Practice Final A (Fall 2023, do yellow questions only, updated)

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Dr. Patrick Convery Econ 106F Corporate Finance Department of Economics, UCLA Spring, 2016 Final Exam June 10, 2016 First Name Last Name UCLA ID # Do not start the exam until instructed to do so.

Problem # Max Score Your Score Mult Choice #1-15 150 16 5 17 15 18 10 19 10 20 10 21 15 22 10 23 10 24 15 25 15

Problem # Max Score Your Score 26 15 27 20 28 15 29 20 30 10 31 15 32 15 33 10 34 15 Total 400

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You may find this table useful for doing some of your calculations more quickly. X (1 + x)^1 (1 + x)^2 (1 + x)^3 (1 + x)^4 (1 + x)^5 (1 + x)^6 1.0% 1.0100 1.0201 1.0303 1.0406 1.0510 1.0615 1.5% 1.0150 1.0302 1.0457 1.0614 1.0773 1.0934 2.0% 1.0200 1.0404 1.0612 1.0824 1.1041 1.1262 2.5% 1.0250 1.0506 1.0769 1.1038 1.1314 1.1597 3.0% 1.0300 1.0609 1.0927 1.1255 1.1593 1.1941 3.5% 1.0350 1.0712 1.1087 1.1475 1.1877 1.2293 4.0% 1.0400 1.0816 1.1249 1.1699 1.2167 1.2653 4.5% 1.0450 1.0920 1.1412 1.1925 1.2462 1.3023 5.0% 1.0500 1.1025 1.1576 1.2155 1.2763 1.3401 5.5% 1.0550 1.1130 1.1742 1.2388 1.3070 1.3788 6.0% 1.0600 1.1236 1.1910 1.2625 1.3382 1.4185 6.5% 1.0650 1.1342 1.2079 1.2865 1.3701 1.4591 7.0% 1.0700 1.1449 1.2250 1.3108 1.4026 1.5007 7.5% 1.0750 1.1556 1.2423 1.3355 1.4356 1.5433 8.0% 1.0800 1.1664 1.2597 1.3605 1.4693 1.5869 8.5% 1.0850 1.1772 1.2773 1.3859 1.5037 1.6315 9.0% 1.0900 1.1881 1.2950 1.4116 1.5386 1.6771 9.5% 1.0950 1.1990 1.3129 1.4377 1.5742 1.7238 10.0% 1.1000 1.2100 1.3310 1.4641 1.6105 1.7716

Multiple choice Question 1 (10 points) Which of the following costs would you consider when making a capital budgeting decision? A) Sunk cost B) Opportunity cost C) Interest expense D) Fixed overhead cost Answer: B Question 2 (10 points) In mid-2012, Cisco Systems had a market capitalization of $101 billion. It had A- rated debt of $16 billion as well as cash and short-term investments of $48 billion, and its estimated equity beta at the time was 1.23. Assuming Cisco’s debt has a beta of zero, the beta of Cisco’s underlying business enterprise is closest too: a) 1.2 b) 1.8 c) 0.2 d) 2.1 Answer: First calculate the Enterprise Value = EV = E + D – C = 101 + 16 – 48 = $69 bil- lion Then calculate the Net Debt = 16 – 48 = –32 Now calculate the asset beta (i.e. unlevered beta) beta_u = (101/69) × 1.23 + (–32/69) × 0 = 1.80

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Question 3 (10 points) Suppose Autodesk stock has a beta of 2.16, whereas Costco stock has a beta of 0.69. If the risk-free interest rate is 4% and the expected return of the market port- folio is 10%, what is the expected return of a portfolio that consists of 60% Auto- desk stock and 40% Costco stock, according to the CAPM? (a) 17.8% (b) 15.3% (c) 13.4% (d) not enough information to determine the answer Answer: C beta = (0.6)(2.16) + (0.4)(0.69) = 1.572 and E[R] = 4 + (1.572)(10 - 4) = 13.432%

