Caterpillar (NYSE:CAT) is a highly profitable company with a sustainable outlook. CAT's strong foothold in its industry along with its keen competitive advantage will enable it to sustain its operations and grow at a favorable, yet variable rate for the next 10 years. Due to findings in academic research, nearly all models used in practice assume that at a point in time the value of a firm or the price of a firm's common stock will continue to grow at a perpetual rate. However, in reality, it is transparent that firms do not grow year after year at a constant rate.

Basic models cannot accommodate nor account for distinct variability among different inputs. Sure, you can model multiple scenarios with the varying inputs, but that stills leaves questions unanswered. What if one variable changes while the other variable remains constant? What if the event only occurs a fraction of the time or only as a result of another event? Answering these questions and accurately forming a conclusion that is statistically significant requires a far more advanced method of modeling. The final output generated by the model is identical in terms of its functional form, but the end result accounts for a wide range of variability basic model fail to incorporate.

In today's world, Monte Carlo Simulation is widely used across the financial industry for variety of different application ranging from complex valuation of various securities and IPOs to multi-variant value at risk models utilized by risk managers. No matter to what level of difficulty the task entails, the fundamental principals of this simulation methodology remain the same. The characteristic feature of this method of simulation is the generation of a large number of random samples from a specified probability distribution or distributions to represent the role of risk in the system. This article is going to show two different valuation models that attempt to place a fair value on CAT's common equity. To test the validity of the assumptions in each model and estimate the probability of the derived price target's occurrence in the model, I will utilize an excel software called Crystal Ball. Crystal Ball, developed by Oracle, is one of the leading spread-sheet based applications for predictive modeling, forecasting, simulation, and optimization. Specifically, it builds on pre-existing Monte Carlo as well as other predictive modeling tools. Crystal Ball's Monte Carlo tools were utilized to run the simulation analysis and carry out the forecast I conducted for CAT. For starters, I am going to begin by walking you through several the assumptions I made in forecasting CAT's financial statement items that are relevant for computing its future free cash flows.

**Financial Statement Analysis And Projections**

In forecasting CAT's financial statements, I took two things into account: historical data and analysts estimates. To forecast CAT's income statement items for FY 2013 to FY 2018, I first extracted CAT's basic income statements items including revenue, cost of goods sold, and operating expenses for FY 2007 to FY 2012. These items allowed me to arrive at the final earnings before interest and taxes (EBIT) figure for each year. The next step involved performing a vertical and horizontal income statement analysis to see the historical averages each account contained as a percentage of total sales as well as the individual growth rate of each item year-over-year. The vertical analysis was useful for estimating the growth rate of revenue because it revealed that over the past five years CAT's revenue increase at an average rate of 13.7% per year. Taking analysts estimates into consideration, in this model I have accounted for total revenue to increase by 10% each year, which I feel is conservative.

*Figure 1: Historical & Forecast Income Statement Items*

**Discounted Free Cash Flow Model**

The discounted free cash flows model is one of the far more accurate models for valuing a firm's common stock. Using CAT's EBIT projections displayed in my forecast above, I computed CAT's expected free cash flows for FY 2013 to FY 2018. The discounted free cash flow model arrive at the per share value by simply dividing the sum of the present value of the free cash flow figure for each year as well as the present value of the terminal value by the number of shares outstanding. Holding CAT's growth rate and its weighted average cost of capital (OTC:WACC) constant, you will see below the derived share price is $105.68. However, due to the presence of uncertainty we must account for the possible variation in CAT's WACC and its perpetual growth rate. Crystal Ball will enable us to arrive at an estimate we are certain has a high probability of occurring.

The first step in Crystal Ball involved defining the assumption and forecast cells, which are both distinguished by the green and aqua highlights below. As you are beginning to understand, the WACC and perpetual growth rate are the two input variables in the model that can vary significantly. Therefore, I have denoted them as assumptions modeling them in a distribution that is suited for each. For CAT's WACC, I used a BetaPERT distribution and analyzed the historical fluctuations in CAT's WACC to determine the minimum, likeliest, and maximum vales. As you will see below, I used CAT's current WACC of 8.3% as the most likely value. For the minimum and maximum values, I used the historical eight year high and low of CAT's WACC. The perpetual growth rate was modeled using a triangular distribution with minimum, likeliest, and maximum values of 4%, 5%, and 6%, respectively. Next, I defined the forecast as the fair value per share for FY 2013 and to increase accuracy I defined the second forecast as the log of the fair value per share.

