Question

Music City, Inc., has no outstanding debt and its total market value is $220,000. Earnings before interest and taxes, EBIT, is projected at $40,000, if economic conditions are normal. If there is a strong expansion in the economy, then EBIT will be 10 percent higher. If there is a recession, then EBIT will be 20 percent lower. The company is considering a debt issue of $135,000 with an interest rate of 4 percent. The funds raised will be used to buy back shares. There are currently 11,000 shares outstanding. Neglect taxes for parts a and b. Assume the company has a market to book value ratio of 1.0.

a-1. Calculate the return on equity (ROE) under each of the three economic scenarios, before any debt is issued. (Do not round intermediate calculations. Enter your answers as a percentage rounded to two decimal places, for example, 32.16.)
a-2. Calculate the percentage changes in ROE when the economy expands or enters a recession. (A negative answer should be indicated with a minus sign. Do not round intermediate calculations. Enter your answers as a percentage rounded to the nearest integer, for example, 32.)
Assume that the company goes ahead with the proposed recapitalization.
b-1. Calculate the return on equity (ROE) under each of the three economic scenarios. (Do not round intermediate calculations. Enter your answer as a percentage rounded to two decimal places, for example, 32.16.)
b-2. Calculate the percentage changes in ROE when the economy expands or enters a recession. (A negative answer should be indicated with a minus sign. Do not round intermediate calculations. Enter your answer as a percentage rounded to two decimal places, for example, 32.16.)
Suppose the company has a tax rate of 35 percent.
c-1. Calculate the return on equity (ROE) under each of the three economic scenarios before any debt is issued. (Do not round intermediate calculations. Enter your answer as a percentage rounded to two decimal places, for example, 32.16.)
c-2. Calculate the percentage changes in ROE when the economy expands or enters a recession. (A negative answer should be indicated with a minus sign. Do not round intermediate calculations. Enter your answer as a percentage rounded to the nearest integer, for example, 32.)
c-3. Calculate the return on equity (ROE) under each of the three economic scenarios, assuming the company goes ahead with recapitalization. (Do not round intermediate calculations. Enter your answers as a percentage rounded to two decimal places, for example, 32.16.)
c-4. Given the recapitalization, calculate the percentage changes in ROE when the economy expands or enters a recession. (A negative answer should be indicated with a minus sign. Do not round intermediate calculations. Enter your answer as a percentage rounded to two decimal places, for example, 32.16.)

Answer 1

To calculate the return on equity (ROE) under each economic scenario and the percentage changes in ROE when the economy expands or enters a recession, we need to analyze the given information and perform the necessary calculations. Additionally, we need to calculate the ROE and percentage changes in ROE after the proposed recapitalization, assuming the company goes ahead with it.

Step-by-step explanation:

Let's calculate the return on equity (ROE) under each of the three economic scenarios before any debt is issued.

Scenario 1: Normal Economic Conditions
EBIT = $40,000
Total market value = $220,000

ROE = (EBIT / Total market value) * 100
ROE = (40,000 / 220,000) * 100 = 18.18%

Scenario 2: Strong Expansion in the Economy
EBIT = $40,000 * 1.1 = $44,000

ROE = (44,000 / 220,000) * 100 = 20%

Scenario 3: Recession
EBIT = $40,000 * 0.8 = $32,000

ROE = (32,000 / 220,000) * 100 = 14.55%

Now, let's calculate the percentage changes in ROE when the economy expands or enters a recession.

Percentage change = ((New ROE - Old ROE) / Old ROE) * 100

Percentage change when the economy expands = ((20 - 18.18) / 18.18) * 100 = 10%

Percentage change when the economy enters a recession = ((14.55 - 18.18) / 18.18) * 100 = -20%

Next, assuming the company goes ahead with the proposed recapitalization:

Total market value after recapitalization = Total market value - Debt issue
Total market value after recapitalization = 220,000 - 135,000 = 85,000

Number of shares outstanding after recapitalization = Shares outstanding - (Debt issue / Market price per share)
Number of shares outstanding after recapitalization = 11,000 - (135,000 / 85,000) * 11,000 = 4,647.06

ROE under each economic scenario after recapitalization:

Scenario 1: Normal Economic Conditions
EBIT = $40,000
ROE = (EBIT / Total market value after recapitalization) * 100
ROE = (40,000 / 85,000) * 100 = 47.06%

Scenario 2: Strong Expansion in the Economy
EBIT = $40,000 * 1.1 = $44,000
ROE = (44,000 / 85,000) * 100 = 51.76%

Scenario 3: Recession
EBIT = $40,000 * 0.8 = $32,000
ROE = (32,000 / 85,000) * 100 = 37.65%

Finally, let's calculate the percentage changes in ROE when the economy expands or enters a recession after recapitalization.

Percentage change when the economy expands = ((51.76 - 47.06) / 47.06) * 100 = 9.98%

Percentage change when the economy enters a recession = ((37.65 - 47.06) / 47.06) * 100 = -20%