## Q. 3.PP.44

A company is trying to decide whether to invest in a new project. Two mutually exclusive projects are available, each requiring an investment of Rs 3,00,000. Project A is expected to generate cash inflows of Rs 2,00,000 per year in the next 2 years. It is estimated that the cash inflows associated with project B would either be Rs 1,80,000, or Rs 2,20,000 (each with 0.5 probability of occurrence) next year. If Rs 1,80,000 is received in the first year, the cash inflow for the second year is likely to be Rs 1,50,000 (probability of 0.3), Rs 1,80,000 (probability of 0.4) and Rs 2,00,000 (probability of 0.3). In case the first year’s cash inflow is Rs 2,20,000, the second year’s likely cash inflow would be Rs 1,80,000 and Rs 2,70,000 (each with 0.3 probability), and Rs 2,20,000 (probability 0.4).
$\,$  The firm uses a 14 per cent minimum required rate of return for deciding whether to invest in projects comparable in risk to the ones under consideration.
$\,$   (i) Calculate the risk adjusted expected NPV for projects A and B.
$\,$  (ii) Identify the best and the worst possible outcomes for B.
$\,$ (iii) Which of the projects, if any, would you recommend? Why?

## Verified Solution

$\,$  (ii) The worst possible outcome is a CFAT of Rs 1,80,000 (year 1) and Rs 1,50,000 (year 2) with the maximum negative NPV as Rs 26,790. The best possible outcome is when NPV is maximum, Rs 1,00,570. It results when CFAT in year 1 is Rs 2,20,000, followed by Rs 2,70,000 in year 2.
$\,$ (iii) The expected NPVs are the same for both projects. However, from the point of view of risk, project A should be chosen as there is no variability of possible events.

(i) $Determination\> of \>expected \>NPV \>of \>project\> A$

 $Total\>PV$ $PV\>factor\>(0.14)$ $CFAT$ $Year$ Rs 1,75,400 0.877 Rs 2,00,000 1 1,53,800 0.769 2,00,000 2 3,29,200 Total present value 3,00,000 $Less$ PV of cash outflows 29,200 NPV
$Determination \>of \>expected\> NPV\> of \>project\>B$
 $Expected$ $NPV$ $Joint$ $probability$ $NPV\>at$ 14% $CFAT_2$ 1 $Time\>0$ (Rs 4,019) 0.20 (Rs 26,790) Rs 1,50,000 (744) 0.20 (3,720) 1,80,000 1,749 0.16 11,660 2,00,000 4,704 0.15 31,360 1,80,000 12,424 0.20 62,120 2,20,000 15,085 0.15 1,00,570 2,70,000 29,199