Question

A 5-year project requires an initial investment of $28 million.  It generates an annual cash flow of $9 million. The unlevered cost of equity is 20%.  A loan of $22.5 million at a rate of 10%.  Principal will be repaid in a lump sum when project ends.  However, the lender will extend the loan for only three years.  The firm’s tax rate is 30%.  Calculate the project’s adjusted present value.  

Answer 1

Present value of cash flows = -28million+(9million/1.2)+(9million/[1.2]^2)+(9million/[1.2]^3)+(9million/[1.2]^4)+(9million/[1.2]^5)

= -28million+7.5million+(9million/1.44)+(9million/1.728)+(9million/2.0736)+(9million/2.48832)

= -28,000,000+7,500,000+6,250,000+5,208,333+4,340,278+3,616,898

= -$1,084,491

Tax savings due to debt per year = Loan amount*interest rate*tax rate

= $22.5million*10%*30% = $675,000

Present value of tax savings = (675,000/1.1)+(675,000/[1.1]^2)+(675,000/[1.1]^3)+(675,000/[1.1]^4)+(675,000/[1.1]^5)

= 613,636+(675,000/1.21)+(675,000/1.331)+(675,000/1.4641)+(675,000/1.61051)

= 613,636+557,851+507,138+461,034+419,122

= $2,558,781

Adjusted present value = Present value of cash flows+Present value of tax savings

= -$1,084,491+$2,558,781

= $1,474,290