Question

A potential buyer of a sportscar is interested in the costs of a vehicle per mile travelled at net present value. The buyer is planning to sell the car after three years of operation at residual value.

The car costs £35000.00 to purchase and the buyer incurs costs for insurance, fuel and mantenance of £1400.00 per year. The car is expected to depreciate in value by £4000.00 per year (straight line depreciation). The buyer is planning to travel 17000 miles per year.

What is the total cost of ownership per mile travelled at net present value, assuming that all payments arise annually and are subject to an annual discount rate of 3%. Note that the miles travelled are not subject to discounting.

Answer 1

Based on given data, pls find below workings:

Based on the below, the ownership cost per mile comes to $ 0.36.

	YEAR
Sports Car ($)	0	1	2	3	Terminal
Initial Cost	-35,000
Depreciation		-4,000	-4,000	-4,000
Residual Value					23,000
No.of Miles		17,000	17,000	17,000
Maintenance Cost		-1,400	-1,400	-1,400
Net Cash Flows	-35,000	-1,400	-1,400	-1,400	23,000
Discount Factor @ 3%	1.0000	0.9709	0.9426	0.9151	0.8885
Discounted Cash Flows	-35,000	-1,359	-1,320	-1,281	20,435
Cumulative Discounted Cash Flows	-35,000	-36,359	-37,679	-38,960	-18,525
NPV	-18,525
Total No.of Miles	51,000
Ownership Cost Per mile $	0.36

Owner ship cost per mile = 18525 / 51000 (NPV / No.of Miles) = 0.36

The Discounting factor is computed based on the formula: For year 0, the discounting factor is 1; For Year 1, it is computed as = Year 0 factor /(1+discounting factor%) ; Year 2 = Year 1 factor/(1+discounting factor %) and so on;