In: Finance
Marsha Jones has bought a used Mercedes horse transporter for
her Connecticut estate. It cost $43,000. The object is to save on
horse transporter rentals.
Marsha had been renting a transporter every other week for $208 per
day plus $1.40 per mile. Most of the trips are 80 or 100 miles in
total. Marsha usually gives Joe Laminitis, the driver, a $35 tip.
With the new transporter she will only have to pay for diesel fuel
and maintenance, at about $0.53 per mile. Insurance costs for
Marsha’s transporter are $1,600 per year.
The transporter will probably be worth $23,000 (in real terms)
after eight years, when Marsha’s horse Spike will be ready to
retire. Assume a nominal discount rate of 9% and a 2% 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.
Given data:
Nominal discount rate is 9% and forecast inflation rate is 2%
Real rate of discount is =(1+r nominal)/(1+inflation rate ) -1
Real rate of discount = (1+0.09)/(1+0.02)-1 =0.0686 i.e 6.86%
Now Calculating the Net Present Value | ||||||||||||
t=0 | t=1 | t=2 | t=3 | t=4 | t=5 | t=6 | t=7 | t=8 | ||||
Investments | -43000 | 23000 | ||||||||||
Savings(refer note1) | 9594 | 9594 | 9594 | 9594 | 9594 | 9594 | 9594 | 9594 | ||||
Insurance | -1600 | -1600 | -1600 | -1600 | -1600 | -1600 | -1600 | -1600 | ||||
Fuel refer note 2 | -1240 | -1240 | -1240 | -1240 | -1240 | -1240 | -1240 | -1240 | ||||
Net CashFlow | -43000 | 6754 | 6754 | 6754 | 6754 | 6754 | 6754 | 6754 | 29754 | |||
FVIF at 6.86% refer note 3 | 1.0000 | 1.0686 | 1.1420 | 1.2203 | 1.3041 | 1.3936 | 1.4892 | 1.5914 | 1.7006 | |||
PV of Cash Flows | -43000 | 6320 | 5914 | 5534 | 5179 | 4846 | 4535 | 4244 | 17496 | |||
NPV of CashFlows | 11069 | |||||||||||
Note1: | ||||||||||||
Annual Savings are calculated as below | ||||||||||||
under old system | 208+35+(1.4*(80+100)/2) | 369.0 | ||||||||||
Renting is done every other week | 26 weeks per year | |||||||||||
Savings | 369*26 | 9594 | ||||||||||
Note 2 | ||||||||||||
Fuel calculation | ((80+100)/2)*0.53*26 | 1240.2 | ||||||||||
Note 3 | ||||||||||||
Formula for FVIF calculation | (1+r)^t |