Question 4 (10 points) Use the information for the question(s) below. Consider a project with free cash flows in one year of $90,000 in a weak economy or $117,000 in a strong economy, with each outcome being equally likely. The ini- tial investment required for the project is $80,000, and the project's cost of capital is 15%. The risk-free interest rate is 5%. 24) Suppose that you borrow $30,000 in financing the project. According to MM proposition II, the firm's equity cost of capital will be closest to: A) 21% B) 15% C) 20% D) 25% Answer: C PV (equity cash flows - unlevered) = (0.5)($90,000 + (0.5)($117,000)/1.15 = $90,000 Given r E = r U + (D/E) (r U - r D ) r E = .15 + 30,000/(90,000 - 30,000) (.15 - .05) = .20 or 20%

Question 5 (10 points) Suppose that Merck (MRK) stock is trading for $36.70 per share with 2.11 billion shares outstanding while Boeing (BA) has 697.5 million shares outstanding and a market capitalization of $38.223 billion. Assume you hold the market portfolio. If you hold 1,000 shares of Merck, then the number of shares of Boeing that you hold is closest to: A) 240 shares B) 330 shares C) 510 shares D) 780 shares Answer: B Shares of Boeing = {(amount of MRK)/Price BA)} * {(Capitalization of BA)/(Capitalization of MRK)} = {($36.70*1000) / (38,223/697.5) }*{ $38,223/($36.70*2110) } = 330.57 shares

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Question 6 (10 points) Which of the following statements is FALSE? A) The levered equity return equals the unlevered return, plus an extra term due to leverage. B) By holding a portfolio of the firm’s equity and its debt, we can replicate the cash flows from holding its levered equity. C) The cost of capital of levered equity is equal to the cost of capital of unlevered equity plus a premium that is proportional to the market value debt-equity ratio. D) If a firm is unlevered, all of the free cash flows generated by its assets are avail- able to be paid out to its equity holders. Answer: B Explanation: B) By holding a portfolio of the firm's equity and its debt, we can replicate the cash flows from holding its unlevered equity. Question 7 (10 points) Which of the following statements is FALSE? A) With no debt, the WACC is equal to the unlevered equity cost of capital. B) With perfect capital markets, a firm's WACC is dependent of its capital struc- ture and is equal to its equity cost of capital only if the firm it is unlevered. C) As the firm borrows at the low cost of capital for debt, its equity cost of capital rises, but the net effect is that the firm's WACC is unchanged. D) Although debt has a lower cost of capital than equity, leverage does not lower a firm's WACC. Answer: B. With perfect capital markets, a firm's WACC is independent of its capital structure and is equal to its equity cost of capital only if the firm it is un-

levered.

Question 8 (10 points) Suppose Johnson & Johnson and the Walgreen Company have expected returns and volatilities shown below, with a correlation of 22%. If the correlation between Johnson & Johnson’s and Walgreen’s stock were to in- crease… how would the expected return of the portfolio change? And how would the volatility of the portfolio change? a) Rise, Rise b) No change, Fall c) Fall, No change d) None of the above Answer: (d) The answer is: No change, Rise The expected return would remain constant, assuming only the correlation changes, 0.5*0.07 + 0.5*0.10 = 0.085. The volatility of the portfolio would increase (due to the correlation term in the equation for the volatility of a portfolio).

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Question 9 (10 points) Kramerica Industries has no debt, total equity capitalization of $600 million, and an equity beta of 1.2. Included in Kramerica’s assets is $90 million in cash and risk-free securities. Assume the risk-free rate is 4% and the market risk premium is 6%. There are no taxes. Kramerica’s WACC is closest to: A) 10.6% B) 11.2% C) 11.8% D) 12.5% Answer: D β U = β U = [ E / (E + D - C) ] β E + [ (D-C) / (E + D - C) ] β D = [600 / (600-90)] × 1.2 + [-90 / (600-90)] × 0 = 1.411765 r wacc = r f + β u (r m - r f ) = 4% + 1.411765(6%) = 12.47%

Question 10 (10 points) Use the following information to answer the question below. Rating AAA AA A BBB BB B CCC Average Default Rate 0.0% 0.1% 0.2% 0.45% 2.2% 5.5% 12.2% Recession Default Rate 0.0% 1.0% 3.0% 3.0% 8.0% 16.0% 48.0% Average Beta 0.05 0.05 0.05 0.10 0.17 0.26 0.31 Company Market Capitaliza- tion ($mm) Total Enterprise Value ($mm) Equity Beta Debt Rating Taggart Transcontinental $4,500 8,000 1.1 BBB Rearden Metal $3,800 7,200 1.3 AAA Wyatt Oil $2,400 3,800 0.9 A Nielson Motors $1,500 4,400 1.75 BB Your estimate of the asset beta for Rearden Metal is closest to: A) 0.42 B) 0.59 C) 0.66 D) 0.71

