Question: The Research and Development (R&D) division of your firm has developed a new product that could be immediately launched on the market. If so, the probability of success is 60%, in which case profit has a present value of €10 million (discounting all future cash flows). In case of flop, you will lose €2 million. You might also delay product launch by 6 months, in order to improve its design. This delay has advantages and disadvantages:

• Product improvement would cost €500,000, but it increases success probability to 90% (without changing hypothetical profits and losses); however, this applies only if no competitor takes advantage of your delay and enters the market, eroding your share (see the last bullet below).

• Delaying product launch has a financial impact, as cash flows are delayed; let us assume that the effect of delay is accounted for by a 5% discount rate for the 6 months. (Note: This is the rate applying to the 6 months, not to 1 year.)

• Delaying product launch has the effect of leaving room for the entry of competitors; we assume that the probability of this entry is 50% and its effect is not on success probability (which is still 90%), but on cash flows: Profit is halved, and loss is doubled, depending on product success or flop.

1. Assuming that you are risk-neutral, what would you do?

2. In practice all of the above probabilities are the result of educated guesswork.

In particular, the entry probability is quite uncertain. Hence, you want to carry out a sensitivity analysis. What is the value of the entry probability (if it exists) that would make you change your mind with respect to the decision above?