A small company heats its building and spends $8,200 per year on natural gas for
ID: 1149900 • Letter: A
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.
Explanation / Answer
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
Annual equivalence cost = PW / P/A(18%, 14) = $70,040.75 / 5.0081** = $13,985.49
**From P/A Factor table
EOY Gas Cost ($) 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