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In the financial world, there are many types of complex instruments called derivatives that derive their value from the value of an underlying asset. Consider the following simple derivative. A stock’s current price is $80 per share. You purchase a derivative whose value to you becomes known a month from now. Specifically, let P be the price of the stock in a month. If P is between $75 and $85, the derivative is worth nothing to you. If P is less than $75, the derivative results in a loss of 100(75-P) dollars to you. (The factor of 100 is because many derivatives involve 100 shares.) If P is greater than $85, the derivative results in a gain of 100(P-85) dollars to you. Assume that the distribution of the change in the stock price from now to a month from now is
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Chapter 11 Solutions
Practical Management Science
- It is January 1 of year 0, and Merck is trying to determine whether to continue development of a new drug. The following information is relevant. You can assume that all cash flows occur at the ends of the respective years. Clinical trials (the trials where the drug is tested on humans) are equally likely to be completed in year 1 or 2. There is an 80% chance that clinical trials will succeed. If these trials fail, the FDA will not allow the drug to be marketed. The cost of clinical trials is assumed to follow a triangular distribution with best case 100 million, most likely case 150 million, and worst case 250 million. Clinical trial costs are incurred at the end of the year clinical trials are completed. If clinical trials succeed, the drug will be sold for five years, earning a profit of 6 per unit sold. If clinical trials succeed, a plant will be built during the same year trials are completed. The cost of the plant is assumed to follow a triangular distribution with best case 1 billion, most likely case 1.5 billion, and worst case 2.5 billion. The plant cost will be depreciated on a straight-line basis during the five years of sales. Sales begin the year after successful clinical trials. Of course, if the clinical trials fail, there are no sales. During the first year of sales, Merck believe sales will be between 100 million and 200 million units. Sales of 140 million units are assumed to be three times as likely as sales of 120 million units, and sales of 160 million units are assumed to be twice as likely as sales of 120 million units. Merck assumes that for years 2 to 5 that the drug is on the market, the growth rate will be the same each year. The annual growth in sales will be between 5% and 15%. There is a 25% chance that the annual growth will be 7% or less, a 50% chance that it will be 9% or less, and a 75% chance that it will be 12% or less. Cash flows are discounted 15% per year, and the tax rate is 40%. Use simulation to model Mercks situation. Based on the simulation output, would you recommend that Merck continue developing? Explain your reasoning. What are the three key drivers of the projects NPV? (Hint: The way the uncertainty about the first year sales is stated suggests using the General distribution, implemented with the RISKGENERAL function. Similarly, the way the uncertainty about the annual growth rate is stated suggests using the Cumul distribution, implemented with the RISKCUMUL function. Look these functions up in @RISKs online help.)arrow_forwardWhich of the following statement is true? O For any type of derivatives, the payoffs will never be negative For any type of derivatives, the profit will never be negative There is no derivative that offers non-negative payoffs There is no derivative that offers non-negative profit All of the statements above are wrongarrow_forwardAssume that one year ago, you bought 240 shares of a mutual fund for $24 per share and that you received an income dividend of $0.31 cents per share and a capital gain distribution of $1.04 per share during the past 12 months. Also assume the market value of the fund is now $26.50 a share. Calculate the total return for this investment if you were to sell it now.arrow_forward
- Find the accumulated value 28 years after the first payment is made of an annuity on which there are 5 payments of $200 each made at four year intervals. The nominal interest rate convertible semiannually is 6% Round your answer to two decimal places. 5130 14arrow_forwardYou have deposited $10,800 into an account that will earn an interest rate of 8% compounded semiannually. How much will you have in this account at the end of 10 years? $16,564.89 $27,213.75 $23,664.13 $28,396.96arrow_forwardPlease answer along with the excel formulas - 1. Sue now has $125. How much would she have after 8 years if she leaves it invested at 8.5% with annual compounding? $205.83 $216.67 $228.07 $240.08 $252.08 2. Suppose you have $1,500 and plan to purchase a 5-year certificate of deposit (CD) that pays 3.5% interest, compounded annually. How much will you have when the CD matures? $1,781.53 $1,870.61 $1,964.14 $2,062.34 $2,165.46 3. Last year Rocco Corporation's sales were $225 million. If sales grow at 6% per year, how large (in millions) will they be 5 years later? $271.74 $286.05 $301.10 $316.16 $331.96arrow_forward
- A project does not necessarily have a unique IRR. (Refer to the previous problem for more information on IRR.) Show that a project with the following cash flows has two IRRs: year 1, 20; year 2, 82; year 3, 60; year 4, 2. (Note: It can be shown that if the cash flow of a project changes sign only once, the project is guaranteed to have a unique IRR.)arrow_forwardA certificate of deposit will often result in a penalty for withdrawing funds before the maturity date. If the penalty involves two months of interest, what would be the amount for early withdrawal on a CD worth $24,000 at 5 percent?arrow_forwardYour company is scheduled to receive 2, 000, 000 euros in 1 year. The euro is currently trading at 1.0813, you can borrow in the US for 1 year at 5.5% or invest in the US at 5.2%. You can borrow in euros at 3.6% or invest in euros at 3.3%. If you use a money market hedge on the receivable, how much will you get in US dollars?arrow_forward
- You purchase 30 bonds with a coupon rate of 6.125% and a current market price of 91.5. The commission charge is $12.50 per bond. The date of the transaction is October 1, and the bond pays interest on January 1 and July 1. What is your total purchase price?arrow_forwardYou have just received a business valuation report that is dated six months ago. Describe the factors that might have changed during the past six months and, therefore, caused the value of the business today to be different from the value six months ago. Which of these changes affect the expected cash flows, and which affect the discount rate that you would use in a discounted cash flow valuation of this company?arrow_forwardUse Table 12-1 to solve. Suppose Jorge Otero has set up an annuity due with a certain credit union. At the beginning of each month, $150 is electronically debited from his checking account and placed into a savings account earning 6% interest compounded monthly. What is the value (in $) of Jorge's account after 17 months? (Round your answer to the nearest cent.)arrow_forward
- Practical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,