A small company heats its building and spends $8,400 per year on natural gas for
ID: 1135353 • Letter: A
Question
A small company heats its building and spends $8,400 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 $9 comma 156 at EOY one). Their maintenance on the gas furnace is $335 per year, and this expense is expected to increase by 15% per year starting one year from now (i.e., the first cash flow for this expense is $385.25 at the EOY one). If the planning horizon is 14 years, what is the total annual equivalent expense for operating and maintaining the furnace? The interest rate is 18% per year.
Explanation / Answer
Working notes:
(i) Cost of gas in year N = Cost of gas in year (N - 1) x 1.09
(ii) Maintenance cost in year N = Maintenance cost in year (N - 1) x 1.15
(iii) Total expense (TE) ($) = Cost of gas + Maintenance cost
We compute Present Worth (PW) of Total Expense as follows. Note that PV Factor in year N = (1.18)-N
Annual equivalent expense = PW of TE / P/A(18%, 14) = $69,010.76 / 5.0081** = $13,779.83
**From P/A factor table
Year Cost of Gas ($) Maintenance Cost ($) TE ($) PV factor @18% Discounted TE ($) (A) (B) (C)=(A)+(B) (D) (C)x(D) 1 9,156 385.25 9,541.25 0.8475 8,085.81 2 9,980.04 443.04 10,423.08 0.7121 7,422.79 3 10,878.24 509.49 11,387.74 0.5984 6,814.93 4 11,857.29 585.92 12,443.20 0.5029 6,257.62 5 12,924.44 673.80 13,598.25 0.4226 5,746.63 6 14,087.64 774.88 14,862.52 0.3551 5,278.07 7 15,355.53 891.11 16,246.64 0.2984 4,848.41 8 16,737.53 1,024.77 17,762.30 0.2508 4,454.39 9 18,243.90 1,178.49 19,422.39 0.2107 4,093.03 10 19,885.85 1,355.26 21,241.12 0.1771 3,761.60 11 21,675.58 1,558.55 23,234.13 0.1488 3,457.60 12 23,626.38 1,792.33 25,418.72 0.1251 3,178.74 13 25,752.76 2,061.18 27,813.94 0.1051 2,922.92 14 28,070.51 2,370.36 30,440.87 0.0883 2,688.22 PW of TE ($) = 69,010.76