Question

Vandelay Industries is considering the purchase of a new machine for the production of latex. Machine A costs $3,072,000 and will last for six years. Variable costs are 35 percent of sales, and fixed costs are $215,000 per year. Machine B costs $5,265,000 and will last for nine years. Variable costs for this machine are 30 percent of sales and fixed costs are $150,000 per year. The sales for each machine will be $10.5 million per year. The required return is 10 percent, and the tax rate is 35 percent. Both machines will be depreciated on a straight-line basis. The company plans to replace the machine when it wears out on a perpetual basis. Calculate the NPV for each machine.

Answer 1

A.

NPV = $16,420,840.31

Particulars	Machine A
Investment	3,072,000
Sales	10,500,000
Variable cost 35% of sales - V	3,675,000
Fixed cost – F	215,000
Total cost per year - TC = (V+F)	3,890,000
Net cash flow = S-TC	6,610,000

Year	Cash outflows	Cash inflows	Depreciation = D = 3072000/6	Net cash flow* = (Co+Ci-D)x(1-35% )+D	Discount factor = Df = 1/(1+10%)^Year	Present Values
0	-3,072,000.00	0.00	0.00	-3,072,000.00	1.000000	-3,072,000.00
	Co	Ci	D	(Co+Ci-D)x(1-35% rate)+D		Df x Net Cash flows
1	-3,890,000.00	10,500,000.00	512,000.00	4,475,700.00	0.909091	4,068,818.18
2	-3,890,000.00	10,500,000.00	512,000.00	4,475,700.00	0.826446	3,698,925.62
3	-3,890,000.00	10,500,000.00	512,000.00	4,475,700.00	0.751315	3,362,659.65
4	-3,890,000.00	10,500,000.00	512,000.00	4,475,700.00	0.683013	3,056,963.32
5	-3,890,000.00	10,500,000.00	512,000.00	4,475,700.00	0.620921	2,779,057.57
6	-3,890,000.00	10,500,000.00	512,000.00	4,475,700.00	0.564474	2,526,415.97
					Total = NPV =	16,420,840.31

B.

NPV = $22,866,391.59

Particulars	Machine B
Investment	5,265,000
Sales – S	10,500,000
Variable cost 30% of sales - V	3,150,000
Fixed cost – F	150,000
Total cost per year - TC = (V+F)	3,300,000
Net cash flow = S-TC	7,200,000

Year	Cash outflows	Cash inflows	Depreciation = D = 5265000/9	Net cash flow* = (Co+Ci-D)x(1-35% )+D	Discount factor = Df = 1/(1+10%)^Year	Present Values
0	-5,265,000.00	0.00	0.00	-5,265,000.00	1.000000	-5,265,000.00
	Co	Ci	D	(Co+Ci-D)x(1-35%)+D		Df x Net Cash flows
1	-3,300,000.00	10,500,000.00	585,000.00	4,884,750.00	0.909091	4,440,681.82
2	-3,300,000.00	10,500,000.00	585,000.00	4,884,750.00	0.826446	4,036,983.47
3	-3,300,000.00	10,500,000.00	585,000.00	4,884,750.00	0.751315	3,669,984.97
4	-3,300,000.00	10,500,000.00	585,000.00	4,884,750.00	0.683013	3,336,349.98
5	-3,300,000.00	10,500,000.00	585,000.00	4,884,750.00	0.620921	3,033,045.43
6	-3,300,000.00	10,500,000.00	585,000.00	4,884,750.00	0.564474	2,757,314.03
7	-3,300,000.00	10,500,000.00	585,000.00	4,884,750.00	0.513158	2,506,649.12
8	-3,300,000.00	10,500,000.00	585,000.00	4,884,750.00	0.466507	2,278,771.93
9	-3,300,000.00	10,500,000.00	585,000.00	4,884,750.00	0.424098	2,071,610.84
					Total = NPV =	22,866,391.59