Question

You own a fleet of food trucks. You are thinking about borrowing $2,496,626 for 10 years at 0.06 to upgrade the stove tops in your trucks. This upgrade has an unlevered NPV of 302,555. The terms of this loan require you to add GPS trackers to your trucks, which will cost you $24,608, and $8,642 per year for the next 10 years. Your tax rate is 0.23. You have little use for the GPS trackers, and would not have purchased them if the loan covenants did not require them. What is the NPV of this upgrade if you take take the loan?

Answer 1

Interest tax shield, ITS = Interest rate x Debt x tax rate = 0.06 x 2,496,626 x 0.23 = 34,453.44

PV of ITS = ITS / r x [1 - (1 + r)^-n] = 34,453.44 / 0.06 x [1 - (1 + 0.06)^-10] = 253,580.31

Incremental cost:

• Upfront cost = C0 = 24,608
• Annual cost = 8,642; Post tax annual cost, C = Pre tax cost x (1 - tax rate) = 8,642 x (1 - 23%) = 6,654.34

PV of the incremental costs = C0 + C / r x [1 - (1 + r)^-n] = 24,608 + 6,654.34 / 0.06 x [1 - (1 + 0.06)^-10] = 73,584.52

Hence, the NPV of this upgrade if you take take the loan

= Unlevered NPV + PV of ITS - PV of the incremental costs

= 302,555 + 253,580.31 - 73,584.52

= $ 482,550.787