Question

A company is looking at investing in a process upgrade. The first option would cost $12,000, with net annual benefits of $2000, and a salvage value of $1000 after 8 years. The second option would cost $20,000, with net annual benefits of $2800, and a salvage value of $4000 after 12 years. The company’s MARR is 8%.

A. Determine the Payback Period for each option.

B. Which alternative should be chosen using the payback period?

C. Determine the NPW of each option.

D. Which alternative should be chosen using the NPW method?

E. Which method would you recommend using to make your decision? Briefly discuss your reasoning…

Answer 1

(A) Payback period (PBP) is the time by when cumulative cash flow equals zero.

OPTION - 1
Year	Cash Flow ($)	Cumulative Cash Flow ($)
0	-12,000	-12,000
1	2,000	-10,000
2	2,000	-8,000
3	2,000	-6,000
4	2,000	-4,000
5	2,000	-2,000
6	2,000	0
7	2,000	2,000
8	3,000	5,000
OPTION - 2
Year	Cash Flow ($)	Cumulative Cash Flow ($)
0	-20,000	-20,000
1	2,800	-17,200
2	2,800	-14,400
3	2,800	-11,600
4	2,800	-8,800
5	2,800	-6,000
6	2,800	-3,200
7	2,800	-400
8	2,800	2,400
9	2,800	5,200
10	2,800	8,000
11	2,800	10,800
12	6,800	17,600

For Option 1, PBP = 6 years

For Option 2, PBP lies between years 7 & 8.

PBP = 7 + (Absolute value of cumulative cash flow, year 7 / Cash flow, year 8)

= 7 + (400 / 2,800) = 7 + 0.14 = 7.14 years

(B) Since Option 1 has lower PBP, this should be chosen.

(C) NPW is computed as follows. Note that PV Factor in year N = (1.08)^-N

OPTION - 1
Year	Cash Flow ($)	PV factor @8%	Discounted Cash Flow ($)
0	-12,000	1.0000	-12,000.00
1	2,000	0.9259	1,851.85
2	2,000	0.8573	1,714.68
3	2,000	0.7938	1,587.66
4	2,000	0.7350	1,470.06
5	2,000	0.6806	1,361.17
6	2,000	0.6302	1,260.34
7	2,000	0.5835	1,166.98
8	3,000	0.5403	1,620.81
		NPW ($) =	33.55
OPTION - 2
Year	Cash Flow ($)	PV factor @8%	Discounted Cash Flow ($)
0	-20,000	1.0000	-20,000.00
1	2,800	0.9259	2,592.59
2	2,800	0.8573	2,400.55
3	2,800	0.7938	2,222.73
4	2,800	0.7350	2,058.08
5	2,800	0.6806	1,905.63
6	2,800	0.6302	1,764.47
7	2,800	0.5835	1,633.77
8	2,800	0.5403	1,512.75
9	2,800	0.5002	1,400.70
10	2,800	0.4632	1,296.94
11	2,800	0.4289	1,200.87
12	6,800	0.3971	2,700.37
		NPW ($) =	2,689.47

(D) Since Option 2 has higher NPW, this shold be chosen.

(E) I would recommend NPW method, because PBP is non-discounted and ignores cash flows after the PBP, but NPW is superior in that it is discounted, includes time value of money, considered all cash flows during project period and gives an absolute dollar value of return.