Question
Jack and Jills Place is a nonprofit nursery school run by the parents of the enrolled children. Since the school is out of town, it
Jack and Jills Place is a nonprofit nursery school run by the parents of the enrolled children. Since the school is out of town, it has a well rather than a city water supply. Lately, the well has become unreliable, and the school has had to bring in bottled drinking water. The schools governing board is considering drilling a new well (at the top of the hill, naturally). The board estimates that a new well would cost $2,966 and save the school $660 annually for 10 years. The schools hurdle rate is 8 percent.
Use Appendix A for your reference.
Note: Use appropriate factor(s) from the tables provided.
Required:
Compute the internal rate of return on the new well. Should the governing board approve the new well?
Future Value and Present Value Tables
Table I
Future Value of $1.00(1 + r)nn
Period | 4% | 6% | 8% | 10% | 12% | 14% | 20% |
---|---|---|---|---|---|---|---|
1 | 1.040 | 1.060 | 1.030 | 1.100 | 1.120 | 1.140 | 1.200 |
2 | 1.082 | 1.124 | 1.166 | 1.210 | 1.254 | 1.300 | 1.440 |
3 | l.125 | 1.191 | 1.260 | 1.331 | 1.405 | 1.482 | 1.728 |
4 | 1.170 | 1.263 | 1.361 | 1.464 | 1.574 | 1.689 | 2.074 |
5 | 1.217 | 1.338 | 1.469 | 1.61l | 1.762 | 1.925 | 2.488 |
6 | 1.265 | 1.419 | 1.587 | 1.772 | 1.974 | 2.195 | 2.986 |
7 | 1.316 | 1.504 | 1.714 | 1.949 | 2.211 | 2.502 | 3.583 |
8 | 1.369 | 1.594 | 1.851 | 2.144 | 2.476 | 2.853 | 4.300 |
9 | 1.423 | 1.690 | l.999 | 2.359 | 2.773 | 3.252 | 5.160 |
10 | l.480 | 1.791 | 2.159 | 2.594 | 3.106 | 3.707 | 6.192 |
11 | 1.540 | 1.898 | 2.332 | 2.853 | 3.479 | 4.226 | 7.430 |
12 | 1.601 | 2.0 12 | 2.513 | 3.139 | 3.896 | 4.818 | 8.916 |
13 | l.665 | 2.133 | 2.720 | 3.452 | 4.364 | 5.492 | 10.699 |
14 | l.732 | 2.261 | 2.937 | 3.798 | 4.887 | 6.261 | 12.839 |
15 | 1.801 | 2.397 | 3.172 | 4.177 | 5.474 | 7.138 | 15.407 |
20 | 2.191 | 3.207 | 4.661 | 6.723 | 9.646 | 13.743 | 38.338 |
30 | 3.243 | 5.744 | 10.063 | 17.450 | 29.960 | 50.950 | 237.380 |
40 | 4.301 | 10.286 | 21.725 | 45.260 | 93.051 | 188.880 | 1,469.300 |
Table II
Future Value of a Series of $1.00 Cash Flows (Ordinary Annuity)(((1+r)nn 1) r)
Period | 4% | 6% | 8% | 10% | 12% | 14% | 20% |
---|---|---|---|---|---|---|---|
1 | 1.000 | 1.000 | 1.000 | l.000 | 1.000 | 1.000 | 1.000 |
2 | 2.040 | 2.060 | 2.080 | 2.100 | 2.120 | 2.140 | 2.220 |
3 | 3.122 | 3. 184 | 3.246 | 3.310 | 3.374 | 3.440 | 3.640 |
4 | 4.247 | 4.375 | 4.506 | 4.641 | 4.779 | 4.921 | 5.368 |
5 | 5.416 | 5.637 | 5.867 | 6.105 | 6.353 | 6.610 | 7.442 |
6 | 6.633 | 6.975 | 7.336 | 7.716 | 8.115 | 8.536 | 9.930 |
7 | 7.898 | 8.394 | 8.923 | 9.487 | 10.089 | 10.730 | 12.916 |
