Question

HopHeart Brewery is considering 3 different bottling machines. It is expected that each machine will be replaceable at the same cost when their useful life ends. The details of the machines are as follows:
Machine X has a useful life of 6 years. It costs $10,000 to purchase and $2,000 per year to maintain.
Machine Y has a useful life of 12 years. It costs $15,000 to purchase, and $1,000 per year to maintain.
Machine Z has a useful life of 8 years. It costs $20,000 to purchase, and $200 per year to maintain.

a) What is the appropriate planning horizon for analyzing these choices?  years

b) Using the planning horizon from part a, analyze the present worth of the cost of each alternative if HopHeart has a MARR of 9.1%/year.
X $  
Y $  
Z $

Answer 1

Present worth = Cost / ((1 + MARR) ^ number of periods)

Net Present Worth = Sum of the present worth of all the costs

Below table has been calculated by the above mentioned formulae.

The appropriate planning horizon for all the choices would be 24 years because each choice can be completed atleast once in the horizon and others can be repeated completely.

Assumption: Every cost is incurred at the end of year. Machine repeated after their useful lives will have added cost at the last year cost. As all cashflows are costs all are taken as positive cashflows for ease of presentation.

Machine X
EOY	Cost	MARR	PV	NPV
0	$10,000.00	9.10%	$10,000.00	$40,791.99
1	$2,000.00	9.10%	$1,833.18
2	$2,000.00	9.10%	$1,680.28
3	$2,000.00	9.10%	$1,540.12
4	$2,000.00	9.10%	$1,411.66
5	$2,000.00	9.10%	$1,293.92
6	$12,000.00	9.10%	$7,115.95
7	$2,000.00	9.10%	$1,087.07
8	$2,000.00	9.10%	$996.40
9	$2,000.00	9.10%	$913.29
10	$2,000.00	9.10%	$837.11
11	$2,000.00	9.10%	$767.29
12	$12,000.00	9.10%	$4,219.73
13	$2,000.00	9.10%	$644.63
14	$2,000.00	9.10%	$590.86
15	$2,000.00	9.10%	$541.58
16	$2,000.00	9.10%	$496.40
17	$2,000.00	9.10%	$455.00
18	$12,000.00	9.10%	$2,502.28
19	$2,000.00	9.10%	$382.26
20	$2,000.00	9.10%	$350.38
21	$2,000.00	9.10%	$321.15
22	$2,000.00	9.10%	$294.36
23	$2,000.00	9.10%	$269.81
24	$2,000.00	9.10%	$247.31

Machine Y
EOY	Cost	MARR	PV	NPV
0	$15,000.00	9.10%	$15,000.00	$29,904.84
1	$1,000.00	9.10%	$916.59
2	$1,000.00	9.10%	$840.14
3	$1,000.00	9.10%	$770.06
4	$1,000.00	9.10%	$705.83
5	$1,000.00	9.10%	$646.96
6	$1,000.00	9.10%	$593.00
7	$1,000.00	9.10%	$543.53
8	$1,000.00	9.10%	$498.20
9	$1,000.00	9.10%	$456.64
10	$1,000.00	9.10%	$418.55
11	$1,000.00	9.10%	$383.64
12	$16,000.00	9.10%	$5,626.30
13	$1,000.00	9.10%	$322.31
14	$1,000.00	9.10%	$295.43
15	$1,000.00	9.10%	$270.79
16	$1,000.00	9.10%	$248.20
17	$1,000.00	9.10%	$227.50
18	$1,000.00	9.10%	$208.52
19	$1,000.00	9.10%	$191.13
20	$1,000.00	9.10%	$175.19
21	$1,000.00	9.10%	$160.58
22	$1,000.00	9.10%	$147.18
23	$1,000.00	9.10%	$134.91
24	$1,000.00	9.10%	$123.65

Machine Z
EOY	Cost	MARR	PV	NPV
0	$20,000.00	9.10%	$20,000.00	$36,854.02
1	$200.00	9.10%	$183.32
2	$200.00	9.10%	$168.03
3	$200.00	9.10%	$154.01
4	$200.00	9.10%	$141.17
5	$200.00	9.10%	$129.39
6	$200.00	9.10%	$118.60
7	$200.00	9.10%	$108.71
8	$20,200.00	9.10%	$10,063.60
9	$200.00	9.10%	$91.33
10	$200.00	9.10%	$83.71
11	$200.00	9.10%	$76.73
12	$200.00	9.10%	$70.33
13	$200.00	9.10%	$64.46
14	$200.00	9.10%	$59.09
15	$200.00	9.10%	$54.16
16	$20,200.00	9.10%	$5,013.67
17	$200.00	9.10%	$45.50
18	$200.00	9.10%	$41.70
19	$200.00	9.10%	$38.23
20	$200.00	9.10%	$35.04
21	$200.00	9.10%	$32.12
22	$200.00	9.10%	$29.44
23	$200.00	9.10%	$26.98
24	$200.00	9.10%	$24.73