Question

Your company doesn't face any taxes and has $760 million in assets, currently financed entirely with equity. Equity is worth $51.00 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	.10	.75	.15
Expect EBIT in State	$110 million	$185 million	$245 million

The firm is considering switching to a 15-percent debt capital structure, and has determined that they would have to pay a 11 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.)

Multiple Choice

• 6.30

• 13.22

• 2.62

• 13.74

Answer 1

No. of Shares = Total value of Equity / Book Value of Equity = 760,000,000 / 51 =14,901,960.78 = 14,901,961

If 15% debt is raised ,as portion of present capital of $760 millions

Debt value = 760,000,000 *0.15 = $114,000,000

Interest on debt @ 11% = $114,000,000 *11% = $12,540,000

EPS = Earning after Interest / No of shares.

Mean EPS() = P₁ * EPS₁ + P₂ * EPS₂ +P₃ * EPS₃

Standard Deviation =

State	Probability	EBIT	Earning after interest	EPS	EPS^2	Standard Deviation
Recession	0.1	110000000	97460000	$6.54	$42.77	2.61
Average	0.75	185000000	172460000	$11.57	$133.93
Boom	0.15	245000000	232460000	$15.60	$243.34
				$11.67	$141.23

option C : 2.62