Question

Randi Corp. is considering the replacement of some machinery that has zero book value and a current market value of $3,700. One possible alternative is to invest in new machinery that costs $30,900. The new equipment has a 5-year service life and an estimated salvage value of $4,400, will produce annual cash operating savings of $10,300, and will require a $3,100 overhaul in year 3. The company uses straight-line depreciation.

Year	FV of $1 at 10%				FV of an ordinary annuity at 10%				PV of $1 at 10%				PV of an ordinary annuity at 10%
1		1.100				1.000				0.909				0.909
2		1.210				2.100				0.826				1.736
3		1.331				3.310				0.751				2.487
4		1.464				4.641				0.683				3.170
5		1.611				6.105				0.621				3.791
6		1.772				7.716				0.564				4.355

Required:

Prepare a net-present-value analysis of Randi’s replacement decision, assuming an 10% hurdle rate and no income taxes. Should the machinery be acquired? (Negative amounts should be indicated by a minus sign. Round calculations to the nearest dollar.)

	Purchase of net machine Sale of old machine Cash operating savings Overhaul Salvage value Total If the machinery should be acquired

Answer 1

Purchase of new machine = $ 30,900

Sale of old machine = $ 3700

Cash operating savings = $ 10,300

Cash operating savings + salvage value in year 5 =  $ 10,300 + $ 4400

Cash operating savings + salvage value in year 5 = $ 14,700

Overhaul = $ 3100 in year 3

Salvage value = $ 4400

Depreciation per year = $ 30,900 5

Depreciation per year = $6,180

Initial investment =  $ 30,900 - $ 3700

Initial investment = $ 27,200

Operating cash flows = ( Cash operating savings - expenses - depreciation) * ( 1 - tax rate) + depreciation

Year	Cash outflows	Depreciation	Cash savings	Operating cash flows
0	$27,200
1	0	$6,180	$10,300	$10,300
2	0	$6,180	$10,300	$10,300
3	$3,100	$6,180	$10,300	$7,200
4	0	$6,180	$10,300	$10,300
5	0	$6,180	$14,700	$14,700

Net present value = - $ 27,200 + $ 10,3001.10¹ +   $ 10,3001.10² +  $ 7,2001.10³ +  $ 10,3001.10⁴ +  $ 14,7001.105

Net present value = $ 12,248.08

Based on the net present value, the machinery should be acquired because the net present value is positive.