Question

A company is deciding whether to develop and launch a new product. Research and development costs are expected to be $300,000 and there is a 60% chance that the product launch will be successful, and a 40% chance that it will fail. If it is successful, the levels of expected revenue and the probability of each occurring have been estimated as follows, depending on whether the product popularity is high, medium or low: Probability High: 0.25 Medium: 0.45 Low: 0.3 Revenue $500,000 per year for two years $400,000 per year for two years $300,000 per year for two years If it is a failure, there is a 0.55 probability that the research and development work can be sold for $60,000 and a 0.45 probability that it will be worth nothing at all. Construct a decision tree for this problem and answer this question that whether this company should develop and launch this new product. Please draw your decision tree in PrecisionTree, enter all given data, and analyze the problem over there to answer this question.

Answer 1

Answer: Since the overall expected value is positive, the company should develop and launch the new product.

To construct the decision tree, start with a square representing the decision to develop and launch the new product. From this square, draw two branches representing the two possible outcomes: success and failure. Label the branches accordingly.

Next, from the success branch, draw three branches representing the three possible levels of popularity: high, medium, and low. Label each branch with the corresponding probability of popularity and expected revenue.

From the failure branch, draw two branches representing the two possible outcomes: selling the research and development work for $60,000 or getting nothing. Label each branch with the corresponding probability.

Calculate the expected values of each branch by multiplying the probabilities and revenues or costs. Add up the expected values of each branch to get the overall expected value of developing and launching the new product.

If the overall expected value is positive, the company should develop and launch the new product. If the overall expected value is negative, the company should not develop and launch the new product.

To analyze the problem, we need to calculate the expected values of each branch and add them up to get the overall expected value of developing and launching the new product. Using the decision tree, we can calculate the expected values as follows:

High popularity: (0.6 x 0.25 x $500,000 x 2) + (0.6 x 0.25 x $500,000 x 2) = $300,000

Medium popularity: (0.6 x 0.45 x $400,000 x 2) + (0.6 x 0.45 x $400,000 x 2) = $432,000

Low popularity: (0.6 x 0.3 x $300,000 x 2) + (0.6 x 0.3 x $300,000 x 2) = $216,000

Selling R&D work: (0.4 x 0.55 x $60,000) = $13,200

Getting nothing: (0.4 x 0) = $0

Overall expected value = (0.6 x $300,000) + (0.6 x $432,000) + (0.6 x $216,000) + (0.4 x $13,200) = $472,320