# NPV

Investing 3M in a project with a potential 50M return over a 10 yr life. The current risk free rate is 5%, equity risk premium is 5%, and project Beta is 2. 22% failure in first 4 years, 13 % thereafter. Indicate if project has a -ve or + NPV and the chance of survival I got survival to be 16% which is corrent. However unsure how to see that NPV is -ve

tmackenz, where are you getting these questions from? they are quite challenging.

schweser practise exam 2 afternoon

1. The chance of survival: (1-0.22)^4 * (1-.13)^16 = 16.05% ~ 16% The chance of failure would therefore be 1-16%=84% 2. Calculate the project’s discount rate: risk free rate + beta * equity risk premium = 5%+2*5%=15% NPV of the project, given that it survives to the end of the tenth year, equals: 50mil/(1+0.15)^10 - 3mil = 9.359mil Expected NPV is a probability weighted average of a successful project and an unsuccessful project 16%*9.359mil - 84%*3mil = -1.023mil Check volume 6, CFAi text, reading 76, page 206 for a similar example.

oh thank you, i kept forgetting to subtract the 0.84*3 for some reason

Why have you used (1-.13)^16 when it’s only a 10 year project? Shouldn’t it be (1-.13)^6?

yes it should

Also, I tried calculating the failiure rate as (0.22^4)*(0.13^6) but I don’t get 84%. Why is that?

yes, it is 6, not 16, sorry.

chad17 Wrote: ------------------------------------------------------- > Also, I tried calculating the failiure rate as > (0.22^4)*(0.13^6) but I don’t get 84%. Why is > that? Think in terms of how it would work if you began with 1000 projects. After year 1, 22% have failed, or 220. Thus, 1-22% or 78% (780) remain. The second year, 78% of the remaining 78% from the first year remain, or (1-0.22)(1-0.22). Then follow the logic the remaining way through. This is why the survival rate is (1-0.22)^4 * (1-.13)^6 = 0.16. If 16% survive, 84% fail. Compare this to your method: (1-0.22)^2 isn’t equal to 1-(0.22)^2. I forgot the technical way to say it (Joey? Anyone? Bueller?)