Question

Fitzgerald Industries has a new project available that requires an initial investment of $4.8 million. The project will provide unlevered cash flows of $852,000 per year for the next 20 years. The company will finance the project with a debt-value ratio of .25. The company’s bonds have a YTM of 7.3 percent. The companies with operations comparable to this project have unlevered betas of 1.07, .95, 1.22, and 1.17. The risk-free rate is 4.5 percent and the market risk premium is 6.1 percent. The tax rate is 22 percent.

  

What is the NPV of this project?

Answer 1

debt to value=   0.25  
so Equity = 1-0.25 =   0.75  
Average of Unlevered betas = (1.07+0.95+1.22+1.17)/4=   1.1025  
Levered beta or Equity beta formula = Unlevered or Asset beta * (1 +( (1-tax rate)*Debt/Equity))      
1.1025*(1+((1-22%)*0.25/0.75))      
1.38915      
cost of Equity = risk free rate +(beta * Market risk Premium)      
4.5% + (1.38915*6.1%)      
0.12973815      
      
Pretax Cost of debt =    0.0730  
Cost of levered Equity =    0.12973815  
      
weighted average cost of capital(wacc)=      
(Weight of equity * cost of equity)+(weight of debt*pretax cost of debt*(1-tax rate))      
(0.75*0.12973815)+(0.25*0.073*(1-22%))      
0.1115386125      
      
So Discount rate (i)=   0.1115386125  
Annual cash inflows =   582000  
      
      
Time (n)=   20  
Initial Investment   -4800000  
      
Present value of annual Cash inflows = Annual amount * (1-(1/(1+r)^n) / r      
582000*(1-(1/(1+0.1115386125)^20))/0.1115386125      
4588408.119      
      
NPV is Sum of present value of all cash flows      
-4800000+ 4588408.12      
-$211,591.88      
      
So NPV of project is   -$211,591.88