Question

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 1

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.)