\n \n2,279,014 / 158,281 = 14.40\n\nTherefore, the weighted average method would lead to a slightly lower turnover ratio compared to the FIFO method (14.54)." ]

[ "What is operating segment disclosure? When does IFRS 8 allow aggregating operating segments?", "Techno sells computer games. Sales are made through the website as well as through brick and mortar stores. The products sold online and in stores are the same. Techno sells new releases for $40 in its stores, but $30 online. Internal reports used by the chief operating decision maker show the results of the online business separately from the stores. However, they will be aggregated together for disclosure in the financial statements.\n\nShould Techno's online business sales and high street stores sales be aggregated into a single segment in the operating segments disclosure?" ]

[ "Operating segment disclosure: A company's disclosure of information about its business components that:\n- Earn revenues and incur expenses.\n- Have separate financial info.\n- Are regularly reviewed by management.\n\nIFRS 8 allows aggregating operating segments if they have similar economic characteristics, products, customers, and distribution methods.", "The online business and the high street stores business should be reported separately as two operating segments instead of aggregated into a single segment.\n\nTechno stores and online business sell similar products to similar customers but have different distribution methods (in-store collection vs. delivery) and significant price differences, leading to different gross margins. This suggests separate disclosure may be more appropriate, as the segments may not be similar enough to aggregate." ]

[ "What is the difference between inherent goodwill and purchased goodwill?", "If XYZ Inc is acquired for a purchase price of $500 million with a fair value of assets of $400 million and no liabilities, what is the purchased goodwill? How will this be recorded on the balance sheet of the company that acquired XYZ Inc?" ]

[ "# Inherent Goodwill\nInherent Goodwill is the value of the business more than the fair value of its separable net assets and cannot be purchased directly. It increases with time due to certain factors such as good reputation of the business, customer loyalty, and brand recognition.\nInherent Goodwill cannot be calculated directly, as it arises from certain factors with the passage of time. Analysts usually use various methods and techniques to estimate the overall value of a business. These techniques include income approach, market approach, discounted cash flow method, cost approach, market capitalization, and so on.\nTherefore, the inherent goodwill of XYZ will include the talented R&D team, and a reputation for cutting-edge technology etc. This will not impact the financial statements because they will not be valued.\n\n# Purchased Goodwill\nPurchased Goodwill arises when a company acquires another company or business. The extra amount paid to acquire the company is considered as purchased goodwill. It is calculated as the value paid to acquire the target company, less the sum of its assets and liabilities that is stated in the target company’s balance sheet.\n\n# Calculation of Purchased Goodwill\nPurchased Goodwill is calculated as follows:\nGoodwill = Purchase price of the target company – (Fair value of Assets + Fair value of Liabilities)", "# Goodwill in case of acquiring XYZ\nPurchase price = $500 million\nFair value of assets = $400 million\nPurchased goodwill = $500 million - $400 million = $100 million\n\nThe excess of $100 million that ABC will pay over the fair value of the net assets of XYZ will be the purchased goodwill. It will be recorded as a long-term asset in the balance sheet and will be tested for impairment annually." ]

[ "How is deferred tax is calculated for long-term assets?", "My company has purchased a manufacturing plant for $100,000. For the company's accounting purposes, the useful life of this asset is five years; however, the tax authority requires depreciation over four years. The current tax in our jurisdiction is 25%. How can I calculate the deferred tax for this?" ]

[ "Deferred tax is the income tax payable in future periods with respect to taxable temporary differences. To calculate the deferred tax for your plant, you need to determine the temporary difference between the depreciation expense for tax purposes and accounting purposes. Temporary differences are defined as differences between the carrying amount of an asset or liability in the statement of financial position and its tax base (i.e. the amount attributed to that asset or liability for tax purposes. If the accounting \n\nTemporary difference = Carrying amount - Tax base\nDeferred tax asset or liability = Temporary difference x Tax rate\nDeferred tax liability (for asset)= carrying amount of asset > tax base\nDeferred tax asset (for asset) = carrying amount of asset < tax base", "1. For tax purposes, the depreciation expense is calculated over four years, resulting in $25,000 of depreciation per year ($100,000 / 4 years). This will leave a tax base amount of $75,000 (100,000 - 25,000).\n2. For accounting purposes, the equipment has depreciated over five years, resulting in $20,000 in depreciation expenses per year ($100,000 / 5 years). This will leave a carrying amount of 80,000 (100,000 - 20,000)\n3. The temporary difference is $5,000 ($80,000 - $75,000). \n4. Then, we multiply the temporary difference $5,000 by the applicable tax rate 25%. \n5. This gives us a deferred tax liability of $1,250." ]

[ "I have purchased $200,000 worth of shares of Apple from a broker by posting only a 40% margin. The broker requires a maintenance margin of 30%. They have told me that I need to ensure my deposit remains above the margin requirement or else the broker will margin call for more deposit. What does this mean?", "At what value of my stock should I expect to receive the call for increasing the deposit?" ]

[ "Maintenance margin, also known as minimum maintenance or variation margin, is the minimum amount of equity an investor must keep in a margin account to avoid a margin call.\n\nSince you have borrowed the funds from the broker to invest in the Apple stock, they have a risk of losing this money. The maintenance margin will protect brokerage firms from default on this loan \n\nA margin call is a request from a broker for an investor to add more funds to their account or liquidate some of their holdings. If an investor doesn't meet the margin call, their position may be automatically liquidated.", "To calculate the value at which the margin call will be received, the following formula can be used\n\nMargin call price = Purchase Price (1 - initial margin / 1 - maintenance margin) \n\n= $200,000 (1 - 0.4 / 1-0.3)\n= $171,428\n\nSo, if the value of your stock falls below this amount, you will be required to deposit funds to meet this minimum requirement." ]

[ "Jack, an investor, buys 1000 shares of Carhub Ltd. at a price of $20 per share in 2020. He plans to hold it for the long run. After a year, the price of one share of Carhub Ltd. increases to $30. After 2 years, the share price of Carhub Ltd. suddenly decreases to $15. Seeing no potential growth in Carhub Ltd. in longer run, Jack sold all his investments in Carhub Ltd.\n\nWhat is the amount of profit/loss Jack has made in 2 years from his investment in Carhub Ltd.?", "Is this profit/loss realized or unrealized? What would be the double entry recorded for this gain/loss?" ]

[ "Cash Outflow = 1,000 * $20 = $20,000\n\nCash Inflow = 1,000 * $15 = $15,000\n\nNet Profit/(Loss) = $15,000 – $20,000 = ($5,000)\n\nThe amount of loss incurred by Jack is $5,000.", "The loss incurred by Jack is realized. Realized Profit/Loss is the actual amount of profit or loss incurred on the sale of the underlying asset or investment. It can be calculated only when the asset is sold. On the other hand, Unrealized Profit/Loss is the increase or decrease in the value of an asset or an investment that an investor holds but has not sold it yet. It is calculated based on the market value of the underlying asset or investment.\n\nIn the case above, since Jack sold his investment in Carhub Ltd., therefore the loss he made was realized.\n\n# Double Entries:\nFor realized loss, the double entry passed in the ledger book would be:\n\n $ $\nDr. Cash 15,000\nDr. Realized Loss on Sale of Shares 5,000\nCr. Investment in Shares 20,000" ]

