Question 14.6: On your first assignment as an engineer, your boss asks you ...
On your first assignment as an engineer, your boss asks you to develop the utility cost portion of an estimate for the cost of a new manufacturing facility. After some research you define the problem as finding the present worth of utility costs, given the following data:
• Your company uses a minimum attractive rate of return (MARR) = 35\% as i. This rate is not adjusted for inflation.
• The project has a useful life of 25 years.
• The utilities to be estimated are electricity, water, and natural gas.
• The 35-year historical data reveal the following increases:
– Electricity costs increase at 8.5\%per year.
– Water costs increase at 5.5\%per year.
– Natural gas costs increase at 6.5\%per year.
• First-year estimates of the utility costs (in today’s dollars) are as follows:
– Electricity will cost \$55,000.
– Water will cost \$18,000.
–Natural gas will cost \$38,000.
For this problem we will take each of the utilities used in our manufacturing facility and inflate them independently at their various historical annual rates. Once we have these actual-dollar amounts (A\$),
we can total them and then discount each year’s total at 35\% back to the present.
| Year | Electricity | Water | Natural Gas | Total |
| 1 | 55,000(1.085)^{0} = \$55,000 | 18,000(1.055)^{0} = \$18,000 | 38,000(1.065)^{0} = \$38,000 | \$111,000 |
| 2 | 55,000(1.085)^{1} = 59,675 | 18,000(1.055)^{1} = 18,990 | 38,000(1.065)^{1}=40,470 | 119,135 |
| 3 | 55,000(1.085)^{2} = 64,747 | 18,000(1.055)^{2} = 20,034 | 38,000(1.065)^{2}=43,101 | 127,882 |
| 4 | 55,000(1.085)^{3} = 70,251 | 18,000(1.055)^{3} = 21,136 | 38,0001.065)^{3}=45.902 | 137,289 |
| 5 | 55,000(1.085)^{4} = 76,222 | 18,000(1.055)^{4} = 22,299 | 38,000(1.065) ^{4}=48,886 | 147,407 |
| 6 | 55,000(1.085)^{5} = 82,701 | 18,000(1.055)^{5} = 23,525 | 38,000(1.065)^{5}=52.063 | 158,290 |
| 7 | 55,000(1.085)^{6} = 89,731 | 18,000(1.055)^{6} = 24,819 | 38,000(1.065)^{6}=55,447 | 169,997 |
| 8 | 55,000(1.085)^{7} = 97,358 | 18,000(1.055)^{7} = 26,184 | 38,000(1.065) ^{7}=59,051 | 182,594 |
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| 24 | 55,000(1.085)^{23} = 359,126 | 18,000(1.055)^{23}=61,671 | 38,000(1.065)^{23}=161,743 | 582,539 |
| 25 | 55,000(1.085)^{24} = 389,652 | 18,000(1.055)^{24}=65,063 | 38,000(1.065)^{24}=172,256 | 626,970 |
The present worth of the total yearly utility costs is
PW = \$111,000(P/F, 35\%, 1) + \$119,135(P/F, 35\%, 2) + \cdots + \$626,970(P/F, 35\%, 25)
= \$5,540,000