Question

Your company doesn't face any taxes and has $757 million in assets, currently financed entirely with equity. Equity is worth $50.70 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	.25	.60	.15
Expect EBIT in State	$107 million	$182 million	$242 million

The firm is considering switching to a 25-percent debt capital structure, and has determined that they would have to pay a 8 percent yield on perpetual debt in either event. What will be the standard deviation in EPS if they switch to the proposed capital structure? (Round your intermediate calculations and final answer to 2 decimal places except calculation of number of shares which should be rounded to nearest whole number.)

Answer 1

Solution:
	Standard deviation of EPS = 3.84 %
Working Notes:
	Interest cost in all cases = Interest rate x 25% x total assets
		=8% x (25%X$757,000,000)
		= $15,140,000
	No. of shares outstanding = 75% X Total assets / Market price per share
	=75% x $757,000,000/$50.70 = 11,198,224.85
	=11,198,225 Shares
	EPS when in capital structure 25% is debt in each situation of economy
	State	Recession	Average	Boom
	EBIT	107,000,000	182,000,000	242,000,000
Less:	Interest	15,140,000	15,140,000	15,140,000
	EBT	91,860,000	166,860,000	226,860,000
Less:	Taxes @ 0%	0	0	0
	Net Income (EAT) (a)	91,860,000	166,860,000	226,860,000
	÷
	No. of shares (b)	11,198,225	11,198,225	11,198,225
	EPS (a/b)	8.20	14.90	20.26
	Probability	0.25	0.60	0.15
	Expected EPS = Sum of (EPS x Prob.)
	=8.20 x 0.25 + 14.90 x 0.60 +20.26 x 0.15
	=14.029
	=14.03
	Standard deviation of EPS = Square root of ( 0.25 x(8.20-14.03)^2 +0.60 x(14.90-14.03)^2 +0.15 x(20.26-14.03)^2)
	Standard deviation of EPS = Square root of ( 14.7733)
	Standard deviation of EPS = ( 14.7733)^(1/2)
	Standard deviation of EPS = 3.843605079
	Standard deviation of EPS = 3.84 %
Please feel free to ask if anything about above solution in comment section of the question.