Spam Corp. is financed entirely by common stock and has a beta of 1.0. The firm

Question

Spam Corp. is financed entirely by common stock and has a beta of 1.0. The firm is expected to generate a level, perpetual stream of earnings and dividends. The stock has a price-earnings ratio of 8 and a cost of equity of 12.5%. The company's stock is selling for $50. Now the firm decides to repurchase half of its shares and substitute an equal value of debt. The debt is risk free, with a 5% interest rate. The company is exempt from corporate income taxes. Assume Modigliani and Miller are correct, calculate the following items after the refinancing:

a. The cost of equity
b. The overall cost of capital (WACC)
c. The price-earnings ratio
d. The stock price
e. The stock's beta

Explanation / Answer

A. The WACC is a weighted average of the cost of debt capital and the cost of equity capital. The weights
in the exercise are 50% debt and 50% equity, and the cost of debt capital is 5% per annum , so

50% × 5% + 50% × r E (cost of equity capital) = 12.5%
A r E (cost of equity capital) = 20.0%.

First assume the marginal tax rate is zero, giving a W ACC of 12.5% and a cost of equity capital of
20%. Then use the actual m arginal tax rate of 35%, giving a revised WACC of

50% × 5% × (1 – 35%) + 50% × 20% = 11.625%

B.This exercise assum es perfect capital m arkets, so capital structure does not affect the worth of the firm . The overall cost of capital (W ACC) does not change. It was 12.5% before the refinancing, so it is 12.5% after the refinancing.

C. The price-earnings ratio is the reciprocal of the earnings per share. Earnings are level and perpetual,
so earnings per share equal the cost of equity capital, or 20%. To show the reasoning, we solve the problem
by first principles as well.

Method: Determ ine the annual earnings before refinancing, subtract the debt costs, and divide by the new
equity value.

Step #1: Before the refinancing, the stock price is $50 and the price-earnings ratio is 8, the annual earnings
per share are $50 / 8 = $6.25.

Step #2: After refinancing, the firm has $50 of debt for each $50 of equity (= one share). Suppose the form
originally had two m illion shares, for total value of $100 m illion and earnings of $12.5 m illion. It now has one
m illion shares worth $50 m illion and $50 m illion of debt. Interest is 5% × $50 m illion = $2.5 m illion. Earnings
are $12.5 m illion – $2.5 m illion = $10 m illion. The shares are worth $50 m illion, so the price-earnings ratio is
$50 / $10 = 20 and earnings per share are $10 / $50 = 20%.

D. The worth of the firm does not change, so the stock price does not change. It was $50 a share before
the refinancing, so it is $50 a share after the refinancing.

The firm has bought back half its stock, so its value to shareholders should decrease by 50%. A past
m odule in this course uses this relation: if a firm pays $1 to shareholders (by a dividend or by a share re-
purchase), its value declines $1. If the firm ’s share price is $50 before a dividend and the firm pays a $1
stockholder dividend, the share price is $49 after the dividend.

The firm ’s value to shareholders declines 50%. But shareholders own only half as m any shares,
so the stock price rem ains $50. The bondholders own the other half of the firm .

Take heed: If the the firm pays a one-tim e dividend to shareholders from the bond proceeds, the num ber of
shares does not change but the value of each share declines. If the firm buys back shares, the value per
share does not change but the num ber of shares held by investors declines.

E. The risk-free rate is 5%. W ith a beta of 1, the cost of equity is 12.5%, so the market risk prem ium is
7.5%. If the new cost of equity capital is 20%, then 20% = 5% + $ × 7.5% A $ = 2.

The beta of the firm ’s assets does not change, but the beta of the firm ’s equity changes. Before the
refinancing, if the overall stock m arket increases 1%, the firm ’s value increases 1%. This is still true after the
refinancing, since the firm ’s assets do not change. The bondholders’ 50% portion of the firm does not change;
they still get a 5% return on their investment. To com pensate, the stockholders’ 50% portion of the firm
increases 2%.

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