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FINE 342 * represents a more difficult problem. 1 Payout Policy/Capital Structure (15 pts) Consider a firm F that generates a single cash-flow in one year which depends on the state of the economy: -Boom (probability 1/2) 5m -Recession (probability 1/2) lm -F has 2,000 bonds outstanding with face value $1,000 and a 6% coupon, one year matu- rity. - There are no taxes, and the risk free rate is 3% -F has 1m cash at the beginning of year 1. -F's cost of debt is 4% regardless of the payout policy they choose. F can distribute at the beginning of year 1 either 70% of its cash or 30% of its cash. The cash retained by the firm is invested at the risk free rate. Stockholders invest the dividend they receive at the beginning of year 1 at the risk free rate as well. 1.1 (5 pts) Which of the two payout policies maximize stockholder payoffs at the end of year 1? 1.2 (5 pts) Anticipating that the firm will choose to payout 70% of its cash at the start of year 1, the market value of the firm's bonds is 1.5m, calculate the expected bankruptcy costs on the firm's assets. 1 FINE 342 1.3* (5 pts) Suppose instead that the market value of the bonds are 2m regardless of the payout policy chosen. The required return on the firm's assets is 10%, and the required return on equity if the firm had zero cash is 12%. Which of the two payout policies will the firm's shareholders optimally undertake and why? 2 Agency Costs (15 points) F generates a single cash-flow in one year. This cash-flow depends on the strategy chosen by the management: - The safe strategy yields a certain cash-flow of $3,500, - The risky strategy yields a high cash-flow of $15,000 with probability 0.2, and a low cash-flow of $625 with probability 0.8. F has 3 stocks outstanding and one bond with a $2,000 face value, a 5% annual coupon and a one-year maturity. All agents are risk neutral and the risk free rate is 5%. 2.1 (3pts) If the bond is non-convertible, which strategy does the management choose and why? 2 FINE 342 2.2 (7pts) If the bond is convertible with a conversion ratio of 4, which strategy does the management choose and why? In what cases do the bondholders convert in what cases do they not convert (they can see the cashflow before converting)? 2.3* (5pts) Suppose the bond has not been issued yet and that both projects cost 2,000. The firm wants to issue the same convertible bond as in 2.2 but must include one of the following covenants to the bond: -Covenant A: restricts the firm to only invest in the safe asset. -Covenant B: restricts the firm to only invest in the risky asset. Assuming the creditors pay market value for the bonds, which covenant will the firm include and why? 3 Agency Costs/Bank Regulation (15 pts) Suppose that you are a bank regulator who knows that there are two types of bank's under your jurisdiction, high quality (H) and low quality (L), who differ in their ability to screen loan applications for credit worthy borrowers. Using past data you estimate that roughly 70% of banks are high quality and 30% are low quality. High quality bank's generate a cashflow per loan of 100k with probability .8 and 0 with probability .2. A low quality bank on the other hand generates a cashflow per loan of 100k with probability .5 and 0 with probability .5. 3 FINE 342 These banks primarily make small loans to local businesses which creates a social benefit of 4% per dollar lent (i.e. if the bank lends $10 then the social benefit is 4%*$10). When a bank fails though, it generates a social cost of 15% per dollar of losses to the banks creditors (i.e. if creditors lose $10 then the social costs is 15%*$10). As a regulator you must choose a "capital requirement, dictating how much the banks can borrow to make loans, in order to maximize the expected social value. Each loan costs $50k and generates the returns described above. Additionally, the bank's start with $50k of their own money to invest. You, as the regulator, are debating whether to let the banks borrow money to issue 0, 1, or 2 additional loans. We assume the bank's find it optimal to issue as many loans as possible but can only raise additional funds by borrowing. This means banks will always make at least 1 loan with their initial $50k and will make an additional 0, 1, or 2 loans with borrowed money depending on how much the regulator allows them to borrow. All loans generate the same cash flow (e.g. if the H-type makes 3 loans then with prob .8 each loan generates a cashflow of 100k and with .2 each loan generates a cash flow of 0. Similarly, the L-type makes 3 loans then each loan generates a cash flow of 100k with prob .5 and each loan generates a cashflow of 0 with probability .5). 