The Fisher Company has identified two mutually exclusive projects, L and S, with

Question

The Fisher Company has identified two mutually exclusive projects, L and S, with the following expected net cash flows:

Expected Net Cash Flows

Year Project S Project L

0 -$1,100 -$2,700

1 550 650

2 600 725

3 100 800

4 100 1,400

Both projects have a cost of capital of 7.50%.

1) What is each project's NPV?

2) What is each project's IRR?

3) Calculate each project's payback period.

4) Calculate the crossover rate.

5) From your answers to Parts 1), 2) and 3), which project would be selected? Are there any conflicts? If so, why do such conflicts occur?

Explanation / Answer

cumulative Project S year net CFs pvif - 7.5% pv pvif - 10% pv pvif - 15% pv CFS 0 -1100 1 550 0.9302 512 0.9091 500 0.8696 478 550 2 600 0.8653 519 0.8264 496 0.7561 454 1150 3 100 0.8050 80 0.7513 75 0.6575 66 1250 4 100 0.7488 75 0.6830 68 0.5718 57 1350 1186 1139 1055 1) NPV = 1186 - 1100 = $86 2) IRR = 10 + 5(39/84) = 12.32% 3) Payback = 1 + 550/600 = 1.92 years cumulative Project L year net CFs pvif - 7.5% pv pvif - 10% pv pvif - 11% pv CFs 0 -2700 1 650 0.9302 605 0.9091 591 0.9009 586 650 2 725 0.8653 627 0.8264 599 0.8116 588 1375 3 800 0.8050 644 0.7513 601 0.7312 585 2175 4 1400 0.7488 1048 0.6830 956 0.6587 922 3575 2924 2747 2681 1) NPV = 2924 - 2700 = $224 2) IRR = 10 + 47/66 = 10.71% 3) Payback = 3 + 525/1400 = 3.38 years 4) Cross over rate: Cash flows S L difference pvif - 10% pv pvif - 11% pv year 0 -1100 -2700 -1600 1 550 650 100 0.9091 91 0.9009 90 2 600 725 125 0.8264 103 0.8116 101 3 100 800 700 0.7513 526 0.7312 512 4 100 1400 1300 0.6830 888 0.6587 856 1608 1560 IRR of the incremental cash flows is the cross over rate = 10 + 8/48 = 10.17% 5) Ranking of projects: S L NPV-$ 86 224 ranking II I IRR-% 12.32 10.71 ranking I II Payback-years 1.92 3.38 ranking I II IRR and payback rank project S as 1, and so S is the choice. NPV ranks project L as 1, hence it is to be selected. Yes, there is conflict of ranking. The conflict in ranking between NPV and IRR, which use the same cash flow numbers and discounting technique, is due to the fact that the NPV uses the Cost of capital (here 7.5%) as the discount rate, whereas the IRR uses the project specific IRR as the discount rate-which is 12.32% for S and 10.71% for L. The difference in interest rates get compounded year after year. This results In cash flows of earlier get more weightage for increased percentages. This aspect of compounding is found to give conflicting ranking of projects under NPV and IRR in the following situations: a) where the life of the mutuall exclusive projects is different. b) where the initial investment is significantly different. c) where the cash flow patterns are different with one project having higher cash flows in the early years and the second project having higher cash flows towards the later years. In the case of the projects L & S, the conflict is due to reasons at (b) & ©.

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