Question

Marsha Jones has bought a used Mercedes horse transporter for her Connecticut estate. It cost $47,000. The object is to save on horse transporter rentals.

Marsha had been renting a transporter every other week for $212 per week plus $1.60 per mile. Most of the trips are 90 miles in total. Marsha usually gives the driver a $50 tip. With the new transporter she will only have to pay for diesel fuel and maintenance, at about $.57 per mile. Insurance costs for Marsha’s transporter are $1,800 per year.

The transporter will probably be worth $27,000 (in real terms) after eight years, when Marsha’s horse Nike will be ready to retire. Assume a nominal discount rate of 9% and a forecasted inflation rate of 3%. Marsha’s transporter is a personal outlay, not a business or financial investment, so taxes can be ignored. Hint: All numbers given in the questions are in real terms. Assume CF at end of year, for simplicity.

Calculate the NPV of the investment. (Do not round intermediate calculations. Round your answer to the nearest whole dollar amount.)

NPV            $   

Answer 1

Real discount rate=nominal discount rate-inflation rate=9%-3%=6%

Considering, 1 year=52 week, yearly rental savings=212*52=$11024

Per mile savings=(1.60-0.57)=$1.03 and hence yearly savings=1.03*90*52=4820.4

Driver's tip savings=52*50=2600

Now,

Year	Initial Investment	Salavage Value	Rental Savings	Driver Tip savings	Fuel Savings	Insurace Cost	Cash Flow (Sum(B:G))	Discounted cashflow (Cash flow/1.06^year)
0	(47,000.00)	-	-	-	-	-	(47,000.00)	(47,000.00)
1	-	-	11,024.00	2,600.00	4,820.40	(1,800.00)	16,644.40	15,702.26
2	-	-	11,024.00	2,600.00	4,820.40	(1,800.00)	16,644.40	14,813.46
3	-	-	11,024.00	2,600.00	4,820.40	(1,800.00)	16,644.40	13,974.96
4	-	-	11,024.00	2,600.00	4,820.40	(1,800.00)	16,644.40	13,183.92
5	-	-	11,024.00	2,600.00	4,820.40	(1,800.00)	16,644.40	12,437.66
6	-	-	11,024.00	2,600.00	4,820.40	(1,800.00)	16,644.40	11,733.65
7	-	-	11,024.00	2,600.00	4,820.40	(1,800.00)	16,644.40	11,069.48
8	-	27,000.00	11,024.00	2,600.00	4,820.40	(1,800.00)	43,644.40	27,383.04
							NPV (Total Present Value)	73,298.43

Hence, NPV=$73298