[ "What is the difference between contingent liability and provision?", "What are the reporting requirements for contingent liabilities?" ]

[ "1. A provision is a present obligation of uncertain amount and timing, as well (e.g. provision for bad debts). Contingent Liability is a possible obligation that results from past events and whose existence will rely upon the happening or non-happening of the future event.\n2. Provision is a recognized liability whose occurrence is certain. A contingent liability is an unrecognized liability, meaning we do not pass any accounting entry for such liability. This is because:\n - It is not foreseeable that the settlement of that liability will need an outflow of funds.\n - An accurate estimation of the amount is not possible.\n3. The occurrence of contingent liability is conditional or uncertain. Whereas the occurrence of provision is certain.\n4. Provision is accounted for at present and arises as a result of past events. Whereas contingent Liability is disclosed at present as a note to account for the outflow of funds which are likely to occur in future.", "Contingent liabilities are liabilities that depend on the outcome of an uncertain event. These obligations are likely to become liabilities in the future.\n\nContingent liabilities must pass two thresholds before they can be reported in financial statements. First, it must be possible to estimate the value of the contingent liability. If the value can be estimated, the liability must have more than a 50% chance of being realized. Qualifying contingent liabilities are recorded as an expense on the income statement and a liability on the balance sheet.\nIf the contingent loss is remote, meaning it has less than a 50% chance of occurring, the liability should not be reflected on the balance sheet. Any contingent liabilities that are questionable before their value can be determined should be disclosed in the footnotes to the financial statements.\n\nCompanies operating in the United States rely on the guidelines established in the generally accepted accounting principles (GAAP). Under GAAP a contingent liability is defined as any potential future loss that depends on a \"triggering event\" to turn into an actual expense.\n\n\nIt's important that shareholders and lenders be warned about possible losses ,an otherwise sound investment might look foolish after an undisclosed contingent liability is realized. There are three GAAP-specified categories of contingent liabilities: probable, possible, and remote. Probable contingencies are likely to occur and can be reasonably estimated. Possible contingencies do not have a more- likely than-not chance of being realized but are not necessarily considered unlikely either. Remote contingencies aren't likely to occur and aren't reasonably possible.\n\nWorking through the vagaries of contingent accounting is sometimes challenging and inexact. Company management should consult experts or research prior accounting cases before making determinations. In the event of an audit, the company must be able to explain and defend its contingent accounting decisions.\n\nAny probable contingency needs to be reflected in the financial statements—no exceptions. Remote contingencies should never be included. Possible contingencies those that are neither probable nor remote should be disclosed in the footnotes of the financial statements.\n\nGAAP accounting rules require probable contingent liabilities ones that can be estimated and are likely to occur to be recorded in financial statements. Contingent liabilities that are likely to occur but cannot be estimated should be included in a financial statement footnotes. Remote (not likely) contingent liabilities are not to be included in any financial statement." ]

[ "What is the beta of a stock? How should you interpret a beta value?", "Blake is considering three companies to suggest his client, William who is trying to invest his money for retirement. Blake wants to select the stock which has the lowest volatility compared to the market.\n\nThe first company is Amazon which has an expected return of 13% with an expected deviation in the return of 25%. Moreover, its correlation with the U.S. stock market is 0.6. The second company is Microsoft with an expected annual return of 16% with an expected deviation in the return of 20%. And its correlation with the market is 0.9. The third company is Meta which has an expected annual return of 12% with an expected standard deviation of 21% and a correlation with the market of 0.7. The standard deviation of the market returns is 15%.\n\nWhich company should Blake suggest to William?" ]

[ "# Formula\n\nBeta is the risk measure that measures the volatility of a stock compared to the market. Beta is measured as follows:\n\nBeta = Correlation(Ri, Rm) * σi / σm\n\nHere: \n\n- Correlation (Ri, Rm) is the correlation between the return of a stock and the market return.\n- σi is the standard deviation of the return of the stock.\n- σm is the standard deviation of the market returns.\n\n# Interpretation\n\nIf a stock has a beta of 1, it moves with the market\nIf a stock has a beta of less than 0, it moves in the opposite direction to the market.\nIf a stock has a beta of >1, it is more volatile than the market.\nIf a stock has a beta of <1, it is less volatile than the market.\n\n.", "# Calculation\n\nBeta = Correlation(Ri, Rm) * σi / σm\n\n## Amazon\n\nBeta = Correlation(Ri, Rm) * σi / σm\nBeta = 0.6 * 0.25 / 0.15\nBeta = 1.0\n\n## Microsoft\n\nBeta = Correlation(Ri, Rm) * σi / σm\nBeta = 0.9 * 0.20 / 0.15\nBeta = 1.2\n\n\n## Meta\n\nBeta = Correlation(Ri, Rm) * σi / σm\nBeta = 0.7 * 0.21 / 0.15 \nBeta = 0.98\n\n# Result\n\nBased on the calculations, Meta has the lowest beta value which means that it is less volatile than the market. Therefore, based on Blake’s criteria, Meta should be suggested to William" ]

[ "What are the formulas for discrete and continuous compounding?", "I have three options to invest my $200,000 savings for the next 8 years. The first option is to invest them at 8% per annum to be compounded continuously. The second option is to deposit this money for a 6% compounded monthly return. The third option is to invest the money at a 7.5% semi annual compounded return. Which option among these three options offers the highest future value?" ]

[ "# Formulas\n\nFuture value of an investment can be found using the following formulas depending on how the compounding takes place.\n\n## Discrete Compounding\n\nFor discrete compounding, the following formula is used:\n\nFV = PV (1+r/m)^nm\n\n- FV = future value\n- PV = present value (value today)\n- r = return\n- m = number of compounding periods\n- n = number of years\n\n## Continuous Compounding\n\nFor continuous compounding, the following formula is used;\n\nFV = PV*e^rt\n\nFV = future value\nPV = present value (value today)\nr = return \nt = time period in years", "# Option 1 (Continuous)\n\n- FV = PV*e^rt\n- FV = $200,000 e^0.08*8\n- FV = 379296\n\n\n# Option 2 (Discrete)\n\n- FV = PV (1+r/m)^nm\n- FV = $200,000 (1+0.06/12)^(12*8)\n- FV = 322828\n\n# Option 3 (Discrete)\n\n- FV = PV (1+r/m)^nm\n- FV = $200,000 (1+0.075/2)^(2*8)\n- FV = 360446\n\n# Result\n\nOption 1 offers the highest future value for the $200,000 investment." ]

[ "I purchased a property that cost $900,000 using a 30-year mortgage for 70% of the total price while funding the remaining amount from a savings account. The mortgage rate is 5.5% annually. \n\nHow much of the first monthly payment will go towards principal? How much will go towards interest?", "What's the total amount of interest to be paid over the entire life of the loan?" ]