Answer: D Because Rearden has a rating of AAA, the appropriate debt beta from the table is 0.05. β U = (E/V)* β E + (E/V)* β D = (3,800/7,200) × 1.3 + ((7,200 - 3,800)/7,200) × 0.05 = 0.709722 Question 11 (10 points) Annabelle Corporation paid dividends per share of $1.50 in 2014, and dividends are expected to grow at a rate (g) per year forever. The stock has a cost of equity of 7.0%. The stock is trading for $92 per share. What would the growth rate (g) in dividends have to be to justify this price? a) 3.8% b) 5.3% c) 6.9% d) Not enough information Answer: (b) The Price per share = $92 = div*(1 + g) / (r – g) = 1.50*(1 + g) / (0.07 – g) Thus, solve this for “g”: 1.50*(1 + g) / (0.070 – g) = $92 g = 92*(0.07 – 1.5) / (92 + 1.5) = 5.3%

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Question 12 (10 points) You expect that Luxor Enterprises will have earnings per share of $2 for the com- ing year. Luxor plans to retain all of its earnings for the next three years. For the subsequent two years, the firm plans on retaining 50% of its earnings. It will then retain only 25% of its earnings from that point forward. Retained earnings will be invested in projects with an expected return of 20% per year. If Luxor’s equity cost of capital is 8%, then the price of a share of Luxor’s stock is closest to: A) $97.25 B) $62.50 C) $108.00 D) $73.75 Answer: (C) Year Earn- ings Divi- dends g 1 $2.00 $0.00 20% 2 $2.40 $0.00 20% 3 $2.88 $0.00 20% 4 $3.46 $1.73 10% 5 $3.80 $1.90 10% 6 $4.18 $3.14 5% P 0 = 1.73/(1.08^4) + 1.90/(1.08^5) + (3.14/(0.08-0.05))*1/(1.08^5) = $73.8 Each g is calculated as the 20% return on the projects × the retention ratio.

Question 13 (10 points) Which of the following statements about correlation and covariance are incorrect? (1) correlation ranges between -1 and +1 (2) a drop in the correlation between the two stocks in a portfolio reduces the ex- pected return on the portfolio (3) covariance ranges between -1 and + 1 (4) correlation ranges between negative infinity and positive infinity (5) if you know the standard deviations of two stocks and the covariance between them, you can calculate correlation (6) if you know the standard deviation of two stocks and the correlation between them, you can calculate covariance (7) covariance ranges between negative infinity and positive infinity (8) a drop in the correlation between two stocks in a portfolio increases the ex- pected return on the portfolio Answer: a. 1, 2, 3, 4 b. 2, 3, 4, 6 c. 1, 3, 4, 5 d. 2, 3, 4, 8 e. 1, 2, 4, 6

Question 14 (10 points) In practice the _______ market index is most widely used as a proxy for the market portfolio in the CAPM. The ________ market index would be the best to use in practice as a proxy for the market portfolio in the CAPM. (pick the best pair) A) Dow Jones Industrial Average, S&P500 B) S&P 500, S&P 500 C) Wilshire 5000, U.S. Treasury Bill D) S&P 500, Wilshire 5000 E) S&P 500, U.S. Treasury Bill Answer: D

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Question 15 (10 points) Consider the following information regarding corporate bonds: Rating AAA AA A BBB BB B CCC Average Default Rate 0.0% 0.1% 0.2% 0.5% 2.2% 5.5% 12.2% Recession Default Rate 0.0% 1.0% 3.0% 3.0% 8.0% 16.0% 48.0% Average Beta 0.05 0.05 0.05 0.10 0.17 0.26 0.31 Trucks R' Us has a market capitalization of $142 billion, $78 billion in BB rated debt, and $10 billion in cash. If Trucks R' Us' equity beta is 1.68, then their under- lying asset beta is closest to: A) 1.00 B) 1.20 C) 1.32 D) 1.48 Answer: B Explanation: B) We can think of Trucks R' Us business assets as a portfolio of eq- uity, plus debt, and less cash. Assuming the beta of cash investments is zero: β U = β E + β D + β C

= × 1.68 + × 0.17 - × 0.0 = 1.199 Alternatively, we estimate asset beta based on its net debt of 78-10=68 m. Using net debt: β U = β E + β D

= × 1.15 + × 0.17 = 1.191 Note that both answers are quite similar. The second approach presumes that TRU's cash reduces the average market risk of its debt (as thought TRU used its cash to repay its senior debt).

