FIN 350 Final Harford FALL 2022

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Apr 3, 2024

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THE LAST PAGE HAS IMPORTANT ASSUMPTIONS FOR THIS EXAM Autumn 2022 Answer Key Page 1 of 5 1. You work at a private company with $10 million in annual cash flows. Your direct competitor is publicly traded and has a price per share of $51 and cash flows per share of $3. What is a reasonable estimate of the value of the private company? [5] P/CF = 51/3 = 17 P/CF x CF = 17 x 10 = $170 million 2. You buy 200 shares of Disney for $100 per share and 600 shares of Coinbase for $50 per share and hold the portfolio for a year. Assume that Coinbase’s equity beta is 1.6 and its stock earns exactly its expected return over the year. Disney’s equity beta is 1.3 and its price rises to $108 by the end of the year, at which point it pays you a $2 per share dividend. a. What was the return on your portfolio? [5] Dollars in Disney: 200 x $100 = $20,000; Dollars in Coinbase: 600 x $50 = $30,000, Total = $50,000 Weights: $20000/$50000 = 40% Disney ; 60% Coinbase Coinbase: Return = Exp Return = .03+1.6(.07) = .142 Disney: (2 + (108-100))/100 = 10/100 = .10 Portfolio Return = (.40)(.10) + (.60)(.142) = .1252 b. Did your portfolio as a whole earn a return that compensated you for its systematic risk? [5] Portfolio beta = (.40)(1.3)+(.60)(1.6) =1.48 Exp Ret = .03+1.48(.07) = .1336 No 3. Why is systematic risk the only risk that is priced (compensated)? [5] Investors can avoid unsystematic risk by diversifying it away in their portfolio. The market will not reward investors for unnecessarily taking-on unsystematic risk. Since it is impossible to avoid systematic risk unless you invest only in the risk-free asset, the capital market must offer a risk premium (higher expected, but not guaranteed) return for investors to be willing to take invest in risky assets. [If you’re interested in a fully complete answer: if you could earn extra return for buying assets with extra unsystematic risk, there would be an arbitrage opportunity because you could buy such assets, put them in a portfolio, eliminate the risk and still earn extra return.] [key points are that you don’t have to hold unsystematic risk, so why should you get rewarded for it, and that you have to provide compensation for taking on systematic risk since investors can’t avoid it other than holding the risk free asset (only way to have an equilibrium where investors buy anything other than the risk- free asset is to give them a risk premium for systematic risk]

THE LAST PAGE HAS IMPORTANT ASSUMPTIONS FOR THIS EXAM Autumn 2022 Answer Key Page 2 of 5 4. Tesla’s equity is worth $601 billion and it has $9 billion in debt. Elon wakes up and realizes that Tesla is probably under-leveraged and so he tweets that Tesla will commence a debt-equity swap whereby it will issue $100 billion in new, permanent debt (3% coupon), and will repurchase (buyback and retire) $100 billion of its equity. a. What will be the effect of the swap on Tesla’s total market value? How much of the total will be equity and how much will be debt? [8] PV(ITS) = .20(100) = 20 New Value = 610 -100 + 100 + 20 = 630, of which 109 is debt and 521 is equity b. Assume that before the repurchase, Tesla has 3 billion shares outstanding. If markets are efficient, what should the price of Tesla’s stock be right after Elon’s tweet? [4] Value created is incorporated immediately into the price, so the market anticipates the $20 billion in added PV(ITS). Thus, before the repurchase commences, the value of equity goes up immediately from $601 billion to $621 billion. Divided by 3 billion shares, you get: 621/3 = $207. c. How many shares will Tesla be able to repurchase for $100 billion? [3] Now Tesla reduces the equity by $100 billion through a repurchase at the market price of $207 per share. $100 billion / $207 = 483,091,787.4 (so 483,091,787 and 483,091,788 are also acceptable) d. Tesla’s equity beta was 2 before the swap. What will Tesla’s new equity beta be after the swap is completed? [5] Find Asset Beta: Ba = BeE% = 2(601/610) = 1.97 New Equity Beta with new capital structure: Be = Ba + Ba(D/E) = 1.97 + 1.97 (109/521) = 2.38

THE LAST PAGE HAS IMPORTANT ASSUMPTIONS FOR THIS EXAM Autumn 2022 Answer Key Page 3 of 5 5. How is knowing the historical market risk premium useful? What does it tell us about the tradeoff between risk and return? [6] The historical market risk premium tells us what the average extra return investors have demanded to invest in the market portfolio instead of a risk-free investment. This is useful because it gives us an estimate of what investors with rational expectations should expect going forward. Further, because it is measured using the market portfolio, it gives us a baseline risk premium that we can scale up and down for investments with more or less systematic risk than the market on average. [key issues are an estimate of what a rational investor should expect and a baseline amount for average market risk that we can scale up and down] 6. SCE’s stock’s beta is 1.0. SCE is financed with $217.8 million in debt and has 22 million shares outstanding. a. If SCE’s dividends are expected as follows, what should be the price per share of SCE’s stock? [6] Years from now: 1 2 3 … ∞ Dividend: $1.21 $1.62 $2.00 Growing by 2% annually Re = .03+ 1(.07) = .10 Price = 1.21/1.10 + 1.62/1.10^2 + ((2/(.1-.02))/1.10^2 = $23.10 b. Find SCE’s asset beta and its after-tax WACC. [6] 22 million shares x $23.10 = $508.2 million in equity Ba = Be (E/(D+E)) = 1(508.2/(508.2+217.8)) = 0.7 After-tax WACC: E% = 508.2/(508.2+217.8) = 0.7, D% = 0.3 So, Re(E%)+Rd(1-Tc)(D%) = .10(.7)+.03(1-.2)(.3) =0.0772

