5) Annual costs of 3 different systems is provided below (the negative number implies a cost). If the MARR is 8%, which system is the most economical of the three? Provide numerical justification.
n |
System A |
System B |
System C |
0 |
0 |
-$2,000,000 |
-$4,000,000 |
1 |
-$9,000,000 |
-$3,800,000 |
-$1,900,000 |
2 |
-$9,000,000 |
-$3,800,000 |
-$1,900,000 |
3 |
-$9,000,000 |
-$3,800,000 |
-$1,900,000 |
4 |
-$9,000,000 |
-$3,800,000 |
-$1,900,000 |
5 |
-$9,000,000 |
-$3,800,000 |
-$1,900,000 |
6 |
-$9,000,000 |
-$3,800,000 |
-$1,900,000 |
7 |
-$9,000,000 |
-$3,800,000 |
-$1,900,000 |
8 |
-$9,000,000 |
-$3,800,000 |
-$1,900,000 |
ANSWER:
We fill find the pw of each system.
1) pw of system a = cash flow from year 1 to year 8(p/a,i,n) = -9,000,000(p/a,8%,8) = -9,000,000 * 5.747 = - 51,723,000
2) Pw of system b = cash flow in year 0 + cash flow from year 1 to year 8(p/a,i,n) = -2,000,000 - 3,800,000(p/a,8%,8) = -2,000,000 - 3,800,000 * 5.747 = - 2,000,000 - 21,838,600 = - 23,838,600
3) Pw of system c = cash flow in year 0 + cash flow from year 1 to year 8(p/a,i,n) = -4,000,000 - 1,900,000(p/a,8%,8) = -4,000,000 - 1,900,000 * 5.747 = - 4,000,000 - 10,919,300 = - 14,919,300
since the pw of system c is the highest and so it will be chosen. (most economical.)
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