Exam 16: Simulation Models

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.)

Which function is often required in simulations where we must model a process over multiple time periods and take the uncertain timing of events into account?

In a marketing and sales model,what might be a good choice for a discrete distribution to model the random timing of sales?

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.

In a bidding model,once we have a bidding strategy that maximizes the expected profit,we should no longer consider the bidder's aversion to risk.

Although we can determine the optimal bid and the expected profit from that bid in a bidding simulation,we usually cannot determine the probability of winning.

Churn is an example of the type of uncertain variable we deal with in financial models.

In investment models,we typically must simulate the random investment weights.

Simulate Amanda's portfolio over the next 30 years and determine how much she can expect to have in her account at the end of that period.At the beginning of each year,compute the beginning balance in Amanda's account.Note that this balance is either 0 (for year 1)or equal to the ending balance of the previous year.The contribution of $5,000 is then added to calculate the new balance.The market return for each year is given by a normal random variable with the parameters above (assume the market returns in each year are independent of the other years).The ending balance for each year is then equal to the beginning balance,augmented by the contribution,and multiplied by (1+Market return). ​ Next,suppose Amanda's broker thinks the stock market may be too risky and has advised her to diversity by investing some of her money in money market funds and bonds.He estimates that this will lower her expected annual return to 10% per year,but will also lower the standard deviation to 10%.Suppose again that Amanda will stop investing in the stock market and transfer all of her retirement into a savings account if and when she reaches $500,000.When can she expect to reach this goal under the more conservative investing strategy?

A @RISK output range allows us to obtain a summary chart that shows the entire simulated range at once.

Which two random variables are typically simulated as inputs in bidding models?

A key objective in cash flow models is often to determine the amount of debt that must be taken out to maintain a minimum cash balance.

In warranty cost models,the key input random variable is product lifetime.

Suppose we are using a marketing simulation model to determine the expected profit under conditions of uncertain customer loyalty.In this case,we should use an optimization model to determine the optimal amount to spend on increasing customer loyalty.

Which of the following is an appropriate distribution,especially when a right-skewed distribution of a nonnegative quantity is desired?

We can use the RISKSIMTABLE function to summarize the results of a single simulation of product lifetime.

A common distribution for modeling product lifetimes is the binomial distribution.

Financial analysts often investigate the value at risk (VAR)with simulation models.VAR is an indicator of _____ for a project.

Cash balance models are an example of which category of simulation application?

The @RISK function RISKUNIFORM (0,1)is essentially equivalent to RAND().