*Figure 2: DFCF Model & Assumptions*

After running a simulation of 500,000 trials, Crystal Ball generated the graph shown below. The simulation revealed a mean and median that were basically identical, which allowed me to assume a normal distribution and to forecast the share price of CAT if it were to fall exactly one standard deviation either above and below the mean. The shaded blue area in the figure below represents the range where CAT's stock price will most likely fall within by the end of FY 2013. To transform the numbers below to a corresponding dollar values shown above in figure 2, I took the exponential function of the mean as well as one standard deviation above and below the mean using the excel function (=EXP). According to the normal distribution, approximately 70% of all observations in the sample fall within one standard deviation above and below the mean (which is the blue area below in figure 3). In conclusion, there is a 70% probability CAT's stock price will be between $87.62 and $195.39 at the end of FY 2013.

*Figure 3: DFCF Simulation Output*

**Dividend Discount Model**

The dividend discount model is similar to the discounted free cash flow model in terms of how both models involve summing all the present values of a future projection, however the dividend discount model replaces the WACC with the required rate of return on equity. Instead of free cash flow estimates, I used dividend projections that at take into account the historical growth rate of CAT's dividends and estimates from several analysts. The historical dividend data and my forecast are shown below in figure 4.

The assumption and forecast cells were defined in the same process as the previous model, except you will notice I have added one additional assumption in this model. Given there are a number of external factors that can potentially impact CAT's dividends, I felt it was only appropriate to account for the variability in the dividend growth rate for each year on a stand alone basis. For this assumption, I assumed a log-normal distribution with a mean and standard deviation of 13% and 17%, respectively. The required rate of return on equity was defined as a BetaPERT distribution with minimum, likeliest, and maximum values of 6.3%, 8.8%, and 11.5%, respectively. These values were assigned based on the differences in CAT's historical required rate of return on equity, which was computed using the Capital Asset Pricing Model (CAPM). The perpetual growth rate was defined as a triangular distribution with the same parameters as in the previous model. Also, the forecast cells deriving the fair value per share and the log of the fair value per share were defined the same as they were in the previous model.

*Figure 4: Dividend Discount Model & Assumptions*

Using the same number of simulation trials, Crystal Ball generated the output shown below. Note I used the log-normal distribution for this model as well. Therefore, it required taking the exponential function of the mean as well as the value of one standard deviation above and below the mean in order to arrive at the range of price estimates. In conclusion, there is a 70% probability that CAT's stock price will be between $67.42 and $152.78 at the end of FY 2013.

*Figure 5: Dividend Discount Simulation Output*

**What To Take From This?**

Every model provides room for variation, but the ability to reduce the possibility and quantity of the variation across the model is the ultimate key to arriving at accurate estimates. As you have seen, the estimates I have provided in this model account for a wide range of variability that incorporate factors that internal to CAT as well as external factors out of CAT's control. It is important to understand these models are intended primarily for risk management and that is why the price target range may seem quite significant. However, you will shortly understand why the interpretation of the model becomes key. To recap, the first model concluded there is a 70% probability of CAT's stock price being between $87.62 and $195.39 at the end of FY 2013. Instead if we look at it differently, what some like to call the glass half empty, we can also conclude there is a 15% probability of CAT's stock price being below $87.62. This also implies there is a 85% probability CAT's stock price will be above $87.62. The second model concluded there is a 70% probability of CAT's stock price being between $67.42 and $152.78 at the end of FY 2013, which is merely the same as saying there is 15% probability CAT's stock price will be below $67.42 at the end of FY 2013.

Overall, these models are excellent tools for evaluating the potential risk of an investment opportunity. Not only do these models allow investors to forecast the probability of a firm's stock falling within a specific price range, but they place a probabilistic measure on the potential downside risk. The ability to account for a broad range of variability makes these models unique and highly accurate. In conclusion, CAT's profitable operations and strong growth prospects support the conclusions of these models. I am long CAT.

*Sources: The graphs were generated using Oracle Crystal Ball and the Excel templates were created by me.*

**Disclosure: **I am long CAT. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.