Annual interest rate = 10%, It is compounded semiannually
Compounded annual interest rate =(1+10%/2)^2-1= 10.25%
Estimated annual cost if overflows = probability of overflow * estimated annual damages
As calculated below present value of total cost over the life for Dam A is -$310,676, Dam B is -$102,762,
Similarly present value of total cost over the life fo Dam C is -93,681, Dam D is -$86,989 and Dam E is -$69,974. (calculations could not be included as it is above the total text limit of the answer (65,000 words)
Dam E has lowest of of -$69,974 among all Dams. Hence Dam E should be chosen.
Dam A |
Capital investment (spread over 40 years) |
Annual damages of overflow over design capacity |
Total cost |
Discount factor (at 10.25%) |
Discounted cash flow |
1 | -2,500 | -30,000 | -32,500 | 0.907 | -29,478 |
2 | -2,500 | -30,000 | -32,500 | 0.823 | -26,738 |
3 | -2,500 | -30,000 | -32,500 | 0.746 | -24,252 |
4 | -2,500 | -30,000 | -32,500 | 0.677 | -21,997 |
5 | -2,500 | -30,000 | -32,500 | 0.614 | -19,952 |
6 | -2,500 | -30,000 | -32,500 | 0.557 | -18,097 |
7 | -2,500 | -30,000 | -32,500 | 0.505 | -16,415 |
8 | -2,500 | -30,000 | -32,500 | 0.458 | -14,889 |
9 | -2,500 | -30,000 | -32,500 | 0.416 | -13,504 |
10 | -2,500 | -30,000 | -32,500 | 0.377 | -12,249 |
11 | -2,500 | -30,000 | -32,500 | 0.342 | -11,110 |
12 | -2,500 | -30,000 | -32,500 | 0.310 | -10,077 |
13 | -2,500 | -30,000 | -32,500 | 0.281 | -9,140 |
14 | -2,500 | -30,000 | -32,500 | 0.255 | -8,291 |
15 | -2,500 | -30,000 | -32,500 | 0.231 | -7,520 |
16 | -2,500 | -30,000 | -32,500 | 0.210 | -6,821 |
17 | -2,500 | -30,000 | -32,500 | 0.190 | -6,187 |
18 | -2,500 | -30,000 | -32,500 | 0.173 | -5,611 |
19 | -2,500 | -30,000 | -32,500 | 0.157 | -5,090 |
20 | -2,500 | -30,000 | -32,500 | 0.142 | -4,616 |
21 | -2,500 | -30,000 | -32,500 | 0.129 | -4,187 |
22 | -2,500 | -30,000 | -32,500 | 0.117 | -3,798 |
23 | -2,500 | -30,000 | -32,500 | 0.106 | -3,445 |
24 | -2,500 | -30,000 | -32,500 | 0.096 | -3,125 |
25 | -2,500 | -30,000 | -32,500 | 0.087 | -2,834 |
26 | -2,500 | -30,000 | -32,500 | 0.079 | -2,571 |
27 | -2,500 | -30,000 | -32,500 | 0.072 | -2,332 |
28 | -2,500 | -30,000 | -32,500 | 0.065 | -2,115 |
29 | -2,500 | -30,000 | -32,500 | 0.059 | -1,918 |
30 | -2,500 | -30,000 | -32,500 | 0.054 | -1,740 |
31 | -2,500 | -30,000 | -32,500 | 0.049 | -1,578 |
32 | -2,500 | -30,000 | -32,500 | 0.044 | -1,431 |
33 | -2,500 | -30,000 | -32,500 | 0.040 | -1,298 |
34 | -2,500 | -30,000 | -32,500 | 0.036 | -1,178 |
35 | -2,500 | -30,000 | -32,500 | 0.033 | -1,068 |
