Use the information for the question(s)below.
Assume that Rose Corporation's (RC)EBIT is not expected to grow in the future and that all earnings are paid out as dividends.RC is currently an all-equity firm.It expects to generate earnings before interest and taxes (EBIT)of $6 million over the next year.Currently RC has 5 million shares outstanding and its stock is trading for a price of $12.00 per share.RC is considering borrowing $12 million at a rate of 6% and using the proceeds to repurchase shares at the current price of $12.00.
-Following the borrowing of $12 million and subsequent share repurchase,the equity cost of capital for RC is closest to:
A)12%.
B)9%.
C)11.0%.
D)10%.

Question

Quizplus · Accepted Answer

Before the share repurchase, the market value of RC was:

Market Value of RC = Number of Shares Outstanding * Price per Share
= 5 million * $12.00 per share
= $60 million

After borrowing $12 million, RC has an initial market value of:

Initial Market Value of RC = Market Value of Equity + Market Value of Debt
= ($60 million - $12 million) + $12 million
= $60 million

Assuming that RC uses the $12 million to repurchase shares at the current price of $12.00 per share, it can buy back:

Number of Shares Repurchased = Amount of Debt / Price per Share
= $12 million / $12.00 per share
= 1 million shares

After the share repurchase, RC will have:

Number of Shares Outstanding = Original Number of Shares - Number of Shares Repurchased
= 5 million shares - 1 million shares
= 4 million shares

The new equity cost of capital for RC can be calculated as:

Equity Cost of Capital = (Earnings Available to Equity / Market Value of Equity)

Assuming RC's EBIT of $6 million remains constant, its earnings available to equity after paying 6% interest on the $12 million in debt will be:

Earnings Available to Equity = EBIT - Interest on Debt
= $6 million - ($12 million * 6%)
= $5.28 million

The new market value of RC after the share repurchase will be:

New Market Value of RC = Number of Shares Outstanding * Price per Share
= 4 million shares * $12.00 per share
= $48 million

Therefore, the new equity cost of capital for RC will be:

Equity Cost of Capital = (Earnings Available to Equity / Market Value of Equity)
= ($5.28 million / $48 million)
= 11.0%

Thus, the best answer is (C) 11.0%.

Use the Information for the Question(s)below