Challenging Venture capital Q

hope u like it. A venture capital investment is expected to yield of payoff of $100 million in five years if it survives. The initial cost is $20 million and the appropriate discount rate is 20%. What is the average annual probability of failure that makes the investment’s NPV = 0? In other words, what is the maximum annual average probability of failure before the investment is not acceptable? A. 13% B. 15% C. 17% D. 20%

A ??

May be C?

Wait a minute - the discount rate should include the prob of failure…

-20p + 100 (1-p) = 0 100-120p = 0 p = 100/120 p = probability of failure the way it has been set up above. so p(success) = 20/120 = 1/6 ~ 17% cp

ok, but we don’t know the breakdown of that! So you are suggesting there is a risk premium built in the 20%? God knows what that is.

A take 20m into FV (at the rate of 20%) (100m multiplied by x, which is the success rate) - 20x(1+20%)^5=200x solve for x --> x=0.4977 now, if we use y as the failure rate – (1-y)^5=0.4977 solve for y --> y=0.1303=13%

seems to me that this should be thought of as jjxx put it, but in slightly different notation… X/(1.2)^5 -20 = 0. Solving for X gets you 49.76. This means that (1-p)*100 = 49.76 with p being the probability of failure. Going further this gives 100 -100p = 49.76. Solving for p (probability of failure) gives you 50.24%. So annualized, as jjxx put it, (1-y)^5 = 50.24% and solving for y gets you 13%.

A N=5 I/Y=20 FV=100 Cpt PV=40.187 -20+40.187(1-r)^5 = 0 (1-r)^5 = 20/40.187 1-r = 0.87 r = 13%

I like heha160’s solution better.

what do i have to do to think like heha160 did there… no seriously , good stuff man

congrats ! This Q looks very nasty but after all I wish to see one like that in the exam