3.1 (9pts) Assume the regulator knows which banks are H-type and which are L-type. What is the expected social value (i.e. social benefit minus expected social cost) if the regulator allows the H-type bank to borrow 0, $50k, or $100k to make additional loans? What bout the L-type bank? How much will the regulator optimally allow the H-type and L-type bank's to borrow? (remember all bank always makes at least 1 loan, so they will either make 1, 2, or 3 loans depending on whether the regulator allows them to borrow 0, $50k, or $100k. Also note that the social cost only applies to borrowed money lost in default, not the bank's initial $50k, and the social benefit applies to money lent, not the realized cashflow). 4. FINE 342 3.2 (3pts) Suppose instead that the regulator cannot tell which bank is H-type and which is L-type. How much will the regulator optimally allow the bank's to borrow? What is the expected social value of this optimal policy? 3.3 (3pts) The regulator is deciding whether to invest in a stress testing technology that will allow them to distinguish H-type banks from L-type banks. How much would the regulator be willing to pay for this technology? 5 FINE 342 4 Excel Exercise (55 points) Excel Instructions: For this question I want all work to be clearly explained in the pdf solutions. Important components to include in the pdf are how the cash flows are derived and discounted for all adjustments, making it clear the discount rates you are using and the time period. Please be explicit: e.g. I want to see "I discount year X cashflows at a rate (1.10% 3" not "I discount year X cashflows at the rate of .7513". Further, I want you to copy and paste the excel cells with your actual calculations and reference that in the pdf document where you explain what you are doing. Failure to include this information in the pdf file and/or copy pasting results that are not identical to what I will find in the Excel file will result in a penalty.2 Excel Sheet Formatting Instructions: Please format the cells you will be using in Excel to include three decimal points and to use commas as 1000 separator (drag and highlight cells you will use, right click, choose Format CellsNumber, Fill in Decimal places: 3, and click the box "Use 1000 separator"). Webticks is a young private firm that provides a streaming service platform to which it charges an annual subscription fee of $15 per user. Data reveals an expected user base of 10m in 2019. Due to the lockdowns from the pandemic and general uncertainty, Webticks' user base is expected to drop by 15% for 2020. Yet, given the high demand for streaming (due to stay at home orders) Webticks is expected to be able to boost its market share during the pandemic resulting in an expected increase in users by 45% in 2021 (from the 2020 level). Analysts' best forecast predicts that, due to the ease of stay at home orders at the end of 2021, Webticks' users would decline in 2022 by 10% of the 2021 level and then continue growing at the pre-pandemic rate of 3% starting in 2023 (i.e. this growth rate does not apply to 2022). The annual operating cost per user of Webticks' operations depends on the number of users and the year and is summarized by the following table: # of Users 2019-2023 0-8,000,000 $16 per user >8,000,000 $8 per user 2024+ $8 per user $8 per user As can be seen, Webticks faces a higher cost per user in the final "start-up years of 1 You can screen shot a selected part of your screen by pressing and holding shift+command+4 on mac or shift+windows+s on windows and then drag the cursor to create a box around the part you want to screenshot and letting go of the cursor. You can then save this image and insert it into your word document (which you will convert to pdf after). 2If you choose not to type your exam you can leave out the copy paste of excel results. I strongly suggest that all students type the exam to avoid being penalized by the curve. 6 FINE 342 2019-2023, but only for the first 8m users. This represents the fixed cost of buying the content that Webticks streams. Starting in 2024 Webticks will own this content outright and therefore faces cost per user of $8 independent of the number of users. The net capital expenditure for this purchase of content has already been accounted for prior to 2019 i.e. we can ignore it) but the purchase is still being accounted for via D&A according to the straight line method at 2m per year with the last year being 2019. Additional Capex from 2019 onward is equal to additional D&A (i.e. not including the 2m D&A in 2019). Additionally, change in NWC is equal to zero as the business requires very little working capital. Webticks is all equity, the required return on Webticks' assets is 20%, and the corporate tax rate is 30%. 