[ "We can calculate the monthly payment using:\nPMT = P * (r * (1 + r)^n) / ((1 + r)^n - 1)\n\nWhere:\n\nPMT = Monthly payment\nP = Loan principal\nr = Monthly interest rate\nn = Number of payments\n\nThis gives us a monthly payment (P&I) of $3,577.07. The interest portion can be calculated as (r * P), which gives us a value of $2,887.50. Therefore, the principal portion of the mortgage will be $3,577.07 - $2,887.50, or $689.57.", "The monthly principal and interest (P&I) payment is $3,577.07, and it will be paid over 360 months.\n\nTotal P&I payments: $3,577.07 × 360 = $1,287,745.20\n\nBreakdown of total payments:\n\nOriginal loan principal: $630,000\nTotal interest paid: $1,287,745.20 - $630,000 = $657,745.20\nThe total interest paid over the life of the loan is $657,745.20." ]

[ "Our company had 5000 laptops, each of them valued at $1000 inventory at the start of the year. During the year, we made purchases of 2000 units at $1200 in January, 1000 at $800 in July and 900 at $750 in September. We sold 3000 units in February, 3000 in August and 2000 in December. \n\nHow would these transactions be recorded on the relevant balance sheets and income statements according to the Weighted Average method, First-in-First-Out (FIFO) method and Last-in-Last-Out (LIFO) method?", "Going forward, which of these would you expect to lead to the highest profit?" ]

[ "# WAC\n\nThe weighted average method assigns the average cost of production to given product. \n\nCost of goods of 3000 in Feb = 3000 x $997 = $2.991M\n\nCost of goods of 3000 in Aug = 3000 x $997 = $2991K\n\nCost of goods of 2000 in Dec = 2000 x $997 = $1994K\n\n(Impact on Income Statement)\nTotal COGS = $7.976M \n\n(Impact on Balance Sheet)\nEnding Balance = Beginning + net purchases - COGS = $5M + $3.875M - $7.976M = $0.899M\n\n# FIFO\n\nFor the FIFO method the oldest cost of an item in an inventory will be removed first when one of those items is sold.\n\nCost of goods of 3000 in Feb = 3000 x $1000 = $3M \n\nCost of goods of 3000 in Aug = 2000 x $1000 + 1000 x $1200 = $2M + $1.2M \n\nCost of goods of 2000 in Dec = 1000 x $ 1200 + 1000 x $800 = $1.2M + $0.8M \n\n(Impact on Income Statement)\nTotal COGS = $8.2M\n\n(Impact on Balance Sheet)\nEnding Balance = Beginning + net purchases - COGS = $5M + $3.875M - $ 8.2M = $0.675 M\n\n# LIFO\n\nLIFO accounting method assumes that latest items bought are the first ones to be sold.\n\nCost of goods of 3000 in Feb = 900 x $750 + 1000 x $800 + 1100 x $1200 = $675K + $800K + $1.32M \n\nCost of goods of 3000 in Aug = 900 x 1200 + 2100 x $1000 = $1.08M + $2.1M \n\nCost of goods of 2000 in Dec = 2000 x $1000 = $2M \n\n(Impact on Income Statement)\nTotal COGS = $7.975M\n\n(Impact on Balance Sheet)\nEnding Balance = Beginning + net purchases - COGS = $5M + $3.875M - $7.975M = $0.9M", "Based on the purchase costs during the year, it is clear that the market prices are decreasing. In this scenario, the LIFO will have the lowest cost of goods sold and the highest profit among the three methods." ]

[ "Walbury had a revenue before taxes of $900 million on which it had to pay a tax of 35%. During the year, it paid $16 million in dividends to the preferred shareholders. It had 220 million weighted average common shares outstanding and it also had 200,000 options outstanding which can be converted to ordinary shares at a price of $30 per share. During the year, the average price per share of Walbury has been $40. \n\nWhat is Walbury's basic EPS?", "What is the difference between Walbury's basic and diluted EPS?" ]

[ "# Step 1\n\nNet income = income before taxes - Taxes\nNet income = $900,000,000 - ($900,000,000 * 35%)\nNet income = $900,000,000 - $315,000,000\nNet income = $585,000,000\n\n# Step 2\n\nBasic EPS = (Net income - preferred share dividends) / Weighted average shares during the year\n\nBasic EPS = ($585,000,000 - $16,000,000) / 220,000,000\n\nBasic EPS = $2.58\n\nWalbury's basic EPS is $2.58", "Diluted EPS = (Net income - preferred dividends) / (Weighted average number of shares + shares that would be issued if options are exercised - Shares that could have been purchased using the cash from options exercise)\n\nDiluted EPS = ($585,000,000 - $16,000,000) / (220,000,000 + 200,000 - 150,000)\n\nDiluted EPS = $2.59\n\n# Difference\n\n$2.66 - $2.59 = $0.07\n\nThe difference between the Basic and Diluted EPS is $0.07" ]

[ "The Manufacturing equipment of a company was valued at $1,000,000 at the beginning of the year on January 1st 2023 when its accumulated depreciation was $450,000. During 2023, an additional depreciation of $50,000 was recorded. \n\nAccording to the cash flow projects, it is expected that the asset will generate cash flows of $80,000 (2024), $86,000 (2025), $90,000 (2026), $60,000 (2027) and $70,000 (2028). The company's discount rate is 2.5% and it has been found that the fair value of the asset in the market is $386,000, with a selling cost of $2,550.\n\nWhat is the impact of the impairment under IFRS?", "What would the impairment be under US GAAP?" ]

[ "The sum of the total undiscounted cash flows is $80,000.00 + $86,000.00 + $90,000.00 + $60,000.00 + $70,000.00 = $386,000.00. \n\nThe present value of these cash flows is computed in the following table.\n\n| Discounted Cash Flows | | | |\n|---------------------------|----------|----------------|--------------------------|\n| Year | Cash Flow | Discount Factor | Discounted Cash Flow |\n| 2024 | $80,000.00 | 0.9756 | $78,048.78 |\n| 2025 | $86,000.00 | 0.9518 | $81,856.04 |\n| 2026 | $90,000.00 | 0.9286 | $83,573.95 |\n| 2027 | $60,000.00 | 0.9060 | $54,357.04 |\n| 2028 | $70,000.00 | 0.8839 | $61,869.80 |\n| Total Discounted Cash Flows | | |$359,705.60|\n\nWe can now summarize the main values we need for the remainder of the question.\n\n| Value at Year Beginning (1 January 2023) | $1,000,000.00 |\n| Accumulated Depreciation (1 January 2023) | $450,000.00 |\n| Depreciation During the Year (2023) | $50,000.00 |\n| Value at Year End (30 December 2023) | $500,000.00 |\n| Value in Use (Discounted Cash Flows) | $359,705.60 |\n| Undiscounted Expected Cash Flows | $386,000.00 |\n| Fair Value | $368,000.00 |\n| Costs to Sell the Asset in the Market | $2,550.00 |\n\n# IFRS\n\nUnder IFRS, the impairment amount is the difference between the carrying amount and the recoverable amount. \n\nImpairment = Carrying Amount - Recoverable Amount\nRecoverable Amount = Higher of Fair Value Less Costs to Sell and Value in Use $365,450.00\n\nCarrying Amount = $500,000 (Value at Year End)\nFair Value less costs to sell = $368,000.00 - $2,550.00 = $365,450\nValue in Use = $359,705.60\nRecoverable Amount = max($365,450, $359,705.60) = $365,450\n\nTherefore, the Impairment under IFRS is $500,000 - $365,450 = $134,550.", "Under US GAAP, the impairment is valid only if the assets are recoverable, meaning that the undiscounted cash flows exceed the carrying value. In this case,\n\nUndiscounted Future Cash Flows = $386,000.00\nCarrying Amount = $500,000\n\nThe impairment is then the carrying amount less the sum of discounted cash flows, or\n\nCarrying Amount - Sum of Discounted Cash Flows = $500,000.00 - $359,705.60 = $140,294.40\n\nTherefore, the Impairment under US GAAP is $500,000 - $365,450 = $140,294.40" ]

