Stackhouse Industries has a new project available that requires an initial inves

Question

Stackhouse Industries has a new project available that requires an initial investment of $5.9 million. The project will provide unlevered cash flows of $815,000 per year for the next 20 years. The company will finance the project with a debt-to-value ratio of .45. The company’s bonds have a YTM of 6 percent. The companies with operations comparable to this project have unlevered betas of 1.29, 1.22, 1.44, and 1.39. The risk-free rate is 3 percent, and the market risk premium is 6.2 percent. The company has a tax rate of 35 percent.

What is the NPV of this project?

Explanation / Answer

Average of unlevered betas = (1.29+1.22+1.44+1.39)/4 = 1.335

Debt to value = 0.45/1

Debt to equity = debt/(value-debt) = .45/(1-.45) = 0.8181

Levered Beta = Unlevered Beta x (1 + ((1 – Tax Rate) x (Debt/Equity)))

= 1.335*(1+((1-0.35)*(0.8181))) = 2.044906

Cost of equity = risk-free rate + beta * (market risk premium) = 3+2.044906*6.2 = 15.678%

WACC = D/A*cost of debt*(1-tax rate)+E/A*cost of equity

= .45*6*(1-0.35)+.55*15.678 = 10.3779%

NPV = -initial investment+20 year annuity of cashflows discounted at WACC

= -5900000+815000*[(1 - (1+ 10.3779/100)^(-20))/(10.3779/100)] = 863279.0549

where annuity formula is C*[(1-(1+i/100)^(-n))/(i/100)]

C = Cash flow per period

i = interest rate

n = number of payments

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