Question

Complicated R&D project:

? Probabilities of success: 0.25, 0.21, 0.17, 0.13, 0.07, and 0.01
? Investment required: 3 mln USD each year that was not successful
? Earnings: 20 mln USD
? Profits = Earnings-Investment
? No interest rates
? Risk-neutral company

How long to invest? When to stop?

Answer 1

Given:

Probabilities of Success

Year	1	2	3	4	5	6
The probability of Success	0.25	0.21	0.17	0.13	0.07	0.01

If the investment fails, there is a loss of 3 million USD but if the investment succeeds, there is an earning of 20 million USD.

Because of the probability of success, there is uncertainty involved in getting the investment's profits. In such a case, one would invest on the basis of expected profits. As long as the expected profits are greater than zero, one should invest.

Expected profits can be calculated using the following formula:

Expected Profits = (Prob. of success * Earnings) + (Prob. of failure * Loss)

• Case 1: Suppose one invests in the 1st year when the probability of success is 0.25
  • Expected profits = (0.25 * 20) + {0.75 * (-3)} = 5 + (-2.25) = 2.75 million dollars.
  • Since the expected profits are greater than zero, one should invest.
• Case 2: Suppose you continue to invest in the second year where the probability of success is 0.21
  • Then, expected profits = (0.21 * 20) + {0.79 * (-3)} = 4.2 - 2.37 = 1.83 million dollars
  • As the expected profits are greater than zero, one should continue to invest.
  • An important point to note is that there are no interest rates. In that situation, profits in the 2nd year are no discounted in the present value.
• Case 3: Investment in 3rd year when the probability of success if 0.17
  • Expected profits = (0.17 * 20) + {0.83* (-3)} = 3.4 - 2.49 = 0.91 million dollars
  • One should still continue to invest
• Case 4: In the 4th year, probability of success is 0.13
  • Expected profits = (0.13 * 20) + {0.87* (-3)} = 2.6 - 2.61 = -0.01 million dollars
  • One can see that the expected profits are now negative.

Therefore, in the given scenario, one should invest for the first 3 years but must stop in the 4th year. Otherwise, the profits from the investment would be negative, and you will be running into losses. Intuitively, this happens because the probability of success falls over time. In other words, your chance of earning 20 million USD decrease over time.