[ "Our software solutions company has a revenue of $28 million and all sales are made on 30 days credit. The average trade receivables balance is $5.37 million and usually, 2% of the credit sales are bad debts. \n\nWe have been trying to reduce the collection period of debts and have spent huge amounts of money but in vain. A factoring company provided us the following option:\n\nAdministration by the factor of our invoicing, sales accounting and receivables collection, on a full recourse basis. The factor would charge a service fee of 0.5% of credit sales revenue per year. We estimate that this would result in savings of $30,000 per year in administration costs. Under this arrangement, the average trade receivables collection period would be 30 days.\n\nPerform a cost/benefit analysis of this option.", "We received an alternative option:\n\nAdministration by the factor of our invoicing, sales accounting and receivables collection on a non-recourse basis. The factor would charge a service fee of 1.5% of credit sales revenue per year. Administration cost savings and average trade receivables collection period would be as Option 1. We would be required to accept an advance of 80% of credit sales when invoices are raised at an interest rate of 9% per year. We pay interest on our overdraft at a rate of 7% per year and the company operates for 365 days per year.\n\nShould we pursue this instead?" ]

[ "# Option 1\n\n## Benefits\nCurrent trade receivables = $5370000\n\nRevised trade receivables = $28000000 * 30/365 = $2301370 \n(With factoring, the average trade receivables balance will be reduced to $2,301,370. This is derived from the 30-day collection period, assuming the same annual sales)\n\nReduction in receivables = $5370000 - $2301370 = $3068630\n\nReduction in financing costs = $3068630 * 0.07 = $214804\n(The reduction in financing costs due to reduced receivables, assuming an overdraft interest rate of 7%)\n\nReduction in admin costs = $30000\n\nTotal benefits = $214804 + $30000 = $244804\n\n## Costs\nFactor's fee = $28000000 * 0.5% = $140000\n(The factor charges a fee of 0.5% of the annual credit sales)\n\n## Net Benefits\nNet benefit = Total benefits - Total costs\nNet benefit = $244804 - $140000 = $104804\n\nThe net benefit of this option would be $104,804.", "# Benefits\nReduction in financing cost = $3068630 * 0.07 = $214804 \nReduction in admin costs = $30000 \nBad debts saved = $28000000 * 0.02 = $560000 \n(Under non-recourse factoring, the factor assumes the bad debts risk, saving the company 2% of the annual credit sales)\n\nBenefits = $214804 + $30000 + $560000 = $804804 \n\n# Costs\n\nIncrease in finance cost = $2301370 * 80% * (9%-7%) = $36822 \n(The factor advances 80% of the credit sales at an interest rate of 2% (the different between offered interest rate of 9% and the current financing cost of 7%). However, we should only consider the cost of financing the remaining receivables after considering the advance. The interest is calculated on the advanced amount)\n\nFactor's fee = $28000000 * 1.5% = $420000 \n(The factor charges a fee of 1.5% of the annual credit sales)\n\nCosts = $36822 + $420000 = $456822 \n\n## Net Benefit\nNet benefit = Benefits - Costs\nNet benefit = $804804 - $456822 = $347982 \n\n\nThis option is better, since it provides a higher net benefit." ]

[ "What is the difference and relationship between FRS 102 and IFRS 9?", "Beto purchased equity shares in another company on May 1st 2022. At the date of acquisition, the investment cost was $11,000 and transaction costs were $2,000. At the reporting date, the shares had a fair value of $13,000.\n\nBeto's finance director has informed the financial accountant that it plans to hold the shares for the long term and therefore wishes to use the alternative treatment in line with IFRS 9 Financial Instruments. The financial accountant has only recently joined the company, having previously worked for a company that applies FRS 102, and is therefore unsure what the finance director is referring to.\n\nWhat is the treatment of the investment in equity shares differs under IFRS 9 and FRS 102 for the year ended December 31st 2022?" ]

[ "FRS 102 provides a baseline for accounting for financial instruments in the UK, and companies can choose to adopt the more advanced IFRS 9 standard for recognition and measurement. As Per IFRS 9 Financial Instruments, investments in equity shares can be classified as fair value through profit or loss, which is the default position, or fair value through other comprehensive income (FVOCI) if an election is made upon initial recognition.\n\nIFRS 9 and FRS 102 are both accounting standards that deal with financial instruments, but they have some key differences:\n- Scope: IFRS 9 is a comprehensive standard that applies to all entities that prepare financial statements under IFRS. FRS 102, on the other hand, is a UK-specific standard that applies to most companies in the UK and Ireland. However, FRS 102 allows companies to voluntarily adopt the recognition and measurement requirements of IFRS 9 for financial instruments.\n- Measurement: IFRS 9 introduces a new expected loss impairment model, while FRS 102 retains the incurred loss model from the previous standard, IAS 39.\n- Hedging: Both standards have similar hedging requirements, but there are some minor technical differences.", "If Beto wishes to designate these shares as FVOCI, then initially the shares should be recognized at fair value plus transaction costs, totaling $13,000 ($11,000 + $2,000).\nOn 31 December 2022, the shares should be measured to the fair value of $13,000, with a gain of $2,000 being recognized in other comprehensive income. As Per FRS 102, the treatment is simplified. Investments in shares should be measured at fair value through profit or loss if their fair value can be reliably measured. There is no alternative FVOCI classification.\nAssuming the fair value of these shares is a reliable measurement, the shares should initially be recognized at their fair value of $11,000. The $2,000 transaction costs should be expensed." ]

[ "What is the relationship between a bonds YTM and its default risk?", "You are given the following information about three bonds issued by different companies. Each bond has a 2-year maturity but differs in terms of face value, coupon rate, and purchase price. Assume the companies have similar credit ratings, are subject to the same market conditions, and are otherwise identical in terms of creditworthiness and risk factors. \n\nBased solely on the Yield to Maturity (YTM), determine which bond likely has the highest default probability and which likely has the lowest default probability. Explain your reasoning.\n\nBond A\n ◦ Issued by Company A\n ◦ Face Value: $1,000\n ◦ Coupon Rate: 10% (semi-annual payments)\n ◦ Purchase Price: $1,000\n ◦ Maturity: 2 years\nBond B\n ◦ Issued by Company B\n ◦ Face Value: $10,000\n ◦ Coupon Rate: 8% (annual payments)\n ◦ Purchase Price: $9,750\n ◦ Maturity: 2 years\nBond C\n ◦ Issued by Company C\n ◦ Face Value: $500\n ◦ Coupon Rate: 12% (annual payments)\n ◦ Purchase Price: $535\n ◦ Maturity: 2 years" ]

