Any good financial model will usually contain scenario and sensitivity analysis functionality, at least to some degree. Scenarios are an important part of financial modelling, and the reason we have left this to near the end of the book is that it is usually a task performed at the end of the model-building process. If the model has been properly designed using best practice, it is not difficult to add, edit, and change scenarios in the model.
Scenarios and sensitivity analysis are great ways to insulate your model from risk. What would be the absolute worst that could happen? If everything that can go wrong does go wrong, will my business/project/venture still be okay? There are usually effects and interactions between multiple variables that may change in the model.
Scenarios can assist with decision analysis. They are laid out in advance so that decision-makers can see the expected impact of each course of action. How close to reality these scenarios are really depends on the accuracy of the assumptions implicit in the model—but that's another story! (See “Document Your Assumptions” in Chapter 3.)
Scenario analysis is a very important part of financial modelling—in fact, in some cases, being able to perform a scenario analysis is almost the whole point of building a financial model in the first place! Many of the principles of best practice in financial modelling discussed in earlier sections were to ensure that the model is set up in such a way that scenarios can easily be included in our model.
There are several different technical methods of creating scenarios and sensitivities in financial models, which we will discuss, but all scenarios involve changing input variables to see the impact of the change on the model outputs. By following good practice when building the model in the first place—particularly when it comes to linking to the source, and only entering data once—creating scenarios and sensitivities in the model is quite simple. (See Chapter 3, “Best Practice Principles of Modelling”.) With a well-built model that has all inputs linked to outputs, it is relatively easy to change inputs and watch the outputs change.
Building scenarios is a task normally best left to the end of the model-building process, because we need to get the model design and layout finalised and make sure the model is working correctly before we can change the input assumptions by adding scenarios. As with many complex model functions, perform a simple task first, then test it, check it, and make sure it is correct, before adding more complexity, such as scenarios.
Scenario analysis, sensitivity analysis, and what-if analysis are really only slight variations of the same thing.
A sensitivity analysis, otherwise known as a what-if analysis, in financial modelling refers to the process of tweaking one key input or driver in a financial model and seeing how sensitive the model is to the change in that variable. Scenarios, on the other hand, involve listing a whole series of inputs and changing the value of each input for each scenario. For example, a worst-case scenario could include interest rates increasing, the number of new customers being less than expected, or unfavourable exchange rates.
Scenarios should really focus on the area or assumption around which we have the least certainty. For example, let's say we are analysing the costs of reducing carbon emissions:
Scenario | Fossil Fuel Prices | Non-fossil Fuel Technology Costs |
Best Case | 10% | +10% |
Likely Case | – | – |
Worst Case | +10% | 10% |
In this very simple example, you could model the prices that you think are most likely and then tweak each of these up or down.
It is possible to create many more than three scenarios in a financial model. I'm often asked how many scenarios should be in a model, and it really depends on the amount of time and the degree of detail and certainty that are required for the model. Three scenarios, as shown in this example, should be a minimum. It's possible to have 20, 30, or even 50 scenarios modelled, but it does become rather unwieldy and confusing so unless you really need them, I'd probably recommend sticking to around a dozen scenarios.
In a volatile economic environment, creating a business case for a new project or product that contains financial projections is an extremely difficult task. Looking at historical data and extrapolating the numbers to create future projections simply doesn't cut it any more. Creating a business case is imperative for companies to plan for the future, attract investor funding, and gain approval for projects, although most of the time there is so much uncertainty involved that financial projections are way off the mark. How do we create a financial model for a business case that is not complete guesswork?
Thorough stress testing, along with scenario and sensitivity analysis, will provide a business case that has the rigour and robustness to cope with various fluctuations in economic inputs. At an absolute minimum, any business case financial model should have a best, base, and worst-case scenario. The scenario analysis may include answers to the following questions, as well as others specific to the industry. Obviously, particular attention should be paid to the downside!
