Question

RAK, Inc., has no debt outstanding and a total market value of $140,000. Earnings before interest and taxes, EBIT, are projected to be $32,000 if economic conditions are normal. If there is strong expansion in the economy, then EBIT will be 12 percent higher. If there is a recession, then EBIT will be 30 percent lower. RAK is considering a $115,000 debt issue with an interest rate of 6 percent. The proceeds will be used to repurchase shares of stock. There are currently 7,000 shares outstanding. Ignore taxes for questions a and b. Assume the company has a market-to-book ratio of 1.0.

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

c-1) Market to book ratio 1.0 means that market value of equity = book value of equity = $140,000

ROE

Particulars	Normal	Expansion	Recession
EBIT	$32000	$32000 x 1.12 = $35840	$32000 x 0.70 = $22400
Less: Interest	$0	$0	$0
EBT	$32000	$35840	$22400
Less: Tax@35%	$11200	$12544	$7840
Net Income (a)	$20800	$23296	$14560
Value of Equity (b)	$140000	$140000	$140000
ROE [ (a / b) x 100 ]	14.86%	16.64%	10.40%

c-2) % change in ROE in case of expansion = (16.64% - 14.86%) / 14.86% = 0.1198 or 11.98%

% change in ROE in case of recession = (10.40% - 14.86%) / 14.86% = (-)0.3001 or (-)30.01%

c-3) Debt to be issued = $115000, Current price of stock = market value / no. of shares = $140000/ 7000 = $20

This amount will be used to purchase stock at the current price of $20.

Shares to be repurchased = $115000 / $20 = 5750

No. of shares remaining = 7000 - 5750 = 1250

Value of equity = 1250 x $20 = $25000

ROE

Particulars	Normal	Expansion	Recession
EBIT	$32000	$32000 x 1.12 = $35840	$32000 x 0.70 = $22400
Less: Interest ($115200 x 6%)	$6900	$6900	$6900
EBT	$25100	$28940	$15500
Less: Tax@35%	$8785	$10129	$5425
Net Income (a)	$16315	$18811	$10075
Value of Equity (b)	$25000	$25000	$25000
ROE [ (a / b) x 100 ]	65.26%	75.24%	40.30%

c-2) % change in ROE in case of expansion = (75.24% - 65.26%) / 65.26% = 0.1529 or 15.29%

% change in ROE in case of recession = (40.30% - 65.26%) / 65.26% = (-)0.3825 or (-)38.25%