Question

A small company heats its building and will spend $9,156 in year 1 on natural gas for this purpose. Cost increases of natural gas are expected to be 9% per year starting year 2. Their maintenance on the gas furnace is going to be $391.00 in the first year and this expense is expected to increase by 15% per year starting year 2. If the planning horizon is 14 years, what is the total annual equivalent expense for operating and maintaining the furnace? The interest rate is 18% per year. (a) The total present worth of operating and maintaining the furnace is $ thousands. (Round to two decimal places.) (b) The total annual equivalent expense for operating and maintaining the furnace is $ thousands (Round to two decimal places.)

Answer 1

(a)

Working notes:

Starting year 2: O&M Cost, year N = O&M Cost, year (N - 1) x 1.15

Starting year 2: Gas cost, year N = Gas cost, year (N - 1) x 1.09

Total cost (TC) = O&M + Gas cost

PV Factor in year N = (1.18)^-N.

PW of total cost is computed as follows.

Year	Gas Cost ($)	O&M Cost ($)	TC ($)	PV Factor @18%	Discounted TC ($)
	(A)	(B)	(C)=(A)+(B)	(D)	(C) x (D)
0				1.0000	0
1	9,156	391	9,547	0.8475	8,091
2	9,980	450	10,430	0.7182	7,490
3	10,878	517	11,395	0.6086	6,936
4	11,857	595	12,452	0.5158	6,423
5	12,924	684	13,608	0.4371	5,948
6	14,088	786	14,874	0.3704	5,510
7	15,356	904	16,260	0.3139	5,104
8	16,738	1,040	17,778	0.2660	4,730
9	18,244	1,196	19,440	0.2255	4,383
10	19,886	1,375	21,261	0.1911	4,062
11	21,676	1,582	23,257	0.1619	3,766
12	23,626	1,819	25,445	0.1372	3,492
13	25,753	2,092	27,845	0.1163	3,238
14	28,071	2,406	30,476	0.0985	3,003
				PW of Costs ($) =	72,175

Total PW = $72.18 (thousand)

(b)

Annual equivalent cost = PW / P/A(18%, 14) = $72,175 / 5.0081 = $14,411 = $14.41 (thousand)