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THE LAST PAGE HAS IMPORTANT ASSUMPTIONS FOR THIS EXAM Autumn 2022 Answer Key Page 4 of 5 7. Ignore taxes for this problem. ORD has two equally-valued divisions, A and B. ORD’s overall asset beta is 0.9. Division A’s direct competitor is MDW, which has an equity beta of 1.2 and is 40% financed with debt. a. What discount rate should ORD use to evaluate typical projects in its Division A? Justify your answer. [5] MDW Ba = 1.2(.6) = 0.72 E[Ra] = .03+.72(.07) = .0804, so 8% Since MDW is Division A’s direct competitor, the risk of its business is the same as the risk of Division A’s business, so we just need to get MDW’s asset beta and then use the CAPM to get a discount rate commensurate with that risk. b. What discount rate should it use in division B? [5] ORD’s overall asset beta is a weighted average of the two divisions’ asset betas. The two divisions are equally valued, so the weights are just 50% each. We know that ORD’s overall asset beta is 0.9 and that Division A’s is 0.72, so we can solve for Division B’s: 0.9 = 0.5(.72)+.5(X) X = 1.08 Using the CAPM, we get the discount rate for Division B: .03+1.08(.07) = .1056 c. Assume that ORD’s market value is $1 billion (all equity) and MDW’s market value is $400 million and that ORD acquires MDW using $240 million in equity and $160 million in debt. After the acquisition, what should the expected return be for stock of the combined firm? [4] This was a stretch problem. So ORD is worth 1000 and MDW is worth 400, so if ORD and MDW combine, they’re worth 1400. That’s where the 1400 comes from. For the 900 and 500, you need to go back to the first part of the problem where it says that ORD has two equally-valued divisions, A & B, so each is worth 500. Division A is just like MDW, so division A’s risk is the same as MDW’s risk. Once they combine, the total value of the assets with Division A (MDW’s) risk is the 500 from division A plus the 400 from MDW, for a total of 900. ORD acquired MDW using 240 E and 160 D (total of 400), so the total equity is ORD’s original 1000+240=1240 and the debt is 160. The combined firm is 1400 million and is 900 million of division A’s risk and 500 million of division B’s risk. Its combined asset beta is .72(900/1400) + 1.08(500/1400) = 0.85 It is now financed 1240 in equity and 160 in debt. Be = Ba + Ba(D/E) = 0.85 + 0.85(160/1240) = 0.96 E[Re] = .03 + .96(.07) = 0.0972 8. You are evaluating a stock and based on its current price, you think it has a higher expected return than it should given its risk. Explain whether the stock is over or underpriced. [6] The stock is underpriced. The only way for a stock to have a higher than necessary expected return is for its price to be too low relative to its expected future price (so that the return to go from the current price to the expected price is too high). Another way to think about this is that if a stock is offering excess expected return, you (and everyone else) want to buy that stock, so it’s underpriced.

THE LAST PAGE HAS IMPORTANT ASSUMPTIONS FOR THIS EXAM Autumn 2022 Answer Key Page 5 of 5 9. ROC has $65 million in common stock with a beta of 1.2. It also has one million shares of preferred stock priced at $10 per share, paying an annual preferred dividend of $0.80 per share. Finally, it has $25 million in debt outstanding priced at par and paying interest of 3%. a. What is ROC’s after-tax WACC? [7] E[Re] =Re= .03 + 1.2(.07) = .114, E% = 65/(65+10+25) = .65 Rpfd = .8/10 = 0.08, P% = 10/(65+10+25) = .10 Rd = .03, D% = 25/(65+10+25) = .25 After-tax WACC = .114(.65) + .10(.08) + .03(1-.2)(.25) = 0.0881 b. If ROC generates a total cash flow of $12 million this year, what will the common stockholders’ return be (in percent)? [5] First, pay interest on the debt, so that after the tax deduction, the cost is (.03)(1-.2)(25million) = $0.6 million. Then, pay the preferred dividend: 1 million shares at $0.8 per share, so $0.8 million What’s leftover goes to common stockholders: $12 million – 0.6 – 0.8 = 10.6 million. The common stockholders have a $65 million investment, so their return is 10.6/65 = 16.3% c. Did the common stockholders get a return sufficient to compensate them for their risk? [4] Yes: 16.3% > 11.4% , but note that if part b is incorrect such that the return calculated in part b is less than 11.4%, then full credit can be awarded here for saying no. 10. Explain in words how to think about what a correlation coefficient of 0.3 between two stocks tells you about them. [6] Correlations are scaled to lie between -1 and +1, so a correlation of 0.3, being in the positive range, means that the two stocks move together more often than they move in opposite directions, but since it is much less than the upper bound (+1), they do not always move together and you can get substantial diversification benefits from holding them together in a portfolio vs. holding them individually. [key issues are to give the reference range of -1 to +1 and to give an intuitive discussion of them moving together more often than not, but not always]

Basic Assumptions for the Exam The risk free rate is 3% . The market risk premium is 7% . The beta of debt is zero, so the cost of debt is always 3% The corporate tax rate is 20% . Capital structure changes don’t have transaction costs and don’t affect investment policy. This is fun!

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