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Homework Questions for Lecture 7 — Valuation Problems Ql. A firm is currently all equity financed. Its equity beta is 1, it has 25 million shares outstanding, and the price per share is $20. (i) The firm recapitalizes by issuing $100 million of perpetual debt and paying its equity holders $150 million in dividends. The additional $50 million in payout comes from excess cash the firm has on its balance sheet. What is the value of the outstanding equity after the recapitalization? Assume while answering this that the tax advantage to debt, 7 ., is 0.4. (i) What is the Weighted Average Cost of Capital for the firm if it is at its target leverage after issuing the debt and paying the dividend? Assume the expected return on the debt is 10%, the risk premium on the market is 8.4%, and the risk free rate is 8%. Q2. In 1989, General Motors (GM) was evaluating the acquisition of Hughes Aircraft Corporation. Recognizing that the appropriate opportunity cost of capital for discounting the projected cash flows for Hughes was different from that of General Motors, GM assumed that Hughes was of approximately the same risk as Lockheed or Northrop which had low-risk defense contracts and products that were similar to those of Hughes. You may assume the data in the following table: Firm Be | DIE GM 1.20 | 0.40 Lockheed { 0.90 | 0.90 Northrop | 0.85 | 0.70 Also assume the following: e The D/E ratios for Lockheed and Northrop are constant over time. The target D/E ratio for acquisition of Hughes is 1. o All after-tax net cash flows are paid out, either as interest or as dividends. e Asofnow (¢ =0), we expect Hughes’ after-tax cash flow from assets (not including debt tax shields) to be $300 million this year (at # = 1), and we expect it to grow thereafter by 5% per year forever. Thus, as of now, we expect the cash flow at date £+1 to be $300(1.05)". Although the market value of these cash flows will fluctuate randomly over time, as of now, the market value of future cash as of any future date, £, can be computed using the perpetuity growth formula as _ $300(1.05) _ EV, (¢ 7= v,(0)(1.05), where Eq denotes the expectation as of today, V() is the value of the assets as of date ¢, and i4 is the opportunity cost of capital for the assets. That is, as of today,

the value of the assets is expected to increase at 5% per year forever. Note that this calculation reflects the assumption that all cash flows up to and including date t have been paid out. ¢ Hughes’ corporate tax rate is 34%. o The risk-free rate is i,= 8%, and the expected risk premium on the market portfolio is 6%. ® Debt of Hughes, Lockheed and Northrup is risk-free, so that the appropriate ip =iy and fp=0. (a) Analyze the Hughes acquisition (which never took place) by first computing the betas of the comparison firms, Lockheed and Northrop, as if they were all equity financed (i.e. by unlevering the betas). (b) Compute S, the beta of the operating assets of the Hughes acquisition by taking the average of the betas of the operating assets of Lockheed and Northrop. (c) Compute Sz for the Hughes acquisition at the target debt ratio. (d) Compute the WACC for the Hughes acquisition. (e) Compute the value of Hughes with the WACC. (f) Now value Hughes using the APV method. HINT: Computing the present value of the debt tax shield is tricky. Start by assuming that, since the value of the unlevered assets is expected to grow at 5% per year, to keep the debt-to-value ratio constant at 0.5, the market value of the debt will need to grow at 5% per year, i.e., we expect next year’s market value of debt will be 5% higher than this year’s, etc. (later you can check to make sure this is correct). This implies that the debt tax shield is also expected to grow at 5% per year, since the debt tax shield in any year is simply ipte times the value of the debt in that year. Now you can use the perpetuity growth formula to calculate the present value of the debt tax shields (what is the opportunity cost of capital for the debt tax shields?), provided you know the initial value of the debt. Well, you don’t know the initial debt value, but you do know that it is 0.5 times the initial value of the levered firm. Adding the value of the debt tax shields, expressed as a function of the value of the levered firm, ¥, to the value of the unlevered assets, V4, will give you a formula in which ¥, appears on both sides. Solve this for V. Q3. Southwestern Industries, a diversified industrial corporation, is considering an acquisition of Cactus Airlines, a small passenger air carrier that operates in the southwestern United States. After the acquisition, Southwestern plans to have a target debt-to-equity (D/E) ratio of 0.15. Cactus Airlines is quite similar in its size and operations to another company, Arizona Air.

You are given the following information: * Risk-free rate =4.3% o Market risk premium = 8.4% e Corporate tax rate = 35% * Southwestern Industries: fg=1, fp=0, ip=4.3% e Cactus Airlines: Sz = 1.5, 8p= 0.3, D/E=0.25 * Arizona Air: f=1.5, fp=02,D/E=0.25 A study of historical data reveals that Cactus Airlines maintains an essentially fixed amount of debt on its balance sheet, while Arizona Air does not. However, although the market value of Arizona Air changes randomly over time, Arizona air constantly rebalances its capital structure to maintain a stable D/E ratio. (a) What are the unlevered asset betas of Cactus Airlines and Arizona Air? (b) Compute the WACC that Southwestern should use to discount the cash flows from the acquisition. Q4. Valuation one more time Your company is currently assessing Timkin Corp as an acquisition target. The balance sheet for the last two years is as follows: 1999 2000 Assets Current Assets 250 300 Net PPE 400 430 Liabilities Current Liabilities 150 180 Deferred taxes 20 40 Long Term Debt 100 110 Equity 380 445 You believe the firm carries too little cash relative to the industry, so you will have to put in $75 million of cash after the acquisition to bring it up to industry levels. The cash will be invested at the risk free rate. The projected net income (Earnings After Depreciation, Interest and Taxes) after the acquisition in 2000 is $60 million. This includes the interest the cash would earn. Assume the firm’s income will grow at 5% and the changes in balance sheet items (in dollar terms, not growth rates) will continue as in the past.

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The equity beta for Sun Corp, a typical firm in the industry is 1.3. It has $400 million of debt outstanding and has had this amount for some time. It also has 300 million shares valued at $4 each. Timkin’s target debt to capital ratio is 0.4, and its debt will be risk free (as is its current debt). Timkin has 20 million shares outstanding. Assume that the risk free rate is 6%, that the market risk premium is 8.4%, and that the corporate tax rate is 34%. i) Determine how much you would pay for each Timkin share using the WACC method. i) Suppose you are told that it would take only $50 million to bring Timken’s cash levels to industry standards. How would your answer change?