Question

Marsha Jones has bought a used Mercedes horse transporter for her Connecticut estate. It cost $50,000. The object is to save on horse transporter rentals. Marsha had been renting a transporter every other week for $215 per day plus $1.75 per mile. Most of the trips are 80 or 100 miles in total. Marsha usually gives the driver, Joe Laminitis, a $40 tip. With the new transporter she will only have to pay for diesel fuel and maintenance, at about $0.60 per mile. Insurance costs for Marsha’s transporter are $1,950 per year. The transporter will probably be worth $30,000 (in real terms) after eight years, when Marsha’s horse Spike, will be ready to retire. Assume a nominal discount rate of 7% and a 3% forecasted inflation rate. Marsha’s transporter is a personal outlay, not a business or financial investment, so taxes can be ignored. Calculate the NPV of the investment.

Answer 1

The answer involves calculating the financial investment's NPV considering costs and savings, including buying price, fuel and maintenance, insurance, and comparison to rental costs. The expected salvage value after 8 years is factored in using a real discount rate calculated from the nominal rate and inflation.

Step-by-step explanation:

Marsha Jones is considering the financial investment aspects of buying a used Mercedes horse transporter for her estate. To determine whether this purchase is a sound investment, we have to calculate the Net Present Value (NPV) which includes all the costs and savings over the lifespan of the transporter, discounted to their present value. We must account for the purchase price, maintenance and fuel costs, insurance, the expected value after 8 years, and compare this to the costs she would otherwise incur from renting a transport twice a month.

Assuming Marsha would rent a transporter for two days every other week, we first calculate the rental costs per year. With 26 weeks a year, that's 26 rentals for two days each, plus mileage and tip. The annual rental cost is therefore (26 * 2 * $215) + (26 * 2 * 90 miles * $1.75) + (26 * $40) for an average trip length of 90 miles. We also add the yearly insurance costs for her transporter and calculate the maintenance and fuel costs per mile over the expected usage.

The salvage value of the transporter after 8 years is factored in at $30,000, discounted to present value using the real discount rate, which is the nominal rate adjusted for inflation. To find the real discount rate, we use the formula (1+nominal rate)/(1+inflation rate) - 1. The NPV is then calculated by finding the present value of all outlays and income (in this case, cost savings), with the real discount rate applied to future values.