Set up the system fequations and then solve it by using an inverse matrix. One safe investment pays 10% per year, and a more risky investment pays 18% per year. A woman has $147,200 to invest and would like to have an income of $20,000 per year from her investments. How much should she invest at each rate? 10% rate $ 18% rate $

Set up the system fequations and then solve it by using an inverse matrix. One safe investment pays 10% per year, and a more risky investment pays 18% per year. A woman has $147,200 to invest and would like to have an income of $20,000 per year from her investments. How much should she invest at each rate? 10% rate $ 18% rate $

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter11: Simulation Models

Section11.3: Financial Models

Problem 13P

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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 stocks 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 normally distributed with mean 1 and standard deviation 8. Let EMV be the expected gain/loss from this derivative. It is a weighted average of all the possible losses and gains, weighted by their likelihoods. (Of course, any loss should be expressed as a negative number. For example, a loss of 1500 should be expressed as -1500.) Unfortunately, this is a difficult probability calculation, but EMV can be estimated by an @RISK simulation. Perform this simulation with at least 1000 iterations. What is your best estimate of EMV?
The IRR is the discount rate r that makes a project have an NPV of 0. You can find IRR in Excel with the built-in IRR function, using the syntax =IRR(range of cash flows). However, it can be tricky. In fact, if the IRR is not near 10%, this function might not find an answer, and you would get an error message. Then you must try the syntax =IRR(range of cash flows, guess), where guess" is your best guess for the IRR. It is best to try a range of guesses (say, 90% to 100%). Find the IRR of the project described in Problem 34. 34. Consider a project with the following cash flows: year 1, 400; year 2, 200; year 3, 600; year 4, 900; year 5, 1000; year 6, 250; year 7, 230. Assume a discount rate of 15% per year. a. Find the projects NPV if cash flows occur at the ends of the respective years. b. Find the projects NPV if cash flows occur at the beginnings of the respective years. c. Find the projects NPV if cash flows occur at the middles of the respective years.
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Using Excel Spreadsheet and formulas for this problem (make sure cell references are unique to your table). Provide all techniques practiced previously: five (5) techniques for Decisions Making under Uncertainty, EMV, EOL, and EVPI. Use α = 0.7 for the Hurwicz. Use the .50 for the probability of a Good Economy and .50 for the probability of a Poor Economy. Show the work on an Excel file. STATE OF NATURE DECISION ALTERNATIVE GOOD ECONOMY POOR ECONOMY Sotck market 80,000 -20,000 Bonds 30,000 20,000 CDs 23,000 23,000
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