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.
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