DS City is known for its vibrant finance industry. A client is responsible for a large VC fund and is seeking your insights how best to invest in the existing portfolio. Can you help?
Your client has funded 1,000 start-ups. If they can achieve a successful exit on a startup, the return is anywhere between $5 and $10 million. Particularly, if startup number i in {0,..,999} succeeds, the expected return is $10-0.005*i million. Alas, most startups fail and return nothing.
To improve the likelihood that a startup succeeds, we can support it with additional funds. A budget of $30 million is available to support the development of the startups. If we invest $S thousand in a startup, its expected likelihood of failure is
Without additional support, a startup therefore has a probability of about 95% that it will fail. The more money we invest to support it, the lower the chances of failure and the higher the probability that we will have an exit for anywhere between $5 to $10 million, depending on the startup. But no matter how much we invest, we cannot lower the failure likelihood below 30%.
The simple question that the client has for you is how to invest the $30 million in the startups. Since this is a simple deterministic optimization problem, surely you can help. Or can you?
Intuitively, is it better to flush fewer startups with money so that their probabilty of success rises close to 70%, or is it better to slightly boost more startups?
Seeker suggests (after sorting all startups by decreasing expected returns):
- Fund the first 167 with $57,000 each.
- Fund the next 176 with $56,000 each.
- Fund the next 149 with $55,000 each.
- Fund another 45 with $54,000 each.
All others receive no extra funding. With this allocation, we expect a total return of $3,046,183,017 on our initial investment plus the additional $30,000,000.