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Payback Period and NPV of a Cost Reduction Proposal—Differential Analysis Katy Zimmerman decided to purchase a...

Payback Period and NPV of a Cost Reduction Proposal—Differential Analysis
Katy 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 $1,200 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.)

Determine the payback period of the incremental investment if gasoline costs $3.50 per gallon.

Answer (in years)

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.)

Answer (in dollars)

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

Answers (4 in gallon)

At $3.50 per gallon, determine the VUE Green combined gas mileage required for a payback period of three years.

Answer (miles per gallon)

Solutions

Expert Solution

Answer:

a) Determine the payback period of the incremental investment if gasoline costs $3.50 per gallon

Payback period = Cost of investment / Net annual cash flow

Where,

Cost of investment = $1200

Net annual cash is,

Units of gasoline used in the year = 12000 / 27 =444 units

Units of gasoline use din the year = 12000 / 23 = 522 units

Incremental savings = 522-444 = 78 gallons

Incremental cash flow = Net annual cash flow = 78*3.50 = $273

Therefore,

Payback period = 1200 / 273 = 4.4 years

b)determine the net present value of the incremental investment at an eight percent time value of money.

Net presesnt value(NPV) = Present value- Cost of investment

Present value of $1 is 5 years at 8% is 3.99271

Present value of $273 for 5 yrs at 8%=$273*3.99271 =$1090

Therefore, NPV= 1090-1200 = -110.

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

Incremental cashflow =$500

Price of gasoline = Incremental cash flow per year / gallons saved per year

= 500 / 78

Price of gasoline =$6.41 per gallon

d)At $3.50 per gallon, determine the VUE Green combined gas mileage required for a payback period of three years.

Pay back period = 3 years

The incremental gallons = 500 / 3.5

=143gallons

Units of gasoline used in year = 12000 / 23 =522 units

Units of gallons to be used by green vue is,

=522-143

=379 units of gallons.

the miles per gallon of vue , = 12000 / 379 = 31.66 miles per gallon

ekkarill92 answered 1 year ago
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