[ "While YTM is not a perfect measure of default probability, it is an important indicator of how investors view the risk of a bond. It is generally correlated with risk, meaning a higher YTM corresponds to a great perception of default probability.", "To approximate the YTM, we can use the following formula: YTM=[C+(FV-PV)/n]/[(FV+PV)/2])\n\nWhere:\nC = coupon payment\nFV = face value\nPV = purchase price\nn = number of periods\n\nDoing so, results in the following: \nBond A: 10.0%\nBond B: ~9.37%\nBond C: ~8.21%\n\nBond A likely has the highest default probability, as its higher YTM indicates that investors perceive greater risk. \n\nBond C likely has the lowest default probability, as its lower YTM implies that investors view it as less risky, even though it has the highest coupon rate." ]

[ "Bob is preparing to file his U.S. federal income taxes for the most recent tax year. He has done his research and is eager to maximize his refund. He plans to claim the standard deduction, as his itemized deductions would only total $3,000. He does not intend to claim any above-the-line deductions.\n\nBob's federal income tax liability, before applying any credits, is calculated to be $5,750. Throughout the year, he worked two jobs and had $5,100 in federal taxes withheld from his wages. With this in mind, Bob believes he will owe $650 in federal taxes before applying an tax credits.\n\nDuring the tax year, he purchased a new electric SUV that qualifies for an $8,500 offset tax credit, which Bob confirmed he's eligible for.\n\nAfter factoring in the tax credit for his new SUV, Bob recalculates his tax liability to be -$1,750. This means he will receive a refund of $7,850. Is Bob's calculation correct?", "What if, instead of an $8,500 non-refundable tax credit, Bob was eligible for a $7,500 fully refundable tax credit? Assuming everything else remains the same, what would his new refund amount be?" ]

[ "Bob's calculation is incorrect. He appears to be assuming that the $8,500 electric vehicle tax credit is fully refundable. However, the question specifies it as an \"offset tax credit,\" meaning it is non-refundable. A non-refundable tax credit can reduce Bob's tax liability to zero but cannot result in a negative liability.\n\nAfter applying the $8,500 credit, Bob's tax liability is reduced to $0. Since the credit cannot be refunded beyond eliminating the tax liability, Bob's refund will consist only of the $5,100 in federal taxes that were withheld during the year. Therefore, Bob's actual refund will be $5,100.", "If Bob now qualifies for a $7,500 fully refundable tax credit instead of the $8,500 non-refundable tax credit, we can calculate his new refund with the following information:\n\n*Initial tax liability: $5,750\n*Federal taxes withheld: $5,100\n*Refundable tax credit: $7,500\n\nBob's $5,750 tax liability will be offset by the $7,500 refundable tax credit:\n7,500 - 5,750 = 1,750\nThis leaves a refundable balance of $1,750.\n\nBob's refund will include the $5,100 withheld from his wages plus the remaining $1,750 refundable portion of the credit:\n5,100 + 1,750 = 6,850\n\nBob’s new refund amount will be 6,850." ]

[ "Sallie is completing her 2024 Form 1040 with a filing status of Single. Her taxable income for the year is $185,000. She paid $7,000 in mortgage interest, $1,800 in property taxes, $1,000 in sales taxes, and $5,300 in state income taxes. She has no other expenses eligible for itemized deductions. Considering the standard deduction for Single filers is $14,600, should Sallie itemize her deductions or take the standard deduction", "Now, imagine that Sallie is married but chooses to file separately from her spouse. Her husband has already filed his 1040 and decided to itemize his deductions. How does this impact Sallie's options?" ]

[ "First, we must determine the maximum amount of itemized deductions available to Sallie:\n • Mortgage Interest: $7,000\n • Property Taxes: $1,800\n • Sales Tax: $1,000\n • State Income Tax: $5,300\nWhile these items total $15,100, Sallie is not permitted to deduct all of these in the same year due to the state and local tax (SALT) deduction limitations.\nThe SALT deduction, capped at $10,000 under the Tax Cuts and Jobs Act (TCJA), allows Sallie to deduct either “state and local income taxes” or “state and local sales taxes,” but not both. Therefore, her options are:\n 1 Mortgage Interest + Property Taxes + Sales Tax
$7,000 + $1,800 + $1,000 = $9,800\n 2 Mortgage Interest + Property Taxes + State Income Tax
$7,000 + $1,800 + $5,300 = $14,100\nIn both scenarios, Sallie’s total itemized deductions are less than the standard deduction of $14,600 available to Single filers in 2024. As a result, Sallie would be better off claiming the standard deduction instead of itemizing.", "In this scenario, Sallie is no longer allowed to claim the standard deduction, even though it would have been more favorable. Filing separately from her husband has resulted in a disadvantage because 26 U.S. Code § 63(c)(6)(A) prohibits one spouse from claiming the standard deduction if the other spouse itemizes deductions." ]

[ "Suppose you're appraising a commercial property, and you've been informed that the appropriate cap rate falls somewhere between 6.5% and 7.25%. Which cap rate would result in a more conservative valuation, and why?", "Assume you are analyzing a commercial property with a reported Net Cash Flow (NCF) of $573,250 for the past year.\n\nYou believe this NCF includes one-time revenue streams that will not be relevant going forward, so you decide to apply a 7% haircut. Additionally, you've observed that similar properties in the area have been appraised using cap rates ranging from 6.5% to 7.25%. Using the adjusted NCF, apply the most conservative cap rate from this range to estimate the property's value." ]

[ "In commercial real estate, the cap rate (capitalization rate) is used to derive a property value based on the Net Cash Flow (NCF). The property value is calculated using the formula:\n\nProperty Value = NCF / Cap Rate\n\nA higher cap rate results in a lower property value. Therefore, the 7.25% cap rate would result in a more conservative (lower) valuation compared to the 6.5% cap rate.", "First, calculate the adjusted NCF:\n$573,250 * (1-0.07) = $533,122.5\n\nBased on the cap rate range of 6.5% to 7.25% provided above, 7.25% would result in the most conservative valuation. \n\nProperty value = Adjusted NCF / Cap Rate:\n\nProperty value = $533,122.5 / 7.25%\n\nProperty value = $7,353,413.79" ]

[ "The Dow Divisor is roughly 0.15173. Today, the share price of AAPL (which is part of the Dow 30) has increased by 5.00 per share. Meanwhile, the Dow is up 0.2%, increasing from 41,800 to 41,883.6. What percentage of the Dow's daily increase can be attributed to AAPL?", "What is the purpose of the Dow Divisor?" ]

