Question

Marsha Jones has bought a used Mercedes horse transporter for her Connecticut estate. It cost $36,000. The object is to save on horse transporter rentals.

Marsha had been renting a transporter every other week for $201 per week plus $1.05 per mile. Most of the trips are 90 miles in total. Marsha usually gives the driver a $45 tip. With the new transporter she will only have to pay for diesel fuel and maintenance, at about $.46 per mile. Insurance costs for Marsha’s transporter are $1,250 per year.

The transporter will probably be worth $16,000 (in real terms) after eight years, when Marsha’s horse Nike will be ready to retire. Assume a nominal discount rate of 10% and a forecasted inflation rate of 4%. 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.)

Answer 1

(1+Dnominal) = (1+Dreal)*(1+Inflation)

Dreal = (1+Dnominal)/(1+inflation) - 1

= (1+10%)/(1+4%) - 1 = 5.77%

Calculation of savings:

	Savings:	Rental		Transporter
	Rent per week ('r)	201
	Miles in one trip (n)	90	Miles in one trip (n)	90
	Cost/mile ('c)	1.05	Cost/mile ('c)	0
(n*c)	Total miles cost (T)	95	Total miles cost (T)	41
(T+r)	Total cost per trip (TC)	296	Cost/year (TC) (T*26)	1,076
	Number of weeks hired (N)	26	Insurance/year (I)	1,250
(TC*N)	Total annual cost	7,683	Total annual cost (TC+I)	2,326
	Net savings	5,357

Calculation of incremental NPV of buying the transporter:

	Discount rate	5.77%
	Life (n)	8
	Initial investment (a)	(36,000)
	Annual savings (b)	5,357
b*((1-(1+Dr)^-n)/Dr	PV of annual savings ('c)	33,569
	Salvage value (d)	16,000
d/(1+Dr)^n	PV of salvage ('e)	10,215
(a+c+e)	NPV	7,784

Thus, NPV of buying the transporter is $7,784.