Mary Zimmerman decided to purchase a new automobile. Being concerned about envir
ID: 2455897 • Letter: M
Question
Mary Zimmerman decided to purchase a new automobile. Being concerned about environmental issues, she is leaning toward the hybrid rather than the gasoline 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 give 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 eigth 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.
Explanation / Answer
Incremental milage due to changing to hybrid model is =27-23 =4.
On an average miles travelled =12,000.
Cost of hybrid model =$1,400.
Quantity of gasoline consumed if the regular model is used= 12000/23 =521.74
Quantity of gasoline consumed if the hybrid model is used =12000/27 =444.44
Cost of gasoline if the regular model is used=521.74*3.60 =$1,878.26---------------(A)
Cost of gasoline if the hybried model is used=444.44*3.60
=$1,600-----------(B)
Savings in the cost of gasoline =A-B =$278.26.
Answer for question no.a:
pay back period = cost of the hybrid model/savings in gasoline cost per year
=$1,400/$278.26.
=5.03 years
Answer for question no.b:
Present value of Savings in perpetuity=Savings per year/cost of capital
=$278.26/.08
=$3,478.25
NPV= Present value of cash inflows- Cash outflow
=$3,478.25 -$1,400
=$2,078.25
Answer for question no.c:
if the pay back period is to be 3 years, then substituting this in the below formula.
pay back period = cost of the hybrid model/savings in gasoline cost per year
3=$1,400/Savings in gasoline cost per year.
Savings in gasolilne cost per year =$1,400/3
=$466.67.
Let x be price of gasoline per gallon.
Savings in changing the model =(12000/23)x -(12,000/27)x
$466.67 =521.73x -444.44x
x=$466.67/77.29
=$6.037 rounded to $6.04.
Answer for question no.d:
Payback period =3 years.
pay back period = cost of the hybrid model/savings in gasoline cost per year
3 = $1,400 /Savings in gasoline cost per year
Savings in gasoline cos per year =$1,400/3
=466.67.per year.
Savings in gasoline cost = difference in mileage * cost per gallon of gasoline.
Cost per gallon of gasoline is $4.15.
Difference in mileage = $466.67/$4.15
=112.449 miles
Gas milegae required for the hybrid engine = 12,000/23 -12,000/x =112.449
=521.74 - 12000/x =112.449
521.74 -112.449 =12000/x
x= 12000/409.289
x=29.319 miles per gallon.
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