In: Economics
Problem 5 (20pts)
Consider two investments with the following cash flows:
n |
Project A |
Project B |
0 |
-100,000 |
-190,000 |
1 |
19,000 |
29,000 |
2 |
17,000 |
27,000 |
3 |
15,000 |
25,000 |
4 |
12,000 |
22,000 |
5 |
22,000 |
32,000 |
6 |
100,000 |
195,000 |
Suppose A and B are mutually exclusive, the MARR is 12%, the rate of return for project A and B is already given, which is 15% and 13% respectively.
Determine which project should be selected using rate of return on incremental investment. In calculation of the rate of return on incremental investment, use the trial and error method.
(Hint: try to draw the cash flows of the incremental investment, then based on the pattern of the cash flows, use appropriate interest factors in determination of the PW)
n |
Project A |
Project B |
Incremental Cash flow between B - A |
0 |
-100,000 |
-190,000 |
-190,000 – 100,000 = -90,000 |
1 |
19,000 |
29,000 |
29,000-19,000 = 10,000 |
2 |
17,000 |
27,000 |
27,000-17,000 = 10,000 |
3 |
15,000 |
25,000 |
25,000 - 15,000 =10,000 |
4 |
12,000 |
22,000 |
22,000 - 12,000 = 10,000 |
5 |
22,000 |
32,000 |
32,000 - 22,000 = 10,000 |
6 |
100,000 |
195,000 |
195,000 - 100,000 = 95,000 |
NPW of the Incremental cash flow of B – A at MARR of 12%
NPW = -90,000 + 10,000 (P/A, 12%, 5) + 95,000 (P/F, 12%, 6)
NPW = -90,000 + 10,000 (3.6048) + 95,000 (0.5066) = -5,825
Decreasing MARR to 10% and calculating NPW
NPW = -90,000 + 10,000 (P/A, 10%, 5) + 95,000 (P/F, 10%, 6)
NPW = -90,000 + 10,000 (3.7908) + 95,000 (0.5645) = 1,535.5
Using interpolation IRR = 10% + 1,535.5 – 0 / [1535.5 – (-5825)] * 2%
IRR for B – A is 10.41% < MARR (12%) – Select A (lowest cost project)