5.1 Scenario 1: (30pts) Give the most accurate possible valuation of Webtixs at the start of 2019 given the above forecasts using the APV method. 5.2 Scenario 2: (10pts) Suppose instead that at the start of 2019 you did not know about the coronavirus outbreak and its potential to disrupt markets. In that case, you simply assumed the company will have 10m users in 2019 and that they are growing at the pre-pandemic rate of 3% after 2019 (all other data is the same). Compare the valuation under this scenario to that of Scenario 1. 5.3 Scenario 3 (hard, 15pts) Suppose that the user base for Webtixs is the same as in Scenario 2 but that Webtixs has 25m outstanding debt at the start of 2019 with an interest rate of 5%, linearly amortized over the next 5 years. In order to understand the required return on Webtixs equity you use data from Netflix from 2016-2019 when it was in a com- parable growth phase (see the attached excel file). Assume Netflix had the same leverage over this sample period as Webtixs starts with in 2019. The annual risk free rate in 2019 is expected to be 2.8% and the annual market return is expected to be 15.3%. Finally, we as- sume that the cost of debt for Webtixs remains constant at 4% over the lifetime of the loan. Give the most accurate possible valuation of Webtixs using the FTE method. You cannot use any estimates for the value of equity when using this approach but you can use ap- propriate estimates for leverage (hint: you will need this to correctly proceed). Was your estimate of leverage accurate? (note that this exercise is labeled hard for a reason and that you MUST use the FTE approach, without using any of the prior calculations of value. You can of course use the same initial calculations as in Scenario 2 so you don't have to repeat the same work. Also note that not all of the exercise is hard so there is potential for partial credit.). 3E.g. if Webticks has 10m users in 2022 then its total operating cost is 8m * 16+ 2m +8, while if it has 10m users in 2024 then its total operating costs is 10m * 8. 7 FINE 342 * represents a more difficult problem. 1 Payout Policy/Capital Structure (15 pts) Consider a firm F that generates a single cash-flow in one year which depends on the state of the economy: -Boom (probability 1/2) 5m -Recession (probability 1/2) lm -F has 2,000 bonds outstanding with face value $1,000 and a 6% coupon, one year matu- rity. - There are no taxes, and the risk free rate is 3% -F has 1m cash at the beginning of year 1. -F's cost of debt is 4% regardless of the payout policy they choose. F can distribute at the beginning of year 1 either 70% of its cash or 30% of its cash. The cash retained by the firm is invested at the risk free rate. Stockholders invest the dividend they receive at the beginning of year 1 at the risk free rate as well. 1.1 (5 pts) Which of the two payout policies maximize stockholder payoffs at the end of year 1? 1.2 (5 pts) Anticipating that the firm will choose to payout 70% of its cash at the start of year 1, the market value of the firm's bonds is 1.5m, calculate the expected bankruptcy costs on the firm's assets. 1 FINE 342 1.3* (5 pts) Suppose instead that the market value of the bonds are 2m regardless of the payout policy chosen. The required return on the firm's assets is 10%, and the required return on equity if the firm had zero cash is 12%. Which of the two payout policies will the firm's shareholders optimally undertake and why? 2 Agency Costs (15 points) F generates a single cash-flow in one year. This cash-flow depends on the strategy chosen by the management: - The safe strategy yields a certain cash-flow of $3,500, - The risky strategy yields a high cash-flow of $15,000 with probability 0.2, and a low cash-flow of $625 with probability 0.8. F has 3 stocks outstanding and one bond with a $2,000 face value, a 5% annual coupon and a one-year maturity. All agents are risk neutral and the risk free rate is 5%. 2.1 (3pts) If the bond is non-convertible, which strategy does the management choose and why? 2 FINE 342 2.2 (7pts) If the bond is convertible with a conversion ratio of 4, which strategy does the management choose and why? In what cases do the bondholders convert in what cases do they not convert (they can see the cashflow before converting)? 