E12-26. Payback Period and NPV of a Cost Reduction Proposal—Differential Analysi

Question

E12-26. 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 gasoline only model. Nevertheless, as a new business school graduate, she wants to determine if there is an economic justification for purchasing the hybrid, which costs $1,400 more than the regular model. She has determined that city/highway combined gas mileage of the hybrid and regular 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.

Required

a. Determine the payback period of the incremental investment if gasoline costs $3.60 per gallon.

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

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

d. At $4.15 per gallon, determine the gas mileage required for a payback period of three years.

Please, show calculations. Thank You!

Explanation / Answer

Gasoline only Hybrid Gallon Required 521.74 444.44 Total Cost 1878.26 1600 Extra 1400 a. Payback period for incremenal investment 5.03125 b. Year 0 1 2 3 4 5 Amount -1400 278.26 278.26 278.26 278.26 278.26 NPV= Rs. -267.58 c. for 3 years payback period Gasoline cost should be $6.04 per gallon (1400/difference per year in gasonline)/ 3 years d. at $4.15 rate milage required= 29.32 miles per gallon

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