Question 1

Perform a simulation assuming the plant will be designed to meet the expected demand. Use RISKSIMTABLE with a range of possible values to help the firm decide what the plant capacity should be. Briefly explain why designing the plant for the expected capacity is clearly not the optimal solution.

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Question 2

Consider a device that requires two batteries to function. If either of these batteries dies, the device will not work. Currently there are two brand new batteries in the device, and there are three extra brand new batteries. Each battery, once it is placed in the device, lasts a random amount of time that is triangularly distributed with parameters 15, 18, and 25 (all expressed in hours). When any of the batteries in the device dies, it is immediately replaced by an extra (if an extra is still available). Use @RISK to simulate the time the device can last with the batteries currently available.

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Question 3

Estimate the mean and standard deviation of the NPV of this project. Assume that cash flows are discounted at a rate of 10% per year.

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Question 4

Estimate the mean and standard deviation of the NPV of this project. Assume that cash flows are discounted at a rate of 10% per year. Now assume that the project has an abandonment option. At the end of each year you can abandon the project for the values given below:  For example, suppose that year 1 cash flow is $400. Then at the end of year 1, you expect cash flow for each remaining year to be $400. This has an NPV of less than $6200, so you should abandon the project and collect $6200 at the end of year 1. Estimate the mean and standard deviation of the project with the abandonment option. How much would you pay for the abandonment option? (Hint: You can abandon a project at most once. Thus in year 5, for example, you abandon only if the sum of future expected NPVs is less than the year 5 abandonment value and the project has not yet been abandoned. Also, once you abandon the project, the actual cash flows for future years will 0. So the future cash flows after abandonment should disappear.)

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Question 5

Perform a simulation assuming the plant will be designed to meet the expected demand. Use RISKSIMTABLE with a range of possible values to help the firm decide what the plant capacity should be. How many units of capacity do you think the plant should be built? Explain.

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Question 6

What is the appropriate distribution for the probability of competitor entry?

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Question 7

Suppose you have invested 25% of your portfolio in four different stocks. The mean and standard deviation of the annual return on each stock are as shown below. The correlations between the annual returns on the four stocks are also shown below. 
-What is the probability that your portfolio's annual return will exceed 20%?

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Question 8

An executive has been offered a compensation package that includes stock options. The current stock price is $30/share, and she has been offered a call option on 2000 shares, which can be exercised five years from now at a price of $42/share. Therefore, if the market price of the shares in five years is more than $42/share, she can buy 2000 shares at $42/share, and then immediately sell the shares at the market price, earning a riskless profit. If the market price of the shares was less than $42/share, she will obviously choose not to exercise the option, and would have zero profit.
Assume the price of the stock can be modeled as exponential growth (compounding), which could be calculated as:  where,  stock price in next period (i.e., price next year)  current stock price  annual growth rate of the stock price, which has been 10%  annual volatility, which is estimated to be 18%  normal random variable with mean of zero and standard deviation of 1
-Simulate the price of the stock in five years by calculating five annual increments (steps) with this model, starting from the current price of $30/share. For each price simulated five years from now, model the exercise decision and calculate the resulting profit, which should then be discounted for five years at the current discount rate (5%) to obtain the present value of the options. What is the expected value of the stock options?

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Question 9

(A) Estimate the mean and median value of your investment after 100 years.
(B) Explain the large difference between the estimated mean and median.

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Question 10

Suppose this new drug will cost $3 million to develop. What is the chance that we could loose money on this project?

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Question 11

What is the appropriate distribution for initial market size?

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Question 12

If the warranty period were reduced to 2 years, how much per year in replacement costs would be saved?

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Question 13

Suppose you have invested 25% of your portfolio in four different stocks. The mean and standard deviation of the annual return on each stock are as shown below. The correlations between the annual returns on the four stocks are also shown below. 
-What is the probability that your portfolio will lose money during the course of a year?

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Question 14

The executive thinks the growth rate could shrink to 7% per year if the company has growing pains, but on the other hand it could be as high as 15% per year if the company prospers. What is the expected value of the stock options in those cases?

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Question 15

Develop an @RISK model to estimate the NPV given an assumed capacity. What are the variable inputs and outputs?

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Question 16

Perform a simulation with this model. What is the expected NPV? What is the standard deviation?

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Question 17

(A) Assuming we are risk neutral, use simulation to find the optimal capacity level.
(B) Using the answer to (A), there a 5% chance that the actual discounted profit will exceed what value?
(C) Using the answer to (A), there is a 5% chance that the actual discounted profit will be less than what value?
(D) If we are risk averse, how might the optimal capacity level change?

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Question 18

What is the appropriate distribution for the market growth rate?

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Question 19

Estimate the fraction of all refrigerators that will have to be replaced.

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Question 20

Perform a simulation assuming the plant will be designed to meet the expected demand. Use RISKSIMTABLE with a range of possible values to help the firm decide what the plant capacity should be. For each simulation what is the probability of exceeding $75,000 in NPV?

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Quiz 16: Simulation Models

Perform a simulation assuming the plant will be designed to meet the expected demand. Use RISKSIMTABLE with a range of possible values to help the firm decide what the plant capacity should be. Briefly explain why designing the plant for the expected capacity is clearly not the optimal solution.

Estimate the mean and standard deviation of the NPV of this project. Assume that cash flows are discounted at a rate of 10% per year.

Perform a simulation assuming the plant will be designed to meet the expected demand. Use RISKSIMTABLE with a range of possible values to help the firm decide what the plant capacity should be. How many units of capacity do you think the plant should be built? Explain.

What is the appropriate distribution for the probability of competitor entry?

(A) Estimate the mean and median value of your investment after 100 years. (B) Explain the large difference between the estimated mean and median.

Suppose this new drug will cost $3 million to develop. What is the chance that we could loose money on this project?

What is the appropriate distribution for initial market size?

If the warranty period were reduced to 2 years, how much per year in replacement costs would be saved?

The executive thinks the growth rate could shrink to 7% per year if the company has growing pains, but on the other hand it could be as high as 15% per year if the company prospers. What is the expected value of the stock options in those cases?

Develop an @RISK model to estimate the NPV given an assumed capacity. What are the variable inputs and outputs?

Perform a simulation with this model. What is the expected NPV? What is the standard deviation?

What is the appropriate distribution for the market growth rate?

Estimate the fraction of all refrigerators that will have to be replaced.

Perform a simulation assuming the plant will be designed to meet the expected demand. Use RISKSIMTABLE with a range of possible values to help the firm decide what the plant capacity should be. For each simulation what is the probability of exceeding $75,000 in NPV?