Capital Structure

Finance I, Problem Set 7 Questions: Capital Structure

1. Companies A and B differ only in their capital structure. The aggregate value of each company is $1 billion. A is financed 30% debt and 70% equity; B is 100% equity financed. The debt of both companies is risk-free and we ignore taxes. The risk-free rate is 5%.

a. A hedge fund owns 1% of the common stock of A. Assume that the hedge fund can borrow at the risk-free rate of 5%. What other investment package would produce identical cash flows for the hedge fund?

1% of A = 1% x 30% x $1bn = $3mm

1% of B = 1% x $1bn = $10mm

Hedge fund would need to borrow $7mm to purchase 1% of B

b. A bank owns 2% of the common stock of B. What other investment package would produce identical cash flows for the bank?

2% of B = 2% x $1bn = $20mm

2% of A = 2% x 30% x $1bn = $6mm

The bank could also own 2% of A which is worth $6mm as opposed to $20mm for 2% of B

c. Assume that the aggregate value of firm B suddenly increased to $1.2 billion while it stayed at $1 billion for firm A. What is the bank and/or the hedge fund likely to do?

Value of the equity of B is now higher, they are likely to want to hold more of B

2. Schuldenfrei AG pays no taxes and is financed entirely by common stock. The aggregate value is £100 million, there are 2 million shares outstanding, and operating profits over the last 12 months were £10 million. Each share costs £50, the equity beta is 0.7, and the expected return on equity is 10%. Schuldenfrei now decides to repurchase half the common stock and finance the repurchase by issuing debt. There are no taxes. If the debt yields a risk-free 6 percent, calculate:

V=£100mm; Shares=2mm; Operating profits=£10mm; Price = £50; βe=0.7, Re=10%; Rf=Rd=6%

a. The beta of the common stock after the refinancing.

Initially: Re = Ra because all equity firm

Re = Rf + βe (Rm – Rf) → 10% = 6% + 0.7 (Rm – 6%) → Rm = (10% - 6%)/0.7 + 6% = 11.7%

Rd = Rf = 6%

After: Re = Ra + (D/E)(Ra – Rd) → Re = 10% + (50/50)(10%-6%) = 14.0%

Re = Rf + βe (Rm – Rf) →14.0% = 6% + βe (11.7% - 6%) → βe = (14.0% - 6%) / (11.7% - 6%) = 1.4

Βe = 1.4

b. The expected return on the stock after the refinancing.

After: Re = Ra + (D/E)(Ra – Rd) → Re = 10% + (50/50)(10%-6%) = 14.0%

Re=14.0%

Assume that the operating profit of the firm is expected to remain constant in perpetuity. What is:

c. The percentage increase in expected earnings per share?

Original EPS = £10mm / 2mm → £5

Shares outstanding after repurchase = 1mm

Earnings = £10mm

EPS = £10mm / 1mm = £10

100% increase in expected earnings per share

d. The new price-earnings multiple?

P / E = £50 / £10 = 5

3. Archimedes Levers is financed by a mixture of debt and equity. You have the following information about its cost of capital: There are no taxes. Can you fill in the blanks?