Tutorial 4 CS-1 Sol revised PDF

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1. Suppose Alpha Industries and Omega Technology have identical assets that generate identical cash flows. Alpha Industries is an all-equity firm, with 14 million shares outstanding that trade for a price of $24 per share. Omega Technology has 22 million shares outstanding as well as debt of $100 million. a.

According to MM Proposition I, what is the stock price for Omega Technology?

b. Suppose Omega Technology stock currently trades for $15 per share. What arbitrage opportunity is available? What assumptions are necessary to exploit this opportunity?

ANSWER a. V(Alpha) = 14 x 24 = 336m = V(Omega) = D + E E = 336 – 100 = 236m  p = $10.73 per share.

b. Omega is overpriced. Sell 16 Omega, buy 10 Alpha, and borrow 100. Initial = 240 – 240 + 100 = 100. Assume we can trade shares at current prices and that we can borrow at the same terms as Omega (or own Omega debt and can sell at same price).

2. Cisoft is a highly profitable technology firm that currently has $5 billion in cash. The firm has decided to use this cash to repurchase shares from investors, and it has already announced these plans to investors. Currently, Cisoft is an all-equity firm with 6 billion shares outstanding. These shares currently trade for $20 per share. Cisoft has issued no other securities except for stock options given to its employees. The current market value of these options is $10 billion. a.

What is the market value of Cisoft’s non-cash assets?

b. With perfect capital markets, what is the market value of Cisoft’s equity after the share repurchase? What is the value per share?

ANSWER

a. Assets = cash + non-cash, Liabilities = equity + options, Non-cash assets = equity + options – cash = 20 × 6 + 10 – 5 = 125 billion.

b.

Equity = 120 – 5 =115.

Per share value



115 $20 4.750 .

5b 0.25b, Repurchase shares 20 

5.750 b shares remain.

3. Schwartz Industry is an industrial company with 103.5 million shares outstanding and a market capitalization (equity value) of $4.41 billion. It has $1.21 billion of debt outstanding. Management have decided to delever the firm by issuing new equity to repay all outstanding debt. a.

How many new shares must the firm issue?

b. Suppose you are a shareholder holding 100 shares, and you disagree with this decision. Assuming a perfect capital market, describe what you can do to undo the effect of this decision.

ANSWER a.

Share price = 4.41b/103.5m = $42.61, Issue 1.21b/42.61 = 28.4 million shares

b. You can undo the effect of the decision by borrowing to buy additional shares, in the same proportion as the firm’s actions, thus re-levering your own portfolio. In this case you should buy 28.4 new shares and borrow $28.4  42.61 = $1,210 (or round it to 29 shares).

4. Explain what is wrong with the following argument: “If a firm issues debt that is risk free, because there is no possibility of default, the risk of the firm’s equity does not change. Therefore, risk-free debt allows the firm to get the benefit of a low cost of capital of debt without raising its cost of capital of equity.”

ANSWER Any leverage raises the equity cost of capital. In fact, risk-free leverage raises it the most (because it does not share any of the risk).

5. Hardmon Enterprises is currently an all-equity firm with an expected return of 12%. It is considering a leveraged recapitalization in which it would borrow and repurchase existing shares. a. Suppose Hardmon borrows to the point that its debt-equity ratio is 0.50. With this amount of debt, the debt cost of capital is 5%. What will the expected return of equity be after this transaction? b. Suppose instead Hardmon borrows to the point that its debt-equity ratio is 1.50. With this amount of debt, Hardmon’s debt will be much riskier. As a result, the debt cost of capital will be 7%. What will the expected return of equity be in this case?

c. A senior manager argues that it is in the best interest of the shareholders to choose the capital structure that leads to the highest expected return for the stock. How would you respond to this argument? ANSWER

a.

re = ru + d/e(ru – rd) = 12% + 0.50(12% – 5%) = 15.5%

b.

re = 12% + 1.50(12% – 7%) = 19.5%

c. Returns are higher because risk is higher—the return fairly compensates for the risk. There is no free lunch.

6. Suppose Visa Inc. (V) has no debt and an equity cost of capital of 9.2%. The average debt-to-value ratio for the credit services industry is 13%. What would its cost of equity be if it took on the average amount of debt for its industry at a cost of debt of 6%? ANSWER

At a cost of debt of 6%: D ( rU  rD ) E 0.13 rE 0.092  (0.092  0.06) 0.87 0.0968 rE rU 

9.68%.

7. Global Pistons (GP) has common stock with a market value of $470 million and debt with a value of $299 million. Investors expect a 13% return on the stock and a 5% return on the debt. Assume perfect capital markets. a. Suppose GP issues $299 million of new stock to buy back the debt. What is the expected return of the stock after this transaction? b. Suppose instead GP issues $71 million of new debt to repurchase stock. i. If the risk of the debt does not change, what is the expected return of the stock after this transaction? ii. If the risk of the debt increases, would the expected return of the stock be higher or lower than in part (i)?

ANSWER

a.

470 299 wacc  13%  5% 9.89% ru (470  299) (470  299) .

b. i.

re ru  d / e ru  rd  9.89% 

370 (9.89%  5%) 15.94% (370  71)

ii. if rd is higher, re is lower. The debt will share some of the risk. 8. Hubbard Industries is an all-equity firm whose shares have an expected return of 10.9%. Hubbard does a leveraged recapitalization, issuing debt and repurchasing stock, until its debt-equity ratio is 0.66. Due to the increased risk, shareholders now expect a return of 17.1%. Assuming there are no taxes and Hubbard’s debt is risk-free, what is the interest rate on the debt? ANSWER 3 2 3 2 wacc  ru 10.9%  17.1%  x  x 10.9%  17.1%  x  x 1.6% 5 5 5 5

9. Yerba Industries is an all-equity firm whose stock has a beta of 0.70 and an expected return of 18.50%. Suppose it issues new risk-free debt with a 6.50% yield and repurchases 5% of its stock. Assume perfect capital markets. a. What is the beta of Yerba stock after this transaction? b. What is the expected return of Yerba stock after this transaction? Suppose that prior to this transaction, Yerba expected earnings per share this coming year of $4.50, with a forward P/E ratio (that is, the share price divided by the expected earnings for the coming year) of 10. c. What is Yerba’s expected earnings per share after this transaction? Does this change benefit shareholders? Explain. d. What is Yerba’s forward P/E ratio after this transaction? Is this change in the P/E ratio reasonable? Explain. ANSWER

a. b.

5   e  u  1  d / e 0.70 1   0.737 95  





re  rf   rm  rf  rm  rf 

18.5  6.5 17.14%  re 6.5  0.737 17.14  19.15% 0.70 from

the CAPM, or 5 re ru  d / e ru  rd  18.5  18.5  6.5  19.15% 95

c. P = 10(4.50) = $45. Borrow 5%(45) = 2.25, interest = 6.5%(2.25) = 0.14625. Earnings = 4.50 – 0.14625 = 4.35375, per share



4.35375 4.58. 0.95

No benefit; risk is higher. The stock price does not change.

d.

45 PE  9.83 4.58 . It falls due to higher risk....