Question

Suppose you are considering purchasing a new car. You and your spouse have narrowed it down to two choices:

a. Sedan Initial Price: $27,300

Annual O&M: $4,456

Expected trade-in value after 5 years: $9,100

b. SUV Initial Price: $38,795

Annual O&M: $3,050

Expected trade-in value after 5 years: $18,544

If you intend to keep your new vehicle for 5 years, then trade it in, determine the net present value (NPV) of each alternative, assuming a discount rate of 4.0%. Which alternative is the better buy, using the NPV criterion?

Answer 1

We shall first compute the NPV of Sedan i.e. part a. by using the below function:

Initial Price + Present value of Annual O & M for 5 years - Present value of Expected trade in value after 5 years

= 27,300 + 4,456 / (1.04)¹ + 4,456 / (1.04)² + 4,456 / (1.04)³ + 4,456 / (1.04)⁴ + 4,456 / (1.04)⁵ - 9,100 / (1.04)⁵

= $ 39,657.78

Now, we shall compute the NPV of SUV i.e. part b. by using the below function:

Initial Price + Present value of Annual O & M for 5 years - Present value of Expected trade in value after 5 years

= 38,795 + 3,050 / (1.04)¹ + 3,050 / (1.04)² + 3,050 / (1.04)³ + 3,050 / (1.04)⁴ + 3,050 / (1.04)⁵ - 18,544 / (1.04)⁵

= $ 37,131.24

Note in both the cases we have used positive signs for cash outflows and negative signs for cash inflow, since we are making a decision which car to buy.

Since the NPV of cash outflow of SUV is lesser than the NPV of cash outflow of Sedan, we shall prefer to buy car SUV i.e. option b.

Feel free to ask in case of any queries regarding this question