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Short Answer Show all your work. Question 16 (5 points) Consider the following two, completely separate, economies. The expected return and volatility of all stocks in both economies is the same. In the first economy, all stocks move together—in good times all prices rise to- gether and in bad times they all fall together. In the second economy, stock returns are independent—one stock increasing in price has no effect on the prices of other stocks. Assuming you are risk-averse and you could choose one of the two economies in which to invest, which one would you choose? For full credit, you must explain your answer. (2-3 sentences should be enough). Answer: Choose the second economy. A risk-averse investor would choose the economy in which stock returns are independent because this risk can be diversified away in a large portfolio, thus leaving them with no risk as at.

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Question 17 (15 points) SA General Electric (GE) expects to pay a dividend of $4.00 per share next year (one year from today), and will grow at 8% for the next 4 years after that (dividends are paid at the end of each year). At that time, the growth rate becomes 2%. Use a discount rate of 7.0%. What is the value of one share of GE stock today? Answer: This is just like what we did in lab #2 to estimate the price of General Electric (GE) stock when using the dividend discount model. There are two phase to calculate, first the period of 7% growth for four years, then the period of 2% growth thereafter. PV1 = $4.00*[ 1/1.07 + (1.08)/(1.07^2) + (1.08^2)/(1.07^3) + (1.08^3)/(1.07^4)] = $15.16 PV2 (at start of phase 2) = use equation 9.13 PV2 (at start of phase 2) = [$4.00*(1.08^4)] * [(1 + 0.02)/(0.07 - 0.02)] = $111.02, and note that this is the PV at the beginning of phase 2. We need to discount that back to the present time. Thus PV2 (at present time) = 111.02 / (1.07^5) = 79.16 Thus, Present Value of Walmart stock = 15.16 + 79.16 = $94.32

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Question 18 (10 points) You have just started your summer internship, and your boss asks you to review a recent analysis that was done to compare three alternative proposals to enhance the firm’s manufacturing facility. You find that the prior analysis ranked the proposals according to their IRR, and recommended the highest IRR option, Proposal A. You are concerned and decide to redo the analysis using NPV to determine whether this recommendation was ap- propriate. But while you are confident the IRRs were computed correctly, it seems that some of the underlying data regarding the cash flows that were estimated for each proposal was not included in the report. For Proposal B, you cannot find information regarding the total initial investment that was required in year 0. And for Proposal C, you cannot find the data regarding additional salvage value that will be recovered in year 3. Here is the information you have: a) Suppose the appropriate cost of capital for each alternative is 10%. Using this information, determine the NPV of each project. Which project should the firm choose? b) Why is ranking the projects by their IRR not valid in this situation? Answer: a. (6 points) Project A: Project B: We can use the IRR to determine the initial cash flow: Thus, Project C: We can use the IRR to determine the final cash flow: Thus,

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b. (4 points) Ranking the projects by their IRR is not valid in this situation because the projects have different scales and different patterns of cash flows over time. Question 19 (10 points) Debt is always cheaper than equity. Therefore, the optimal debt ratio is all debt. Is this true or false? Explain your answer Answer: This is False. While debt is always cheaper than equity, taking on more debt will make you a riskier firm. This will then push up the costs of both debt and equity. This negative effect could offset the positive effect of replacing more expensive equity with less expensive debt. Question 20 (10 points) A firm that has no debt has a market value of $100 million and a cost of equity of 11%. In the Modigliani-Miller (MM) world, a) What happens to the value of the firm as leverage is changed? (Assume no taxes) b) What happens to the cost of capital as leverage is changed? (Assume no tax- es) c) How would your answers to (a) and (b) change if there are taxes? Answer: a) In the MM world with no taxes, the value of the firm will be $100M no matter what the debt ratio. b) The cost of capital will always be 11%. With taxes, the value of the firm will increase as the debt is increased (because of the tax benefits of debt) and the cost of capital will go down (due to the interest tax savings)

