Question

Nippon Steel’s expenses for heating and cooling a large manufacturing facility are expected to increase according to an arithmetic gradient beginning in year 2. If the cost is $550,000 this year (year 0) and will be $550,000 again in year 1, but then it is estimated to increase by $58,000 each year through year 12, what is the equivalent annual worth in years 1 to 12 of these energy costs at an interest rate of 14% per year? The equivalent annual worth is determined to be $

Answer 1

We need to calculate Equivalent Annual worth in years 1 to 12 which is

= r(NPV)/{1-(1+r)^-n}

Year	Cost	Discount rate @ 14%	NPV
1	550000	0.877193	482456.1404
2	608000	0.769468	467836.2573
3	666000	0.674972	449531.0298
4	724000	0.59208	428666.1208
5	782000	0.519369	406146.2955
6	840000	0.455587	382692.7001
7	898000	0.399637	358874.3156
8	956000	0.350559	335134.4564
9	1014000	0.307508	311813.0541
10	1072000	0.269744	289165.3638
11	1130000	0.236617	267377.6358
12	1188000	0.207559	246580.2137
Total			4426273.583

Equivalent Annual worth = 0.14(4426273.583)/[1-(1+0.14)^-12]

= 619678.3017/(1-0.207559)

= 619678.3017/0.792441

= $ 781986.7747