A company is considering two mutually exclusive projects X and Y$.$ Project X costs

Rs$\mathrm{.}30,000$ and Project Y Rs$\mathrm{.}36,000.$ You have been given below the net present

value probability distribution for each project:

Project X

Project Y

NPV estimate $($Rs$.)$

Probability

NPV estimate $($Rs$.)$

Probability

$3,000$

$6,000$

$12,000$

$15,000$

$0\mathrm{.}1$

$0\mathrm{.}4$

$0\mathrm{.}4$

$0\mathrm{.}1$

$3,000$

$6,000$

$12,000$

$15,000$

$0\mathrm{.}2$

$0\mathrm{.}3$

$0\mathrm{.}3$

$0\mathrm{.}2$

$($i$)$ Compute the expected net present value of projects X and Y$.$

$($ii$)$ Compute the risk attached to each project i$.$e$.,$ standard deviation of each probability distribution.

$($iii$)$ Which project do you consider more risky and why?

$($iv$)$ Compute the profitability index of each project.