[ "The Dow has increased by approximately 0.20%, which amounts to 83.60 (41,883.6 - 41,800). The stated divisor value of 0.15173 indicates that each $1.00 change in an underlying stock price corresponds to a 6.5906 change in the Dow (1.00 / 0.15173).\n\nThe 83.60 change in the Dow correlates to a cumulative change of 12.684 in the underlying stock prices of the index.\n\nIn other words, the $5.00 increase in Apple stock accounts for 39.4% of the Dow's daily gains (5 / 12.684).", "The Dow Divisor is crucial for calculating the Dow Jones Industrial Average, which tracks the stock prices of 30 major companies and serves as a measure of the overall performance of the U.S. stock market.\n\nThe Dow Divisor helps ensure that changes in the index's components—such as stock splits or the addition or removal of companies—do not distort the value of the DJIA. It keeps the index focused on actual price changes, minimizing the impact of other factors." ]

[ "L Brands is currently trading at $35.00 per share with 275 million shares outstanding. The company has announced a $1.5 billion share buyback. Assuming stable market conditions, how would investors likely interpret these buybacks?", "Assuming L Brands' quarterly net income and stock price remain constant at $35.00 during the buyback, calculate how the buyback will impact the company's quarterly EPS one year from now." ]

[ "The buyback will likely be viewed positively by investors, signaling that management believes its stock is undervalued and a good investment. By reducing the number of shares outstanding, the buyback will increase EPS and make shares more scarce. All else equal, these factors should push the stock price higher in the short term.", "At a stock price of $35 per share, the $1.5 billion buyback will repurchase approximately 42.857 million shares. As a result, the number of shares outstanding will decrease from 275 million to 232.14 million (275 million - 42.857 million). This represents a 15.59% reduction in shares outstanding (42.857 million / 275 million). \n\nOld EPS = Earnings/275,000,000\nNew EPS = Earnings/(275,000,000 - 42,857,000) = Earnings/232,143,000\n\nPercent Change in Earnings = (2750,000,000 / 232,143,000) - 1 = 0.1846\n\nAll else equal, the percent change in EPS will be roughly 18.46%" ]

[ "My company's debt cost of capital of 5% and an equity cost of capital of 8%. Let's say our debt-to-equity ratio is 0.7. What is our pre tax WACC?", "Now let's say the corporate tax rate is 40%. What is the impact of the interest rate tax shield on our WACC?" ]

[ "The WACC, or weight average cost of capital,\n\nWACC = (E / (E + D)) * r_e + (D / (E + D)) * r_d\n\nWhere:\nE = equity\nD = debt\nr_e = cost of equity\nr_d = cost of debt\n\nSInce the debt to equity ratio is 0.7, we know that:\nD / E = 0.7\nD = 0,7 E\nE = 1.428 D\n\nWhich means that:\n\nE / (E + D) = E / (E + 0.7 E) = 1 / 1.7 = 0.588\nD / (E + D) = 0.7 E / (E + 0.7 E) = 0.411\n\nFilling this in then gives us:\n\nWACC = 0.588 * 0.08 + 0.411 * 0.05 = 0.06759\n\nTherefore, our pre-tax WACC is approximately 6.759%.", "The interest rate tax shield reduces our tax burden which in turn reduces our WACC. The post tax WACC can be computed as,\n\nWACC = (E / (E + D)) * r_e + (D / (E + D)) * r_d * (1 - t) = pre-tax WACC - ((D / (E + D)) * r_d * t\n\nWhere t is the tax rate. \n\nPlugging in our values:\n((D / (E + D)) * r_d * t = 0.411 * 0.08 * 0.4 = 0.013152\n\nTherefore, accounting for tax will reduce the WACC by approximately 1.31% to 5.44%." ]

[ "What is the main difference between WACC-based valuation and APV valuation?", "My company is considering an acquisition of another company for $100 million. Our current best estimate is that this new company will generate cash flows of $1 million dollars per year, and this will grow indefinitely at a rate of 4% per year. Our cost of capital is 5% and the interest rate on the loan is 8%. \n\nTo afford this acquisition, we will fund 25% of the acquisition through debt. What is the APV? Assume the corporate tax rate is 50% and we will keep our debt-to-equity ratio constant." ]

[ "The main difference lies in how they try to account for the interest rate tax shield. The WACC method tries to roll this into its estimate for the required rate of return. APV instead tries to first compute the unlevered value and then directly incorporate the value of the interest rate tax shield.", "First, we need to compute the unlevered value of this company. Since it is going to generate a constantly growing stream of cash flows, we can use:\n\nPV = C / (g - r) = 1e6 / (5% - 4%) = $100,000,000\n\nThis means that the unlevered value of the acquisition is $100 million.\n\nWe can do the same calculation to estimate the value of the tax shield. SInce we are funding 25% of the $100 million in debt, that means that we have $25 million. In the first year, we will be required to pay 0.08 * 25 = $2 million dollars. Since the tax rate is 50% that means that we have a tax shield of 2 * 0.5 = $1 million in the first year. However, since we are keeping the debt-to-equity ratio constant, we need to value not only the $1 million dollars of tax shield that this acquisition will support, but the tax shield from all of the additional debt as well. Since this value is growing as a perpetuity, this will grow as a perpetuity as well. This means that its value is also:\n\nPV = C / (g - r) = 1e6 / (5% - 4%) = $100,000,000\n\nTherefore,\n\nAPV = Unlevered Present Value + Present Value of Interest Rate Tax Shield = 100 + 100 = $200 Million." ]

[ "ABC llc made $1,604,299 in profits in the year 2023; $224,000 in Australia, $248,389 in Canada, $128,763 in the United Kingdom, $524,682 in the United States and $478,465 in India.\nIt paid corporate tax of $22,400 in Australia, $62,097.25 in Canada, $51,505.20 in the United Kingdom, $178,391.88 in the United States and $112,439.28 in India. \n\nWhat is the effective tax rate of ABC in the year 2023?", "ABC llc has a reporting date of April 30, 2023. The company obtains tax relief of $2 million for research and development expenditure on a cash paid basis in Canada. The recognition of a material development asset during the year, in accordance with IAS 38, created a significant taxable temporary difference as of April 30, 2023.\n\nOn 6 June 2023, the Canadian government passed legislation to lower the company tax rate to 20% from 1 January 2024 onward.\n\nWhat will be the company's deferred tax liability for the year ended 30 April 2024?" ]