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Question 21 (15 points) Benchmark Metrics, Inc. (BMI), an all-equity financed firm, just reported EPS of $5.00 per share for 2008. Despite the economic downturn, BMI is confident re- garding its current investment opportunities. But due to the financial crisis, BMI does not wish to fund these investments externally. The Board therefore decides to suspend its stock repurchase plan and cut its dividend to $1 per share (vs. almost $2 per share in 2007), and retain these funds instead. The firm has just paid this 2008 dividend, and BMI plans to keep its dividend at $1 per share in 2009 as well. In subsequent years, it expects its growth opportunities to slow, and it will still be able to fund its growth internally with a target 40% dividend payout ratio, and rei- nitiating its stock repurchase plan for a total payout rate of 60%. (All dividends and repurchases occur at the end of each year.) Suppose BMI’s existing operations will continue to generate the current level of earnings per share in the future. Assume further that the return on new investment is 15%, and that reinvestments will account for all future earnings growth (if any). Finally, assume BMI’s equity cost of capital is 10%. a) Estimate BMI’s EPS in 2009 and 2010 (before any share repurchases). b) What is the value of one share of BMI stock at the start of 2009? Answer: a) (5 points) To calculate earnings growth, we can use the formula: g = (retention rate) × (re- turn on new investment). In 2008, BMI retains $4 of its $5 in EPS, for a retention rate of 80%, and an earnings growth rate of 80% × 15% = 12%. Thus, EPS2009 = $5.00 × (1.12) = $5.60. In 2009, BMI retains $4.60 of its $5.60 in EPS (because it only pays $1.00 in dividends in 2009), for a retention rate of 82.14% and an earnings growth rate of 82.14% × 15% = 12.32%. So, EPS2010 = $5.60 × (1.1232) = $6.29. b) (10 points) From 2010 on, the firm plans to retain 40% of EPS, for a growth rate of 40% × 15% = 6%. We are told total Payouts in 2010 are 60% of EPS, or 60% × $6.29 = $3.774. Thus, the value of the stock at the end of 2009 is, given the 6% future growth rate, P2009 = $3.77/(10% – 6%) = $94.35.

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Given the $1 dividend in 2009, we get a share price in 2008 of P2008 = ($1 + 94.35)/1.10 = $86.68. Question 22 (10 points) Bauer Industries is an automobile manufacturer. Management is currently evaluat- ing a proposal to build a plant that will manufacture lightweight trucks. Bauer plans to use a cost of capital of 8.0% to evaluate this project. Based on extensive research, it has prepared the following incremental free cash flow projections (in millions of dollars): What is the NPV of the plant to manufacture lightweight trucks? Answer: Note that FCF for years 1-10 can be thought of as an annuity. The NPV of the es- timated FCF is therefore: NPV = -150 + (35/0.08)*[1 – (1/1.08)^5)] + 48/(1.08^6) = $20M

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Question 23 (10 points) Orchid Biotech Company is evaluating several development projects for experi- mental drugs. Although the cash flows are difficult to forecast, the company has come up with the following estimates of the initial capital requirements and NPVs for the projects. Given a wide variety of staffing needs, the company has also esti- mated the number of research scientists required for each development project (all cost values are given in millions of dollars). a) Suppose that Orchid has a total capital budget of $60 million and no restriction on scientists. How should it prioritize these projects? b) Suppose in addition that Orchid currently has only 12 research scientists and does not anticipate being able to hire any more in the near future. How should Orchid prioritize these projects? c) If instead, Orchid had 15 research scientists available, which projects should it choose now? Answer: a. (2 points) The PI rule selects projects V, III, II. These are also the optimal projects to under- take (as the budget is used up fully taking the projects in order). b. (5 points) Project PI NPV/Headcount I 1.01 5.1 II 1.27 6.3 III 1.47 5.5 IV 1.25 8.3 V 2.01 5.0 .

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The PI rule using the headcount constraint alone selects IV, II, III, I, and V, because the project with the next highest PI (in terms of NPV/Headcount), V, cannot also be undertaken without vio- lating the resource constraint. These projects are also feasible to do under the current capital budget because they happen to require exactly $60 million in capital. The only other feasible possibility is to take only project V, which generates a lower NPV, so this choice of projects is optimal. c. (3 points) Now choose V and IV.

