Payback Period and NPV of Alternative Automobile Purchase Wendy Li decided to pu

Question

Payback Period and NPV of Alternative Automobile Purchase Wendy Li decided to purchase a new Honda Civic. Being concerned about environmental issues she is leaning toward a Honda Civic Hybrid rather than the completely gasoline-powered LX model. Nevertheless, she wants to determine if there is an economic justification for purchasing the Hybrid, which costs $4,950 more than the LX. Based on a mix of city and highway driving she predicts that the average gas mileage of each car is 40 MPG for the Hybrid and 30 MPG for the LX. Wendy also anticipates she will drive an average of 12,000 miles per year and that gasoline will cost an average of $2.75 per gallon over the next four years. She also plans to replace whichever car she purchases at the end of four years when the resale values of the Hybrid and the LX are predicted to be $12,000 and $8,500 respectively. Required a. Determine the payback period of the incremental investment associated with purchasing the Hybrid. years b. Determine the net present value of the incremental investment associated with purchasing the Hybrid at a ten percent time value of money. Use a negative sign with your answer, if appropriate. Round answer to the nearest whole number. c Determine the cos f asoline required for a payack period of three ears an the Incremental investment. Round answer to two decimal places Check

Explanation / Answer

Answer a.
The extra cost of Honda civic hybrid is $4950
incremental salvage value = 12,000-8500 = 3500
Thus incremental investment = 4950-3500 = 1450

and the cost per mile per gallon of gasoline given gasoline rtae of $2.75 and mileage for hybrid at 40MPG and LX at 30MPG
Hybrid = 2.75/40 = 0.06875
LX = 2.75/30 = 0.09167

Thus travelling 12000 miles a year the costs are:
Hybrid = 0.06875*12000 = 825
LX = 0.09176*12000 = 1101.12
Hence cost saved by Hybrid = 1101.2-825 = $276.12 per year

So payback period = 1450/276.12 = 5.25 years



Answer b.
Initail outlay for hybrid = -4950
Operating cashflow = 276.12 (for four years)
Terminal value = incremental salvage value = 12,000-8500 = 3500 (this will get added to 4th year operating cashflow)

Thus NPV at 10% discount rate is as below:

Years

Cashflows

0

-4950

1

276.12

2

276.12

3

276.12

4

3776.12

NPV at 10%

-$1,531.08

The NPV for hybrid is -$1531


Answer c.
The incremental investment is 1450
and if the payback is required in 3 years, per year saving should be 1450/3 = 483.33
and the total amount of gasoline required by each car is:
Hybrid = 12000/40 = 300
LX = 12000/30 = 400
Let the price of gasoline be X

Thus 400x-300x=483.33
100x = 483.33
x=483.33/100
X = 4.83

Thus the price of gaoline should be $4.83 per gallon for hybrid to break even in 3 years

Years

Cashflows

0

-4950

1

276.12

2

276.12

3

276.12

4

3776.12

NPV at 10%

-$1,531.08

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