Answering a)
Project A | |||||||||||||||||||||
Year | 0 (Initital investment) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
Cash flows | -47 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 |
PV of Cash Flows | -47 | 6.25 | 5.58 | 4.98 | 4.45 | 3.97 | 3.55 | 3.17 | 2.83 | 2.52 | 2.25 | 2.01 | 1.80 | 1.60 | 1.43 | 1.28 | 1.14 | 1.02 | 0.91 | 0.81 | 0.73 |
Cost of capital | 12% | ||||||||||||||||||||
NPV | 5.29 | ||||||||||||||||||||
IRR | 13.76% |
We Arrive at PV of Cash Flows by discounting them by the cost of capital = 12% for the number of years required to shift it to t = 0. For e.g. cash flow of 7 million of year 3 is calculated as 7 / (1.12)^3 to arrive its value of 4.98 at t = 0.
We calculate the NPV by summing all the PV of Cash Flows, Hence
E.g. NPV for Project A = (6.25 + 5.58 + 4.98 + ....... + 0.73) = 5.29
We calculate IRR using
Project B | |||||||||||||||||||||
Year | 0 (Initial Investment) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
Cash flows | -13 | 3.1 | 3.1 | 3.1 | 3.1 | 3.1 | 3.1 | 3.1 | 3.1 | 3.1 | 3.1 | 3.1 | 3.1 | 3.1 | 3.1 | 3.1 | 3.1 | 3.1 | 3.1 | 3.1 | 3.1 |
PV of Cash Flows | -13 | 2.77 | 2.47 | 2.21 | 1.97 | 1.76 | 1.57 | 1.40 | 1.25 | 1.12 | 1.00 | 0.89 | 0.80 | 0.71 | 0.63 | 0.57 | 0.51 | 0.45 | 0.40 | 0.36 | 0.32 |
Cost of capital | 12% | ||||||||||||||||||||
NPV | 10.16 | ||||||||||||||||||||
IRR | 23.50% |
b) The Cash Flows for project A are shown in the above table & also given below:
For year 0 = (-47 million) (negative as it is Cash Outflow)
For year 1 - 20 = +7 million each year = 140 million ( positive as it is Cash Inflow)
While the NPV and the IRR values remain the same as Project A. i.e
NPV = 5.29 and IRR = 13.76 %
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