Probability/NPV Exercise – Venture Capital Example

Question:

A venture capitalist is planning to invest in a bio-technology startup. It is expected that the startup will have 0.5, 0.4, 0.4 and 0.1 failure probabilities respectively in the first 4 years. If it is successful, the payoff will be $2M. For the risk taken, the discount rate is 30%, how much is he willing to invest today?

Answer:

If you are not clear what this question is asking, let’s first draw the time line and the binary tree. So, the investment horizon is 4 years and we put t=0 (i.e. now) to t=4. In the first year, it has 50% of chance to fail. The return will be 0. But if it is successful (which has 1-50%=50% of chance), we will go to the next year. Again in the next year, there 40% of chance to fail and you will get 0 return. Similarly if it is successful, we will move to the 3^rd year. We repeat this process until the end of the 4^th year. So, the venture capitalist will only get $2 million return if it is success all the way to the end of the 4^th

year (Go through the black arrows). And this rate is calculated as

P(success) = (1-0.5)*(1-0.4)*(1-0.4)*(1-0.1)=0.162.

If it fails at any stage, he will have 0 return. So the expected return by the end of the 4^th year is the weight average of the return

E(return)= P(failure)* 0 + P(Success)*2M =324K.

Investing in start-up is a high risk investment. Therefore, the discount rate is priced at 30% to account for the risk. And to decide how much he will invest, we need to find the NPV.

PV of E(return) =324K / (1+30%)^4 =113.4K

Investor will only be willing to invest if it is less than 113.4k today so that it will have a positive NPV!