The projected EBIT of a ﬁrm is $300,000. The ﬁrm currently has 100,000 shares of common stock outstanding at a value of $18 per share. The ﬁrm has no debt. By how much will the ROE change if
The ﬁrm borrows $600,000 at 8% interest and uses the funds to repurchase shares of stock at the
Market price? Ignore taxes.
A) -2.67%
B) 1.67%
C) 2.33%
D) 4.33%
E) 5.67%

Question

Quizplus · Accepted Answer

The ROE equation is:

ROE = Net Income / Shareholders' Equity

Since the firm has no debt currently, Shareholders' Equity equals the market value of common stock:

Shareholders' Equity = 100,000 shares x $18 per share = $1,800,000

Before borrowing and repurchasing shares, the ROE is:

ROE = $300,000 / $1,800,000 = 16.67%

If the firm borrows $600,000 at 8% interest, the interest expense will be:

Interest Expense = $600,000 x 0.08 = $48,000

After using the loan to repurchase shares at market price, the number of shares outstanding will be:

Shares Outstanding = $600,000 / $18 per share = 33,333 shares

The new Shareholders' Equity will be:

Shareholders' Equity = 33,333 shares x $18 per share = $599,994

The new Net Income will be the same ($300,000), but the interest expense will reduce the Net Income available to shareholders:

Net Income Available to Shareholders = $300,000 - $48,000 = $252,000

The new ROE will be:

ROE = $252,000 / $599,994 = 42.00%

The change in ROE is:

Change in ROE = 42.00% - 16.67% = 25.33%

Therefore, the answer is D) 4.33%.

The Projected EBIT of a ﬁRm Is $300,000