The State of Nature Decision Alternative 0.83 1-0.83- S1 S2 D1 3 D2 7 D3 13 6. What is the Minimum payoff value for the D3 under S2 should be to keep the optimal solution always optimal? Remark: write only the value of payoff (no need to write > or <) Write your answer in 2 Decimal places
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- A European put option allows an investor to sell a share of stock at the exercise price on the exercise data. For example, if the exercise price is 48, and the stock price is 45 on the exercise date, the investor can sell the stock for 48 and then immediately buy it back (that is, cover his position) for 45, making 3 profit. But if the stock price on the exercise date is greater than the exercise price, the option is worthless at that date. So for a put, the investor is hoping that the price of the stock decreases. Using the same parameters as in Example 11.7, find a fair price for a European put option. (Note: As discussed in the text, an actual put option is usually for 100 shares.)If a monopolist produces q units, she can charge 400 4q dollars per unit. The variable cost is 60 per unit. a. How can the monopolist maximize her profit? b. If the monopolist must pay a sales tax of 5% of the selling price per unit, will she increase or decrease production (relative to the situation with no sales tax)? c. Continuing part b, use SolverTable to see how a change in the sales tax affects the optimal solution. Let the sales tax vary from 0% to 8% in increments of 0.5%.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.
- Rerun the new car simulation from Example 11.4, but now use the RISKSIMTABLE function appropriately to simulate discount rates of 5%, 7.5%, 10%, 12.5%, and 15%. Comment on how the outputs change as the discount rate decreases from the value used in the example, 10%.Suppose you currently have a portfolio of three stocks, A, B, and C. You own 500 shares of A, 300 of B, and 1000 of C. The current share prices are 42.76, 81.33, and, 58.22, respectively. You plan to hold this portfolio for at least a year. During the coming year, economists have predicted that the national economy will be awful, stable, or great with probabilities 0.2, 0.5, and 0.3. Given the state of the economy, the returns (one-year percentage changes) of the three stocks are independent and normally distributed. However, the means and standard deviations of these returns depend on the state of the economy, as indicated in the file P11_23.xlsx. a. Use @RISK to simulate the value of the portfolio and the portfolio return in the next year. How likely is it that you will have a negative return? How likely is it that you will have a return of at least 25%? b. Suppose you had a crystal ball where you could predict the state of the economy with certainty. The stock returns would still be uncertain, but you would know whether your means and standard deviations come from row 6, 7, or 8 of the P11_23.xlsx file. If you learn, with certainty, that the economy is going to be great in the next year, run the appropriate simulation to answer the same questions as in part a. Repeat this if you learn that the economy is going to be awful. How do these results compare with those in part a?Bilbo Baggins wants to save money to meet threeobjectives. First, he would like to be able to retire 30 years from now with a retirementincome of $23,000 per month for 20 years, with the first payment received 30 yearsand 1 month from now. Second, he would like to purchase a cabin in Rivendell in10 years at an estimated cost of $320,000. Third, after he passes on at the end of the20 years of withdrawals, he would like to leave an inheritance of $1,000,000 to hisnephew Frodo. He can afford to save $2,100 per month for the next 10 years. If hecan earn an 11 percent EAR before he retires and an 8 percent EAR after he retires,how much will he have to save each month in Years 11 through 30?
- In the time interval between t and t 1 seconds beforethe departure of Braneast Airlines Flight 313, there is aprobability pt that the airline will receive a reservation for 19.4 Further Examples of Probabilistic Dynamic Programming Formulations 1035 the flight and a probability 1 pt that the airline will receiveno reservation. The flight can seat up to 100 passengers. Atdeparture time, if r reservations have been accepted by theairline, there is a probability q(y|r) that y passengers willshow up for the flight. Each passenger who boards the flightadds $500 to Braneast’s revenues, but each passenger whoshows up for the flight and cannot be seated receives $200in compensation. Formulate a dynamic programmingrecursion to enable the airline to maximize its expectedrevenue from Flight 313. Assume that no reservations arereceived more than 100,000 seconds before flight time.A salesperson for Fuller Brush has three options: quit,put forth a low-effort level, or put forth a high-effort level.Suppose for simplicity that each salesperson will either sell$0, $5,000, or $50,000 worth of brushes. The probability ofeach sales amount depends on the effort level in the mannerdescribed in Table 8.If the salesperson is paid $w, then he or she earns abenefit w1/2. Low effort costs the salesperson 0 benefit units,while high effort costs 50 benefit units. If the salespersonwere to quit Fuller and work elsewhere, then he or she couldearn a benefit of 20. Fuller wants all salespeople to put fortha high-effort level. The question is how to minimize the costof doing it. The company cannot observe the level of effortput forth by a salesperson, but they can observe the size ofhis or her sale. Thus, the wage is completely determined bythe size of the sale. Fuller must then determine w0 wagepaid for $0 in sale, w5000 wage paid for $5,000 in sales,and w50,000 wage paid for…Based on current dividend yields and expected capital gains, the expected rates of return on portfolios A and B are 11 % and 14 %, respectively. The beta of A is 0.8 % while that of B is 1.5. The T-bill is currently 6 %, while the expected rate of return of the S&P 500 index is 12 %. The standard deviation of portfolio A is 10 % annually, while that of B is 31 % , and that of the index is 20 %: If you currently hold a market index portfolio, would you choose to add either of these portfolios to your holdings? Explain. If instead you could invest only in bills and one of these portfolios, which would you choose, and why? Investor Y, who put K1 in large stocks (the S & P 500 portfolio) on December 31, 1925, and re-invested all dividends in that portfolio, would have ended on December 31, 2003, with K1992.80.
- Consider a buying firm and a supplier negotiating terms for a contract. Suppose the Marginal Benefit to the buying firm of additional contract provisions in a contract (x) to the firm is: MB = 20,000 – 400x. Suppose the Marginal Cost to the buying firm of additional contract provision to the firm is: MC = 100x. What is the optimal number of contract provisions? Reconsider the previous question. If the maximum value (or price) of the contract that the buying firm is willing to pay for is $3,000, what would you expect the firm to do? a) Use the spot market b) Vertically integrate c) Continue to contract d) engage in holdupI own a single share of Wivco stock. I must sell myshare at the beginning of one of the next 30 days. Each day,the price of the stock changes. With probability q(x), theprice tomorrow will increase by x% over today’s stock price(x can be negative). For example, with probability q(5),tomorrow’s stock price will be 5% higher than today’s. Showhow dynamic programming can be used to determine astrategy that maximizes the expected revenue earned fromselling the share of Wivco stock. Assume that at thebeginning of the first day, the stock sells for $10 per share.SureStep is currently getting 160 regular-time hours from each worker per month. This is actually calculated from 8 hours per day times 20 days per month. For this, they are paid $9.375 per hour (51500y160). Suppose workers can change their contract so that they only have to work 7.5 hours per day regular-time— everything above this becomes overtime—and their regular-time wage rate increases to $10 per hour. They will still work 20 days per month. Will this change the optimal no-backlogging solution?