Question

Fabrice is looking to buy a new plug-in hybrid vehicle. The purchase price is $14,000 more than a similar conventional model. However, he will receive a $6,300 federal tax credit that he will realize at the end of the year. He estimates that he will save $1,300 per year in gas over the conventional model; these cash outflows can be assumed to occur at the end of the year. The cost of capital (or interest rate) for Fabrice is 6%. How long will Fabrice have to own the vehicle to justify the additional expense over the conventional model? In other words, what is the DISCOUNTED payback period in years? Discount future cash flows before calculating payback rounded UP to a whole year. (Enter just the number without comma and round off decimals.)

Answer 1

The net present value after 8 years is:

$NPV = -14000 + 7600/1.06 + 1300/1.06^2 + 1300/1.06^3 + 1300/1.06^4 + 1300/1.06^5 + 1300/1.06^6 + 1300/1.06^7 + 1300/1.06^8 = 16.13.$

So, the DISCOUNTED payback period is approximately 8 years.