# SS 13 question

A private equity investor expects to realize a return on her venture capital investment in two years and expects to sell the firm for \$30 million. She estimates that a discount rate of 30% is reasonable but expects that there is a 20% probability of failure in any given year. The post-money value of her investment today, adjusted for failure, is closest to: A) \$11.20. B) \$14.20. C) \$11.36. In this question, how come I shouldn’t use scenario analysis to calculate?

(1+.3)/(1-.2) = 1.625 so Post money value = 30 / (1.625^2) = 11.36? C

it’s correct…but if I use scenario analysis, the answer would be (\$30 x 0.8) + (0 x 0.2) = 24 24/(1.3 x 1.3) = 14.2 how come I shouldn’t use scenario analysis?

doesn’t selling of the firm happen when the firm is assured of success? don’t know about scenario analysis. Is this the Level 1 material on Venture capital stuff that you are trying to use? In that case, there was no mention of Post Money, Pre-Money etc. there.

I am not sure what this scenario analysis either, but i think there is a simple way of solving this problem. The problem takes place over 2 yrs. So in yr 1 there is a 20% chance of failure, same in yr 2. When i see this problem, the first thing I do is ask myself, what is the chance this investment actually pays me money in the end? (what is the chance of survival?) Well that is 80% in yr 1, and 80% in yr 2. So if you take the probability it makes it thru both years, it would be .80 * .80 = .64. The business has a 64% chance of making it to the end of 2 yrs. So if you have 30 million invested and discount that at 30%, the PV is roughly 17,750,000. If 17.750M is the PV are looking for and there is only a 64% chance you see this 17.750M, what is the most you would pay? .64 * 17.750 = 11.360

Using Scenario Analysis method of adjusting firm value and using the unadjusted discount rate we have, 30 million is the end value which you will receive if the project does not fail in any of the 2 years So, Actual value received after accounting for failure probability = 30*(probability of not failing in year1)*(probability of not failing in year2) = 30*(1-0.20)*(1-0.20) = 30*0.80*0.80 = 19.2 POST=19.2/(1.3*1.3) =19.2/1.69 =11.360946 = C Ideally, it should work with both ways, but I prefer the one where we adjust r and then do TVM calculation (as cp dide above)

Thank you very much for the explanation!