1. Part I: Checking the Data
The first part of this chapter focuses on checking the data you are using.
2. Importance of Checking Projections
Garbage-In Garbage-Out. The valuation you perform is only as good as the inputs and assumptions you use. The projections are comprised of many different elements and getting comfortable with all of them is important. Typically, the other elements in financial projections are modeled as a function of revenues, such as a percentage of revenue or a percentage of change in revenue.
In this chapter, we will show two common techniques that you can use to test the revenue projections. These are through visual inspection and trend analysis.
3. Visually Inspecting the Data
The first approach sounds simple. It entails plotting the data in a bar chart. To do this in R, we use the barplot() command. For our purposes, we want to separate the historical data from the projected data, so we can use different colors to easily distinguish the two when plotted. We do this by splitting the revenue data into two vectors: hist and proj. Notice that both vectors have 15 elements. The hist vector has the nonzero numbers for the first 10 elements and 0 for the last five, while the proj vector has 0 for the first 10 elements and values for the last five. We combine the two vectors into one data object using rbind(). Then, we can use the barplot() command. The "col" argument allows us to add colors to the barplot and the "main" argument allows us to add a title to the chart.
We then use the "legend" argument of the "legend" command to add labels and then the "fill" argument to add the color marker to the legend that matches the bars. We place the legend in the top-left of the chart because the bars during the first few years appear much lower. In practice, you may have to resort to trial-and-error to find the best position for the legend.
4. Bar Plot
Here is the result of bar chart you created. if we can see a clear break in the historical versus projected trend, we may be able to begin our inquiry of why the projection period is different than the historical period here. However, because the trend seems consistent going through the projection period, we may consider performing a more formal quantitative test on the data.
5. Using Trend Analysis
The setup is a little different. We put both the historical and projected revenues in one vector.
Then, we add a "trend" variable, which takes on the value of 1 for the first observation, 2 for the second observation, and so on. We use the seq() command to do this in R.
Next, we add a dummy variable that equals 0 during the historical period and 1 during the projection period. We use two rep() commands but you can also manually enter the numbers. The first is rep(0, 10), which reflects the historical data. A "0" for the first 10 years. The next is rep(1, 5), which reflects the five years of projections. A "1" for the last five years.
6. Regression Result
Then, we fit a linear regression model using the lm() command and view the summary() of the output. As we can see, the shift variable is positive and is not statistically significant with a p-value of 0.76. This means that there is no significant increase in the revenue trend when going from the historical revenues to the projected revenues. If the increase in revenue trend were statistically significantly, we may have to investigate the cause of the shift. But our revenue projections have passed both the visual inspection and the regression-based trend analysis tests.
7. Let's practice!
Let's practice!