Question

A small company heats its building and spends $8,200 per year on natural gas for this purpose. Cost increases of natural gas are expected to be 9​% per year starting one year from now​ (i.e., the first cash flow is $8,938 at EOY​ one). Their maintenance on the gas furnace is ​$355 per​ year, and this expense is expected to increase by 12​% per year starting one year from now​ (i.e., the first cash flow for this expense is $397.60 at the EOY​ one). 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.

Answer 1

Annual Total cost (TC) = Cost of gas + Maintenance cost

First, we compute the Present worth (PW) of TC as follows. Note that

PV Factor, year N = (1.18)^-N

EOY	Gas Cost ($)	Maintenance ($)	TC ($)	PV Factor @18%	Discounted TC ($)
	(A)	(B)	(C)=(A)+(B)	(D)	(C)x(D)
1	8,938.00	397.60	9,335.60	0.8475	7,911.53
2	9,742.42	445.31	10,187.73	0.7182	7,316.67
3	10,619.24	498.75	11,117.99	0.6086	6,766.75
4	11,574.97	558.60	12,133.57	0.5158	6,258.36
5	12,616.72	625.63	13,242.35	0.4371	5,788.35
6	13,752.22	700.71	14,452.93	0.3704	5,353.82
7	14,989.92	784.79	15,774.71	0.3139	4,952.08
8	16,339.01	878.97	17,217.98	0.2660	4,580.64
9	17,809.52	984.44	18,793.97	0.2255	4,237.21
10	19,412.38	1,102.58	20,514.96	0.1911	3,919.68
11	21,159.50	1,234.89	22,394.38	0.1619	3,626.08
12	23,063.85	1,383.07	24,446.92	0.1372	3,354.60
13	25,139.60	1,549.04	26,688.64	0.1163	3,103.56
14	27,402.16	1,734.92	29,137.09	0.0985	2,871.43
				PW ($) =	70,040.75

Annual equivalence cost = PW / P/A(18%, 14) = $70,040.75 / 5.0081** = $13,985.49

**From P/A Factor table