Of course, if you count on the worst-case scenario, you'll probably end up doing nothing, and you definitely won't get any funding or approval! However, by creating a well-built, robust financial model, we can know exactly what the possible outcomes are so that we can show we are prepared for the best or worst eventualities.
Following the global financial crisis, there was quite a lot of discussion on the importance of stress testing businesses, and I need to point out that this is quite different from stress testing a financial model. Stress testing a business involves putting the business's financial forecasts through scenario modelling. Stress testing a financial model is more about testing the technical inner workings of the model (i.e., varying the inputs to see how much the outputs change).
Strategies to stress test a model include:
Stress testing your financial model by way of scenario and sensitivity analysis will help you be prepared for varying outcomes as a result of fluctuating external factors. Once you have completed your financial model, you should stress test the workings of the model to ensure that it is robust and accurate.
Many people will create a financial model and save it as a base case. Then they change all the numbers and save it as a worst case. Then they change all the numbers again and save it as a best case. Whilst this method will work, it's not a very efficient way of performing scenario analysis. If a subsequent change needs to be made to the model, it will need to be made several times, and there is a high possibility that an error will be made between the different versions.
Let's take a look at the technical methods available in Excel for creating scenarios and sensitivities, which will provide a much better way of building models. Essentially, there are three ways:
Creating scenario analysis using manual drop-down boxes means that you can only view one scenario at a time.
In-Cell Drop-Downs (Using Data Validation) In an in-cell drop-down, the value sits within the cell of data validation drop-down box. See Figure 11.1.
In this case, the modeller has limited the valid entries to this cell to one of three options: Best Case, Base Case, or Worst Case. This is the easiest and most commonly used type of drop-down box.
See “Bulletproofing Your Model” in Chapter 7 for how to create a data validation drop-down box, and “Comparing Scenario Methods” later in this chapter for a practical exercise on how to use them in scenario analysis.
Object Drop-Downs (Using Combo Boxes) There is very little difference from the user perspective with a combo box drop-down, but it's built very differently. See Figure 11.2.
This type of box is an object that sits on top of the sheet, rather than within the cell itself. If you look very closely, you can see that the box is sitting across several cells instead of within a single cell. This type of box is a little more difficult to build, but is easier for the user, as the drop-down arrow appears all the time, rather than only when the cell is selected.
See “Form Controls” in Chapter 7 for how to create a combo box drop-down, and “Comparing Scenario Methods” later in this chapter for a practical exercise on how to use them in scenario analysis.
Scenario Manager is an Excel tool in which you can create multiple scenarios. Once it is set up, the user can select a scenario, and input cells will change automatically. Scenario Manager is fairly limited and is not particularly helpful in large and complex models. It is therefore not a very widely used tool for scenarios in financial modelling. See Figure 11.3.
Scenario Manager is a tool that has been grouped together with Goal Seek and Data Tables in the What-if Analysis section of the Data tab. Being grouped with other tools that are so useful would lead the aspiring modeller to believe that Scenario Manager is also a critical tool to know. However, despite its useful-sounding name and the good company it keeps, Scenario Manager is quite limited in its functionality and is not particularly helpful in large and complex financial models. It is therefore not commonly used by expert financial modellers; however, for the sake of completeness, we will cover it very briefly in this chapter.
Let's take a very simple example of a person creating her personal budget for next year. Let's assume that she does not know what her mortgage payments will be, due to the changing rate of interest, or how much her travel railcard will cost.
You can define different scenarios and then switch between them to do what-if analysis to see if she will end up in debt or be able to afford a holiday. Scenarios work best on complex spreadsheets where there is a large knock-on effect from changes in the variable data.
Scenarios are created and managed using the Scenario Manager in the following 13 steps:
As we can see, Scenario Manager is a rudimentary tool, which simply changes hardcoded numbers. It's not very easy to see, display, or print the different options unless we go into the Scenario Manager tool. Using the summary tool creates a summary report of the scenarios created, but they are not dynamic or interactive and are therefore of little use as a modelling tool. The biggest downfall of Scenario Manager is that the user cannot see the results on the sheet unless she actually goes in to view the scenarios.
