Question

1. Suppose you are in the market for a new car. You identify two models that you like and are considering a final purchase decision. The vehicle details are as follows:

• One is a high fuel efficient vehicle with a fuel cost per mile of $0.10 and the other is a low fuel efficient vehicle with a fuel cost per mile of $0.15.
• The high efficiency vehicle costs $47,500 in time period 0 (no discounting); the low efficiency vehicle costs $32,500
• You plan to drive the car for five years (time periods 1 to 5)
• In addition to the fuel costs in period 5, you also face depreciation costs of $17,500 for the low efficient vehicle and depreciation costs of $40,000 for the high efficient vehicle

1. 1. Suppose you drive 10,000 miles per month and have an internal discount rate of 5%. Which car has the lower total cost of ownership? Show your work on a separate page or attach a printout of your excel model, clearly labeled.
2. 2. Suppose you drive 17,000 miles per month and have an internal discount rate of 5%. Which car has the lower total cost of ownership? Show your work on a separate page or attach a printout of your excel model, clearly labeled.
3. 3. Suppose you drive 7,500 miles per month and have an internal discount rate of 20%. Which car has the lower total cost of ownership? Show your work on a separate page or attach a printout of your excel model, clearly labeled.
4. 4. In general, what characteristics (in terms of driving habits and discount rates) describe an individual that finds a lower total cost of ownership in high fuel efficient vehicles?

Answer 1

The high fuel efficient car has a cost of $47500 and fuel cost of $0.10 per mile.
The depreciation cost is $40000 which is assumed to be spread over 5 years.

The low fuel efficient car has a cost of $32500 and fuel cost of $0.15 per mile.
The depreciation cost is $17500.

The residual value is not categorized in the question but it should be either considered as salvage value or must be regarded as initial cost.

a) 10000 miles per month is equivalent to 120000 mile per year

High fuel efficient car
120000 * 0.10 = 12000

Total Cost = Fuel Cost + Depreciation Cost
12000 + (40000 / 5) = 20000

Low fuel efficient car
120000 * 0.15 = 18000
Total Cost = Fuel Cost + Depreciation Cost
18000 + (17500 / 5) = 21500

The PW of the cash flow can be calculated using the following formula
PW = Cash Flow * (1+Interest Rate) ^ Duration

High Efficiency Car Year 0
(42500 - 40000) = 2500

High Efficiency Car Year 1
20000 / 1.05 = 19047.62

We can create a table here
The residual value if assumed to be salvage value

Year		High Efficiency			Low Efficiency
	10000 miles	17000 miles	7500 miles	10000 miles	17000 miles	7500 miles
0
1	20000	28400	17000	21500	34100	17000
2	20000	28400	17000	21500	34100	17000
3	20000	28400	17000	21500	34100	17000
4	20000	28400	17000	21500	34100	17000
5	17500	25900	14500	6500	19100	2000
	PW @ 5%	PW @ 5%	PW @ 20%	PW @ 5%	PW @ 5%	PW @ 20%
1	19047.62	27047.62	14166.67	20476.19	32476.19	14166.67
2	18140.59	25759.64	11805.56	19501.13	30929.71	11805.56
3	17276.75	24532.99	9837.96	18572.51	29456.86	9837.96
4	16454.05	23364.75	8198.30	17688.10	28054.15	8198.30
5	13711.71	20293.33	5827.22	5092.92	14965.35	803.76
Total	84630.72	120998.32	49835.71	81330.86	135882.26	44812.24

If the residual amount is considered to be initial cost

Year		High Efficiency			Low Efficiency
	10000 miles	17000 miles	7500 miles	10000 miles	17000 miles	7500 miles
0	2500	2500	2500	15000	15000	15000
1	20000	28400	17000	21500	34100	17000
2	20000	28400	17000	21500	34100	17000
3	20000	28400	17000	21500	34100	17000
4	20000	28400	17000	21500	34100	17000
5	20000	28400	17000	21500	34100	17000
	PW @ 5%	PW @ 5%	PW @ 20%	PW @ 5%	PW @ 5%	PW @ 20%
0	2500	2500	2500	15000	15000	15000
1	19047.62	27047.62	14166.67	20476.19	32476.19	14166.67
2	18140.59	25759.64	11805.56	19501.13	30929.71	11805.56
3	17276.75	24532.99	9837.96	18572.51	29456.86	9837.96
4	16454.05	23364.75	8198.30	17688.10	28054.15	8198.30
5	15670.52	22252.14	6831.92	16845.81	26718.24	6831.92
Total	89089.53	125457.14	53340.41	108083.75	162635.15	65840.41

The cost of ownership is lower for high fuel efficient car when considered for 10k miles per month and 17k miles per month.
However, the ownership cost is lower for low fuel efficient car if we consider 7500 miles per month and 20% discount rate. The calculation are given in the table above.

d) The discount rate is different here for the 3rd option or 7500 miles per month. The calculation shows that cost is directly related to the miles driven and higher the miles driven the lower cost of ownership for the high fuel efficient car.