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You own a fleet of food trucks. You are thinking about borrowing $2,118,992 for 10 years...

You own a fleet of food trucks. You are thinking about borrowing $2,118,992 for 10 years at 0.05 to upgrade the stove tops in your trucks. This upgrade has an unlevered NPV of 356,960. The terms of this loan require you to add GPS trackers to your trucks, which will cost you $27,539, and $6,408 per year for the next 10 years. Your tax rate is 0.31. 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?

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Expert Solution

Loan amount = 2,118,992

Time of loan = 10 years

Rate = 0.05

Tax rate = 0.31

Unlevered NPV = 356,960

Cost of GPS trackers at Year 0 = 27,539

Per year cost for 10 years cost = 6,408

Incremental costs to be incurred on GPS trackers because of loan = 27,539 + PV of 6,408-10 year Annuity

PV of Annuity Formula = (Payment / R) * (1 - (1+R)-T)

Loan rate will be used for discount rate since that is cost of capital in our case

PV of 6,408-10 year Annuity = (6,408 / 0.05) * (1 - (1+0.05)-10) = 49,480.88

Total Incremental costs on GPS trackers because of loan = 27,539 + 49,480.88 = $ 77,019.9

Now we will find the Tax shield because of loan.

Interest Tax Shield each year = Loan amount * Interest rate * Tax-rate = 2,118,992 * 0.05 * 0.31 = 32,844.38

As the tax shield will remain equal each year, we can calculate its Present value as an annuity at 0.05 discount rate for 10 years

PV of Annuity Formula = (Payment / R) * (1 - (1+R)-T)

PV of Interest Tax-shield = (32844.38 / 0.05)*(1 - (1+0.05)-10) = $ 253,615.6

Incremental NPV after Loan = PV of Interest Tax shield - Incremental costs on GPS trackers after loan

Incremental NPV after loan = 253,615.6 - 77,019.9 = $ 176,595.70

NPV of the upgrade after loan = 356,960 + 176,595.70 = 533,555.70 or $ 533,556

Hence, the Levered NPV of the upgrade is $ 533,556. As Incremental NPV after loan is positive, therefore, Loan should be taken.

jeff jeffy answered 2 years ago
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