DA Corp is a smart audio equipment manufacturer. The company has to decide if it should invest in developing a new product to be launched by the second half of 2019. The project requires an initial investment of either $1 million or $2 million in January 2019. However, the company does not know whether the product could be completed by June 2019 or not.
The company believes that, if it invests $1 million in January 2019, the product will be completed in June 2019 with probability 0.6; if it invests $2 million instead, the product will be completed in June 2019 with probability 0.8.
If the product is not completed by June 2019, DA has the option to either invest another $2 million to continue the project or to terminate the project. If it does invest $2 million in June 2019, it will certainly finish the product by October 2019.
DA Corp has a competitor, Cyber Inc., who is working on a competing product. DAbelieves that Cyber is equally likely to finish its producteither by June 2019 or October 2019. DA will know with certainty in June 2019 whether Cyber has finished its product at that time or not.
If the two companies finish their products at the same time, they will each make $10million profits from marketing and sales. Otherwise, the one who finishes first will make $4 million profits from marketing and sales, and the one who finishes later will make only $1 million from marketing and sales. If a company does not finish a product, it will not make any profit.
Assume DA Corp is risk neutral. Ignores the effects of any time value of money in your analysis.
- Draw a decision tree representing DA Corp decision problem. Determine the company’s optimal decision policy and certainty equivalent. (10 marks)
- Plot the risk profiles for the company’s two initial decision alternatives on a common graph paper. (10 marks)
- Is there any first or second order stochastic dominance among the two initial alternatives? Explain your answers. (5 marks)
- What is the value of clairvoyance to DA Corp on whether Cyber Inc. will finish its product by the end of June 2019 or not? Show your computations. (10 marks)
- John, an ex-employee of Cyber offers to help DA assess whether Cyber would complete the product by June or October 2019. However, as John had left the company months ago, his assessment will not be perfect. If Cyber can complete by June 2019, John will predict it correctly with probability 0.75.
On the other hand, if Cyber completes the product in October 2019 instead, John will predict it correctly with probability of 0.9. How much is John’s assessment worth to DA? Show your computations (15 marks)
You may use computer software (treeplan and others) for your computations but you must show your workings in the submission.
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