Economics of Innovation Homework

1. (10 points) Suppose that you are considering an idea (v,c). There is uncertainty over the true value v. Looking at similar ideas from the past, you estimate that the probability that v = 1000 is 1/5 and the probability that v = 100 is 4/5. With certainty, you know that c = 300 and R = 1. a. Should this idea be invested in given the above probabilities? Why or why not? b. Now, suppose that you decide to consult an expert to better determine whether v = 1000 or v = 100. The expert excels at conrming high-value ideas but is rather poor at conrming low-value ideas. Suppose that when the true value is v = 1000, the expert declares the value as v = 1000 with probability 4/5. However, when the true value is v = 100, the expert incorrectly declares the value at v = 1000 with probability 1l2 and correctly declares the value at v = 100 with probability 1/2. Use Bayes' rule to determine the probability that v = 1000 when the expert declared that the value is v = 1000. c. Suppose you consulted this expert and the expert claimed that v=1000. Should this idea be invested in given the updated probabilities? Why or why not? 2. (10 points) Suppose your company is considering developing a new product. The company spent $300 million in research and development over the previous five years. Ifthe company chooses to invest, it receives the following schedule of benefits and costs: Year 0 Year 1 Year 2 Year 3 Revenues of $25 million Costs of $90 million Revenues of $25 million Revenues of $25 million Revenues of $25 million Should your company develop this innovative new product if the interest rate (discount rate) is a. 1% (0.01)? b. swans)? c. 10%(o.10)? d. 20%(020)? (10 points) Suppose your company is considering developing a new product. The company spent $75 million in research and development over the previous five years. Ifthe company chooses to invest, it receives the following schedule of benefits and costs: Year 0 Year 1 Year 2 Year 3 0 Costs of $65 million - Revenues of $25 million - Revenues of $25 million o Revenues of $25 million Should your company develop this innovative new product if the interest rate (discount rate) is a. 1%? b. 5%? c. 10%? d. 20%? (10 points) A firm has $25 million today that it can invest in any or all of the projects listed below. All investments must be made today. Which projects, if any, should the firm invest in and why? Remember that the firm only has $25 million on hand and must pay all investment costs up front. Project A: Year 0 Years 1 until forever Investment cost of $15 Sale price: 53 million Expected sales (units): 2,000,000 Cost per unit sold: 51 Other operating expenses: $400,000 Project B: Year 0 Years 1 until forever Investment cost of $15 million Sale price: 55 Expected sales (units): 500,000 Cost per unit sold: 52 Other operating expenses: $400,000 Project C: Year 0 Year 1 Year 2 Year 3 Year 4 Investment Sale price: 52 Sale price: 52 Sale price: 54 Sale price: 53 cost of 515 Expected sales: Expected sales: Expected sales: Expected sales: million 10 million 10 million 10 million 10 million Cost per unit: 51 Other expenses: 55 million Cost per unit: 51 Other expenses: 55 million Cost per unit: 52 Other expenses: 55 million Cost per unit: 52 Other expenses: 55 million (10 points) A firm is trying to decide whether to invest in a t-shirt factory. The factory can be built instantly at a cost $5,000,000 and will produce 500,000 units per year forever (starting right away). The current profit per unit of a t-shirt is $3 and all 500,000 t-shirts are sold each year. Next year the profit per unit may increase to $4 with probability 0.25 or it may decrease to $2 with probability 0.75. After that change, the profit per unit will remain constant forever. Operating costs are $1,000,000 per year. The interest rate is 10%. The rm must make this decision today and cannot delay until the uncertainty is resolved. What do you recommend? (show how you came up with your recommendation). Would your decision change if the interest rate is 5%? 6. (10 points) You are the international operations manager for ExxonMobil and you are considering investing in an offshore oil rig. The development can be done instantly at a cost of $10,000,000. The oil company can extract 30,000 barrels of oil per year forever at a cost of $50 per barrel (the initial extraction can be done immediately after making the investment). The current price of a barrel of oil is 5100. Next year, the price of a barrel may increase to $150 or it may decrease to $50 with equal probability. After that, the price will remain constant. The interest rate is 10%. Should ExxonMobil invest today, wait one year until the uncertainty is resolved (if so, under what conditions should ExxonMobil invest?), or never