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 week plus $1.75 per mile. Most of the trips are 90 miles in total. Marsha usually gives the driver a $40 tip. With the new transporter she will only have to pay for diesel fuel and maintenance, at about $.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 Nike will be ready to retire. Assume a nominal discount rate of 7% 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

	Transporter		Rental
Rent/week (a)	215	Number of trips/year (a)	26
Weeks rented (b)	26	Miles/trip (b)	90
Total rent (c = a*b)	5,590	Total miles (c = a*b)	2,340
Miles/trip (d)	90	Price/mile (d)	0.60
Price/mile ('e)	1.75	Total price (e = c*d)	1,404
Total price (f = b*d*e)	4,095	Insurance cost (f)	1,950
Tip/trip (g)	40
Total tips (h = g*b)	1,040
Total cost (I = c+f+h)	10,725	Total cost (G = e+f)	3354
Net savings (I-G)	7,371

Real discount rate d = (n-i)/(1+i) where n = nominal discount rate and i = forecasted inflation

d = (7%-3%)/(1+3%) = 3.88%

Formula	Initial investment (II)	(50,000)
	Life (N)	8
	Salvage value (SV)	30,000
	Discount factor (D)	3.88%
	PMT	7,371
PV(D,N,PMT)	PV of PMT (a)	49,867
PV(D,N,0,FV)	PV of salvage value (b)	22,118
(II + a + b)	NPV	21,985

NPV of the investment = 21,985