PROBLEM SET 4 (STRATEGIC DECISION-MAKING) Please provide your answers on a separ

Question

PROBLEM SET 4 (STRATEGIC DECISION-MAKING) Please provide your answers on a separate sheet. Write as neatly as possible, show all your work and clearly note your final answer Section I As a New Year's gift to yourself, you buy your roommate's 1976 Ford Pinto. She has given you the option of two payment plans. Under Plan A. you pay $500 now, plus $500 at the beginning of each of the next two years. Under Plan B, you would pay nothing down, but $800 at the beginning of each of the next two years 1. Calculate the net present value of each plan's payments if interest rates are 10% Should you choose plan A or plan B Section 2 You have a Bernoulli utility function given by u() I+10000, where / is income. You are considering two job opportunities. The first pays a salary of $40,000 for sure. The second pays a base salary of $20,000. However, it also offers the possibility of a $40,000 bonus on top of your base salary (for a total salary of $60,000). You believe that you will earn the bonus with a probability of 2. Prove that the "more is better" assumption holds for your utility function. 3. Prove that the utility function exhibits decreasing marginal utility. . Calculate the expected utility under each offer. Which job opportunity should you choose? Explain 5. Calculate the certainty equivalent of the second job opportunity Section 3 Suppose you are the CEO of Asus (a risk neutral mega-corporation) and you are trying to determine whether or not you should introduce a new high end tablet that runs Windows 10. Developing this new tablet will cost $45 mil. You know that demand for the tablet will either be high (h) or low (). If demand is high you will generate $60 mil in revenue; if it is low the tablet will generate only $10 mil in revenue. From your personal experience you believe that the probability there will be high demand is P(h)- and the probability there will be low demand is P 6. Calculate the expected revenue from the tablet given your initial beliefs about the demand for the product This is a really big decision so you decide to hire a market research firm to help. They will hold several focus groups and then tell you if they think demand will be high or low. You have worked with this particular firm before so you know that they are really good at determining when demand for a product will be low, but their ability to determine if demand will be high is a little hit or miss. In particular you know PCHI»-2. Pal»-2,P(HD- nd Pun 7. Calculate P(L). 8. Calculate P(h|L)and P(TIL). 9. Suppose that the market research firm reports that demand will be low (L), what is the expected revenue of the tablet? 10. Assuming that Asus is risk neutral, should you develop the product if you get a report of low demand?

Explanation / Answer

ANS SECTION 1:

1. present worth of plan A = 500 + 500/(1+r) + 500/(1+r)^2 where r = 10%

= 1367.7685

present worth of plan B = 800/(1+r) + 800 / (1+r)^2 where r = 10%

= 1388.4297

so, you should choose plan A as it costs less.

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