Engineering Calculations | Table of Contents | Electric Rate Structure

Financial Calculations

Internal Rate of Return on Investment

Each 28-kW micro-turbine generator3 costs $36,000. The cost of a heat exchanger14 is approximately $400. Assume that maintaining the turbines approximately costs 3% per year of their original cost1. Maintenance of the heat exchangers is negligible because they have no moving parts.

3% ($36,000) = $1,080 per year

$1,080 (10 years) = $10,800

$36,000 + 400 + 10,800 = $47,200

The Simple Pay Back Period for an 84-kW system is found on Figure 6-8b, using $1685.70/kW, to be 6.8 years. This means that three turbines and three heat exchangers would be purchased. Figure 6-8a shows the annual utility savings to be $20,800. To find the internal rate of return on the investment (IRRI), use the following equation15:

Initial Investment + (Net Annual Savings)(P/A, IRRI, Y) = 0

where Y is the number of years that the system is assumed to last. Then the Discrete Compounding tables15 must be used to obtain P/A factors and these must be interpolated with their respective interest rates to find the IRRI. Typical system components last from 10 to 34 years1. Therefore, it is reasonable to calculate benefits over possible turbine lives of 10, 15 and 20 years. Using the cost of three turbines and therefore tripling the cost of maintenance:

$109,200 + (20,800 - 3,240)(P/A, IRRI, Y) = 0

(P/A, IRRI, Y) = 6.219

Note that this equation yields the actual pay back period15 of the investment, 6.2 years. The Discrete Compounding tables report the following:

(P/A, 9%, 10) = 6.4177 and (P/A, 10%, 10) = 6.1446

(P/A, 12%, 15) = 6.8109 and (P/A, 15%, 15) = 5.8474

(P/A, 15%, 20) = 6.2593 and (P/A, 18%, 20) = 5.3527

Therefore, linearly interpolating between P/A factors at Y = 10 years yields the following results:

Interpolating between P/A factors at Y = 15 years gives an IRRI of 13.8%, and at Y = 20 years the rate of return is 15.1%.

Partial Loan with Ten-Year Life

If 80% of the initial investment is borrowed at an interest rate higher than 9.73%, assuming the life of the turbine is 10 years, then the value of IRRI will decrease. Contrarily, if a loan is borrowed at a lower interest rate, the IRRI will increase15. For an 84-kW system,

20%($109,200) + (20,800 - 3,240 - loan payment)(P/A, IRRI, 10) = 0

Using a sample loan interest rate of 7%,

(A/P, 7%, 10) = 0.1424

And,

loan payment = 80%($109,200)(A/P, 7%, 10)

= 80%($109,200)(0.1424)

= $12,440.06

Also,

(P/A, IRRI, 10) = 4.266

Interpolating between (P/A, 18%, 10) = 4.4941 and (P/A, 20%, 10) = 4.1925 gives the result for this scenario, IRRI = 19.5%.

Profit from Emissions Reduction

Figure 6-10 shows that an 84-kW cogeneration system reduces carbon emissions by 46.7 tons of carbon per year. To find out how much is saved while reducing emissions, the equivalent annual savings15 of the system must be found to compare with the emissions reduction. This is the same as assuming that the entire cost of the cogeneration system is borrowed. Using an interest rate of 7.5% for the hypothetical loan,

loan payment = $109,200(A/P, 7.5%, Y)

The A/P factors are found in the aforementioned Discrete Compounding tables15. A 10-year loan results in annual payments of $15,910.44. A 15-year loan costs $12,372.36 per year and a 20-year loan costs $10,717.98 per year. The loan payments are subtracted from the annual savings minus maintenance costs to obtain the net equivalent annual savings:

$20,800 - 3,240 - loan payment = equivalent annual savings

For the 10-year assumption, the equivalent annual savings is $1649.56, for the 15-year assumption it is $5187.64 and for the 20-year assumption $6842.02. Dividing each of these by 46.7 tons of carbon per year results, respectively, in profits of $35.32, $111.08 and $146.51 per ton of carbon over a 10-year, 15-year and 20-year life.