Question

Triad Corporation has established a joint venture with Tobacco Road Construction, Inc., to build a toll road in North Carolina. The initial investment in paving equipment is $197 million. The equipment will be fully depreciated using the straight-line method over its economic life of five years. Earnings before interest, taxes, and depreciation collected from the toll road are projected to be $29.3 million per annum for 20 years starting from the end of the first year. The corporate tax rate is 23 percent. The required rate of return for the project under all-equity financing is 15 percent. The pretax cost of debt for the joint partnership is 8.7 percent. To encourage investment in the country’s infrastructure, the U.S. government will subsidize the project with a $130 million, 15-year loan at an interest rate of 5.2 percent per year. All principal will be repaid in one balloon payment at the end of Year 15.

  

What is the adjusted present value of this project?

Answer 1

Answer: Adjusted Present value of the Project would be

APV = NPV + Sd + Sl + VI

NPV = Net present value of the Cash flows that we will receive over 20 years

Sd = Present value of Depreciation Tax shield

Sl = Present value of Tax shield from the loan

Vl = Present value of loan repayment

Annual Cash flow for the Project = $29.3 million * (1 - tax rate)

Corporate tax rate =23%

Annual Cash flow for the Project = $29.3 million * ( 1- 0.23) = $22.561 million

NPV = Cash flow * PVIFA _{15%,20 yrs,}- Initial Investment = (22.561 * 6.2593 ) million - $197 million = 141.2161 - 197 = -55.7839 million

Present value of depreciation Tax shield = Initial Investment / no of years * corporate tax rate * present value interest factor of annuity.

Putting the values

Use the PVIFA table

197 / 5 * 23% * PVIFA _{15%, 5 years}  = 39.4*0.23 * 3.3522 = $ 30.37764 million

Present value of tax shield from the Loan = 130 million * 5.2% * 23% * PVIFA _{15%, 15 years} = 130* 0.052 * 0.23 * 5.8474 = 9.091538

Present value of Loan Repayment (Vl) = 130 million -( 130 * 5.2% * 5.8474) - 130 * PVIF _{15%,15 years} = 130 - 39.52 -130*0.1229

= 130 -39.52 - 15.977 = $74.49 million

Adjusted Present Value would be -$55.7839 + $30.37764 + $9.091538 + $74.49 = $58.17982 million.