Astromet is financed entirely by common stock and has a beta of 1.10. The firm pays no taxes.

Astromet is financed entirely by common stock and has a beta of 1.10. The firm pays no taxes. The stock has a price-earnings multiple of 10.0 and is priced to offer a 11.0% expected return. The company decides to repurchase half the common stock and substitute an equal value of debt.

Assume that the debt yields a risk-free 5.0%.

a.	Calculate the beta of the common stock after the refinancing. (Round your answer to 1 decimal place.)

Beta of the common stock

b.	Calculate the required return and risk premium on the common stock before the refinancing. (Round your answers to 1 decimal place.)

Required return	%
Risk premium	%

c.	Calculate the required return and risk premium on the common stock after the refinancing. (Round your answers to 1 decimal place.)

Required return	%
Risk premium	%

d.	Calculate the required return on the debt. (Round your answer to 1 decimal place.)

Required return

%

e.	Calculate the required return on the company (i.e., stock and debt combined) after the refinancing. (Do not round intermediate calculations. Round your answer to 1 decimal place.)

Required return

%

Assume that the operating profit of the firm is expected to remain constant.

f.	Calculate the percentage increase in earnings per share after the refinancing. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Percentage increase

%

g-1.	Calculate the new price-earnings multiple. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

New price-earnings multiple

g-2.	Has anything happened to the stock price?
	Unchanged

Explanation:

Some values below may show as rounded for display purposes, though unrounded numbers should be used for the actual calculations.

Currently, with no outstanding debt, βequity = 1.10.

Therefore: βassets = 1.10

Also: requity = 11.0% rassets = 11.0%

Finally: rdebt = 5.0%

The firm plans to refinance, resulting in a debt-to-equity ratio of 1.10 and a debt-to-value ratio of debt/(debt + equity) = 0.5.

a.

(βequity × 0.5) + (βdebt × 0.5) = βassets = 1.10

(βequity × 0.5) + 0 = 1.10 βequity = 1.10/0.5 = 2.2

b.

requity = rassets = 11.0%

Risk premium = requity − rdebt = 11.0% − 5.0% = 6.0%

(Note that the debt is risk-free.)

c.

requity = rassets + [D/E × (rassets − rdebt)] = 11.0% + [1 × (11.0% − 5.0%)] = 17.0%

Risk premium = requity − rdebt = 17.0% − 5.0% = 12.0%

e.

rassets = (0.5 × requity) + (0.5 × rdebt) = (0.5 × 17.0%) + (0.5 × 5.0%) = 11.0%

This is unchanged.

f.

Suppose total equity before the refinancing was $1,000. Then expected earnings were 11.0% of $1,000, or $110. After the refinancing, there will be $500 of debt and $500 of equity, so interest expense will be $25.0. Therefore, earnings fall from $110 to $85, but the number of shares is now only half as large. Therefore, EPS increases by 54.55%:

EPS after	=	85/(original shares/2)	=	1.55
EPS before		110.0/original shares

g.

The stock price is unchanged, but earnings per share have increased by a factor of 1.55. Therefore, the P/E ratio must decrease by a factor of 1.55, from 10.0 to:

10.0/1.55 = 6.47

So, while expected earnings per share increase, the earnings multiple decreases, and the stock price is unchanged.