Question

# 5) Annual costs of 3 different systems is provided below (the negative number implies a cost)....

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

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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