8 | 9.214 | 9.898 | I0.637 | Il.436 | 12.300 | 13.233 | 16.499 |
9 | 10.583 | ll.491 | 12.488 | 13.580 | 14.776 | 16.085 | 20.799 |
10 | 12.006 | 13.181 | 14.487 | 15.938 | 17.549 | 19.337 | 25.959 |
11 | 13.486 | 14.972 | 16.646 | 18.531 | 20.655 | 23.045 | 32.150 |
12 | 15.026 | 16.870 | 18.977 | 21.385 | 24.133 | 27.271 | 39.580 |
13 | 16.627 | 18.882 | 21.495 | 24.523 | 28.029 | 32.089 | 48.497 |
14 | 18.292 | 21.015 | 24.215 | 27.976 | 32.393 | 37.581 | 59.196 |
15 | 20.024 | 23.276 | 27.152 | 31.773 | 37.280 | 43.842 | 72.035 |
20 | 29.778 | 36.773 | 45.762 | 57.276 | 75.052 | 91.025 | 186.690 |
30 | 56.085 | 79.058 | 113.283 | 164.496 | 241.330 | 356.790 | l,181.900 |
40 | 95.026 | 154.762 | 259.057 | 442.597 | 767.090 | 1.342.000 | 7,343.900 |
Table III
Present Value of $1.00 (1 (1+r)nn)
Period | 4% | 6% | 8% | 10% | 12% | 14% | 16% | 18% | 20% | 22% | 24% | 26% | 28% | 30% | 32% |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | .962 | .943 | .926 | .909 | .893 | .877 | .862 | .847 | .833 | .820 | .806 | .794 | .781 | .769 | .758 |
2 | .925 | .890 | .857 | .826 | .797 | .769 | .743 | .718 | .694 | .672 | .650 | .630 | .610 | .592 | .574 |
3 | .889 | .840 | .794 | .751 | .712 | .675 | .641 | .609 | .579 | .551 | .524 | .500 | .477 | .455 | .435 |
4 | .855 | .792 | .735 | .683 | .636 | .592 | .552 | .516 | .482 | .451 | .423 | .397 | .373 | .350 | .329 |
5 | .822 | .747 | .681 | .621 | .567 | .519 | .476 | .437 | .402 | .370 | .341 | .315 | .291 | .269 | .250 |
6 | .790 | .705 | .630 | .564 | .507 | .456 | .410 | .370 | .335 | .303 | .275 | .250 | .227 | .207 | .189 |
7 | .760 | .665 | .583 | .513 | .452 | .400 | .354 | .314 | .279 | .249 | 222 | .198 | .178 | .159 | .143 |
8 | .731 | .627 | .540 | .467 | .404 | .351 | .305 | .266 | .233 | .204 | .179 | .157 | .139 | .123 | .108 |
9 | .703 | .592 | .500 | .424 | .361 | .308 | .263 | .225 | .194 | .167 | .144 | .125 | .108 | .094 | .082 |
10 | .676 | .558 | .463 | .386 | .322 | .270 | .227 | .191 | .162 | .137 | .116 | .099 | .085 | .073 | .062 |
11 | .650 | .527 | .429 | .350 | .287 | .237 | .195 | .162 | .135 | .112 | .094 | .079 | .066 | .056 | .047 |
12 | .625 | .497 | .397 | .319 | .257 | .208 | .168 | .137 | .112 | .092 | .076 | .062 | .052 | .043 | .036 |
13 | .601 | .469 | .368 | .290 | .229 | .182 | .145 | .116 | .093 | .075 | .061 | .050 | .040 | .033 | .027 |
14 | .577 | .442 | .340 | .263 | .205 | .160 | .125 | .099 | .078 | .062 | .049 | .039 | .032 | .025 | .021 |
15 | .555 | .417 | .315 | .239 | .183 | .140 | .108 | .084 | .065 | .051 | .040 | .031 | .025 | .020 | .016 |
20 | .456 | .312 | .215 | .149 | .104 | .073 | .051 | .037 | .026 | .019 | .014 | .010 | .007 | .005 | .004 |
