Question

RAK, Inc., has no debt outstanding and a total market value of $250,000. Earnings before interest and taxes, EBIT, are projected to be $42,000 if economic conditions are normal. If there is strong expansion in the economy, then EBIT will be 18 percent higher. If there is a recession, then EBIT will be 30 percent lower. RAK is considering a $100,000 debt issue with an interest rate of 8 percent. The proceeds will be used to repurchase shares of stock. There are currently 10,000 shares outstanding. Ignore taxes for questions a and b. Assume the company has a market-to-book ratio of 1.0. 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

c-1

ROE = EBIT*(1-tax rate)/Market value

Recession

ROE = EBIT*(1-recession impact%)*(1-tax rate)/market value

ROE=42000*(1-0.3)*(1-0)/250000

ROE=11.76

Normal

ROE = EBIT*(1-tax rate)/Market value

ROE=42000*(1-0)/250000

ROE=16.8

Expansion

ROE = EBIT*(1+Growth impact%)*(1-tax rate)/Market value

ROE=42000*(1+0.18)*(1-0)/250000

ROE=19.82

c-2

%age change in ROE for Recession

=(ROE recession/ROE normal-1)*100

=(0.1176/0.168-1)*100

=-30%

%age change in ROE for Growth

=(ROE Growth/ROE normal-1)*100

=(0.1982/0.168-1)*100

=17.98%

c-3

New market value = old market value-debt

=250000-100000

=150000

ROE = (EBIT-debt*interest%)*(1-tax rate)/new market value

Recession

ROE = (EBIT*(1-recession impact%)-debt*interest %age)*(1-tax rate)/new market value

ROE=(42000*(1-0.3)-100000*0.08)*(1-0)/150000

ROE=14.27

Normal

ROE = (EBIT-debt*interest%)*(1-tax rate)/new market value

ROE=(42000-100000*0.08)*(1-0)/150000

ROE=22.67

Expansion

ROE= (EBIT*(1+growth impact%)-debt*interest %age)*(1-tax rate)/new market value

ROE=(42000*(1+0.18)-100000*0.08)*(1-0)/150000

ROE=27.71

c-4

%age change in ROE for Recession

=(ROE recession/ROE normal-1)*100

=(0.1427/0.2267-1)*100

=-37.05%

%age change in ROE for Growth

=(ROE Growth/ROE normal-1)*100

=(0.2771/0.2267-1)*100

=22.23%