Data tables are one of the more advanced and complex financial modelling tools. They can be used for scenarios and sensitivity analysis, but they are not as commonly used as drop-down scenarios, mostly because users don't know much about them. Because data tables use array formulas, they are unlike most other formulas in that you cannot trace dependents, and they are very difficult to follow unless you are familiar with them.
Note that a modeller who is not familiar with data tables will be unable to edit the table, or make any changes.
Let's create an interest rate calculator upon which we can test the sensitivity of monthly repayments to changes in interest rates and loan terms.
One-Variable Data Table The data table presents a body of data derived from a function. The rows and columns of the table are drawn from one or two of the inputs or variables fed to the function. In this case, the data comes from the results of the PMT function, using the interest rate variable (cell B8).
Limitations of Data Tables We can see from the example above that data tables are a great way to look at multiple scenarios or sensitivity analyses one at a time. Instead of manually changing the interest rate or the term of the loan, we can display at a glance the impact of these changes.
However, data tables have a few limitations that make them inappropriate for some scenarios or sensitivity analysis situations. These three limitations are:
Data tables are extremely useful when, as in the example shown above, you want to see the incremental change of one or two inputs on a single output. For example, how much does my profit margin change if I change my price from $450 to $460, $470, $480, $490, or $500? A data table would not be an appropriate solution if the output of your financial model were a full set of financial statements, for example. In this situation, a drop-down scenario would be most appropriate.
A data table is a good opportunity to use conditional formatting with a formula. We can use advanced conditional formatting to enhance a two-variable data table, making it more visually interesting and interactive for the user.
Our final result will look similar to Figure 11.11, using the term of the loan and the interest rate as the two variables to drive the conditional formatting. You can find the completed version as shown in Figure 11.11 at www.plumsolutions.com.au/book. If you change the interest rate in cell B8 from 7.5 to 7 percent, the row currently being highlighted will change from row 10 to row 9. Similarly, if the term of the loan is changed in cell B10 from 25 to 30, the column currently being highlighted will change from column G to column H. In this way, we can see at a glance which inputs have been selected currently in the model.
For a review of the basics, see “Conditional Formatting” in Chapter 7. As you know, conditional formatting allows you to apply formats to a cell or range of cells and have that formatting change depend on the value of the cell (or the value of a formula).
In this particular example, we want the interest rate and term to intersect at the appropriate repayment instalment. As the variables to the PMT function are changed, the intersection point will move to spotlight the repayment amount.
One way we can accomplish this is to apply conditional formatting by means of a formula to each row within the table and, likewise, to each column. For instance, in Figure 11.12, we can stipulate that if cell E10 is equal to the interest rate (B8), then Excel must colour row 10 within the table.
This would require 10 formulas if we were to cover each of the six interest rates and each of the four terms. However, we can accomplish the exercise with two formulas only: the first locks either the rows or columns with absolute references; the second allows other elements of the cell address to float across the row or up and down the column by using relative references. This exercise illustrates how this is done.
Let's create a very simple property development feasibility model to demonstrate the difference between the methods of scenario analysis. You are considering purchasing an empty block upon which you are considering developing a residential villa complex. You can find this template, along with the accompanying models to the rest of the screenshots in this book, at www.plumsolutions.com.au/book.
The assumptions are:
To create the working model, follow these eight steps:
We have now completed the workings of the model and are ready to add some scenarios. Note that this is a very simple one-page model, which we will use to demonstrate how to build scenarios. Your model can be a lot more complex than this, containing many more pages and calculations, but the methodology for creating a scenario will be exactly the same.
The two input variables that we think are the most likely to change are the building cost and the sale price per square metre. Note that because of the way we have built this model, with these assumptions hardcoded and all the calculations linking to these inputs, we can quite easily change these inputs manually and this will affect the output of the model. We can see that if the building costs were to decrease from $1,500 to $1,200 per square metre, this would increase the profit margin to 24 percent. Additionally, if the sale price were to increase from $3,000 to $3,300 per square metre, this would increase the profit margin further to 31 percent.
