Question

2) You work for GrubHub delivering takeout to people who ask for delivery. You need to purchase a vehicle and are trying to decide between two choices. The first is a gasoline car that currently sells for $27,500, gets 20 miles to the gallon, has a resale value of $8,500 in 10 years and has maintenance costs of $750 per year. The alternative is an electric car that costs $35,000, has a resale value of $15,000 in 10 years, and has maintenance costs of $500 per year. You expect to drive 12,000 miles per year, and the cost of gasoline is $2.00 per gallon while the price of electricity is $.0666667 per mile. a) Graph the NPV profiles for both cars. (8) b) Which car would you choose? Explain in detail. (8) c) Assume the discount rate is 5%. What would the price of gasoline have to be to make you indifferent between the gas and electric cars?

Answer 1

Initial cost of gasoline car = -27500

Annual cash-flow from year 1-9 of gasoline car = -Annual maintenance - Cost of running the gasoline car 12000 miles

Annual cash-flow from year 1-9 of gasoline car = -750-12000*2/20

Annual cash-flow in year 10 of gasoline car = -750+8500-12000*2/20

Initial cost of electric car = -27500

Annual cash-flow from year 1-9 of electric car = -Annual maintenance - Cost of running the electric car 12000 miles

Annual cash-flow from year 1-9 of electric car = -500-12000*0.0666667

Annual cash-flow in year 10 of electric car = 15000-500-12000*0.0666667

Year	Gasoline car	Electric car
0	-27500	-35000
1	-1950	-1300
2	-1950	-1300
3	-1950	-1300
4	-1950	-1300
5	-1950	-1300
6	-1950	-1300
7	-1950	-1300
8	-1950	-1300
9	-1950	-1300
10	6550	13700

Discount rate	NPV Gasoline	NPV Electric
1%	-38274.10472	-33733.39536
2%	-38043.08021	-34372.1396
3%	-37809.09726	-34927.85838
4%	-37573.95133	-35410.70523
5%	-37339.12046	-35829.55969
6%	-37105.81415	-36192.19446
7%	-36875.01502	-36505.41943
8%	-36647.51408	-36775.20618
9%	-36423.94066	-37006.79548
10%	-36204.7879	-37204.79035
11%	-35990.43435	-37373.23679
12%	-35781.16239	-37515.69365
13%	-35577.17382	-37635.29347
14%	-35378.60313	-37734.79528
15%	-35185.52882	-37816.63063
16%	-34997.98295	-37882.9436
17%	-34815.95932	-37935.62583
18%	-34639.42031	-37976.34698
19%	-34468.3028	-38006.58143
20%	-34302.52311	-38027.63164
21%	-34141.98119	-38040.64855
22%	-33986.56415	-38046.6495
23%	-33836.1493	-38046.53395
24%	-33690.6066	-38041.09729
25%	-33549.80083	-38031.04294
26%	-33413.59331	-38016.99303
27%	-33281.84342	-37999.49777
28%	-33154.40976	-37979.04373
29%	-33031.15122	-37956.06115
30%	-32911.92775	-37930.93033

a)

b) The discount rate is 5%. At this discount rate, the NPV of Electric vehicle is higher than that of Gasoline vehicle. Hence, we prefer the Electric vehicle

c) We would be indifferent if the NPV of both the alternatives is the same.

We use excel solver with the following constraints to find the price of the gasoline for the NPV to be the same

Solving, we get

Year	Gasoline car	Electric car
0	-27500	-35000
1	-1754.504975	-1300
2	-1754.504975	-1300
3	-1754.504975	-1300
4	-1754.504975	-1300
5	-1754.504975	-1300
6	-1754.504975	-1300
7	-1754.504975	-1300
8	-1754.504975	-1300
9	-1754.504975	-1300
10	6745.495025	13699.9996
NPV	-35829.55969	-35829.55969

Hence, the price of the gasoline for the NPV to be the same = $1.674