RAK, Inc., has no debt outstanding and a total market value of $250,000. Earning
ID: 2767451 • Letter: R
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 $40,000 if economic conditions are normal. If there is strong expansion in the economy, then EBIT will be 20 percent higher. If there is a recession, then EBIT will be 20 percent lower. RAK is considering a $105,000 debt issue with an interest rate of 4 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.
a1- Calculate return on equity (ROE) under each of the three economic scenarios before any debt is issued.
a2- Calculate the percentage changes in ROE when the economy expands or enters a recession.
Assume the firm goes through with the proposed recapitalization.
b1- Calculate the return on equity (ROE) under each of the three economic scenarios.
b2- Calculate the percentage changes in ROE when the economy expands or enters a recession.
Assume the firm has a tax rate of 35 percent.
c1- Calculate return on equity (ROE) under each of the three economic scenarios before any debt is issued.
c2- Calculate the percentage changes in ROE when the economy expands or enters a recession.
c3- Calculate the return on equity (ROE) under each of the three economic scenarios assuming the firm goes through with the recapitalization.
c4- Given the return on equity (ROE) under each of the three economic scenarios assuming the firm goes through with the recapitalization.
Explanation / Answer
Part A
Calculation of EPS before any Debt issue is shown In the following table:
Recession
Normal
Expansion
EMT
32,000
40,000
48,000
Less: Interest
0
0
0
EST
32,000
40,000
48,000
Less: Taxes
0
0
0
Net Income(A)
32,000
40,000
48,000
Shareholders’ equity(B)
250,000
250,000
250,000
ROE (A/B)
0.128
0.16
0.192
Percentage change in ROE when Economy changes from Normal to Expansion: Percentage change = (ROE under Expansion— ROE under Normal) / ROE under Normal *100 = (0.192 —0.16/0.16*100 = 20%
Percentage change in ROE when Economy changes from Normal to Recession: Percentage change = (ROE under recession— ROE under Normal)/ ROE under Normal* 100
= (0.128-0.16)/0.16*100 = - 20%
Part b
To calculate the revised ROE, we need to calculate the revised number of outstanding shares. The company would utilize the amount of $60,000 to repurchase stock which will reduce the number of outstanding shares. The revised outstanding shares have been calculated as follows:
Current Market Value of Stock = Total Market Value/Number of Shares= 250,000/10,000 = $25 per share
Number of Shares Bought Back = Value of Debt/Current Market Value of Stock =105,000/25 = 4,200 shares
Revised Number of Shares Outstanding= Current Shares Outstanding - Number of Shares Bought Back = 10,000 -4,200 =5,800 shares
Calculation of ROE after Debt issue is shown in the following table
Recession
Normal
Expansion
EBIT
32,000
40,000
48,000
Less: Interest (105,000*4%)
4,200
4,200
4,200
EBT
27,800
35,800
43,800
Less: Taxes
0
0
0
Net income(A)
27,800
35,800
43,800
Shareholders’ equity(b)
145,000
145,000
145,000
ROE
0.191
0.2469
0.302
Percentage Change in ROE when Economy Changes from Normal to Expansion:
Percentage Change = (ROE under Expansion - ROE under Normal)/ROE under Normal*100
= (0.302 -0.247)/0.247*100 = 22.34%
Percentage Change in ROE when Economy Changes from Normal to Recession:
Percentage Change = (ROE under Recession- ROE under Normal)/ROE under Normal*100
= (0.191 -0.2469)/0.2469*100 =-22
Recession
Normal
Expansion
EMT
32,000
40,000
48,000
Less: Interest
0
0
0
EST
32,000
40,000
48,000
Less: Taxes
0
0
0
Net Income(A)
32,000
40,000
48,000
Shareholders’ equity(B)
250,000
250,000
250,000
ROE (A/B)
0.128
0.16
0.192
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