Question

HiLo, Inc., doesn’t face any taxes and has $53.9375 million in assets, currently financed entirely with equity. Equity is worth $5 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 Pessimistic Optimistic

Probability of state 0.45 0.55

Expected EBIT in state $ 1,553,400 $ 16,138,100

The firm is considering switching to a 20-percent-debt capital structure, and has determined that it would have to pay a 12 percent yield on perpetual debt in either event. What will be the standard deviation in EPS if the firm switches to the proposed capital structure?

I keep getting 8,253,985/8,630,000 which comes out to 0.956, which is obviously wrong. What am I doing wrong?

Answer 1

Total Assets = $53,937,500

Value of Equity = 80% * $53,937,500
Value of Equity = $43,150,000

Number of shares outstanding = Value of Equity / Value per share
Number of shares outstanding = $43,150,000 / $5
Number of shares outstanding = 8,630,000

Value of Debt = 20% * $53,937,500
Value of Debt = $10,787,500

Interest Expense = Interest Rate * Value of Debt
Interest Expense = 12% * $10,787,500
Interest Expense = $1,294,500

Expected EPS = 0.45 * $0.03 + 0.55 * $1.72
Expected EPS = $0.9595

Variance = 0.45 * (0.03 - 0.9595)^2 + 0.55 * (1.72 - 0.9595)^2
Variance = 0.706885

Standard Deviation = (0.706885)^(1/2)
Standard Deviation = $0.84

So, standard deviation in EPS is $0.84