# HOMER Grid 1.1

The net present cost (or life-cycle cost) of a Component is the present value of all the costs of installing and operating the Component over the project lifetime, minus the present value of all the revenues that it earns over the project lifetime. HOMER calculates the net present cost of each Component in the system, and of the system as a whole.

Example: A diesel generator has an initial capital cost of \$96,000, a replacement cost of \$48,000, and a lifetime of 3.52 years. Its cost of operation and maintenance (O&M) is \$2,471/yr, and its fuel cost is \$34,969/yr. What is the net present cost of this generator over a 25-year project lifetime at an annual real discount rate of 6%?

To perform this calculation, HOMER produces a Cash Flow table such as the one below. Except for the salvage value that occurs at the end of the 25th year, all of these cash flows are costs, so they appear as negative numbers in the table.

The first column shows the time at which each cash flow occurs, in years since the start of the project. The capital cost occurs at the start of the project, or year zero. The annual O&M and fuel costs occur at the end of each year. The replacement costs occur every 3.52 years.

The second column, highlighted in yellow, contains the discount factor. The columns highlighted in green contain the nominal cash flows. The columns highlighted in purple contain the same cash flow discounted to year zero. HOMER calculates the discounted costs by multiplying the nominal costs by the discount factor.

The bottom row below the purple discounted cash flow columns contains the net present value of each category of cash flow, as well as the total net present value, shown in red, with a value of -\$725,240. The net present value and the net present cost differ only in sign, so the net present cost of this generator over the 25-year project lifetime is \$725,240.

HOMER does a similar analysis for each Component in the system, and for the system as a whole.

 Year Discount Nominal Cash Flows Discounted Cash Flows Factor Capital Replace-ment Salvage O&M Fuel Total Capital Replace-ment Salvage O&M Fuel Total 0 1.000 -96,000 -96,000 -96,000 -96,000 1 0.943 -2,471 -34,969 -37,441 -2,331 -32,990 -35,321 2 0.890 -2,471 -34,969 -37,441 -2,200 -31,123 -33,322 3 0.840 -2,471 -34,969 -37,441 -2,075 -29,361 -31,436 3.52 0.815 -48,000 -48,000 -39,098 -39,098 4 0.792 -2,471 -34,969 -37,441 -1,958 -27,699 -29,657 5 0.747 -2,471 -34,969 -37,441 -1,847 -26,131 -27,978 6 0.705 -2,471 -34,969 -37,441 -1,742 -24,652 -26,394 7 0.665 -2,471 -34,969 -37,441 -1,644 -23,257 -24,900 7.04 0.663 -48,000 -48,000 -31,847 -31,847 8 0.627 -2,471 -34,969 -37,441 -1,551 -21,940 -23,491 9 0.592 -2,471 -34,969 -37,441 -1,463 -20,698 -22,161 10 0.558 -2,471 -34,969 -37,441 -1,380 -19,527 -20,907 10.56 0.540 -48,000 -48,000 -25,941 -25,941 11 0.527 -2,471 -34,969 -37,441 -1,302 -18,421 -19,723 12 0.497 -2,471 -34,969 -37,441 -1,228 -17,379 -18,607 13 0.469 -2,471 -34,969 -37,441 -1,159 -16,395 -17,554 14 0.442 -2,471 -34,969 -37,441 -1,093 -15,467 -16,560 14.08 0.440 -48,000 -48,000 -21,130 -21,130 15 0.417 -2,471 -34,969 -37,441 -1,031 -14,592 -15,623 16 0.394 -2,471 -34,969 -37,441 -973 -13,766 -14,738 17 0.371 -2,471 -34,969 -37,441 -918 -12,986 -13,904 17.60 0.359 -48,000 -48,000 -17,212 -17,212 18 0.350 -2,471 -34,969 -37,441 -866 -12,251 -13,117 19 0.331 -2,471 -34,969 -37,441 -817 -11,558 -12,375 20 0.312 -2,471 -34,969 -37,441 -771 -10,904 -11,674 21 0.294 -2,471 -34,969 -37,441 -727 -10,286 -11,013 21.12 0.292 -48,000 -48,000 -14,020 -14,020 22 0.278 -2,471 -34,969 -37,441 -686 -9,704 -10,390 23 0.262 -2,471 -34,969 -37,441 -647 -9,155 -9,802 24 0.247 -2,471 -34,969 -37,441 -610 -8,637 -9,247 24.64 0.238 -48,000 -48,000 -11,420 -11,420 25 0.233 43,120 -2,471 -34,969 5,679 10,047 -576 -8,148 1,323 Total -96,000 -336,000 43,120 -61,784 -874,234 -1,324,899 -96,000 -160,668 10,047 -31,593 -447,026 -725,239

Note that HOMER uses the discount factor to account for the time value of money, not inflation. Inflation is factored out of the analysis by using the real discount rate instead of the nominal discount rate. All costs in the table above are in year-zero dollars. This explains why the fuel and O&M costs remain the same for each year of the project lifetime.

Even with inflation removed from the analysis, the time value of money dictates that a future cash flow is worth less than a present cash flow of the same amount. The discount factor accounts for this effect; its value decreases with the increasing number of years from the start of the project.

Total net present cost

Annualized cost

Present value

Future value

Salvage value

Real Discount rate

Discount factor

Cash Flow table

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