A small company heats its building and spends $8,200 per year on natural gas for this...

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.

Expert Solution

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

Rahul Sunny answered 1 year ago

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