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Question 24 (15 points) One year ago, your company purchased a machine used in manufacturing for $110,000. You have learned that a new machine is available that offers many ad- vantages; you can purchase it for $150,000 today. It will be depreciated on a straight-line basis over 10 years, after which it has no salvage value. You expect that the new machine will produce EBITDA (earnings before interest, taxes, depreciation, and amortization) of $40,000 per year for the next 10 years. The current machine is expected to produce EBITDA of $20,000 per year. The cur- rent machine is being depreciated on a straight-line basis over a useful life of 11 years, after which it will have no salvage value, so depreciation expense for the current machine is $10,000 per year. All other expenses of the two machines are identical. The market value today of the current machine is $50,000. Your company’s tax rate is 45%, and the oppor- tunity cost of capital for this type of equipment is 10%. Is it profitable to replace the year-old machine? Answer: Replacing the machine increases EBITDA by 40,000 – 20,000 = 20,000. Deprecia- tion expenses rise by $15,000 – $10,000 = $5,000. Therefore, FCF will increase by (20,000) × (1-0.45) + (0.45)(5,000) = $13,250 in years 1 through 10. In year 0, the initial cost of the machine is $150,000. Because the current machine has a book value of $110,000 – 10,000 (one year of depreciation) = $100,000, sell- ing it for $50,000 generates a capital gain of 50,000 – 100,000 = –50,000. This loss produces tax savings of 0.45 × 50,000 = $22,500, so that the after-tax proceeds from the sales, including this tax savings, is $72,500. Thus, the FCF in year 0 from replacement is = –150,000 + 72,500 = –$77,500. NPV of replacement = –77,500 + 13,250 × (1 / .10)(1 – 1 / 1.10 10 ) = $3916. There is a small profit from replacing the machine.

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Question 25 (15 points) IDX Technologies is a privately held developer of advanced security systems based in Chicago. As part of your business development strategy, in late 2008 you initiate discussions with IDX’s founder about the possibility of acquiring the busi- ness at the end of 2008. Estimate the value of IDX per share using a discounted FCF approach and the following data: • Debt: $30 million • Excess cash: $110 million • Shares outstanding: 50 million • Expected FCF in 2009: $45 million • Expected FCF in 2010: $50 million • Future FCF growth rate beyond 2010: 5% • Weighted-average cost of capital: 9.4% Answer: From 2010 on, we expect FCF to grow at a 5% rate. Thus, using the growing per- petuity formula, we can estimate IDX’s Terminal Enterprise Value in 2009 = $50/(9.4% – 5%) = $1136. Adding the 2009 cash flow and discounting, we have Enterprise Value in 2008 = ($45 + $1136)/(1.094) = $1080. Adjusting for cash and debt (net debt), we estimate an equity value of Equity Value = $1080 + 110 – 30 = $1160. Dividing by number of shares: Value per share = $1160/50 = $23.20.

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Question 26 (15 points) Suppose Intel’s stock has an expected return of 26% and a volatility of 50%, while Coca-Cola’s has an expected return of 6% and volatility of 25%. If these two stocks were perfectly negatively correlated (i.e., their correlation coefficient is − 1), (a) Calculate the portfolio weights that remove all risk. (b) If there are no arbitrage opportunities, what is the risk-free rate of interest in this economy? Answer: 10) points) (a) If the two stocks are perfectly correlated negatively, they fluctuate due to the same risks, but in opposite directions. Because Intel is twice as volatile as Coke, we will need to hold twice as much Coke stock as Intel in order to offset Intel’s risk. In other words, our portfolio should be 2/3 Coke and 1/3 Intel. (full credit is given for part (a) with the above answer. However, they may also provide an answer analytically by stating that we must solve eq. 11.9 as shown below) (5 points) (b) From Eq. 11.3, the expect return of the portfolio is Because this portfolio has no risk, the risk-free interest rate must also be 12.67%.

