You are the CEO of a privately held company. Your company has a project regarding the development and marketing of a new product. The project requires an initial investment (at t=0) of $100m, and will generate a payoff only during the following period, t=1. The payoff at t=1 is random, and depends on your marketing strategy at that time. In particular, you will be able to follow either a conservative strategy (strategy C) or an aggressive strategy (strategy A). Payoffs under the two strategies are given by:
Payoff from strategy C: 150m (probability 50%) 110m (probability 50%)
Payoff from strategy A: 200m (probability 50% 30m (probability 50%)

The strategy you will choose remains private information to you. You have
20m cash, and you must raise the $80m required for the initial investment
with outside financing. The appropriate discount rate for this project is the
risk-free rate, which is zero.

You first consider a bank loan. What is the promised payment F (principal
plus interests) that a rational banker, aware of your incentives, will ask to loan
you the $80m you need? (Hint: you need determine which strategy the firm
will follow if it is debt-financed…)
Before signing up for a loan, you also check with an investment banker
about issuing equity in an IPO. The banker advises you that if you wish to
issue equity in an IPO you should expect to sell shares at 20% discount with
respect to their fair market value. What fraction of the firm must you sell to
receive the desired $80m financing?

Which alternative do you prefer: the bank loan or the IPO? Explain your
results. How your answer would change if you are able to sell equity in the IPO at a 10% discount?