Question

Daddi Mac, Inc., doesn’t face any taxes and has $300.40 million in assets, currently financed entirely with equity. Equity is worth $32 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

Expected EBIT in state $ 4,731,300 $ 10,964,600 $ 17,948,900

The firm is considering switching to a 20-percent-debt capital structure, and has determined that it would have to pay an 9 percent yield on perpetual debt regardless of whether it changes the capital structure. What will be the standard deviation in EPS if the firm switches to the proposed capital structure? (Do not round intermediate calculations and round your final answer to 2 decimal places.)

Answer 1

The 1st step will be to compute EPS for each state of economy if debt is issued.

Interest amount = total asset value*percentage of debt in capital*yield

= $300.4 million*20%*9%

= $5,407,200

Now in case of recession expected EBIT = 4,731,000. Net income = EBIT-Interest = 4,731,300-5,407,200 = 675,900 (loss).

Thus EPS = Net income/no. of shares

No. of shares = $300.4 million/32*0.8 = 7,510,000

So EPS = -675,900/7,510,000 = -0.09

Similarly EPS have been computed for each scenario:

Probability	EBIT	Int	Net Income	No of shares	EPS
0.25	$          4,731,300	$      5,407,200	$     (675,900)	7,510,000.00	$    (0.09)
0.6	$        10,964,600	$      5,407,200	$    5,557,400	7,510,000.00	$       0.74
0.15	$        17,948,900	$      5,407,200	$ 12,541,700	7,510,000.00	$       1.67

Using the above EPS figures standard deviation will be computed:

Probability	EPS	EPS*probability	(EPS*probability)^2	(EPS*probability)^2*probability
0.25	$                   (0.09)	$                  (0.02)	$                             0.48	0.119889063
0.6	0.74	0.444	$                             0.05	0.0306456
0.15	1.67	0.2505	$                             0.18	0.026397038
	Total	$                    0.67		0.1769317

Thus standard deviation = 0.1769317^0.5

= 0.4206 or 42.06%

Thus standard deviation = 42.06%