2.3* (5pts) Suppose the bond has not been issued yet and that both projects cost 2,000. The firm wants to issue the same convertible bond as in 2.2 but must include one of the following covenants to the bond: -Covenant A: restricts the firm to only invest in the safe asset. -Covenant B: restricts the firm to only invest in the risky asset. Assuming the creditors pay market value for the bonds, which covenant will the firm include and why? 3 Agency Costs/Bank Regulation (15 pts) Suppose that you are a bank regulator who knows that there are two types of bank's under your jurisdiction, high quality (H) and low quality (L), who differ in their ability to screen loan applications for credit worthy borrowers. Using past data you estimate that roughly 70% of banks are high quality and 30% are low quality. High quality bank's generate a cashflow per loan of 100k with probability .8 and 0 with probability .2. A low quality bank on the other hand generates a cashflow per loan of 100k with probability .5 and 0 with probability .5. 3 FINE 342 These banks primarily make small loans to local businesses which creates a social benefit of 4% per dollar lent (i.e. if the bank lends $10 then the social benefit is 4%*$10). When a bank fails though, it generates a social cost of 15% per dollar of losses to the banks creditors (i.e. if creditors lose $10 then the social costs is 15%*$10). As a regulator you must choose a "capital requirement, dictating how much the banks can borrow to make loans, in order to maximize the expected social value. Each loan costs $50k and generates the returns described above. Additionally, the bank's start with $50k of their own money to invest. You, as the regulator, are debating whether to let the banks borrow money to issue 0, 1, or 2 additional loans. We assume the bank's find it optimal to issue as many loans as possible but can only raise additional funds by borrowing. This means banks will always make at least 1 loan with their initial $50k and will make an additional 0, 1, or 2 loans with borrowed money depending on how much the regulator allows them to borrow. All loans generate the same cash flow (e.g. if the H-type makes 3 loans then with prob .8 each loan generates a cashflow of 100k and with .2 each loan generates a cash flow of 0. Similarly, the L-type makes 3 loans then each loan generates a cash flow of 100k with prob .5 and each loan generates a cashflow of 0 with probability .5). 3.1 (9pts) Assume the regulator knows which banks are H-type and which are L-type. What is the expected social value (i.e. social benefit minus expected social cost) if the regulator allows the H-type bank to borrow 0, $50k, or $100k to make additional loans? What bout the L-type bank? How much will the regulator optimally allow the H-type and L-type bank's to borrow? (remember all bank always makes at least 1 loan, so they will either make 1, 2, or 3 loans depending on whether the regulator allows them to borrow 0, $50k, or $100k. Also note that the social cost only applies to borrowed money lost in default, not the bank's initial $50k, and the social benefit applies to money lent, not the realized cashflow). 4. FINE 342 3.2 (3pts) Suppose instead that the regulator cannot tell which bank is H-type and which is L-type. How much will the regulator optimally allow the bank's to borrow? What is the expected social value of this optimal policy? 3.3 (3pts) The regulator is deciding whether to invest in a stress testing technology that will allow them to distinguish H-type banks from L-type banks. How much would the regulator be willing to pay for this technology? 5 FINE 342 4 Excel Exercise (55 points) Excel Instructions: For this question I want all work to be clearly explained in the pdf solutions. Important components to include in the pdf are how the cash flows are derived and discounted for all adjustments, making it clear the discount rates you are using and the time period. Please be explicit: e.g. I want to see "I discount year X cashflows at a rate (1.10% 3" not "I discount year X cashflows at the rate of .7513". Further, I want you to copy and paste the excel cells with your actual calculations and reference that in the pdf document where you explain what you are doing. Failure to include this information in the pdf file and/or copy pasting results that are not identical to what I will find in the Excel file will result in a penalty.2 Excel Sheet Formatting Instructions: Please format the cells you will be using in Excel to include three decimal points and to use commas as 1000 separator (drag and highlight cells you will use, right click, choose Format CellsNumber, Fill in Decimal places: 3, and click the box "Use 1000 