A small company heats its building and spends $8,400 per year on natural gas for
ID: 1188664 • 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 $9156 at EOY one). Their maintenance on the gas furnace is $350 per year, and this expense is expected to increase by 12% per year starting one year from now. If the planning horizon is 13 years, what is the total annual equivalent expense for operating and maintaining the furnace? The interest rate is 15% per year?
Explanation / Answer
Calculation of annual equivalent expense:
Calculation of present value (PV) is as below
Year
Natural gas (N)
Maintenance (M)
Cash flow (F) = N + M
15% factor {1 / (1+0.15)^year
PV
1
9,156
392
9,548
0.8696
8,302.94
2
9,980
439.04
10,419.04
0.7561
7,877.84
3
10,878.24
491.72
11,369.96
0.6575
7,475.75
4
11,857.27
550.73
12,408
0.5718
7,094.89
5
12,924.38
616.82
13,541.20
0.4972
6,732.68
6
14,087.58
690.83
14,778.41
0.4323
6,388.71
7
15,355.46
773.73
16,129.19
0.3759
6,062.96
8
16,737.45
866.57
17,604.02
0.3269
5,754.75
9
18,243.83
970.57
19,214.40
0.2843
5,462.65
10
19,885.76
1,087.03
20,972.79
0.2472
5,184.47
11
21,675.47
1,217.49
22,892.96
0.2149
4,919.69
12
23,626.25
1,363.59
24,989.84
0.1869
4,670.60
13
25,752.63
1,527.22
27,279.85
0.1625
4,432.98
-90,360.91
PV should be represented as in negative figure, since the amount is for expenses.
Annual equivalent expense = Rate × PV [(1 + 0.15)^13 / {(1 + 0.15)^13 – 1}
= 0.15 (-90,360.91) × 1.1940
= -$16,183.63 (Answer)
Year
Natural gas (N)
Maintenance (M)
Cash flow (F) = N + M
15% factor {1 / (1+0.15)^year
PV
1
9,156
392
9,548
0.8696
8,302.94
2
9,980
439.04
10,419.04
0.7561
7,877.84
3
10,878.24
491.72
11,369.96
0.6575
7,475.75
4
11,857.27
550.73
12,408
0.5718
7,094.89
5
12,924.38
616.82
13,541.20
0.4972
6,732.68
6
14,087.58
690.83
14,778.41
0.4323
6,388.71
7
15,355.46
773.73
16,129.19
0.3759
6,062.96
8
16,737.45
866.57
17,604.02
0.3269
5,754.75
9
18,243.83
970.57
19,214.40
0.2843
5,462.65
10
19,885.76
1,087.03
20,972.79
0.2472
5,184.47
11
21,675.47
1,217.49
22,892.96
0.2149
4,919.69
12
23,626.25
1,363.59
24,989.84
0.1869
4,670.60
13
25,752.63
1,527.22
27,279.85
0.1625
4,432.98
-90,360.91