Question

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?

Answer 1

Ans.

Payoff from strategy C = 150 * 50% + 110 * 50%

= 75 + 55

$ 130 m

Payoff from strategy A = 200m * 50% + 30 * 50%

= 100 + 15

= $ 115 m

Payoff from strategy C is better. Besides it also conservative strategy. So, company should follow strategy C as minimum returns of $ 110 m will also provide profits to company on investment.

Loan required by company = $ 80m

Promised payment F (principal plus interests) that a rational banker, aware of your incentives, will ask to loan you

= $ 110 m - $ 20 m

= $ 90 m

Reason that banker will loan up to $ 90 m is that even at it's minimum company is going to earn $ 110m, out of which $ 90m would be sufficient to fund principal & interest of bank loan.

Amount that company needs to raise @ 20% discount in IPO = 80 / 0.80

= $ 100 m

Company should prefer bank loan as it's cost is less than IPO by $ 10m ($ 100m - $ 90m).

If company is able to sell equity in the IPO at a 10% discount:

Amount that company needs to raise @ 10% discount in IPO = 80 / 0.90

= $ 88.89 m

Company should prefer IPO as it's cost is less than bank loan by $ 1.11m ($ 90m - $ 88.89m).