Question

A company has a need for a snow removal machine. The machine can be purchased for the cost of $25,000. The machine is expected to have a life of 6 years with no salvage value. The annual operating cost amounts to $5,000. Alternatively, the machine can be rented at the cost of $400 per day payable at the end of the year. (a) Determine Net Present Worth for buying option. Use an interest rate of 10% per year. (5 points) (b) Determine the number of days per year that snow removal is required in order to justify the purchase decision. Use an interest rate of 10% per year.(10 points) (c) If the machine was needed for 30 days only every year, should the company BUY or RENT the machine? Justify your answer(5 points)

Answer 1

(a) Net Present Value for buying option @ 10% discount rate is 46,776 $

(b) No. of days per year that snow removal is required to justify the purchase decision should be equal to the number of days for which discounted net present value of rent is same as purchase. As per working below, the machine is required for atleast 29.2 days to justify the purchase decision.

(c) If the machine was needed for 30 days, the company should still BUY the machine since as the NPV for rent charges is still higher than BUY option.

Please refer to the table below for complete working

	Particulars	Year 0	Year 1	Year 2	Year 3	Year 4	Year 5	Year 6	Total
	Buy
	Initial Investment	$25,000	$5,000	$5,000	$5,000	$5,000	$5,000	$5,000
	Discount Rate	10%	10%	10%	10%	10%	10%	10%
	DCF	1	$0.909	$0.826	$0.751	$0.683	$0.621	$0.564
(A)	Buy - Net Present Value @ 10%	$25,000	$4,545	$4,132	$3,757	$3,415	$3,105	$2,822	$46,776
	Rent
	Cost incurred @ 400 $ per day for 365 Days		$146,000	$146,000	$146,000	$146,000	$146,000	$146,000
	Discount Rate		10%	10%	10%	10%	10%	10%
	DCF		$0.909	$0.826	$0.751	$0.683	$0.621	$0.564
(B)	Rent - Net Present Value @ 10%		$132,727	$120,661	$109,692	$99,720	$90,655	$82,413	$635,868
(B) / (A)	No. of days at which Buy & Rent are same		$29.20	$29.20	$29.20	$29.20	$29.20	$29.20
	Cost incurred @ 400 $ per day for 30 Days		$12,000	$12,000	$12,000	$12,000	$12,000	$12,000
	Discount Rate		10%	10%	10%	10%	10%	10%
	DCF		$0.909	$0.826	$0.751	$0.683	$0.621	$0.564
	Rent for 30 days - Net Present Value @ 10%		$10,909	$9,917	$9,016	$8,196	$7,451	$6,774	$52,263