Question

Pendergast, Inc., has no debt outstanding, and has a total market value of $180,000. Earnings before interest and taxes (EBIT) are projected to be $23,000 if economic conditions are normal. If there is a strong expansion in the economy, then EBIT will be 20% higher. If there is a recession, then EBIT will be 30% lower. Pendergast is considering a $75,000 debt issue with a 7% interest rate. The proceeds will be used to repurchase shares of stock. There are currently 6,000 shares of stock outstanding, and the relevant tax rate is 35%.

a- Calculate ROE and EPS under each of the economic scenarios before any debt is issued.

b- Repeat part a, assuming that the company goes through with the capitalization.

c- Calculate the percentage changes in EPS when the economy expands or enters a recession.

Answer 1

a) ROE and EPS

EPS= Earnings / No. of shares

ROE= Earnings / Value of Equity

Earnings = (EBIT- Interest)(1-Taxes)

Using the given details and above formula, we solve

Economy	Recession	Normal	Boom
EBIT	16100	23000	27600
Less Interest	0	0	0
EBT	16100	23000	27600
Less Taxes	-5635	-8050	-9660
Profit	10465	14950	17940
No. Of shares	6000	6000	6000
EPS	1.74	2.49	2.99
Market Value	180000	180000	180000
Debt	0	0	0
Market value of Equity	180000	180000	180000
ROE	5.81%	8.31%	9.97%

b) Company uses 75000 debt to repay the equity. Number of equity shares that can be paid = 75000/ Price per share

= 75000 Divide (180000 / 6000)

75000 divide 30

= 2500 shares

Balance number of shares = 6000 - 2500 = 3500 shares

Market Value of equity = Value of firm - Value of debt

We assume value of firm remains the same as per MM approach, hence value of equity = value of firm - debt

= 180000 - 75000 = 105000

We do the same calculation as in part a)

Economy	Recession	Normal	Boom
EBIT	16100	23000	27600
Less Interest	-5250	-5250	-5250
EBT	10850	17750	22350
Less Taxes	-3797.5	-6212.5	-7823
Profit	7052.5	11538	14528
No. Of shares	3500	3500	3500
EPS	2.02	3.30	4.15
Market Value	180000	180000	180000
Debt	-75000	-75000	-75000
Market value of Equity	105000	105000	105000
ROE	6.72%	10.99%	13.84%

c) Chnage in EPS

Without Debt

	Recession	Normal	Boom
EPS	1.74	2.49	2.99
% Change in EPS	-30%		20%

With debt

	Recession	Normal	Boom
EPS	2.02	3.30	4.15
% Change in EPS	-39%		26%

We observe that, EPS becomes more sensitive to change in EBIT, this is because leverage increases.