Question

NoNuns Cos. has a 25 percent tax rate and has $302.40 million in assets, currently financed entirely with equity. Equity is worth $30 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		0.20				0.55				0.25
Expected EBIT in state	$	5,846,400			$	11,995,200			$	18,950,400

   

The firm is considering switching to a 25-percent-debt capital structure, and has determined that it would have to pay an 10 percent yield on perpetual debt in either event. What will be the standard deviation in EPS if NoNuns switches to the proposed capital structure? (Do not round intermediate calculations and round your final answer to 2 decimal places.)

	Standard deviation in EPS %

Answer 1

Equity=Assets=302.40 million

Old Number of shares=Equity/Share price=302.40/30=10.08 million

Old Debt=0

New Debt=0.25*302.4=75.6 million

New equity=302.4-75.6=302.8 million

New number of shares=10.08-75.6/30=7.56 million

Recession PAT=(5.846400-75.6*10%)-25%*max(5.846400-75.6*10%,0)=-1.7136

Average PAT=(11.995200-75.6*10%)-25%*max((11.995200-75.6*10%),0)=3.3264

Boom PAT=(18.950400-75.6*10%)-25%*max((18.950400-75.6*10%),0)=8.5428

Standard devaition of EPS will be equal to standard deviation of PAT/number of shares because number of shares is the same in all cases

Average PAT=0.2*(-1.7136)+0.55*3.3264+0.25*8.5428=3.6225 million

Standard deviation of EPS=Standard deviation of PAT/number of shares=sqrt((0.2*(-1.7136-3.6225)^2+0.55*(3.3264-3.6225)^2+0.25*(8.5428-3.6225)^2))/7.56=0.454290503

The correct approach to this question would have been below:

Value of the levered firm=Value of unlevered frim+Debt*tax rate

Let total value be x

Then Debt will be 0.25x and Equity will be 0.75x

So,

x=302.40+0.25x*25%

=>x=322.56 million

Hence, New Debt=0.25*322.56=80.64 million

New Equity=241.92 million

New number of shares=10.08-80.64/30=7.392 million