RAK, Inc., has no debt outstanding and a total market value of $150,000. Earning

Question

RAK, Inc., has no debt outstanding and a total market value of $150,000. Earnings before interest and taxes, EBIT, are projected to be $36,000 if economic conditions are normal. If there is strong expansion in the economy, then EBIT will be 15 percent higher. If there is a recession, then EBIT will be 25 percent lower. RAK is considering a $95,000 debt issue with an interest rate of 8 percent. The proceeds will be used to repurchase shares of stock. There are currently 6,000 shares outstanding. Ignore taxes for questions a and b. Assume the company has a market-to-book ratio of 1.0. a-1 Calculate 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 percent rounded to 2 decimal places, e.g., 32.16.) ROE Recession 18 % Normal 24 % Expansion 27.6 % a-2 Calculate the percentage changes in ROE when the economy expands or enters a recession. (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) % change in ROE Recession -6 % Expansion 3.6 % Assume the firm goes through 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 answers as a percent rounded to 2 decimal places, e.g., 32.16.) ROE Recession 21.6 % Normal 31.6 % Expansion 37.6 % b-2 Calculate the percentage changes in ROE when the economy expands or enters a recession. (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) % change in ROE Recession % Expansion % Assume the firm has a tax rate of 35 percent. c-1 Calculate 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 percent rounded to 2 decimal places, e.g., 32.16.) ROE Recession % Normal % Expansion % c-2 Calculate the percentage changes in ROE when the economy expands or enters a recession. (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) % change in ROE Recession % Expansion % c-3 Calculate the return on equity (ROE) under each of the three economic scenarios assuming the firm goes through with the recapitalization. (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) ROE Recession % Normal 51.64 % Expansion % c-4 Given the recapitalization, calculate the percentage changes in ROE when the economy expands or enters a recession. (Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places. (e.g., 32.16)) % change in ROE Recession 35.45 % Expansion 12.48 %

Explanation / Answer

a) Since the company has a market-to-book ratio of 1.0, the total equity of the firm is equal to the market value of equity. Using the equation for ROE:

ROE=NI/$150,000

The ROE for each state of the economy under the current capital structure and no taxes is:      
Recession Normal Expansion
       ROE 27,000/150,000 36,000/150,000 41,400/150,000
ROE 0.18 0.24 0.276

Sensitivity Analysis: Normal to Recession

%ROE = (0.18 - .0.24)/0.24 = -0.25 or -25%

Sensitivity Analysis: Normal to Expansion

%ROE = (0.276 - 0.24)/0.24 = 0.15 or 15%

b) If the firm goes forward with recapitalization, the new equity value will be:

Equity = $150,000 - $95,000 or $55,000 [due to reduction of shares outstanding]  

So, the ROE for each state of the economy is: ROE = NI/$55,000

Recession Normal Expansion

ROE $19400/55000 $28400/55000 $33800/55000

ROE 0.35 0.52 0.61

Sensitivity Analysis: Normal to Recession

%ROE = (0.35-0.52)/0.52= -0.3269 or 32.69%

Sensitivity Analysis: Normal to Expansion

%ROE = (0.61-0.52)/0.52 = 0.1730 or 17.30%

c) Recession Normal Expansion

EBIT $27,000 $36,000 $41,400

LESS:Interest 7,600 7,600 7,600

EBT $19,400 $28,400 $33,800

LESS:TAX@35% 6790 9940 11830

NI $12,610 $18,460 $21970

ROE 0.2292 0.3356 0.3994

Sensitivity Analysis: Normal to Recession

%ROE = (0.2292-0.3356)/0.3356 = -0.3170 or -31.70%

Sensitivity Analysis: Normal to Expansion

%ROE = (0.3994-0.3356)/0.3356= 0.1901or 19.01%

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