Problem 1. Sunrise Industries Corp, is planning to repurchase part of its common stock in the open market by issuing corporate debt. As a result, the debt-to-equity ratio is expected to rise from 40 percent to 50 percent. The annual interest payment on its outstanding debt amounts to $0.75 million with an interest rate at 10 percent. The expected earnings before interest are $3.75 million. There are no taxes in the country where Sunrise operates. (Treat the debt and earnings as perpetuities to simplify calculation.)
a. What is the total value of Sunrise Industries Corp?
b. What is the expected return on equity before and after the announcement of the stock?
c. How would the stock price change at the announcement of the repurchase?
Solution:
a.
current debt = 0.75 / 10% = $7.5 mln
current equity = 7.5 / 40% = $18.75 mln
total firm value = 7.5 + 18.75 = $26.25 mln
b.
rS = earnings after interest / total equity value = (3.75 - .75) / 18.75 = 16%
rB = 10%
r0 = (.4/1.4) 10% + (1/1.4) 16% = 14.29%
rS after repurchase = 14.29% + 50% (14.29% - 10%) = 16.44%
So, the return on equity would increase from 16% to 16.44% with the completion of the planned stock repurchase.
c.
The stock price wouldn’t change because in an MM world, there’s no added value to a change in firm leverage. In other words, it’s a zero NPV transaction.
Problem 2. Berk, DeMarzo 14.5
Suppose Alpha Industries and Omega Technology have identical assets that generate identical cash flows. Alpha industries is an all-equity firm, with 10 million shares outstanding that trade for a price of $22 per share. Omega Technology has 20 million shares outstanding as well as debt of $60 million.
- According to MM Proposition I, what is the stock price for Omega Technology?
- Suppose Omega Technology stock currently trades for $11 per share. What arbitrage opportunity is available? What assumptions are necessary to exploit this opportunity?
Solution:
a.V(alpha) = 1022 = 220m = V(omega) = D + E E = 220 – 60 = 160m p = $8 per share.
b.Omega is overpriced. Sell 20 Omega, Buy 10 alpha and borrow 60. Initial = 220 – 220 + 60 = 60. Assumes we can trade shares at current prices & Assumes we can borrow at same terms as Omega (or own Omega debt and can sell at same price).
Problem 3. Ross, Westerfield and Jaffe 15.8.
Strom, Inc., has 250,000 outstanding shares of stock that sell for $20 per share. Strom, Inc., currently has no debt. The appropriate discount rate for the firm is 15%. Strom’s earnings last year were $750,000. The management expects that if no changes affect the assets of the firm, the earnings will remain $750,000 in perpetuity. Strom pays no taxes.
Strom plans to buy out a competitor’s business at a cost of $300,000. Once added to Strom’s current business, the competitor’s facilities will generate earnings of $120,000 in perpetuity. The competitor has the same risk as Strom, Inc.
1)Construct the market-value balance sheet for Strom before the announcement of the buyout is made.
2)Suppose Strom uses equity to fund the buyout.
a)According to the efficient-market hypothesis, what will happen to Strom’s price?
b)Construct the market-based balance sheet as it will look after the announcement.
c)How many shares did Strom sell?
d)Once Strom sells the new shares of stock, how will its account look?
e)After the purchase is finalized, how will the market-based balance sheet look?
f)What is the return to Strom’s equityholders?
3)Suppose Strom uses 10-percent debt to fund the buyout.
a)Construct the market-based balance sheet as it will look after the announcement.
b)Once Strom sells the bonds, how will the accounts look?
c)What is the cost of equity?
d)Explain any difference in he cost of equity between the two plans.
e)Use MM Proposition II to verify the answer in c)
Problem 4.Berk, DeMarzo 14.14
Indell stock has a current market value of $120 million and a beta of 1.50. Indell 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 the beta of Indell stock be after this transaction.
Solution:
Indell 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
Problem 5. Berk, DeMarzo 14.15
Yerba Industries is an all-equity firm whose stock has a beta of 1.2 and an expected return of 12.5%. Suppose it issues new risk-free debt with a 5% yield and repurchases 40% 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 $1.50, with a forward P/E ratio (that is, the share price divided by the expected earnings for the coming year) of 14.
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.
Solution:
a.
b. from the CAPM, or
- . Borrow 40%(21) = 8.4, interest = 5%(8.4) = 0.42. Earnings = 1.50 – 0.42 = 1.08, per share
No benefit; risk is higher. The stock price does not change.
- . It falls due to higher risk.