Payback Period and NPV of a Cost Reduction Proposal$-$Differential Analysis

Mary Zimmerman decided to purchase a new automobile. Being concerned about environmental issues, she is leaning toward the hybrid rather than the completely gasoline four$-$cylinder model. Nevertheless, as a new business school graduate, she wants to determine if there is an economic justification for purchasing the hybrid, which costs $$1,500$ more than the regular VUE. She has determined that city$/$highway combined gas mileage of the Green VUE and regular VUE models are $27$ and $23$ miles per gallon respectively. Mary anticipates she will travel an average of $12,000$ miles per year for the next several years. $($Round your answers to two decimal places.$)$

$($a$)$ Determine the payback period of the incremental investment if gasoline costs $$3\mathrm{.}50$ per gallon.

years

$($b$)$ Assuming that Mary plans to keep the car five years and does not believe there will be a trade$-$in premium associated withthe hybrid model, determine the net present value of the incremental investment at an eight percent time value of money. $($Use a negative sign with your answer.$)$

$

$($c$)$ Determine the cost of gasoline required for a payback period of three years.

$ per gallon

$($d$)$ At $$3\mathrm{.}50$ per gallon, determine the VUE Green combined gas mileage required for a payback period of three years.

miles per gallon