1. Calculate the rate of return on abc’s equity

3. (Capital Structure) Company ABC has common stock with a market value of $200 million and debt with a value of $100 million. Investors expect a rate of return of 10% on the debt. The rate of return on ABC’s assets is 40%, i.e., the rate of return rU if ABC were an all equity-financed firm. Assume perfect capital markets.
1. Calculate the rate of return on ABC’s equity.
Answer:
The formula is
rU = E/[D + E]* rE + D/[D + E]* rD
Hence rE = [D + E] / E*rU – [D/E]*rD = rU + [D/E]*(rU − rD)
0.4 + 100/200*(0.4 − 0.1) = 0.55
2. Suppose that ABC issues $100 million of new shares to buy back the debt. What is the expected return of the stock (i.e., rE) after this transaction?
Answer:
rE = rU + [D/E]*(rU − rD)
0.4 + 0/300*(0.4 − 0.1) = 0.4
3. Suppose instead ABC issues $40 million of new debt to repurchase stock. If the risk of the debt does not change, what is the expected return rE of the stock after this transaction?
Answer:
rE = rU + [D/E] (rU − rD)
0.4 + 140/160*(0.2 − 0.05) = 0.6625