Business

Problem 16-9

Solution:

Currently, with no outstanding debt, Bequity = 1.

Therefore, Bassets = 1.

Also, requity = 10%, so rassets = 10%. Finally, rdebt = 5%.

The firm plans to refinance, resulting in a debt-to-equity ratio of 1.0, and debt-to-value ratio: debt/(debt + equity) = .5.

a. Bequity  .5 + Bdebt  .5 = Bassets = 1

Bequity  .5 + 0 = 1

Bequity = 1/.5 = 2.0

b. requity = rassets = 10%

Risk premium = requity - rdebt = 10% - 5% = 5%.

(Note that the debt is risk-free.)

c. requity = rassets + D/E  (rassets - rdebt)

= 10% + 1  (10% - 5%) = 15%

Risk premium = requity - rdebt = 15% - 5% = 10%

d. Required rate of return is 5% (same as risk-free rate).

e. rassets = .5  requity + .5  rdebt

= .5  15% + .5  5% = 10%

This is unchanged from beta before the refinancing.

f. Suppose total equity before the refinancing was $1000. Then expected earnings were 10% of $1000, or $100. After the refinancing, there will be $500 of debt and $500 of equity, so interest expense will be $25. Therefore, earnings fall from $100 to $75, but the number of shares is now only half as large. Therefore, EPS rises by 50%:

EPS afterEPS before = 75/(Original shares/2)100/Original shares = 1.5

g. The stock price is unchanged, but earnings per share have increased by a factor of 1.5. Therefore, the P/E ratio must fall by a factor of 1.5, from 10 to 10/1.5 = 6.67. So, while expected earnings per share rise, the earnings multiple falls, and the stock price is unchanged.

Problem 16-30

Solution:

a. V = EBIT(1  Tc)r = 25,000(1  .35).10 = $162,500

b. The value of the firm increases by the present value of the interest tax shield, or .35  $50,000 = $17,500.

c. The expected cost of bankruptcy is .30  $200,000 = $60,000. The present value of this cost is $60,000/(1.10)3 = $45,079.

Since this is greater than the PV of the potential tax shield, the firm should not issue the debt.

Problem 17-9

Solution: