Decision tree, sensitivity and Monte Carlo (Chapter 9)

Question 1

What is a decision tree?

Answer 1

Decisions are often made in several stages. Decision tree analysis is a graphical representation of the alternatives available in each period and the likely consequences of our choices. It estimates what is expected net present value when it is conditional on decisions and outcomes of stochastic variables during earlier stages of the project.
* Decisions: E.g., investment level, technology choice
* Stochastic variables: E.g., sales.

This graphical representation helps identify the best course of action.

Question 2

What is a sensitivity analysis?

Answer 2

“What if”-analysis - examines how sensitive a particular NPV calculation is to changes in the underlying assumptions.

Algorithm for sensitivity analysis:
1. Specify the NPV equation, including cash flow equation
2. Specify base values for stochastic variables in the NPV equation (base assumptions)
3. Calculate NPV using base values
4. For each stochastic variable:
- Decide upon alternative outcomes for the variable (e.g. -20% drop, +20% rise etc.)
- Calculate the NPV under alternative outcomes
- Under sensitivity analysis, one input is varied at a time while all other inputs are assumed to meet their expectations (base assumption)
5. Analyze the effect of alternative outcomes on NPV
- Find which variables have the greatest effect, e.g. by using a ”spider” (also called “star”) diagram.

Question 3

Advantages and disadvantages of sensitivity analysis

Answer 3

Advantages of sensitivity-analysis:
* Recognizes the uncertainty associated with the variables
* Shows how significant any variable is in determining a project’s NPV
* Help in anticipating and preparing for the ”what if” questions that are asked in presenting and defending a project
* Does not depend on probabilities associated with outcomes of variables
* Can be used when there is little information, resources and time for more sophisticated techniques

Disadvantages of sensitivity-analysis:
* Variables are often interrelated
* Sensitivity analysis provides no explicit probabilistic measure of risk exposure
* How likely is a pessimistic or expected or optimistic value and how likely is the corresponding outcome value?
* In other words, sensitivity analysis provides information on the effects of different outcomes of variables on project NPV, but not on the likelihood of these outcomes, and the associated probability distribution of NPV.

Question 4

Scenario analysis

Answer 4

Scenario analysis examine different scenarios, where each scenario involves a confluence of factors. Scenario analysis allow us to look at different but consistent combination of variables.

What happened if Janus biggest competitor starts to make a similar type of underwear?

Question 5

Break-even analysis

Answer 5

Common tool for analyzing the relationship between sales volume and profitability. The focus is on how far sale could fall before the project begins to lose money

Is break-even analysis important?
* Very much so: All corporate executives fear losses. Break-even analysis determines how far down sales can fall before the project is losing money

There are three common break-even measures
* Accounting break-even: sales volume at which net income = 0
* Cash break-even: sales volume at which operating cash flow = 0
* Financial break-even: sales volume at which net present value = 0
We will look at accounting break-even and financial break-even.

Would you be happy about investing in a stock that after 5 years gave you a total rate of return of zero?
* A zero return does not compensate you for the time value of money or the risk you have taken.
* A project that simply breaks even on accounting basis gives you your money back, but does not cover the opportunity cost of capital tied up in the project

Question 6

Monte Carlo simulation

Answer 6

Monte Carlo attempts to model real-world uncertainty and is seen as a step beyond sensitivty or scenario analysis.

Algorithm for Monte Carlo:
1. Specify the basic model

2. Estimate or assume a probability distribution of stochastic variables, e.g. a normal, uniform, lognormal

3. Draw a number from each probability distribution

4. Calculate NPV (or other measures) using the values from step 3

5. Replicate step 3 and 4 many times, e.g. 10000 times.

6. Sort the estimated NPVs and construct the simulated probability distribution.
 If there are 10000 draws, then each value will represent 1/10000 = 0.0001 of the simulated probability distribution

Question 7

Advantages and diadvantages of Monte Carlo-simulation

Answer 7

• A simulation model that attempts to be realistic will also be complex. Difficult to model the underlying probability distribution of each variable. Difficult to model the interactions between variables
• Simulation analysis is sensitive to assumption affecting the input parameters
• GIGO principle: “Garbage in, garbage out”
• Simulation can provide useful information that sensitivity- or scenario analysis cannot give us.

Question 8

Real options

Answer 8

One of the fundamental insights of modern finance theory is that options have value. The phrase “We are out of options” is surely a sign of trouble.

Corporations make decisions in a dynamic environment Choice of options should be considered in project valuation.

The Option to Expand
Has value if demand turns out to be higher than expected

The Option to Abandon
Has value if demand turns out to be lower than expected

The Option to Delay
Has value if the underlying variables are changing with a favorable trend

Real option = flexibility
* The investment flexibility is equal to a call/put option on a stock
* It gives the right, but not the obligation, to make an investment expenditure/abandon the investment
* What is this option worth?