Calculate the NPV and IRR of each project.

A company is considering to select a project out of the two mutually exclusive projects. The company’s cost of capital is 10% and the net after tax cash flow of the project are as follows:

Year                              0                 1                 2                3                   4              5

Project   X (Rs.)    2,00,000                      35,000      80,000      90,000      75,000     20,000

Project Y (Rs.)      2,00,000     2,18,000    10,000     10,000         4,000       3,000

(i)                   Calculate the NPV and IRR of each project.

(ii)                 State with reasons which project you would recommend

The discount factors are as follows:

Year                              0        1             2             3             4              5

Discount factor

At 10%                         1        0.91       0.83      0.75      0.68         0.62

At 20%                         1        0.83       0.69      0.58      0.48         0.41

Ans:        (i)

                Net Present Value at 20%:

Year	Project X			Project Y
	Net Cash income (Rs.)	Discount Factor	PV Rs.	Net Cash income (Rs.)	Discount Factor	PV Rs.
0	2,00,000	1	2,00,000	2,00,000	1	2,00,000
1	35,000	0.83	29050	2,15,000	0.83	1,78,450
2	80,000	0.69	55200	10,000	0.69	6,900
3	90,000	0.58	52200	10,000	0.58	5,800
4	75,000	0.48	36000	4000	0.48	1,920
5	20,000	0.41	8200	3,000	0.41	1,230
			3,80,0650			3,94,300

Net Present Value at 10%:

Year	Project X			Project Y
	Net Cash income (Rs.)	Discount Factor	PV Rs.	Net Cash income (Rs.)	Discount Factor	PV Rs.
0	2,00,000	1	2,00,000	2,00,000	1	2,00,000
1	35,000	0.91	31850	2,15,000	0.91	1,95,650
2	80,000	0.83	66,400	10,000	0.83	8300
3	90,000	0.75	67500	10,000	0.75	7500
4	75,000	0.68	51000	4000	0.68	2720
5	20,000	0.62	12400	3,000	0.62	1860
			4,29,150			4,16,030

               

                Internal Rate of Return: IRR = LRD + NPR x R / PV

                LRD = Lower rate of discount

                NPVR = Net present value at lower rate of discount

                PV = Difference in present value of lower and higher

                R = Difference between two rates of discount

The Finance Director of Ritoria Ltd thinks that the project with the higher NPV should be chosen whereas its Managing Director thinks that the one with the higher IRR should be undertaken

The Finance Director of Ritoria Ltd thinks that the project with the higher NPV should be chosen whereas its 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                                         0                      1          2          3          4          5

            (Cash Flows figs 000)

            Project X                             Rs. (200)                 35         80         90         75         20

            Project Y                             Rs. (200)               218         10         10           4          3

 

           You are required to :

1. Calculate the NPV and IRR of each project.
2. State, with reasons, which of the two mutually exclusive projects you would recommend.
3. Explain the reasons for inconsistency in the ranking of the two projects. 

Solution: BY NPV METHOD:

NPV is the sum of all terms  ,

-200/(1.1)=-200

 35/1.1=31.82

 80/1.21=66.21

 90/1.331=67.62

 75/1.4641=51.23

 20/1.61051=12.42     here 200-all 5 above

200-229.21=  -29.21 for x

For y:

-200/1.1=-200

218/1.1=198.18

10/1.21=8.26

10/1.331=7.51

4/1.4641=2.73

3/1.61051=1.86

Here 200- all 5 above

200-218.54 = -18.54

BY IRR METHOD:

rate of return is given by r in:

-200+31.82+66.12+67.62+51.23+12.42 = 29.3 for x

-200+198.18+8.26+7.51+2.73+1.86 = 18.54 for y

The Finance Director of Ritoria Ltd thinks that the project with the higher NPV should be chosen whereas its 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

The Finance Director of Ritoria Ltd thinks that the project with the higher NPV should be chosen whereas its 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	0	1	2	3	4	5
(Cash Flows figs 000)
Project X	Rs. (200)	35	80	90	75	20
Project Y	Rs. (200)	218	10	10	4	3

You are required to :

a.   Calculate the NPV and IRR of each project.

Factor Factor Project X PV 10% PV 20% Project Y PV 10% PV 20%

b.   State, with reasons, which of the two mutually exclusive  projects you would recommend.

c.   Explain the reasons for inconsistency in the ranking of the two projects.

10%	20%	000	000	000	000	000	000
1.000	1.000	(200)	(200.00)	(200.00)	(200)	(200.00)	(200.00)
0.909	0.833	35	31.82	29.16	218	198.16	181.59
0.826	0.694	80	66.08	55.52	10	8.26	6.94
0.751	0.579	90	67.59	52.11	10	7.51	5.79
0.683	0.482	75	51.23	36.15	4	2.73	1.93
0.621	0.402	20	12.42	8.04	3	1.86	1.21
		NPV	29.14	(19.02)	NPV	18.52	(2.54)

@10% NPV Project X = £29,140

@10% NPV Project Y = £18,520

@20% NPV Project X = (£19,020)

@20% NPV Project Y = (£2,540) IRR Project X=16%

IRR Project Y=18%

(b) Undertake Project X:

it has a positive NPV, indicating that it exceeds the company’s cost of capital;

assuming that the company’s objective is to maximise the present value of future cash flows X offers the higher NPV.

X offers a higher NPV, whereas Y offers a high IRR. Where such conflicting indications appear  it is generally  appropriate  to accept the NPV result, NPV being regarded  as technically more sound than IRR.

(c) The two projects have redically different time projiles. X’s cash inflows are grouped in the three middle years of the project. This leads to Y showing a higher IRR.

Risk, uncertainty and timing of cash flows may be considered by the directors in making the final investment decisions.