Question

NoNuns Cos. has a 25 percent tax rate and has $302.40 million in assets, currently financed entirely with equity. Equity is worth $30 per share, and book value of equity is equal to market value of equity. Also, let’s assume that the firm’s expected values for EBIT depend upon which state of the economy occurs this year, with the possible values of EBIT and their associated probabilities as shown below:

State	Recession				Average				Boom
Probability of state		0.20				0.55				0.25
Expected EBIT in state	$	5,846,400			$	11,995,200			$	18,950,400

   

The firm is considering switching to a 25-percent-debt capital structure, and has determined that it would have to pay an 10 percent yield on perpetual debt in either event. What will be the standard deviation in EPS if NoNuns switches to the proposed capital structure? (Do not round intermediate calculations and round your final answer to 2 decimal places.)

	Standard deviation in EPS %

Answer 1

First we calculate the EPS with all equity assets

Number of shares = 302,400,000/30 = 10,080,000 shares

The EPS is calculated as shown in the table below:

State	Recession	Average	Boom
Probability	0.2	0.55	0.25
EBIT	5846400	11995200	18950400
Taxes at 25%	-1461600	-2998800	-4737600
Net Income	4384800	8996400	14212800
Number of shares	10080000	10080000	10080000
EPS	0.435	0.8925	1.41
EPS (Weigted average)	$                        0.930375

Mow we calculate the EPS with the debt issue

25% of debt means = 0.25*302,400,000 = 75,600,000

Number of shares to be repurchased = 75,600,000/30 = 2,520,000 shares

Number of shares outstanding = 10,080,000 - 2,520,000 = 7,560,000 shares

Interest on debt = 75,600,000*0.10 = 7,560,000

The EPS after debt issue is calculated as follows:

State	Recession	Average	Boom
Probability	0.2	0.55	0.25
EBIT	5846400	11995200	18950400
Interest	-7560000	-7560000	-7560000
EBT	-1713600	4435200	11390400
Taxes at 25%	428400	-1108800	-2847600
Net income	-1285200	3326400	8542800
Number of shares	7560000	7560000	7560000
EPS	-0.170	0.440	1.130
EPS (Weigted average)	$                             0.4905

Now we calculate the std. deviation in EPS using stdev()

EPS all equity	0.930375
EPS with 25% debt	0.4905
Sd. Deviation	31.104%

Standard deviation in EPS = 31.10% (Rounded to 2 decimals)