Payback Period and NPV of a Cost Reduction Proposal—Differential Analysis Hermio

Question

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

a. In the given problem, Incremental Cash Outflow = $1,595

Incremental Annual Cash Inflow = Annual Cash Saving on Gasoline

= 1375-1100 = $275

Incremental Payback Period = Incremental Cash Outflow/ Incremental Cash Inflow

= 1595/275

= 5.8 years

b. Hermoine intends to keep the car for six years because of which she will have an annual cash inflow of 275 per year.

Present Value of Incremental Cash Inflow = 275* Present Value Annuity Factor at 6% for 6 years

= 275* 4.9173

= $ 1,352.26

Incremental Net Present Value = Incremental Cash Outflow - Present Value of Incremental Cash Inflow

= 1,595-1352.26

= $ 242.74

c. We know that Payback Period = Incremental Cash Outflow/ Incremental Cash Inflow

That is, 3 = 1,595/Incremental Cash Inflow

Incremental Cash Inflow= 1595/3 = 531.67

Incremental Cash Inflow is the annual incremental gasoline expense. It is calculated as,

Per unit cost of gasoline*Incremental saving on gasoline consumption

That is , Incremental Cash Inflow = Per unit cost of gasoline * (500-400)

531.67= Per unit cost of gasoline* 100

Per unit Cost of gasoline = 531.67/100 = 5.3167

Thus, for a payback period of 3 years, total cost of gasoline = $531.67 and per unit cost of gasoline = $5.3167

d. As calculated in (c), the total cost of gasoline for a payback period of 3 is $531.67

Total Cost of gasoline = Per unit cost of gasoline * Incremental saving on gasoline consumption

531.67 = 4.60*Gas Consumption

Incremental saving on gasoline consumption = 531.67/4.60 = 115.58 gallons

We know that gasoline consumprion for the regular model = 500 gallons

Thus, gasoline consumption for hybrid model = 500-115.58 = 384.42 gallons

Gas Mileage required = Distance to be covered/ Gas consumption for hybrid model

= 12,000/384.42

= 31.22 miles per gallon

Particulars Hybrid Regular A. Distance to be covered in a year 12,000 miles 12,000 miles B. Gas Mileage 30 24 C. Gasoline required in a year (A/B) 400 gallon 500 gallon D. Annual Cost of Gasoline at 2.75 per gallon 1100 1375

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