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 $81.8 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 $13.9 million per annum for 20 years starting from the end of the first year. The corporate tax rate is 34 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 10.3 percent. To encourage investment in the country’s infrastructure, the U.S. government will subsidize the project with a $26.8 million, 15-year loan at an interest rate of 6.8 percent per year. All principal will be repaid in one balloon payment at the end of Year 15. The company issued subsidized debt instead of issuing debt at the terms it normally would. Assume the face amount and maturity of the debt issue are the same. Calculate the gain or loss from subsidized debt.

Answer 1

Before moving to calculation of gain or loss of subsidized debt, calculate the annual present value of the project.

Annual Present Value = NPV (All Equity) + NPV (All debt)

Calculation of NPV of All Equity

Depreciation = Purchase Cost / Number of Years

                        = $81,800,000 / 5

                        = $16,360,000

Note: Depreciation is calculated for 5 years and hence, it is discounted for 5 years.

NPV (All Equity) = ([Present Value of Earnings after consideration of corporate tax + Present Value of depreciation tax shield] - Purchase Cost)

PV of earnings after taxes = 1,39,00,000 * (1-0.35) * PVIFA (15% for 20 years)

                                               = 1,39,00,000 * (0.66) * 6.2593

                                               = 57,422,818.2

PV of depreciation tax shield = Depreciation Amount x Corporate Tax (%) x PVIFA (15% for 5 years)

                                                    = 16,360,000 x 0.34 x 3.3522

                                                    = 18,646,277.28

Purchase Price = 81,800,000

NPV (All Equity) = ([Present Value of Earnings after consideration of corporate tax + Present Value of depreciation tax shield] - Purchase Cost)

                              =57,422,818.2 + 18,646,277.28 – 81,800,000

                              = -5,730,904.52

Calculation of Debt Interest after tax = Debt Value x Coupon Rate x Corporate Tax

                                                   = 26,800,000 x 6.8% x (1-0.34)

                                                   = 1,202,784

NPV(Debt) = Amount Borrowed – Present value of after tax interest payments – Present Value of Loan Payments

Amount Borrowed = 26,800,000

Present value of after tax interest payments = Loan Amount x Coupon Rate x Corporate Tax x PVIFA (6.8% for 15 years)

                                                                                = [1,202,784] x PVIFA (6.8% for 15 years)

                                                                                = 1,202,784 x 9.2241

                                                                                = 11,094,599.89

Present value of loan repayment = Loan Amount / (1.068)^15

                                                           = 26,800,000 x 2.6826

                                                           = 9,990,307.91

  

NPV (All Debt) = 26,800,000 – 11,094,599.89 – 9,990,307,91

                              = 5,715,092.2          

  

Since, NPV of Debt is positive, there is a gain from the subsidized debt.

   NPV positive implies that you are paying less than what is expected to pay.

   The gain from subsidized debt = NPV (All Debt) = 5,715,092.2