36 | -2,500 | -30,000 | -32,500 | 0.030 | -969 |
37 | -2,500 | -30,000 | -32,500 | 0.027 | -879 |
38 | -2,500 | -30,000 | -32,500 | 0.025 | -797 |
39 | -2,500 | -30,000 | -32,500 | 0.022 | -723 |
40 | -2,500 | -30,000 | -32,500 | 0.020 | -656 |
Total cost over the life of dam | -310,676 |
Excel formula:
Dam B |
Capital investment (spread over 40 years) |
Annual damages of overflow over design capacity |
Total cost |
Discount factor (at 10.25%) |
Discounted cash flow |
1 | -3,750 | -7,000 | -10,750 | 0.907 | -9,751 |
2 | -3,750 | -7,000 | -10,750 | 0.823 | -8,844 |
3 | -3,750 | -7,000 | -10,750 | 0.746 | -8,022 |
4 | -3,750 | -7,000 | -10,750 | 0.677 | -7,276 |
5 | -3,750 | -7,000 | -10,750 | 0.614 | -6,600 |
6 | -3,750 | -7,000 | -10,750 | 0.557 | -5,986 |
7 | -3,750 | -7,000 | -10,750 | 0.505 | -5,429 |
8 | -3,750 | -7,000 | -10,750 | 0.458 | -4,925 |
9 | -3,750 | -7,000 | -10,750 | 0.416 | -4,467 |
10 | -3,750 | -7,000 | -10,750 | 0.377 | -4,052 |
11 | -3,750 | -7,000 | -10,750 | 0.342 | -3,675 |
12 | -3,750 | -7,000 | -10,750 | 0.310 | -3,333 |
13 | -3,750 | -7,000 | -10,750 | 0.281 | -3,023 |
14 | -3,750 | -7,000 | -10,750 | 0.255 | -2,742 |
15 | -3,750 | -7,000 | -10,750 | 0.231 | -2,487 |
16 | -3,750 | -7,000 | -10,750 | 0.210 | -2,256 |
17 | -3,750 | -7,000 | -10,750 | 0.190 | -2,046 |
18 | -3,750 | -7,000 | -10,750 | 0.173 | -1,856 |
19 | -3,750 | -7,000 | -10,750 | 0.157 | -1,684 |
20 | -3,750 | -7,000 | -10,750 | 0.142 | -1,527 |
21 | -3,750 | -7,000 | -10,750 | 0.129 | -1,385 |
22 | -3,750 | -7,000 | -10,750 | 0.117 | -1,256 |
23 | -3,750 | -7,000 | -10,750 | 0.106 | -1,139 |
24 | -3,750 | -7,000 | -10,750 | 0.096 | -1,034 |
25 | -3,750 | -7,000 | -10,750 | 0.087 | -937 |
26 | -3,750 | -7,000 | -10,750 | 0.079 | -850 |
27 | -3,750 | -7,000 | -10,750 | 0.072 | -771 |
28 | -3,750 | -7,000 | -10,750 | 0.065 | -700 |
29 | -3,750 | -7,000 | -10,750 | 0.059 | -634 |
30 | -3,750 | -7,000 | -10,750 | 0.054 | -576 |
31 | -3,750 | -7,000 | -10,750 | 0.049 | -522 |
32 | -3,750 | -7,000 | -10,750 | 0.044 | -473 |
33 | -3,750 | -7,000 | -10,750 | 0.040 | -429 |
34 | -3,750 | -7,000 | -10,750 | 0.036 | -390 |
35 | -3,750 | -7,000 | -10,750 | 0.033 | -353 |
36 | -3,750 | -7,000 | -10,750 | 0.030 | -320 |
37 | -3,750 | -7,000 | -10,750 | 0.027 | -291 |
38 | -3,750 | -7,000 | -10,750 | 0.025 | -264 |
39 | -3,750 | -7,000 | -10,750 | 0.022 | -239 |
40 | -3,750 | -7,000 | -10,750 | 0.020 | -217 |
Total cost over the life of dam | -102,762 |
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