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Question 27 (20 points) You have been asked by AB Corporation to evaluate its capital structure. The company currently has 20 million shares outstanding trading at $20 per share. In addition, it has $250 million public debt outstanding, rated AA and with a yield to maturity of 8%. The beta for the company is 1.0, the current Treasury bond rate is 6%, and the market risk premium is 5.5%. The tax rate is 40%. AB Corporation is proposing to borrow an additional $150 million to use as follows: • Repurchase $30 million worth of stock • Pay $80 million in dividends • Invest $40 million in a project with a NPV of $30 million. The additional borrowing will cause the bond rating to fall to BBB, which current- ly carries a yield to maturity of 10%. How will the firm’s cost of capital change with this additional borrowing? (hint: to simplify your calculations, assume the total firm value used in computing WACC does not have to consider the change in firm value due solely to the change in total cost of capital) Answer: Current value of equity = $400 million Current value of debt = $250 million Cost of equity = .06 + 1.0*.055 = 11.5% Cost of debt = 8% Current WACC = 250/650*8%*(1-.4) + 400/650*11.5% = 8.92% NPV of project accrues to equity, so Equity = $400 – $30 - $80 + $30 = $320 Debt = $250 + $150 = $400 New D/E ratio = 400/320 Unlevered beta = 1/(1+0.6*250/400) = 0.727 New levered beta = 0.727*(1+0.6*400/320)) = 1.27 New cost of equity = .06 + 1.27*.055 = 13% New WACC = 400/720*10%*(1-.4) + 320/720*13% = 9.11%

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Question 28 (15 points) Use the following information to answer the question below. Rating AAA AA A BBB BB B CCC Average Default Rate 0.0% 0.1% 0.2% 0.45% 2.2% 5.5% 12.2% Recession Default Rate 0.0% 1.0% 3.0% 3.0% 8.0% 16.0% 48.0% Average Beta 0.05 0.05 0.05 0.10 0.17 0.26 0.31 Suppose that because of the large need for steel in building railroad infrastructure, Taggart Transcontinental and Rearden Metal decide to form into one large con- glomerate. What is your estimate of the asset beta for this new conglomerate? Answer: Because Taggart has a rating of BBB, the appropriate debt beta from the table is 0.10. β U = (E/V) β E + (E/V) β D = (4,500/8,000) × 1.1 + [(8,000 - 4,500)/8,000] × 0.10 = 0.6625 Because Rearden has a rating of AAA, the appropriate debt beta from the table is 0.05. β U = (E/V) β E + (E/V) β D = (3,800/7,200) × 1.3 + [(7,200 - 3,800)/7,200] × 0.05 = 0.709722 β U conglomerate = W TT β UTT + W RM β URM = [8,000/(8,000 + 7,200)](0.6625) + [7,200/(8,000 + 7,200)](0.709722) = 0.685

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Question 29 (20 points) Acort Industries owns assets that will have an 80% probability of having a market value of $50 million in one year. There is a 20% chance that the assets will be worth only $20 million. The current risk-free rate is 5%, and Acort’s assets have a cost of capital of 10%. a) If Acort is unlevered, what is the current market value of its equity? b) Suppose instead that Acort has debt with a face value of $20 million due in one year. According to MM, what is the value of Acort’s equity in this case? c) What is the expected return of Acort’s equity without leverage? What is the expected return of Acort’s equity with leverage? d) What is the lowest possible realized return of Acort’s equity with and without leverage? Answer: (5 points each) (a) E[value in one year] = 0.8(50M)+0.2(20M) = 44M E = 44M/1.10 = $40M (b) D = 20/1.05 = 19.048. Therefore, E = 40-1.048 = $20.952M (c) without leverage, r = (44/40 -1) = 10% with leverage, r = (44-20)/20.952 - 1 = 14.55% (d) without leverage, r = (20/40 - 1) = -50% with leverage, r = 0/20.952 - 1 = -100%

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Question 30 (10 points) Cerano Biotech stock has a current market value of $120 million and a beta of 1.50. Cerano Biotech currently has risk-free debt as well. The firm decides to change its capital structure by issuing $30 million in additional risk-free debt, and then using this $30 million plus another $10 million in cash to repurchase stock. With perfect capital markets, what will be the beta of Cerano Biotech stock after this transaction? Answer: Cerano Biotech increases its net debt by $40 million ($30 million in new debt + $10 million in cash paid out). Therefore, the value of its equity decreases to 120 – 40 = $80 million. If the debt is risk-free: where D is net debt, and EV is enterprise value . The only change in the equation is the value of equity. Therefore

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Question 31 (15 points) (a) What is the risk premium of a zero-beta stock? Explain your answer. (b) Can you can lower the volatility of a market portfolio without changing its expected return by substituting out any zero-beta stock in a portfolio and replacing it with the risk-free asset? Explain your answer. Answer: (5 points) (a) Risk premium = 0. It is uncorrelated with the market, so there is no incremental risk from adding it to your portfolio. (10 points) (b) Because the stock is positively correlated with itself (which is part of the mar- ket), to have zero beta it must be negatively correlated with the other stocks. Thus, it offsets risk that other stocks have. Thus, taking it out will not reduce risk.

