Casey must determine if it is economically preferable to use higher octane gasol
ID: 1221419 • Letter: C
Question
Casey must determine if it is economically preferable to use higher octane gasoline in his new car. The higher octane gas has a cost of S0.20/gallon higher than that of the low octane gas. Casey uses approximately 500 gallons of gas per year. He believes that if he uses the higher octane gas, he will extend the life of her car by one year (from a useful life of nine years to a useful life of ten years). His car has an initial cost of 522,000 and an assumed salvage value of $0. Given an interest rate of 8% compounded annually, should Casey use the higher octane gas?Explanation / Answer
Lets calculate NPV in each case as follows
Lets assume, Gasoline is costing $1 for low octane gasoline, so high octan gasoline = 1 + 0.2 = $1.2
Cashflows for low octane are as follows
NPV =NPV(8%,F3:F11)+F2 = -25,123.44
High Octane cash flows are as follows
NPV =NPV(8%,F3:F12)+F2 = -26,026.05
We cannot directly compare the NPV's because they are as for different numbers of years. So lets calculate annual benefit each yeaer as follows
Low Octane = PMT(8%,9,-25123.44,0,0) = -$4,021.75
High Octane = PMT(8%,10,-26026.05,0,0) = -$3,878.65
Since high octane costs are less than Low octane gasoline costs, Casey should go for High Octane gasoline
Notez;
NPV is nt present value. For a capital budgeting project, it is best used method to choose to project. Once you enter these cash flows in an excel sheet, this is the formula to calculate NPV.
As mentioned in the answer, NPV for 2 projects can be compared only when they are same duration. If they are not of same duration, we have to convert this into effective annual return with PMT formula in excel.