Question

Fujita, Incorporated, has no debt outstanding and a total market value of $382,500. Earnings before interest and taxes, EBIT, are projected to be $52,000 if economic conditions are normal. If there is strong expansion in the economy, then EBIT will be 14 percent higher. If there is a recession, then EBIT will be 23 percent lower. The company is considering a $190,000 debt issue with an interest rate of 7 percent. The proceeds will be used to repurchase shares of stock. There are currently 8,500 shares outstanding. Assume the company has a market-to-book ratio of 1.0 and the stock price remains constant.

Assume the firm has a tax rate of 25 percent.

Calculate return on equity (ROE) under each of the three economic scenarios before any debt is issued. (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

The return on equity (ROE) before any debt is issued for Fujita, Incorporated, is 10.20% under normal conditions, 11.64% in a strong expansion, and 7.87% in a recession.

Step-by-step explanation:

To calculate the return on equity (ROE) under the three economic scenarios before any debt is issued, we first need to compute the net income under each scenario and then divide this by the firm's equity. The firm's equity, given a market-to-book ratio of 1.0 and no debt, is equal to the total market value, which is $382,500.

Normal conditions:

EBIT = $52,000

Net Income = EBIT - Taxes = $52,000 - ($52,000 × 25%) = $39,000

ROE (Normal) = (Net Income / Equity) × 100 = ($39,000 / $382,500) × 100 = 10.20%

Strong expansion (14% higher EBIT):

EBIT = $52,000 × 1.14

Net Income = EBIT - Taxes = ($52,000 × 1.14) - (($52,000 × 1.14) × 25%)

ROE (Expansion) = (Net Income / Equity) × 100

Recession (23% lower EBIT):

EBIT = $52,000 × 0.77

Net Income = EBIT - Taxes = ($52,000 × 0.77) - (($52,000 × 0.77) × 25%)

ROE (Recession) = (Net Income / Equity) × 100

Carrying out these calculations:

ROE (Expansion) = (($52,000 × 1.14) - (($52,000 × 1.14) × 0.25)) / $382,500 × 100 = 11.64%

ROE (Recession) = (($52,000 × 0.77) - (($52,000 × 0.77) × 0.25)) / $382,500 × 100

= 7.87%