1.17 Trading in a Car to Save on MPGs (Solution)
To solve this problem, we first need to figure the annual gas savings of the new car and next, the present value of the calculated savings over the five anticipated years of use.
| Annual gas savings | Current gas consumption (gallons): (5,000) ÷ (12) = | 416.67 g. | |
| Expected gas consumption: (5,000) ÷ (25) = | 200.00 g. | ||
| Dollar value of gas savings: (216.67 g.) ($4) = | $866.68 | ||
| PV of annual savings (at 6% for 5 years) | ($866.68) (4.2124) = | $3,650.75 |
Now that we have this information, we may compare the savings over the anticipated life of the new investment, against the initial net cost of the trade-in. Again, we assume that other costs of the new vehicle are the same as the old vehicle’s and, hence, do not figure any such costs into the analysis. (This, in fact, may or may not be the case.) No salvage cost or similar horizon-figures are assumed.
| Initial Net Cost | ($15,000) | |
| Annual gas savings | $866.68 | |
| PV of gas savings | $3,650.75 | |
| NPV | ($11,349.25) |
Judging from this analysis, it does not appear that the trade-in pays off. The NPV is negative. Do you agree with this analytic approach and decision rule? What may have been omitted?
