Question

The supervisor of the county Department of Transportation (DOT) is considering the replacement of some machinery. This machinery has zero book value but its current market value is $840. One possible alternative is to invest in new machinery, which has a cost of $39,400. This new machinery would produce estimated annual operating cash savings of $12,700. The estimated useful life of the new machinery is four years. The DOT uses straight-line depreciation. The new machinery has an estimated salvage value of $2,040 at the end of four years. The investment in the new machinery would require an additional investment in working capital of $3,000, which would be recovered after four years. If the DOT accepts this investment proposal, disposal of the old machinery and investment in the new equipment will take place on December 31, 20x1. The cash flows from the investment will occur during the calendar years 20x2 through 20x5. Use Appendix A for your reference. (Use appropriate factor(s) from the tables provided.) Required: Prepare a net-present-value analysis of the county DOT’s machinery replacement decision. The county has a 10 percent hurdle rate. (Round your "Discount factors" to 3 decimal places and final dollar amounts to whole dollars. Negative amounts should be indicated by a minus sign.)

Answer 1

Net Present value means PV of Cash inflows minus PV of cash outflows. As per time value of money concept, we need to calculate present values by discounting various estimated inflows and outflows at different points in time using given hurdle rate.

In the tabulated presentation below,it has been assumed that T0 is Dec 31, 2001 i,e, the day disposal of old machinery is done and new machinery has been acquired.

Calculation showing NPV analysis for Machine replacement decision
Particulars	Dec 31, 2001	Dec 31, 2002	Dec 31, 2003	Dec 31, 2004	Dec 31, 2005
PVF of 10%	0	0.909	0.826	0.751	0.683
Cash Inflows
Disposal value of old machinery	$ 840
Estimated Annual Operating cash savings per year $12700 discounted using appropriate PVF as above		$ 11,544	$ 10,490	$ 9,538	$ 8,674
Salvage value of new machinery discounted using PVF of 2005					$1,393
Tax benefit on Depreciation amount discounted using appropriate PVF as above		$ 8,490	$ 7,715	$ 7,014	$ 6,379
(39400 - 2040)/4 = $9340
Recovery of additional working capital done in 2001. Present value at the end of 2005 is calculated using the PVF of 2005					$ 2,049
PV of cash infows	$ 840	$ 20,034	$ 18,205	$16,552	$ 18,496
Cash Outflows
Additional working capital investment for the year of new machinery purchase	$ -3,000
Cost of new machinery	$ -39,400
PV of cash outflows	$-42,400

NPV if the replacement decision is taken is calculated as follows:-

NPV	Amount
Sum of PV of Cash Inflows	$                74,127.08
840 + 20034 + 18205 + 16552 + 18495
Minus PV of Cash outflow	$              -42,400.00
NPV	$                31,727.08

Since the NPV is positive , DOT must go ahead with machine replacement decision.