Question 15.11: PW for a Dam The dam will supply annual recreation benefits ...
PW for a Dam
The dam will supply annual recreation benefits of $500K for 250 users per day and 200 days per year at $10 per user-day. However, its main purpose is to generate electricity. It will save $3 million in fuel costs for Arctic Power & Light. The dam will cost $400K annually for labor to run and maintain and $40 million to build.
Calculate the PW using a real interest rate of 4% and a 25-year life. The differential interest rates are 0% for recreation, 2% for fuel cost, and 1% for labor. There is a 5% inflation rate for the economy ( f ).
First, the year-1 dollars of CF_{1} are chosen as the constant-value unit. In this case, f is used only to state the first cost in year-1 dollars, since the real interest rate and each of the differential inflation rates are given. Each annual benefit, savings, and expense is shown as a column in Exhibit 15.8, with the differential rate for each applied. Note that all cash flows in the table are stated in $1000’s, and the initial data for annual cash flows are assumed to be year-1 dollars. The first cost is assumed to be in year-0 dollars. Thus, cell E13 multiplies the first cost by (1 + f ) to state it in year-1 dollars. Column D includes the time-0 expense and totals the annual cash flows in constant-dollar terms. ThePWof columnDat an interest rate of4%is found using {E13+ NPV(A10, E14: E38)}.
EXHIBIT 15.8 PW of a dam
| E | D | C | B | A | |
| All costs are in $1000s | 1 | ||||
| first cost for the dam | -$40,000 | 2 | |||
| recreation benefits | $500 | 3 | |||
| savings in fuel costs | $3,000 | 4 | |||
| labor to operate | -$400 | 5 | |||
| f = CPI | 5% | 6 | |||
| f(delta-rec) | 0% | 7 | |||
| f(delta-fuel) = differential rate for fuel | 2% | 8 | |||
| f(delta-labor) = differential rate for labor | 1% | 9 | |||
| real interest rate | 4% | 10 | |||
| 11 | |||||
| Total CF(t) in year-1 $s | Labor Constant $ Cash Flow | Fuel Savings Constant $ Cash Flow | Recreation Constant $ Cash Flow | Year | 12 |
| -42,000 | 0 | 13 | |||
| 3,100 | -400 | 3000 | 500 | 1 | 14 |
| 3,156 | -404 | 3060 | 500 | 2 | 15 |
| 3,213 | -408 | 3121 | 500 | 3 | 16 |
| 3,272 | -412 | 3184 | 500 | 4 | 17 |
| 3,331 | -416 | 3247 | 500 | 5 | 18 |
| 3,392 | -420 | 3312 | 500 | 6 | 19 |
| 3,454 | -425 | 3378 | 500 | 7 | 20 |
| 3,517 | -429 | 3446 | 500 | 8 | 21 |
| 3,582 | -433 | 3515 | 500 | 9 | 22 |
| 3,648 | -437 | 3585 | 500 | 10 | 23 |
| 3,715 | -442 | 3657 | 500 | 11 | 24 |
| 3,784 | -446 | 3730 | 500 | 12 | 25 |
| 3,854 | -451 | 3805 | 500 | 13 | 26 |
| 3,926 | -455 | 3881 | 500 | 14 | 27 |
| 3,999 | -460 | 3958 | 500 | 15 | 28 |
| 4,073 | -464 | 4038 | 500 | 16 | 29 |
| 4,149 | -469 | 4118 | 500 | 17 | 30 |
| 4,227 | -474 | 4201 | 500 | 18 | 31 |
| 4,306 | -478 | 4285 | 500 | 19 | 32 |
| 4,387 | -483 | 4370 | 500 | 20 | 33 |
| 4,470 | -488 | 4458 | 500 | 21 | 34 |
| 4,554 | -493 | 4547 | 500 | 22 | 35 |
| 4,640 | -498 | 4638 | 500 | 23 | 36 |
| 4,728 | -503 | 4731 | 500 | 24 | 37 |
| 4,817 | -508 | 4825 | 500 | 25 | 38 |
| PW = $16,579 | 39 | ||||