You can see that we can also manually change the sales commission and the total number of square metres in the development, although we have determined that these are unlikely to change.
Creating Built-In Scenarios Using a Data Validation Drop-Down Tweaking these input variables manually is a form of sensitivity or what-if analysis, but it's difficult to control and not very auditable. It's much better practice to build some predefined scenarios into the model, and allow the user to switch between the scenarios using a drop-down box.
Let's build some scenarios using this 10-step method:
Creating Scenarios Using a Combo Box Drop-Down Now that we've got our scenarios working, let's take a look at what we could achieve using a combo box drop-down instead. To review how to create a combo box, refer to the “Form Controls” section in Chapter 7.
If you are using the template provided, choose the next tab across, called “Combo Drop-Down”. If you are creating this model from scratch, then leave the scenario model we've just created intact, and make a copy of the sheet by right-clicking on the sheet tab at the bottom. Select Move or Copy and then select Create a Copy and click OK.
What's the Difference Between a Data Validation and Combo Box Drop-Down? From the user perspective, the data validation and the combo box drop-down should be almost indistinguishable from each other. They both work in the same way: the user selects from a drop-down list, and the model will change. However, there are a few key differences from the model developer's perspective:
As shown in Figure 11.24, combo boxes will not work if the source data is oriented horizontally instead of vertically.
Let's take a look to see if we could achieve the same result on our property development feasibility model using a data table method of scenario analysis instead of a drop-down box.
If you are using the template provided, choose the next tab across, called “Data Table”. If you are creating this model from scratch, then leave the scenario model we've just created intact, and make a copy of the sheet by right-clicking on the sheet tab at the bottom. Select Move or Copy, then select Create a Copy and click OK.
Instead of creating base, best, and worst-case scenarios from which users need to select the scenario that they want to display, we are instead going to create a single matrix in six steps, where users can see simultaneously the results of different inputs. If you've copied the sheet, then you'll need to change the design of the model to look like Figure 11.25 in order to create this scenario analysis using a data table instead.
This gives us exactly the same results as the drop-down box options, but instead of having to flick through the drop-downs, the user can see at a glance all the results of the different scenarios simultaneously.
In this situation, the data table is an appropriate option for displaying the sensitivity of our profit margin to changes in inputs (because the inputs and outputs are all on one page, and we are only interested in a single output). We do lose some detail by using the data table method, as we cannot see, for example, the building cost amount under each different scenario, only the final outcome.
This feasibility model shows clearly the difference between three of the scenario methods. We have chosen not to use Scenario Manager because, even though it is perfectly possible for this model, it is not a particularly useful tool. In this example, the data validation drop-down, combo box drop-down, and data table scenario analysis methods are all suitable. However, it really depends on the size, layout, and required output of the model as to which method is best to use.
After completing the last exercise, we can see from the results of our sensitivity analysis—as shown in the completed data table in Figure 11.27—that the expected profit margin from our financial model will be anywhere between a profit of 29 percent and a loss of 5 percent. In order to actually help the decision-making process, a good financial modeller will try to narrow down the possible outcomes. One way of doing this is to apply some probability to each outcome and then calculate the probability-weighted predicted outcome.
Let's assume that the base case is the most likely, and assign a probability of 50 percent to that outcome under each variable. We then need to assign probabilities to the worst and best cases as well.
In this chapter, we have covered the different tools that are available in Excel for scenarios and sensitivity analysis. Depending on the inputs and outputs for the scenarios, different tools are most appropriate.
As discussed, the drop-down method is the most popular, as that allows for many different scenario inputs as well as outputs. Scenario Manager is not a particularly useful tool, and data tables are most useful for sensitivity analysis where there are a maximum of two input variables, and only one output that needs to be shown. Whilst there are several different scenario tools available, the methodology and logic behind creating the scenarios remain the same.
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