Question 5.S2.EQ.6: The cash flows of two mutually exclusive projects are as und......
The cash flows of two mutually exclusive projects are as under:
Required:
(i) Estimate the net present value (NPV) of the Project ‘P’ and ‘J’ using 15 per cent as the hurdle rate. (ii) Estimate the internal rate of return (IRR) of the Project ‘P’ and ‘J’. (iii) Why there is a conflict in the project choice by using NPV and IRR criterion? (iv) Which criteria you will use in such a situation? Estimate the value at that criterion. Make a project choice.
The present value interest factor values at different rates of discount are as under:
(CA—May, 2004)
| t_0 | t_1 | t_2 | t_3 | t_4 | t_5 | t_6 | |
| Project ‘P’ | (Rs) (40,000) | 13,000 | 8,000 | 14,000 | 12,000 | 11,000 | 15,000 |
| Project ‘J’ | (Rs) (20,000) | 7,000 | 13,000 | 12,000 | — | — | — |
| t_0 | t_1 | t_2 | t_3 | t_4 | t_5 | t_6 | |
| 0.15 | 1.00 | 0.8696 | 0.7561 | 0.6575 | 0.5718 | 0.4972 | 0.4323 |
| 0.18 | 1.00 | 0.8475 | 0.7182 | 0.6086 | 0.5158 | 0.4371 | 0.3704 |
| 0.20 | 1.00 | 0.8333 | 0.6944 | 0.5787 | 0.4823 | 0.4019 | 0.3349 |
| 0.24 | 1.00 | 0.8065 | 0.6504 | 0.5245 | 0.4230 | 0.3411 | 0.2751 |
| 0.26 | 1.00 | 0.7937 | 0.6299 | 0.4999 | 0.3968 | 0.3149 | 0.2499 |
(i) Determination of NPV of projects P and J
(ii) Determination of IRR
Project P: Rs 40,000 = Rs 13,000/(1 + r)¹ + Rs 8,000/(1 + r)² + Rs 14,000//(1 + r)³ + Rs 12,000/(1 + r)^4 + Rs 11,000//(1 + r)^5 + Rs 15,000//(1 + r)^6
The fake pay back period is (Rs 40,000/Rs 12,167 Average CFAT) = 3.287. From Table A-4, the value closest to the fake pay back of 3.287 against 6 years is 3.245 against 21 per cent. Since the actual cash flow stream in the year 2 is lower than the average CFAT, the IRR is likely to be marginally lower than 21 per cent. Let us try with 20 and 19 per cent.
Project J: Rs 20,000 = Rs 7,000/(1 + r)¹ + Rs 13,000/(1 + r)² + Rs 12,000/(1 + r)³
The fake pay back period is (Rs 20,000/Rs 10,667 Average CFAT) = 1.875. From Table A-4 the value closest to the fake pay back of 1.875 against 3 years is 1.896 against 27 per cent. Since the actual cash flows in the initial year is lower than the average CFAT, the IRR is likely to be lower than 27 per cent. Let us try at 25 and 26 per cent.
(iii) There is conflict in the ranking of projects between NPV and IRR methods. While project ‘P’ is ranked first under the NPV method, IRR ranks Project J first. The reason of conflict is due to reinvestment rate assumption.
IRR method assumes that the intermediate CFAT are reinvested at IRR. With the NPV method, the assumption is that the funds released are reinvested at the rate of cost of capital. The assumption of the NPV method is considered to be superior (for details refer to text).
(iv) In general, NPV ranking is preferred to that of IRR. The present situation is unequal project lives. In projects of unequal expected lives, the computation of equivalent annual net present value (EANPV) is appropriate. The EANPV is determined dividing the NPV of project by the annuity factor corresponding to the life of the project at the given cost of capital. The project with higher EANPV is preferred.
Determination of EANPV:
Project P = Rs 5,363.9/3.784 = Rs 1,417.52
Project J = Rs 3,806.5/2.283 = Rs 1,667.32
Since the EANPV of Project J is higher than that of project P, Project P is recommended.
| Year (t) | CFAT | PV factor at 0.15 |
Total PV | ||
| Project P | Project J | Project P | Project J | ||
| 1 | Rs 13,000 | 7,000 | 0.8696 | Rs 11,304.8 | Rs 6,087.2 |
| 2 | 8,000 | 13,000 | 0.7561 | 6,048.8 | 9,829.3 |
| 3 | 14,000 | 12,000 | 0.6575 | 9,205.0 | 7.890.0 |
| 4 | 12,000 | — | 0.5718 | 6,861.6 | — |
| 5 | 11,000 | — | 0.4972 | 5,469.2 | — |
| 6 | 15,000 | — | 0.4323 | 6,484.5 | — |
| Gross present value | 45,363.9 | 23,806.5 | |||
| Less cash outflows | 40,000.0 | 20,000.0 | |||
| Net present value | 5,363.9 | 3,806.5 | |||
| Year | CFAT | PV factor | Total PV | ||
| (0.19) | (0.20) | (0.19) | (0.20) | ||
| 1 | Rs 13,000 | 0.840 | 0.833 | Rs 10,920 | 10,829 |
| 2 | 8,000 | 0.706 | 0.694 | 5,648 | 5,552 |
| 3 | 14,000 | 0.593 | 0.579 | 8,302 | 8,106 |
| 4 | 12,000 | 0.499 | 0.482 | 5,988 | 5,784 |
| 5 | 11,000 | 0.419 | 0.402 | 4,609 | 4,422 |
| 6 | 15,000 | 0.352 | 0.335 | 5,280 | 5,025 |
| Gross present value | 40,747 | 39,718 | |||
| Less cash outflows | 40,000 | 40,000 | |||
| Net present value | 747 | (282) | |||
IRR is between 19 and 20 per cent. By interpolation IRR is 19 per cent + (Rs 747/Rs 1,029) i.e., 0.726 = 19.73 per cent
| Year | CFAT | PV factor | Total PV | ||
| (0.25) | (0.26) | (0.25) | (0.26) | ||
| 1 | Rs 7,000 | 0.800 | 0.794 | Rs 5,600 | Rs 5,558 |
| 2 | 13,000 | 0.640 | 0.630 | 8.320 | 8,190 |
| 3 | 12,000 | 0.512 | 0.500 | 6,144 | 6,000 |
| Gross present value | 20,064 | 19,748 | |||
| Less cash outflows | 20,000 | 20,000 | |||
| Net present value | 64 | (252) | |||
IRR is 25 per cent + (Rs 64/Rs 316) i.e., = 0.2 = 25.2 per cent