Question

Your company doesn't face any taxes and has $752 million in assets, currently financed entirely with equity. Equity is worth $50.20 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	$102 million	$177 million	$237 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.)

Answer 1

Value of Assets = $752,000,000
Price per share = $50.20

Value of Debt = 15% * Value of Assets
Value of Debt = 15% * $752,000,000
Value of Debt = $112,800,000

Interest Expense = 11% * Value of Debt
Interest Expense = 11% * $112,800,000
Interest Expense = $12,408,000

Value of Equity = Value of Assets - Value of Debt
Value of Equity = $752,000,000 - $112,800,000
Value of Equity = $639,200,000

Number of shares outstanding = Value of Equity / Price per share
Number of shares outstanding = $639,200,000 / $50.20
Number of shares outstanding = 12,733,068

Expected EPS = 0.10 * $7.04 + 0.75 * $12.93 + 0.15 * $17.64
Expected EPS = $13.05

Variance in EPS = 0.10 * (7.04 - 13.05)^2 + 0.75 * (12.93 - 13.05)^2 + 0.15 * (17.64 - 13.05)^2
Variance in EPS = 6.783025

Standard Deviation in EPS = (6.783025)^(1/2)
Standard Deviation in EPS = $2.60