Investing in Start-ups [Use Excel's Decision Tree]

A regional government has created a Venture Fund (VF) to support early-stage start-up companies that could benefit the local economy. Those are risky, but when start-ups succeed, VF can recoup its investments, sometimes with substantial profits, and re-invest in new budding companies.

VF is considering a $2 million investment in H2Op, a start-up company that has patented a novel technology for efficient water purification or desalination. Considering the uncertainties surrounding whether the new technology will lead to commercialization, VF managers estimate that investing $2m in H2Op would lead to one of three equally likely outcomes (1/3 chance each):

1) Success: the start-up thrives, and VF will be able to sell their share in it for $7m (in present value), that is, they will earn a net payoff of $5m.

2) "Living dead": the start-up manages to bring a product to market but with mediocre results; VF will be able to just recoup their $2m investment, i.e., a breakeven.

3) Failure: the patented technology does not yield a viable product and the start-up fails, the business is worth nothing; VF will not recoup anything, i.e., a net loss of $2m.

a) Construct a decision tree to help evaluate this investment opportunity. What is its expected value? What should VF do if they make decisions based on expected value?

VF can negotiate an option to invest more resources to grow the business before selling out if the start- up succeeds. If H2Op succeeds, the option will give VF the right to further invest $1m to develop markets and attempt to grow the business before selling. The additional $1m investment would give VF a 50% chance of increasing its share value from $7m to $10.5 million (in present value), and 50% chance of no significant impact, that is, VF's payoff will remain at $7m. Under the option, VF could also choose to decline investing more money and just sell out for $7m.

b) Add to the decision tree from (a) to incorporate the option of further investing in the business. Does this expansion option add value to the investment?

For the rest of the exercise, ignore the option discussed in Part (b), revert to the decision tree from (a).

Suppose a diagnostic study could determine with 100% reliability whether the technology can be developed into a viable product or not. This would provide perfect information that predicts just whether the start-up will fail or not; in case of no failure, it would not predict the market outcome (Success or Living-dead).

c) Add a branch to your decision tree from Part (a) to show the alternative, described above, of seeking perfect information on failure. Based on expected value, what is the most VF would be willing to pay for that information?

Instead of putting $2m in H2Op, suppose VF splits it between two ventures: invest $1m in H2Op (and earn half of the eventual payoff, whatever it turns out to be), and $1m in another independent venture, that has a 50% chance to succeed and be worth $3.5m (i.e., net profit of $2.5m), and 50% chance to fail and generate no payoff.

d) Add a branch to your decision tree from Part (a) to show the alternative, described above, of investing in both start-ups simultaneously. What is the expected value of that alternative? Based on expected value, what is the best decision?