Dataware is trying to determine whether to give a $10 rebate, cut the price $6, or have no price change on a software product. Currently, 40,000 units of the product are sold each week for $45 apiece. The variable cost of the product is $5. The most likely case appears to be that a $10 rebate will increase sales 30%, and half of all people will claim the rebate. For the price cut, the most likely case is that sales will increase 20%. a. Given all other assumptions, what increase in sales from the rebate would make the rebate and price cut equally desirable? b. Dataware does not really know the increase in sales that will result from a rebate or price cut. However, the company is sure that the rebate will increase sales by between 15% and 40% and that the price cut will increase sales by between 10% and 30%. Perform a sensitivity analysis (two-way data table) that could be used to help determine Dataware’s best decision

Dataware is trying to determine whether to give a $10 rebate, cut the price $6, or have no price change on a software product. Currently, 40,000 units of the product are sold each week for $45 apiece. The variable cost of the product is $5. The most likely case appears to be that a $10 rebate will increase sales 30%, and half of all people will claim the rebate. For the price cut, the most likely case is that sales will increase 20%. a. Given all other assumptions, what increase in sales from the rebate would make the rebate and price cut equally desirable? b. Dataware does not really know the increase in sales that will result from a rebate or price cut. However, the company is sure that the rebate will increase sales by between 15% and 40% and that the price cut will increase sales by between 10% and 30%. Perform a sensitivity analysis (two-way data table) that could be used to help determine Dataware’s best decision

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter11: Simulation Models

Section11.3: Financial Models

Problem 22P: In the financial world, there are many types of complex instruments called derivatives that derive...

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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?
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.)
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.
The file P02_41.xlsx contains the cumulative number of bits (in trillions) of DRAM (a type of computer memory) produced and the price per bit (in thousandth of a cent). a. Fit a power curve that can be used to show how price per bit drops with increased production. This relationship is known as the learning curve. b. Suppose the cumulative number of bits doubles. Create a prediction for the price per bit. Does the change in the price per bit depend on the current price?
Rework the previous problem for a case in which the one-year warranty requires you to pay for the new device even if failure occurs during the warranty period. Specifically, if the device fails at time t, measured relative to the time it went into use, you must pay 300t for a new device. For example, if the device goes into use at the beginning of April and fails nine months later, at the beginning of January, you must pay 225. The reasoning is that you got 9/12 of the warranty period for use, so you should pay that fraction of the total cost for the next device. As before, how-ever, if the device fails outside the warranty period, you must pay the full 300 cost for a new device.
An automobile manufacturer is considering whether to introduce a new model called the Racer. The profitability of the Racer depends on the following factors: The fixed cost of developing the Racer is triangularly distributed with parameters 3, 4, and 5, all in billions. Year 1 sales are normally distributed with mean 200,000 and standard deviation 50,000. Year 2 sales are normally distributed with mean equal to actual year 1 sales and standard deviation 50,000. Year 3 sales are normally distributed with mean equal to actual year 2 sales and standard deviation 50,000. The selling price in year 1 is 25,000. The year 2 selling price will be 1.05[year 1 price + 50 (% diff1)] where % diff1 is the number of percentage points by which actual year 1 sales differ from expected year 1 sales. The 1.05 factor accounts for inflation. For example, if the year 1 sales figure is 180,000, which is 10 percentage points below the expected year 1 sales, then the year 2 price will be 1.05[25,000 + 50( 10)] = 25,725. Similarly, the year 3 price will be 1.05[year 2 price + 50(% diff2)] where % diff2 is the percentage by which actual year 2 sales differ from expected year 2 sales. The variable cost in year 1 is triangularly distributed with parameters 10,000, 12,000, and 15,000, and it is assumed to increase by 5% each year. Your goal is to estimate the NPV of the new car during its first three years. Assume that the company is able to produce exactly as many cars as it can sell. Also, assume that cash flows are discounted at 10%. Simulate 1000 trials to estimate the mean and standard deviation of the NPV for the first three years of sales. Also, determine an interval such that you are 95% certain that the NPV of the Racer during its first three years of operation will be within this interval.
A local finance company quotes a 16 percent interest rate onone-year loans. So, if you borrow $26,000, the interest for the year will be $4,160. Because you must repay a total of $30,160 in one year, the finance company requiresyou to pay $30,160y12, or $2,513.33, per month over the next 12 months. Is this a15 percent loan? What rate would legally have to be quoted? What is the effectiveannual rate?
A buyer for a large sporting goods store chain must place orders for professional footballs with the football manufacturer six months prior to the time the footballs will be sold in the stores. The buyer must decide in November how many footballs to order for sale during the upcoming late summer and fall months. Assume that each football costs the chain $45. Furthermore, assume that each can be sold for a retail price of $90. If the footballs are still on the shelves after next Christmas, they can be discounted and sold for $35 each. The probability distribution of consumer demand for these footballs (in hundreds) during the upcoming season has been assessed by the market research specialists and is presented below. Finally, assume that the sporting goods store chain must purchase the footballs in lots of 100 units. Demand (in hundreds) Probability 4 0.30 5 0.50 6 0.20 a) Construct a decision tree to identify the buyer’s course of action that maximizes the expected profit…
BADLY NEED YOUR HELP PLEASE. 1.) True or false? Briefly explain. _____ Your firm has the opportunity to invest $20 million in a new project. The interest rate on the firm’s debt is 7% and the cost of equity is 14%. The cost of capital for the project depends on whether the firm finances the project with new debt or new equity. _____ You are thinking about investing in either stock A or stock B. Both stocks have an expected return of 12%, but stock A has a standard deviation of 25% annually and stock B has a standard deviation of 35% annually. You should invest in stock A since it is less risky. _____ Your firm currently has a debt-to-equity ratio of 10%: debt = $50 million and equity = $500 million (market values). The interest rate on the firm’s debt (rD) is 8% and the cost of equity (rE) is 13%. Since the cost of debt rD is lower than the cost of equity rE, the firm can lower its overall cost of capital by borrowing more. Ignore taxes.
Two companies are producing widgets. It costs the first company q12 dollars to produce q1 widgets and the second company 0.5q22 dollars to produce q2 widgets. If a total of q widgets are produced, consumers will pay 200 - q dollars for each widget. If the two companies want to collude in an attempt to maximize the sum of their profits, how many widgets should each company produce? (The model for this type of problem is called a collusive duopoly model.)
When a company offers a new product or service, they estimate how much of that product or service people will want at different prices. This is referred to as the product or service demand. As the price of a product or service increases, the demand usually decreases, and this drives the price down. Companies use the estimated demand to determine how much of a product or service they are willing to supply at different prices. As the price of a product or service increases, companies are willing to supply more of it because they will earn more money. If you graph the demand and the supply curves on the same xy-plane, they will sometimes intersect at the point where the price and the supply are in equilibrium. Consider the scenario below. Yaseen is a local artist who wants to increase the amount of money she earns every month by selling at-home painting kits. These kits will include a photograph of the finished painting, a link and password to Yaseen’s YouTube channel where she will…