separator"). Webticks is a young private firm that provides a streaming service platform to which it charges an annual subscription fee of $15 per user. Data reveals an expected user base of 10m in 2019. Due to the lockdowns from the pandemic and general uncertainty, Webticks' user base is expected to drop by 15% for 2020. Yet, given the high demand for streaming (due to stay at home orders) Webticks is expected to be able to boost its market share during the pandemic resulting in an expected increase in users by 45% in 2021 (from the 2020 level). Analysts' best forecast predicts that, due to the ease of stay at home orders at the end of 2021, Webticks' users would decline in 2022 by 10% of the 2021 level and then continue growing at the pre-pandemic rate of 3% starting in 2023 (i.e. this growth rate does not apply to 2022). The annual operating cost per user of Webticks' operations depends on the number of users and the year and is summarized by the following table: # of Users 2019-2023 0-8,000,000 $16 per user >8,000,000 $8 per user 2024+ $8 per user $8 per user As can be seen, Webticks faces a higher cost per user in the final "start-up years of 1 You can screen shot a selected part of your screen by pressing and holding shift+command+4 on mac or shift+windows+s on windows and then drag the cursor to create a box around the part you want to screenshot and letting go of the cursor. You can then save this image and insert it into your word document (which you will convert to pdf after). 2If you choose not to type your exam you can leave out the copy paste of excel results. I strongly suggest that all students type the exam to avoid being penalized by the curve. 6 FINE 342 2019-2023, but only for the first 8m users. This represents the fixed cost of buying the content that Webticks streams. Starting in 2024 Webticks will own this content outright and therefore faces cost per user of $8 independent of the number of users. The net capital expenditure for this purchase of content has already been accounted for prior to 2019 i.e. we can ignore it) but the purchase is still being accounted for via D&A according to the straight line method at 2m per year with the last year being 2019. Additional Capex from 2019 onward is equal to additional D&A (i.e. not including the 2m D&A in 2019). Additionally, change in NWC is equal to zero as the business requires very little working capital. Webticks is all equity, the required return on Webticks' assets is 20%, and the corporate tax rate is 30%. 5.1 Scenario 1: (30pts) Give the most accurate possible valuation of Webtixs at the start of 2019 given the above forecasts using the APV method. 5.2 Scenario 2: (10pts) Suppose instead that at the start of 2019 you did not know about the coronavirus outbreak and its potential to disrupt markets. In that case, you simply assumed the company will have 10m users in 2019 and that they are growing at the pre-pandemic rate of 3% after 2019 (all other data is the same). Compare the valuation under this scenario to that of Scenario 1. 5.3 Scenario 3 (hard, 15pts) Suppose that the user base for Webtixs is the same as in Scenario 2 but that Webtixs has 25m outstanding debt at the start of 2019 with an interest rate of 5%, linearly amortized over the next 5 years. In order to understand the required return on Webtixs equity you use data from Netflix from 2016-2019 when it was in a com- parable growth phase (see the attached excel file). Assume Netflix had the same leverage over this sample period as Webtixs starts with in 2019. The annual risk free rate in 2019 is expected to be 2.8% and the annual market return is expected to be 15.3%. Finally, we as- sume that the cost of debt for Webtixs remains constant at 4% over the lifetime of the loan. Give the most accurate possible valuation of Webtixs using the FTE method. You cannot use any estimates for the value of equity when using this approach but you can use ap- propriate estimates for leverage (hint: you will need this to correctly proceed). Was your estimate of leverage accurate? (note that this exercise is labeled hard for a reason and that you MUST use the FTE approach, without using any of the prior calculations of value. You can of course use the same initial calculations as in Scenario 2 so you don't have to repeat the same work. Also note that not all of the exercise is hard so there is potential for partial credit.). 3E.g. if Webticks has 10m users in 2022 then its total operating cost is 8m * 16+ 2m +8, while if it has 10m users in 2024 then its total operating costs is 10m * 8. 7

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