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 Hermione 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 $1,595 more than the regular model. She has determined that city/highway combined gas mile- age of the hybrid and regular models are 30 and 24 miles per gallon respectively. Hermione 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 $2.75 per gallon. b. Assuming that Hermione plans to keep the car about six years and does not believe there will be a trade-in premium associated with the hybrid model, determine the net present value of the incre- mental investment at six percent time value of money. c. Determine the cost of gasoline required for a payback period of three years. d. At $4.60 per gallon, determine the gas mileage required for a payback period of three years.

Explanation / Answer

Soln : We need to calculate the payback period for incremental investment , i.e. for $1595

Hybrid model wil lrun extra miles = 30-24 = 6 miles per gallon

Now, in an year miles covered = 12000, Total gallons saved using hybrid = 12000/24- 12000/30 = 100 gallons

Cost saved = 2.75*100 = $275

Payback period = 1595/275 = 5.8 years or we can say approx. 6 years.

b) Required to calculate the NPV of these 6 years, Please refer the table:

Total value is -$242.74, means premium not to be charged.

c) Cost of gasoline lets say is C , payback period = 3 years

So, as calculated in part a) we can say that C*100 = 1595/3, C = $5.32 per gallon

d) Let the gas mileage be X, then total no. of gallons saved in 3 years = 3*(12000/24 - 12000/X)

Now,  3*(12000/24 - 12000/X) *cost of per gallon = 1595

500-12000/X = 1595/(3*4.60) or 12000/X = 500- 115.58 , X = 31.22

Gas mileage should be 31.22 for 3 year payback period with given cost.

Year 0.00 1.00 2.00 3.00 4.00 5.00 6.00 Cash outflow -1595.00 Cash inflow 275 275 275 275 275 275 rate 1.06 1.06 1.06 1.06 1.06 1.06 1.06 PV -1595.00 259.43 244.75 230.90 217.83 205.50 193.86 Total -242.74

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