Question

Your initial investment for research and development (R&D) is estimated to be $9000 total and there’s a 50-50 chance that it will be successful. If the results of the R&D phase turn out to be successful, you will need a total of $20,000 to invest in the product’s development. If the product goes through the development phase, uncertainty remains about the product’s demand on market and thus uncertainty about the profit will be realized. You categorize the product demand as high, medium and low with respective probabilities of 0.5, 0.3 and 0.2. Your best estimate of revenue projection under high demand is $75000; at medium demand, revenue is projected at $55,000; and, at a low demand for the product, revenue is projected at $21,000. Another option is that if the R&D phase is successful, you could sell the rights of the product for an estimated $18,000 and not engage its development.

Develop the decision tree and solve it according to the EMV decision criterion. State the optimal decision according to the EMV decision criterion.

Answer 1

Data Provided:

1.  Research and Development (R&D) is estimated to be $9,000 total and there’s a 50-50 chance that it will be successful.

2. If the R&D phase turns out to be successful, you will need a total of $20,000 to invest in the product’s development.

3. Revenue projection under high demand for the product is $75,000 with an associated probability of 0.5.

4. Revenue projection under medium demand for the product is $55,000 with an associated probability of 0.3.

5. Revenue projection under low demand for the product is $21,000 with an associated probability of 0.2.

6. If the R&D phase turns out to be successful, then there is another alternative to sell the rights of the product for an estimated $18,000 and not engage its development

Answer:

Based on the information provided we constructed the decision tree as shown in the image below:

Explanation of the Decision Nodes and the Chance Nodes:

Chance Node (1): After R&D, there is a probability of either success or failure and each is equally probable

Decision Node(3): After R&D was successful, we need to take a decision of whether to do the path of Product development which will need an additional investment of $20,000 or sell the rights of the product at $ 18,000.

Chance Node(2): After the product development there are chances of high, medium or low demand and each of these demands has a different probability associated with them.

Expected Value of Money:

If we take the Product development path then the expected value of money given the 3 different types of demand in market is: $58,200 = [($75000*0.5) +   ($55000*0.3) + ($21000*0.2)]

Now if we do product development with an additional investment of $ 20,000, the expected value of money is $ 58,2000, and reducing the product development investment of $ 20,000, have a higher expected EVM value compared to selling the rights of the product without product development.

So we will go for the product development way and not sell the rights of the product.

Summary:

So the decision tree path that we will follow: