Question

Wendy Li decided to purchase a new Honda Civic. Being concerned about environmental issues she is leaning toward a Honda Civic Hybrid rather than the completely gasoline-powered LX model. Nevertheless, she wants to determine if there is an economic justification for purchasing the Hybrid, which costs $5,100 more than the LX. Based on a mix of city and highway driving she predicts that the average gas mileage of each car is 40 MPG for the Hybrid and 30 MPG for the LX. Wendy also anticipates she will drive an average of 12,000 miles per year and that gasoline will cost an average of $3.30 per gallon over the next four years. She also plans to replace whichever car she purchases at the end of four years when the resale values of the Hybrid and the LX are predicted to be $12,000 and $8,500 respectively. Required a. Determine the payback period of the incremental investment associated with purchasing the Hybrid. Answer 0 years b. Determine the net present value of the incremental investment associated with purchasing the Hybrid at a ten percent time value of money. Use a negative sign with your answer, if appropriate. Round answer to the nearest whole number. $Answer 0 c. Determine the cost of gasoline required for a payback period of three years on the incremental investment. Round answer to two decimal places

Answer 1

a. To calculate payback period, we need to calculate how long will it take to payback the incremental investment of $5100 associated with buying the hybrid. Refer the below table:

time period	0	1	2	3	4
incremental cash outflow with purchasing hybrid	-5100
cost of gas per gallon		3.3	3.3	3.3	3.3
miles driven per year		12000	12000	12000	12000
Gallons used by Hybrid with 40MPG average		300	300	300	300
Gallons used by LX with 30MPG average		400	400	400	400
Total cost of gas driving hybrid		990	990	990	990
Total cost of gas driving LX		1320	1320	1320	1320
cost saving by driving hybrid		330	330	330	330
resale value of hybrid					12000
resale value of LX					8500
net cash inflow associated with driving hybrid		330	330	330	3830

As seen from above table, the total cash inflow over 4 years after purchasing hybrid is $4820 which is less than initial investment of $5100. Thus, the payback period is longer than her time horizon of 4years. Payback period is indeterminable since at the end of 4years, the car will be replaced and it is not possible to estimate further cashflows

b. Net Present value with a 10% time value of money can be calculated extending the above table:

time period	0	1	2	3	4
incremental cash outflow with purchasing hybrid	-5100
net cash inflow associated with driving hybrid		330	330	330	3830
discounted cash flow at 10%		=330/(1+10%)^1 =300	=330/(1+10%)^2 =272.7	=330/(1+10%)^3 =247.9	=3830/(1+10%)^4 =2615.9
NPV	= -5100+300+272.7+247.9+2615.9 = -1663.4

Hence, NPV is -$1663. This implies that it's not economically justified to drive Hybrid instead of LX

c. In part c, we have to estimate the cost of gasoline which gives payback period of 3years. Now initial investment is 5100, thus we need cost saving of 1700 annually for payback period to be  3years.

No. of miles driven per year would be same i.e. 12000

Additional gas used by LX annually = 12000/40 - 12000/30 = 100gallons

To save $1700 annually on gas, price per gallon of gas should be equal to 1700/100 = $17.00