SmallCompany Plc is considering which two mutually exclusive projects it should

Question

SmallCompany Plc is considering which two mutually exclusive projects it should undertake. The finance director thinks that the project with the higher NPV should be chosen whereas the managing director thinks that the one with the higher IRR should be undertaken especially as both projects have the same initial outlay and length of life. The company anticipates a cost of capital of 10% and the net after tax cash flows of the projects are as follows: Year Project X ( '000) 0,-200,-200 1,35,218 3,90,10 4,75,4 5,20,3 Required: Calculate the NPV and IRR of each project Recommend with reasons, which project would you undertake (if either) Explain the inconsistency in ranking of the two projects in view of the remarks of the directors. Identify the cost of capital at which your recommendation in (B) would be reversed and comment.

Explanation / Answer

A) NPV & IRR of the Projects are calculated below: PROJECT X pvif @ pvif @ pvif @ year cash flow 10% pv 15% pv 16% pv 0 -200 1 35 0.9091 31.82 0.8696 30.43 0.8621 30.17 2 80 0.8264 66.12 0.7561 60.49 0.7432 59.45 3 90 0.7513 67.62 0.6575 59.18 0.6407 57.66 4 75 0.6830 51.23 0.5718 42.88 0.5523 41.42 5 20 0.6209 12.42 0.4972 9.94 0.4761 9.52 300 229.20 202.93 198.23 NPV = 229.20 - 200 = 29.20 IRR = 15 + 2.93/4.7 = 15.62% PROJECT Y pvif @ pvif @ pvif @ pvif @ year cash flow 10% pv 15% pv 16% pv 19% pv 0 -200 1 218 0.9091 198.18 0.8696 189.57 0.8621 187.93 0.8403 183.19 2 10 0.8264 8.26 0.7561 7.56 0.7432 7.43 0.7062 7.06 3 10 0.7513 7.51 0.6575 6.58 0.6407 6.41 0.5934 5.93 4 4 0.6830 2.73 0.5718 2.29 0.5523 2.21 0.4987 1.99 5 3 0.6209 1.86 0.4972 1.49 0.4761 1.43 0.4190 1.26 218.55 207.48 205.41 199.44 NPV = 218.55 - 200 = 18.55 IRR = 16 + (5.41/5.97)*3 = 18.72% B) The project to be undertaken is the one with the higher NPV. Here it is project X. Hence it should be selected. The reason is that NPV gives the absolute addition to the shareholders present worth. C) The inconsistency in the ranking of the projects is due to the difference in the pattern of cash flows. Project Y has a huge cash flow in the first year followed by insignificant cash flows in the next four years. In contrast Project X has cash flows which increase from year 1 to 3 and then decrease. NPV uses the WACC (10%) as the discount rate for both the projects. In contrast, the IRR uses 15.62% for Project X and 18.72% for project Y as the discount rate. Since, discounting magnifies difference in PVs as the discount rate goes up, more so for the later years, the NPV and IRR are found to give conflicting rankings in certain situations. Conflicting rankings arise in situations where the lives of the projects are differenct or initial investment size is markedly different or where the cash flow patterns are very widely varying, as in this case. D) The decision would be reversed if the cost of capital is about 14%. (the exact point is between 13% and 14%) X Y X Y X Y year cash flow cash flow pvif @13% pv pv pvif @14% pv pv 1 35 218 0.8850 30.97 192.92 0.8772 30.70 191.23 2 80 10 0.7831 62.65 7.83 0.7695 61.56 7.69 3 90 10 0.6931 62.37 6.93 0.6750 60.75 6.75 4 75 4 0.6133 46.00 2.45 0.5921 44.41 2.37 5 20 3 0.5428 10.86 1.63 0.5194 10.39 1.56 212.85 211.76 207.80 209.60 At about 14%, the decision would be reversed as Project has higher NPV. ` This proves that selection of projects or its ranking under NPV depends on the discount rate used.

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