Maria Company is financed entirely by common stock that is priced to offer a 20%

Question

Maria Company is financed entirely by common stock that is priced to offer a 20% expected rate of return. The stock price is $60 and the earnings per share are $12. The company wishes to repurchase 50% of the stock and substitutes an equal value of debt yielding 8%. Suppose that before refinancing, an investor owned 100 shares of Learn and Earn common stock. If an investor wishes to ensure that risk and expected return on his investment are unaffected by this refinancing, he sold 50 shares and purchased $3,000 of 8% debt (bonds).

Prove that the new expected return for him will remain at 20% (1)

Explanation / Answer

Half shares are converted into debt bearing an interest rate of 8%

so interest per share will be = $60 * .05 *.08 = $2.40

So now the new earning per share will be the = Old EPS - the interest per share

( as debt holders are paid before equity holders)

As only half applied for debt

New EPS = (12- 2.40 )/.05 = $19.20

so now return = 19.20/60 = 32%

Prrof

.2 = We *.32 + Wd *.008

we know that We + wd = 1

.2 = .32 W + (1- We) *.008

W = .05

thus at half shares (60 *100 = $6000)

$3000 in equity and $3000 in debt return will be equal

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