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 % Normal % Expansion % 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 % Expansion % 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 % Normal % Expansion % 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 % 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 % Expansion %

Answer 1

Without Taxes

RAK	Expansion	Normal	Recession
EBIT	41,400	36,000	27,000
ROE	27.60%	24.00%	18.00%
% Change	15.0%		-25.0%
With Debt	Boom	Normal	Recession
EBIT	41,400	36,000	27,000
Interest	-7,600	-7,600	-7,600
Profits	33,800	28,400	19,400
ROE	61.45%	51.64%	35.27%
% Change	19.0%		-31.7%

With Taxes

RAK	Expansion	Normal	Recession
EBIT	41,400	36,000	27,000
Taxes (35%)	-14,490	-12,600	-9,450
Profits	26,910	23,400	17,550
ROE	17.94%	15.60%	11.70%
% Change	15.0%		-25.0%
With Debt	Boom	Normal	Recession
EBIT	41,400	36,000	27,000
Interest	-7,600	-7,600	-7,600
EBT	33,800	28,400	19,400
Taxes (35%)	-11,830	-9,940	-6,790
Profits	21,970	18,460	12,610
ROE	39.95%	33.56%	22.93%
% Change	19.0%		-31.7%

Without debt, Equity = 150,000 and with debt, Equity = 150,000 - 95,000 = 55,000

Interest expense = 95,000 x 8% = 7,600

ROE = Profits / Equity