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You own a fleet of food trucks. You are thinking about borrowing $2,367,487 for 10 years...

You own a fleet of food trucks. You are thinking about borrowing $2,367,487 for 10 years at 0.07 to upgrade the stove tops in your trucks. This upgrade has an unlevered NPV of 342,464. The terms of this loan require you to add GPS trackers to your trucks, which will cost you $20,414, and $7,903 per year for the next 10 years. Your tax rate is 0.24. 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?

Solutions

Expert Solution

Solution:-

Interest tax shield(ITS) = interest * debt * tax rate

= 0.07 * $2,367,487 * 0.24

= $39,773.7816

PV of ITS = ITS / r * [1-(1+r)-n]

= $39,773.7816 / 0.07 * [1-(1+0.07)-10]

= $39,773.7816 / 0.07 * 0.4916

= $279,325.5862

Incremental cost:

Upfront cost =C0 = $20,414

Annual cost = $7,903;post tax annual cost,C = pre tax cost * (1-tax rate)

= 7,903 * 76%

= 6,006.28

PV of the Incremental costs = C0 + C/r *[1-(1+r)-10]

= $20,414 + 6,006.28 / 0.07 (0.4916)

= $20,414 + $42,181.24

= $62,595.24

Hence NPV of this upgrade = Unlevered NPV + PV of ITS - PV of Inremental costs

= $342,464 + $279,325.58 -$62,595.24

= $559,194.34

jeff jeffy answered 2 years ago
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