Question

Your company doesn't face any taxes and has $501 million in assets, currently financed entirely with equity. Equity is worth $40.10 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:

	Recession	Average	Boom
EBIT	$51,000,000	$101,000,000	$171,000,000
− Interest	-10,020,000	-10,020,000	-10,020,000
= EBT/NI	40,980,000	90,980,000	160,980,000
Shares = $51,000,000 x (1-.20) = $40,800,000/$40.10 = 1,017,456
EPS	4.10	9.10	16.11

The firm is considering switching to a 20-percent debt capital structure, and has determined that they would have to pay a 10 percent yield on perpetual debt in either event. What will be the level of expected 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.)

The expected EPS will be equal to (.20 x 4.10) + (.50 x 9.10) + (.30 x 16.11) = $10.20

Answer 1

Value of Assets = $501,000,000

Value of Debt = 20% * Value of Assets
Value of Debt = 20% * $501,000,000
Value of Debt = $100,200,000

Interest Expense = 10% * Value of Debt
Interest Expense = 10% * $100,200,000
Interest Expense = $10,020,000

Value of Equity = 80% * Value of Assets
Value of Equity = 80% * $501,000,000
Value of Equity = $400,800,000

Price per share = $40.10

Shares outstanding = Value of Equity / Price per share
Shares outstanding = $400,800,000 / $40.10
Shares outstanding = 9,995,012

Recession Average Boom 51,000,000 $ 101,000,000 $ 171,000,000 10,020,000 $ 40,980,000 $ $ EBIT 10,020,000 $ 90,980,000 $ 160,980,000 $ Less: Interest 10,020,000 EBT Shares outstanding 9,995,012 9,995,012 9,995,012 4.10 $ 9.10 $ EPS 16.11

Expected EPS = Probability of Recession * EPS under Recession + Probability of Average * EPS under Average + Probability of Boom * EPS under Boom
Expected EPS = 0.20 * $4.10 + 0.50 * $9.10 + 0.30 * $16.11
Expected EPS = $10.20