Question

Pendergast, Inc., has no debt outstanding, and has a total market value of $180,000. Earnings before interest and taxes (EBIT) are projected to be $23,000 if economic conditions are normal. If there is a strong expansion in the economy, then EBIT will be 20% higher. If there is a recession, then EBIT will be 30% lower. Pendergast is considering a $75,000 debt issue with a 7% interest rate. The proceeds will be used to repurchase shares of stock. There are currently 6,000 shares of stock outstanding, and the relevant tax rate is 35%.
Required:

(a) Calculate the return on equity (ROE) under each of the three economic scenarios before any debt is issued. (Round your answers to 2 decimal places. (e.g., 32.16)).

(b) Calculate the percentage changes in ROE when the economy expands or enters a recession. (Negative amounts should be indicated by a minus sign.)

Answer 1

Answer:

return on equity (ROE) = net income / shareholders' equity

shareholders' equity = $180,000

economic scenarios:

1. normal ⇒ EBIT = $23,000
2. economic expansion ⇒ EBIT = $27,600
3. economic recession ⇒ EBIT = $16,100

additionally, $75,000 in debt will be used to repurchase stocks, so shareholders' equity = $180,000 - $75,000 = $105,000

interest on the loan = $75,000 x 7% = $5,250

tax rate = 35%

net income in 3 economic scenarios:

1. normal ⇒ ($23,000 - $5,250) x 0.65 = $11,537.50
2. economic expansion ⇒ ($27,600 - $5,250) x 0.65 = $14,527.50
3. economic recession ⇒ ($16,100 - $5,250) x 0.65 = $7,052.50

A) ROE under 3 different economic scenarios:

1. normal = $11,537.50 / $105,000 = 10.99%
2. economic expansion = $14,527.50 / $105,000 = 13.84%
3. economic recession = $7,052.50 / $105,000 = 6.72%

B)

When the economy expands, the ROE will increase by 11.46% compared to the normal economic activity [= (13.84% - 10.99%) / 10.99%]

When the economy enters a recession, the ROE will decrease by -38.85% compared to the normal economic activity [= (6.72% - 10.99%) / 10.99%]