Question

- A company purchased a quality control system for $12,783 which requires $5,677 per year maintenance fees for the first 5 years, after which the maintenance fees will increase by 12% per year for the upcoming 7 years (i.e. the first increase will happen at year 6.) Determine the equivalent total present worth value of preached system during the 12 years operation at i = 15% per year.

Answer 1

Working notes:

• Starting year 6, Cost in year N = Cost in year (N - 1) x 1.12
• PV Factor in year N = (1.15)^-N

Present worth of costs is computed as follows.

Year	Cost ($)	PV Factor @15%	Discounted Cost ($)
0	12,783	1.0000	12,783.00
1	5,677	0.8696	4,936.52
2	5,677	0.7561	4,292.63
3	5,677	0.6575	3,732.72
4	5,677	0.5718	3,245.84
5	5,677	0.4972	2,822.47
6	6,358.24	0.4323	2,748.84
7	7,121.23	0.3759	2,677.13
8	7,975.78	0.3269	2,607.30
9	8,932.87	0.2843	2,539.28
10	10,004.81	0.2472	2,473.04
11	11,205.39	0.2149	2,408.52
12	12,550.04	0.1869	2,345.69
		PW of Costs ($) =	49,612.99

PW (rounded off) = $49,613