Question

Making Money, Inc. is considering the purchase of a new truck so it can make more money. The truck costs $120,000.

Making Money, Inc. had been renting the truck every week for $500 per week plus $1.20 per mile. On average, the truck is traveling 75 miles per week.

If Making Money, Inc. purchases the truck, it will only have to pay for diesel fuel and maintenance, at about $.50 per mile. Insurance costs for the new truck are $5,000 per year.

The truck will probably be worth $20,000 (in real terms) after six years, when the company would be looking to sell the truck.

Assume a nominal discount rate of 10% and a forecasted inflation rate of 2.5%. The tax code is rapidly changing, so we are going to ignore taxes for now.

WHAT IS THE NPV of BUYING vs RENTING? (round to nearest whole dollar)

Hint: All numbers given in the questions are in real terms. Assume CF at end of year, for simplicity.

Hint #2:

Step 1: list assumptions

Step 2: calc real interest rate

Step 3: Calc cost (NPV) to rent

Step 4: Calc cost (NPV) to buy

Step 5: subtract NPVs

Answer 1

1. Assumptions:

For renting:

• Cost incurred are rent of $500 per week plus $1.20 per mile
• Truck travels 75 miles per week.

For buy option:

• Cost of truck = $120,000
• Useful life = 6 years
• Salvage value = $20,000
• Diesel and maintenance cost = $0.50 per mile
• Insurance cost = $5,000

Step 2:

Nominal discount rate = 10%

Inflation rate = 2.5%

Real interest rate = Nominal rate - Inflation rate =10% - 2.5% = 7.5%

Step 3:

NPV calculation to rent:

Weekly rent = $500 + $1.20 * 75 = $590

Number of weeks in a year = 52

Annual rent = $590 * 52 = $30,680

Present Value Interest Factors for a One-Dollar Annuity Discounted at 7.5% for 6 years = 4.693846

NPV = 4.693846 * (- $30,680) = - $144,007

Step 4:

Calculate NPV for buy option:

Diesel fuel and maintenance cost = $.50 per mile

Annual Diesel fuel and maintenance cost = $0.50 * 75 * 52 = $1950

NPV is calculated as below:

Step 5

NPV of Buy option - NPV of rent option = -$139,663 - ( - $144,007) = $4,344

Buying option is better and should be chosen.