[ "To compute the effective tax rate, we can use the following formulas:\n\nTax Rate = Taxes Paid / Net Profits\nProfits Percentage = Net Profit / Total Profit\nProfit weighed share of the profits = Profits Percentage * Tax Rate\nEffective tax rate = Sum of the Profit weighed share of the profits in the individual countries\n\nWe can use these to fill out the following table:\n\n\n| | Australia | Canada | United Kingdom | United States | India | Total |\n|-------------------|-------------|---------------|----------------|---------------|-------------|---------------|\n| Net Profits | $224,000.00 | $248,389.00 | $128,763.00 | $524,682.00 | $478,465.00 | $1,604,299.00 |\n| Taxes Paid | $22,400.00 | $62,097.25 | $51,505.20 | $178,391.88 | $112,439.28 | |\n| Tax Rate | 10.00% | 25.00% | 40.00% | 34.00% | 23.50% | |\n| Profits Percentage | 13.96% | 15.48% | 8.03% | 32.70% | 29.82% | |\n| Profit weighed share of the profits | 1.40% | 3.87% | 3.21% | 11.12% | 7.01% | |\n\nEffective Tax Rate = 1.40% + 3.87% + 3.21% + 11.12% + 7.01% = 26.61% \n\nTherefore, the effective tax rate was 26.61%.", "Tax liability = 25% * $2 million = $0.5 million\n\nDeferred tax liabilities and assets should be measured using the tax rates expected to apply when the asset is realized. This tax rate must have been enacted or substantively enacted by the end of the reporting period. The government enacted the 20% tax rate after the period end. Therefore, it should not be used when calculating the deferred tax liability for the year ended 30 April 2023. The current 22% rate should be used instead.\n\nAs per IAS 10, changes in tax rates after the end of the reporting period are a non-adjusting event. However, if the change in the tax rate is deemed to be material, then AZ should disclose this rate change and an estimate of the financial impact.\n\nAccording to IAS 12, changes in tax rates and deferred tax liabilities are addressed as follows:\n- Measure deferred tax liabilities using the tax rate expected to apply when the liability is settled or reversed.\n- Adjust deferred tax liabilities for changes in tax rates.\n- Recognize the effect of tax rate changes in profit or loss, except to the extent it relates to items previously recognized outside profit or loss (e.g., goodwill or revaluation surplus).\n- Adjust the carrying amount of deferred tax liabilities when tax rates change, with no impact on the statement of financial position.\n- Consider the expected tax rate when the temporary difference is expected to reverse, rather than the current tax rate." ]

[ "Kyle is a fund manager who manages wealth for high-worth investors in Iowa. One of his private equity funds which he manages as a general partner has $500 million of committed capital. The limited partners included a hurdle rate of 10% in the initial contract along with a full catchup clause. Moreover, there is no management fee. The limited partners are going to get 80% and Kyle will only get carried interest of 20% above the preferred return of the investors. Furthermore, the fund has a deal-by-deal structure with a clawback provision and the fund distribution cannot take place before six years.\n\nIn the past 6 years from 2017 to 2023, Kyle has made 5 investments which have performed as follows:\n\n| Investment | Invested Amount | Year Invested | Year Sold | Sale Amount |\n|------------|------------------|----------------|------------|--------------|\n| 1 | $100 million | 2017 | 2020 | $120 million |\n| 2 | $150 million | 2019 | 2020 | $160 million |\n| 3 | $60 million | 2018 | 2022 | $88 million |\n| 4 | $90 million | 2019 | 2023 | $67 million |\n| 5 | $100 million | 2022 | 2023 | $90 million |\n\nHow much is kyle's total carried interest (performance fees) from 2017 to 2023?", "What is the annual geometric rate of return for the limited partners over this six year period (ignoring taxes or fees other than the performance fee)?" ]

[ "# Investment 1:\nInvestment: $100 million\nSold for: $120 million\nGain: $20 million\nGeometric Mean: ($120m - $100m) / $100m * 100 = 20%\n\nThe return is above the hurdle rate so the profit will be shared according to 80/20.\n\nShare of Limited Partners = 80% of $20 m = $16m\nShare of General partner (Kyle) = $20m - $16m = $4m\n\n\n# Investment 2:\nInvestment: $150 million\nSold for: $160 million\nGain: $10 million\nPercentage: ($160m - $150m) / $150m * 100 = 6.67%\n\nThe return is above the hurdle rate so the profit will be shared according to 80/20.\n\nShare of Limited Partners = 80% of $10 m = $8m\nShare of General partner (Kyle) = $10m - $8m = $2m\n\n\n# Investment 3:\nInvestment: $60 million\nSold for: $88 million\nGain: $22 million\nPercentage: ($88m - $60m) / $60m * 100 = 36.67%\n\nThe return is above the hurdle rate so the profit will be shared according to 80/20.\n\nShare of Limited Partners = 80% of $22 m = $17.6m\nShare of General partner (Kyle) = $22m - $17.6m = $4.4m\n\n\n# Investment 4:\nInvestment: $90 million\nSold for: $67 million\nLoss: $23 million\nPercentage: ($67m - $90m) / $90m * 100 = - 25.56%\n\nSince the return is negative, it fails to meet the hurdle rate requirement. Therefore, the clawback provision will get activated and the gains of the general partner (Kyle) will be reduced according to the 80/20 division rule. Since the fund cannot be distributed before six years, the accumulated carried interest of the general partner (Kyle) will have accumulated will get reduced.\n\nShare of Limited Partners = 80% of $(-25.56m) = -($20.45m)\nShare of General partner (Kyle) = 20% of $(-25.56m) = (-$5.11m)\n\n# Investment 5:\nInvestment: $100 million\nSold for: $90 million\nLoss: $10 million\nPercentage: ($90m - $100m) / $100m * 100 = (-10%)\n\nSince the return is negative, it fails to meet the hurdle rate requirement. Therefore, the clawback provision will get activated and the gains of the general partner (Kyle) will be reduced according to the 80/20 division rule. Since the fund cannot be distributed before six years, the accumulated carried interest of the general partner (Kyle) will have accumulated will get reduced.\n\nShare of Limited Partners = 80% of $(-10m) = (-$8m)\nShare of General partner (Kyle) = 20% of $(-10m) = (-$2m)\n\n\nTotal Carried Interest of the general partner\nInvestment 1: $4m\nInvestment 2: $2m\nInvestment 3: $4.4m\nInvestment 4: -$5.11m\nInvestment 5: -$2m\n\nTotal = $4m + $2m + $4.4m + (-$5.11m) + (-$2m) = $3.29m \n\nThe General Partner (Kyle) will have earned $3.29m in performance fees.", "We can compute the geometric rate of return here with:\n\nGRR = (Final Value / Initial Value)^{1/n} - 1\n\nThe investors all put in $500 million in capital. The total fund value was 120 + 160 + 88 + 67 + 90 = $525 million. From this we need to subtract Kyle's carried interest of $3.29 million to get $521.71 million. This would then mean the geometric mean of these returns would be:\n\nGRR = (521.71 / 500)^(1/6) - 1 = 0.71%\n\nThe geometric return of the investors was 0.71%. Nice job Kyle." ]

[ "Our company has leased a supercomputer for the next five years.\n\nWhat will be the two ways in which this transaction will show up on our income statement in the following years?", "The supercomputer has a fair value of $12,000,000. The lease payment is $2,400,000 per year (with the first payment due at the start of 2024). Our company's interest rate for a similar type of debt is 4.79%. The useful life of the supercomputer is 7 years; however, we only intend to use it till 2028. \n\nCalculate the total charge to our income statement in the year 2026 (assuming straight line depreciation)?" ]