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Question 32 (15 points) Your company operates a steel plant. On average, revenues from the plant are $30 million per year in perpetuity. All of the plants costs are variable costs and are con- sistently 80% of revenues, including energy costs associated with powering the plant, which represent one quarter of the plant’s costs, or an average of $6 million per year. Suppose the plant has an asset beta of 1.25, the risk-free rate is 4%, and the market risk premium is 5%. The tax rate is 40%, and there are no other costs. a) Estimate the value of the plant today assuming no growth. b) Suppose you enter a long-term contract which will supply all of the plant’s ener- gy needs for a fixed cost of $3 million per year (before tax). What is the value of the plant if you take this contract? c) How would taking the contract in (b) change the plant’s cost of capital? Explain. Answer: a. FCF = (30 – 0.8(30))(1 – 0.40) = 3.6 million Ru = 4% + 1.25 × 5% = 10.25% V= 3.6/0.1025 = 35.12 million b. FCF without energy = (30 – 18)(1 – 0.40) = 7.2 Cost of capital = 10.25% Energy cost after tax = 3(1 – 0.40) = 1.8 Cost of capital = 4%, because this is a fixed cost i.e. no risk V = 7.2/.1025 – 1.8/0.04 = 70.24 – 45 = 25.24 million c. FCF = 7.2 – 1.8 = 5.4 5.4/25.24 = 21.4% Risk is increased because now energy costs are fixed. Thus a higher cost of capital is appropriate.

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Question 33 (10 points) You currently have $100,000 invested in a portfolio that has an expected return of 12% and a volatility of 8%. Suppose the risk-free rate is 5%, and there is another portfolio that has an expected return of 20% and a volatility of 12%. a. What portfolio has a higher expected return than your portfolio but with the same volatility? b. What portfolio has a lower volatility than your portfolio but with the same ex- pected return? Answer: Invest an amount x in the other portfolio and the expected return and volatility are a) So to maintain the volatility at 8%, x = 8%/12% = 0.66667 thus, you should invest $66,667 of your original $100,000 in the other portfolio and the re- maining $33,333 in the risk-free investment. Your expected return will then be 15%. b) Alternatively, to keep the expected return equal to the current value of 12%, x must satisfy 5% + x (15%) = 12%, so x = 46.667%. Now you should invest $46,667 in the other portfolio and $53,333 in the risk-free investment, lower- ing your volatility to 5.6%

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Question 34 (15 points) Use the following information for Wyatt Oil to answer the question below. Division of Wyatt Oil Asset Beta Next Period's Expected Free Cash Flow ($mm) Expected Growth Rate Oil Exploration 1.4 450 4.0% Oil Refining 1.1 525 2.5% Gas & Convenience Stores 0.8 600 3.0% The risk-free rate of interest is 3% and the market risk premium is 5%. The overall cost of capital for Wyatt Oil is: Answer: Oil Exploration Division: r i = r rf + β (r m - r rf ) = .03 + 1.4(.05) = .10 or 10.0% V = FCF/(r - g) = $450/(10% - 4%) = $7,500 Oil Refining: r i = r rf + β (r m - r rf ) = .03 + 1.1(.05) = .085 or 8.5% V = FCF/(r - g) = $450/(8.5% - 2.5%) = $8,750 Convenience Store: r i = r rf + β (r m - r rf ) = .03 + 0.8(.05) = .07 or 7.0% V = FCF/(r - g) = $600/(7% - 3%) = $15,000

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Total Value = 7,500 + 8,750 + 15,000 = $31,250 r WO = w OE r OE + w OR r OR + w CS r CS = ($7,500/$31,250)(.10) + ($8,750/$31,250)(.085) + ($15,000/$31,250)(.07) = .0814

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Practice Final A (Fall 2023, do yellow questions only, updated)

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