Engineering Economic Analysis

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Cash FlowsThat Inflate at Different Rates 457

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%asi.

· The project has a useful life of 25 years.

·Utilities to be estimated include electricity, water, and natural gas.

· The 35-year historical data reveal:

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 cost will be $55,000

Water cost will be $18,000

Natural gas will be $38,000

SOLUTION

For this problem we will take each of the utilities used in our manufacturing facility and inflate

them independently at their respective historical annual rates. Once we have these actual dollar

amounts(A$),we can total them and then discount each year's total at 35% for the appropriate

number of periods back to the present.

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24 55,000(1.085)23= 359,126

25 55,000(1.085)24= 389,652

38,000(1.065)23 = 161,743

38,000(1.065)24 = 172,256

18,000(1.055)23= 61,671

18,OOO(1.055}24= 65,063

582,539

626,970

The present worth of the total yearly utility costsis:

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'PW = $Qf,OOO(P/F,35"%,1)+$119';135(P/F, 35%, 2) +... +$6+6,970(P/F, 35%, 25)

• $5,,540,000

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Year Electricity Water Natural Gas Total

1 55,000(1.085)° =$ 55,000 18,000(1.055)°=$18,000 38,000(1.065)° =$ 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 55,000a.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 38,000(1.065)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