Chapter 7: Innovation and Technological Change: The Future Is Now
The expected net revenue, Rn, from your research and development project equals
where Rn represents net revenue in millions of dollars and t is time measured in years. Your time-cost trade-off function is
where C is development cost in millions of dollars and t is again time. In order to determine the optimal time frame for the project’s completion, take the following steps:
1. Note that the expected profit, π, from the project equals net revenue minus the development cost represented by the time-cost trade-off function.
Thus,
2. In order to maximize profit, take the derivative of profit, π, with respect to time, t.
This derivative equals
3. Set the derivative equal to zero and solve for t.
Thus, the project’s optimal time frame is four years. Substituting t equals 4 into the expected profit equation indicates that the expected profit is $4 million.
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