[ "The impact on the income statement will come in two forms: \n1. The interest expense associated with the lease.\n2. The amortization of the lease asset itself.", "We can start by looking at the present value of the lease, starting right before the first payment in 2024.\n\nPV = 2,400,000 / (1 + 0.0479)^0 + 2,400,000 / (1 + 0.0479)^1 + 2,400,000 / (1 + 0.0479)^2 + 2,400,000 / (1 + 0.0479)^3 + 2,400,000 / (1 + 0.0479)^4 = $10,951,959.84 \n\n# Step 1: Interest Expense\n\nStarting carrying amount is = PV of lease payments - the payment made at the beginning = 10,951,959.84 - 2,400,000= $8,551,959.84\n\nInterest Expense = Carrying Amount * interest rate\n\nThe remaining amount of the payment reduces the carrying about for the following year. We can repeat this process to find the interest expense in 2026. \n\n| Year | Carrying amount | Interest expense | Payment (Lease payment) - at the end of the period | Principal repayment (Lease payment - Interest expense) | Ending Carrying amount (Opening carrying amount - principal repayment) |\n|-----------------------------|--------------|----------------|-----------|--------------------|--------------------|\n| 2024 | $8,551,959.84 | $409,638.88 | $0.00 | $0.00 | $8,551,959.84 |\n| 2025 | $8,551,959.84 | $409,638.88 | $2,400,000.00 | $1,990,361.12 | $6,561,598.72 |\n| 2026 | $6,561,598.72 | $314,300.58 | $2,400,000.00 | $2,085,699.42 | $4,475,899.30 |\n\n# Step 2: Amortization of the Lease Asset\n\nThe deferred tax asset is recorded at the present value of the lease payments in the first year, which we calculated as $10,951,959.84.\n\nWith straight line depreciation, we will amortize a constant amount of the asset over the five year lease term. This amount is the total initial carrying amount (the PV of the loan, $10,951,959.84) divided by the total number of years (5). So, $10,951,959.84 / 5 = $2,190,391.97 per year through 2029.\n\n# Step 3: Charge to the income statement in 2026\n\nThe amount charged to the income statement in the year 2026 will include:\n1. The interest expense in that year: $314,300.58\n2. The amortization of the lease asset recognized at the beginning: $2,190,391.97\n\nTherefore, the total charge = $314,300.58 + $2,190,391.97 = $2,504,692.55" ]

[ "| Asset Description | A Corp ($) | B Corp ($) |\n|------------------------------|--------------|--------------|\n| Servers and Data Centres | 48,050 | 64,867.5 |\n| Office Buildings | 48,704 | 65,750.4 |\n| Receivables | 18,368 | 24,796.8 |\n| Marketable Securities | 48,048 | 64,864.8 |\n| Furniture and Fixtures | 478,075 | 645,401.25 |\n| Vehicles | 48,204 | 65,075.4 |\n| Land | 45,820 | 61,857 |\n| Inventory | 47,868 | 64,621.8 |\n| Computer Hardware | 1,800,000 | 2,430,000 |\n| Networking Equipment | 45,806 | 61,838.1 |\n| Cash | 78,048 | 105,364.8 |\n| Prepaid Expenses | 5,580 | 7,533 |\n\nWhich of these are current v.s. non-current assets?", "A Corp had sales of $5,980,546 and B Corp had sales of $6,780,452, what are their fixed asset turnover ratios?" ]

[ "Let's divide these assets into current and noncurrent assets. \n\nCurrent: \nReceivables\nMarketable Securities\nInventory\nCash\nPrepaid Expenses\n\nNon-Current:\nServers and Data Centres\nOffice Buildings\nFurniture and Fixtures\nVehicles\nLand\nComputer Hardware\nNetworking Equipment", "To compute the fixed assets turnover, we need to compute the ratio of Sales to the total value of the fixed (non-current) assets.\n\n# A Corp\nNon-current Assets = 48,050 + 48,704 + 478,075 + 48,204 + 45,820 + 1,800,000 + 45,806 = $2,514,659\n\nFixed Assets Turnover (Revenue / Fixed Assets) = 5,980,546.00 / 2,514,659.00 = 2.38\n\n# B Corp\nNon-current Assets = $3,394,789.65\nFixed Assets Turnover (Revenue / Fixed Assets) = 6,780,452 / 3,394,789.65 = 2.0\n\n\nA Corp had a fixed asset turnover ratio of 2.38 and B Corp had a ratio of 2.0." ]

[ "Shortly after the reporting date, a major credit customer of Cheetah Inc. went into liquidation due to heavy trading losses. It is expected that little or none of the customer's $22,500 debt will be recoverable. $20,000 of the debt relates to sales made prior to the 2021 year-end, and $2,500 relates to sales made in the first two days of the 2022 financial year. In the 2021 financial statements, the whole debt has been written off. However, one of the directors suggests that the debt should not be written off but disclosed by note in Cheetah's 2021 financial statements, and the debt written off in the 2022 financial statements. \n\nFirst, which accounting standard would be applicable here?", "How much of the debt should be written off in the 2021 financial statements?" ]

[ "The relevant standard is IAS 10, which covers everts that occur between the financial period end and the date on which the financial statements are approved by the board of directors.", "In this case, $20,000 of the receivable existed at the reporting date and the liquidation of the major customer provides more information about that receivable. This is an adjusting event that would require the debt existing at the reporting date to be written off in the 2021 financial statements. \n\nTherefore, $20,000 should be written off in the 2021 financial statements. The remaining receivable did not exist at the reporting date and should therefore be written off in the 2022 financial statements." ]

[ "Mark & Co., a software company, enters into a contract with Chris Builders, a manufacturing company, to make a software that suits the daily operations and business needs of Chris Builders. The software project’s development cost is estimated to cost $5 million. The software is expected to generate cash flows in the future for the company. The company is keen to complete the project before the year end. Chris Builders paid half of the amount in advance to Mark & Co. for building the required software. Chris Builders plans to use the software for the next few years as it will help in automating the business operations. However, the team hired to build that software lacks the necessary skills and expertise level. They are not considering to hire additional team members from outside as it will be too much costly. \n\nHow would the cost of $5 million be treated in the accounts of Chris Builders?", "What will be the impact of this transaction on the balance sheet and income statement if the $5 million software development costs are expensed compared to if they are capitalized?" ]

[ "The cost of $5 million would be recorded as an expense in the company’s accounts. \n\nAs per IAS 38 Intangible Assets, the development cost can be capitalized only if the following six criteria points are met: \n• Probable economic benefits\n• Intention to complete the project\n• Resources available to complete the project\n• Ability to use or sell the item\n• Technically feasible\n• Expenses on the project can be identified. \n\nIn this case, all the criteria points are met except the point “technically feasible,” since the team hired for the building and development of software has limited expertise and skill set. \n\nDue to this, the overall development cost cannot be capitalized as an asset. Rather, it should be recognized as an expense.", "Since the transaction resulted in expense, the net income will be reduced. Moreover, the balance sheet will not be affected as the $5 million expense will not be capitalized. \n\nOn the other hand, if the software development costs were capitalized, the assets would increase in the balance sheet and an amortization expense would be charged to the income statement." ]