Question

Marsha Jones has bought a used Mercedes horse transporter for her Connecticut estate. It cost $41,000. The object is to save on horse transporter rentals.

Marsha had been renting a transporter every other week for $206 per week plus $1.30 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 $.51 per mile. Insurance costs for Marsha’s transporter are $1,500 per year.

The transporter will probably be worth $21,000 (in real terms) after eight years, when Marsha’s horse Nike will be ready to retire. Assume a nominal discount rate of 8% 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.)

Answer 1

ANNUAL COST OF RENTING A TRANSPORTER = $206 X 26 weeks + $1.30 X 90 X 26 + $45 X 26 = $9,568

ANNUAL COST OF OWNING A TRANSPORTER = $0.51 X 90 X 26 + $1,500 = $2693.4

ANNUAL SAVING IN COSTS = $9,568 - $2693.4 = $6874.6

PURCHASE PRICE OF TRANSPORTER = $ 41,000

SALVAGE VALUE OF TRANSPORTER AT THE END OF 8th YEAR = $21,000

RATE OF INFLATION = 3%

NORMAL DISCOUNT RATE  = 8%

ANNUAL SAVINGS AT THE END OF THE YEAR = $6874.6

PRESENT VALUE OF SAVINGS CAN BE CALCULATED AS = PRESENT VALUE OF GROWING ANNUITY OF $6874.6 AT GROWTH RATE OF 3% DISCOUNTING AT 8% FOR 8 YEARS + PRESENT VALUE OF $21,000

= COST SAVING [ 1 - {( 1+ g) \ (1 + r)}ⁿ] \ ( r - g ) + 21,000 X PVF r%,n

= 6874.6 [ 1 -  { ( 1+ 0.03) \ (1 + 0.08 ) }⁸ \( 0.08 - 0.03)] + 21,000 X PVF 8% , 8

= 6874.6 X 6.3120708 + 21,000 X 0.540

= 43,392.9619 + 11,340

= 54,732.9619

PRESENT VALUE OF ALL BENEFITS AND SALVAGE VALUE = 54732.9619

NPV = $54,732.9619 - $41,000

= $13732.9619