30 | .308 | .174 | .099 | .057 | .033 | .020 | .012 | .007 | .004 | .003 | .002 | .001 | .001 | ||
40 | .208 | .097 | .046 | .022 | .011 | .005 | .003 | .001 | .001 |
Table IV
Present Value of Series of $1.00 Cash Flows 1/r (1 (1 (1+rnn)))
Period | 4% | 6% | 8% | 10% | 12% | 14% | 16% | 18% | 20% | 22% | 24% | 25% | 26% | 28% | 30% |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 0.962 | 0.943 | 0.926 | 0.909 | 0.893 | 0.877 | 0.862 | 0.847 | 0.833 | 0.820 | 0.806 | 0.800 | 0.794 | 0.781 | 0.769 |
2 | 1.886 | 1.833 | 1.783 | 1.736 | 1.690 | 1.647 | 1.605 | 1.566 | 1.528 | 1.492 | 1.457 | 1.440 | 1.424 | 1.392 | 1.361 |
3 | 2.775 | 2.673 | 2.577 | 2.487 | 2.402 | 2.322 | 2.246 | 2.174 | 2.106 | 2.042 | 1.981 | 1.952 | 1.923 | 1.868 | 1.816 |
4 | 3.630 | 3.465 | 3.312 | 3.170 | 3.037 | 2.914 | 2.798 | 2.690 | 2.589 | 2.494 | 2.404 | 2.362 | 2.320 | 2.241 | 2.166 |
5 | 4.452 | 4.212 | 3.993 | 3.791 | 3.605 | 3.433 | 3.274 | 3.127 | 2.991 | 2.864 | 2.745 | 2.689 | 2.635 | 2.532 | 2.436 |
6 | 5.242 | 4.917 | 4.623 | 4.355 | 4.111 | 3.889 | 3.685 | 3.498 | 3.326 | 3.167 | 3.020 | 2.951 | 2.885 | 2.759 | 2.643 |
7 | 6.002 | 5.582 | 5.206 | 4.868 | 4.564 | 4.288 | 4.039 | 3.812 | 3.605 | 3.416 | 3.242 | 3.161 | 3.083 | 2.937 | 2.802 |
8 | 6.733 | 6.210 | 5.747 | 5.335 | 4.968 | 4.639 | 4.344 | 4.078 | 3.837 | 3.619 | 3.421 | 3.329 | 3.241 | 3.076 | 2.925 |
9 | 7.435 | 6.802 | 6.247 | 5.759 | 5.328 | 4.946 | 4.607 | 4.303 | 4.031 | 3.786 | 3.566 | 3.463 | 3.366 | 3.184 | 3.019 |
10 | 8. 111 | 7.360 | 6.710 | 6.145 | 5.650 | 5.216 | 4.833 | 4.494 | 4.192 | 3.923 | 3.682 | 3.571 | 3.465 | 3.269 | 3.092 |
11 | 8.760 | 7.887 | 7.139 | 6.495 | 5.938 | 5.453 | 5.029 | 4.656 | 4.327 | 4.035 | 3.776 | 3.656 | 3.544 | 3.335 | 3.147 |
12 | 9.385 | 8.384 | 7.536 | 6.814 | 6.194 | 5.660 | 5.197 | 4.793 | 4.439 | 4.127 | 3.851 | 3.725 | 3.606 | 3.387 | 3.190 |
13 | 9.986 | 8.853 | 7.904 | 7.103 | 6.424 | 5.842 | 5.342 | 4.910 | 4.533 | 4.203 | 3.912 | 3.780 | 3.656 | 3.427 | 3.223 |
14 | 10.563 | 9.295 | 8.244 | 7.367 | 6.628 | 6.002 | 5.468 | 5.008 | 4.611 | 4.265 | 3.962 | 3.824 | 3.695 | 3.459 | 3.249 |
15 | 11.118 | 9.712 | 8.559 | 7.606 | 6.811 | 6.142 | 5.575 | 5.092 | 4.675 | 4.315 | 4.001 | 3.859 | 3.726 | 3.483 | 3.268 |
20 | 13.590 | 11.470 | 9.818 | 8.514 | 7.469 | 6.623 | 5.929 | 5.353 | 4.870 | 4.460 | 4.110 | 3.954 | 3.808 | 3.546 | 3.316 |
30 | 17.292 | 13.765 | 11.258 | 9.427 | 8.055 | 7.003 | 6.177 | 5.517 | 4.979 | 4.534 | 4.160 | 3.995 | 3.842 | 3.569 | 3.332 |
40 | 19.793 | 15.046 | 11.925 | 9.779 | 8.244 | 7.105 | 6.234 | 5.548 | 4.997 | 4.544 | 4.166 | 3.999 | 3.846 | 3.571 | 3.333 |
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