Q & A Part - 4; Question - 4.24

Here the respective probability of outflow and inflows have been given in the question. It is not mentioned that the values of the outflows are dependent upon that of inflows. I solved the question by finding the expected value of inflows and then discounted them for three years each for 45 & 25. On the other hand I again found out the expected values of outflow in 4 possible scenarios and discounted them accordingly. Both these calculations for inflows and outflows were independent. Then I solved for total NPV.
In the solution the overall probability of the scenario has been taken by multiplying the probability of inflow to outflow. Individually NPV for each scenario has been calculated and then the total NPV has been found.
Both our answers differ.
I want to know that are both the solutions are correct or am I missing something somewhere. It would be grateful I someone could guide me. Hope am clear in my question.
Thank You.

 

Sir I also calculated my values assuming both the inflows and the outflows incurring at the beginning of the year. But I didn't take a single probability for an entire scenario as taken in the solutions. I calculated independently the EPV of inflows & the EPV of outflows, and then found out the total NPV of the project. Whereas in the solutions they found out the various combinations of cashflows, found out an individual probability for each scenario and then calculated the total NPV.
And obviously our answers would differ because they are taking a single probability for each scenario whereas I used the probabilities for inflows and outflows separately.
And Sir I got NPV = 15.48911
So is my method correct or am I missing out on any information ?

 

EPV of inflow = [45*(2/3)*v^3*annuity advance for 3 years] + [25*(1/3)*v^3*annuity advance for 3 years] = 78.78456

EPV of outflow = [50 * (1/4)] + [60 * (1/4)] + [{50 + 20v} * (3/8)] + [{60 + 24v} * (1/8)] = 63.29545

NPV = 15.48911

 

I was making a mistake in discounting the overall inflows to time 0 as you rightly said it must be (v^2) instead of (v^3), which gave the same result as in the solutions. All my doubts are clear. Thank you so much Sir.