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

Question

Payback Period and NPV of a Cost Reduction Proposal—Differential Analysis Mary Zimmerman decided to purchase a new Saturn VUE automobile. Being concerned about environmental issues, she is leaning toward the hybrid VUE Green 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 VUE Green, which costs $1,300 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 $3.50 per gallon. Answer 5.03 Incorrect years (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. $Answer 3,478.25 Incorrect (c) Determine the cost of gasoline required for a payback period of three years. $Answer 0 Incorrect per gallon (d) At $3.50 per gallon, determine the VUE Green combined gas mileage required for a payback period of three years. Answer 0 Incorrect miles per gallon

Explanation / Answer

Ans:

(a)

Calculation of Payback period for the Incremental Investment in a new Saturn VUE Automobiles

Incremental initial investment = $1300

Incremental cost saving per year a new VUE Green= $3.5 (12000/27-12000/23)

Cost Saving (incremental) per year= $270.53 ( Cost saving is equal to revenue earned)

Payback Period = Initial Investment/ Yearly Cash Flow

Payback period= $1300/$270.53

Payback period= 4.81 Years

(b)

Calculation of Net Present Value for the proposal of new VUE Green

Here cost of new investment is 8% hence discounting rate = 8%

NPV=( Present value of initial investment) - (Present Value of Inflow )

Present Value of Initial investment= $1300

Present Value of Yearly cost saving = Yearly Cost Saving X( PVAF for 5 year @ 8 %)

Where PVAF ( Present Value of Annuity Factor)= 3.993

Present value of yearly cost saving = $270.53 x3.993

PV of Yearly cost saving= $1080.21

NPV= $1300- $1080.21

NPV= -$219.79 (negative NPV)

(C ) Cost of Gasoline for a payback period of three years.

Payback period means a period in which cost of investment is recovered.

If required payback period is 3 years , it means $ 1300 is need to be recovered in three years.

Payback Period = Initial Investment/ Yearly Cost saving

3= $1300/ Yearly cost saving

Yearly cost saving= $1300/3

Yearly saving = $433.3333

$433.3333= (1200/23-1200/27) * Cost of gasoline / gallon

$433.3333= 77.2947 gallon * Cost of gasoline

Cost of gasoline= $433.33/77.2947

Gasoline Cost= $5.61 per gallon

(d)

Yearly cost saving = Saving in yearly consumption of gasoline X Cost per gallon

$433.33= Saving in yearly consumption X $3.5

Consumption saving= 123.81 gallons

Lets assume mileage is M miles per gallon

Saving in yearly consumption= 12000/23- 12000/M

123.81= 521.74 gallons-12000/M

12000/M= 397.93 gallons

M (required mileage)= 30 .16 miles per gallon

Payback period= 4.81 Years

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