Yenki Ltd. is considering two mutually exclusive projects A and B. Project A costs Rs. 30,000 and Project B Rs. 36,000. The NPV probability distribution for each project is as given below:

Yenki Ltd. is considering two mutually exclusive projects A and B. Project A costs Rs. 30,000 and Project B Rs. 36,000. The NPV probability distribution for each project is as given below:

Project A		Project B
NPV Estimate	Probability	NPV Estimate	Probability
Rs. 3,000	0.1	Rs. 3,000	0.2
6,000	0.4	6,000	0.3
12,000	0.4	12,000	0.3
15,000	0.1	15,000	0.2

You are required to compute:

i) the expected Net Present value of Projects A and B.

ii) The risk attached to each project i.e., Standard deviation each probability distribution.

iii) The profitability Index of each project.

Which project do you consider more risky and why?

Solution.

COMPUTATION OF EXPECTED NET PRESENT VALUE

i) Expected NPV = Σ Estimated NPV x Prob.

Expected Net Present Value of both the Projects are Rs 9000

(i)

COMPUTATION OF RISK ATTACHED TO EACH PROJECT

(STANDARD DEVIATION)

PROJECT “A”

NPV                Prob     Expected          NPV         X -

X                     P              PX R                                  d                             d²                Pd²

3000             .1             300                     −6000         36000000    3600000

6000             .4              2400                   −3000        9000000      3600000

12000           .4              4800                   3000            9000000      3600000

15000           .1              1500                   6000            36000000    3600000

                                      ΣPR=9000                                                 ΣPd2 = 14400000

X = ΣPR

Risk (S.D) = √ΣPd2 = √14400000 = 3794.73

PROJECT “B”

NPV                   Prob      Expected NPV      X −

X                        P               PXR              d                   d2                Pd2

3000                   .2              600            −6000          36000000    7200000

6000                   .3              1800          −3000          9000000      2700000

12000                 .3              3600          3000            9000000      2700000

15000                 .2              3000          6000            36000000    7200000

                                            ΣPR=9000                                         ΣPd2 = 19800000

X = ΣPR

Risk (S.D.) = √ΣPd2 = √19800000 = 4449.72

(ii) PROFITABILITY INDEX = (Estimated NPV/Expected NPV) / Initial Outflow

Project A = 9000/30000 = 0.3

Project B = 9000/36000 = .25

Standard deviation measures the risk attached to the project. If in case of two mutually projects, one is to be selected based on risk then that project should be selected which has the lower standard deviation.

In the above case Project B has greater risk i.e. Rs. 4449.72 as compared to A i.e. Rs 3794.73. Hence project B is more risky than the Project A.

Calculate each project’s payback period, net present value (NPV), and internal rate of return (IRR).

You are a Financial Analyst for Amazon Electronics Company. The director of capital budgeting has asked you to analyze two proposed capital investment projects P and Q.  Each project has a cost of Rs. 10,000,  and the cost of capital for each project is 12 percent. The projects’ expected net cash flows are as follows:

                                                               Expected Net Cash Flows

            Year                              Project P                     Project Q

              0                                (Rs.10,000)                   (Rs. 10,000)

              1                                        6,500                             3,500

              2                                         3,000                            3,500

              3                                        3,000                             3,500

              4                                        1,000                             3,500                                                      

a.                   Calculate each project’s payback period, net present value (NPV), and  internal rate of return (IRR).

b.                   Which project or projects should be accepted if they are independent?

c.                   Which project should be accepted if they are mutually exclusive?

d.                   How might a change in the cost of capital, produce a conflict between the NPV and IRR rankings of these two projects? Would this conflict exist if k were 5 percent?

e.                   Why does the conflict exist?      

    

Solution. (a)

CALCULATION OF PAYBACK PERIOD

Project P

Rs. 10000 is covered in 3rd year, therefore, payback period is:

= 2 years + (12 months/3000) x 500

= 2 year and 2 months

Project Q

Rs. 10000 is covered in 3rd year, therefore, payback period is:

= 2 years + (12 months x 3500) x 3000

= 2 year and 10.28 months

or 2 years, 10 months and (.28 x 30 days)*

or 2 years, 10 months and 8 days

*.28 month can be converted into days by multiplying .28 month with days in month. Therefore .28 is multiplied with 30 (days in month) to convert it in days.

CALCULATION OF NET PRESENT VALUE

Year	Amount		Discounting Factor	Present Value
	Project P	Project Q		Project P	Project Q
0	(10000)	(10000)	1	(10000)	(10000)
1	6500	3500	.893	5804.5	3125.5
2	3000	3500	.797	2391	2789.5
3	3000	3500	.712	2136	2492
4	1000	3500	.636	636	2226
Net Present Value				967.5	633

CALCULATION OF INTERNAL RATE OF RETURN

CALCULATION OF NET PRESENT VALUE

(AT DISCOUNTING FACTOR 8 %)

Year	Amount		Discounting Factor	Present Value
	Project P	Project Q		Project P	Project Q
0	(10000)	(10000)	1	-10000	-10000
1	6500	3500	.926	6019	3241
2	3000	3500	.857	2571	2999.5
3	3000	3500	.794	2382	2779
4	1000	3500	.735	735	2572.5
Net Present Value				1707	1592

CALCULATION OF NET PRESENT VALUE

(AT DISCOUNTING FACTOR 14%)

Year	Amount		Discounting Factor	Present Value
	Project P	Project Q		Project P	Project Q
0	(10000)	(10000)	1	-10000	-10000
1	6500	3500	0.877	5700.5	3069.5
2	3000	3500	0.769	2307	2691.5
3	3000	3500	0.675	2025	2362.5
4	1000	3500	0.592	592	2072
Net Present Value				624.5	195.5

Internal Rate of Return

Project P

8% + 6% x (1707 / 1082.5)

 = 8% + 9.46%

= 17.46%

Project Q

8% + 6% x (1592 / 1396.5)

 = 8% + 6.84%

= 14.84%

b) If projects are independent then company can accept both the projects because both the projects have positive NPV.

c) If projects are mutual exclusive then company should accept Project P because it has more NPV.

d) Calculation of NPV when cost of capital is 5%

Year	Amount		Discounting Factor	Present Value
	Project P	Project Q		Project P	Project Q
0	-10000	-10000	1	-10000	-10000
1	6500	3500	0.952	6188	3332
2	3000	3500	0.907	2721	3174.5
3	3000	3500	0.864	2592	3024
4	1000	3500	0.823	823	2880.5
Net Present Value				2324	2411

Conclusion: When cost of capital is taken 5% then the NPV of both the projects is positive but project P has lower NPV then the project Q, which shows that if both projects are mutual exclusive then project Q should be accepted.

But, if decision is taken by considering the IRR then project P should be accepted because project P has higher IRR (calculated in part A).

e) The conflict arises due to reinvestment rate. The basic presumption behind the two is different.

1. In case of NPV, it is assumed that intermediate cash inflows are reinvested at cut off rate.

2. In case of IRR, it is assumed that intermediate cash inflow is reinvested at IRR rate.

That is why NPV is more reliable. Because it is possible to reinvest at cut off rate not at IRR rate, which is very high at different times.