# Single Stage FCFF Model

We now have a fair understanding of what the concepts of free cash flow to the firm is. We also know how to calculate this metric under various circumstances. It is now time to use this metric to arrive at the final valuation for a given firm which is the objective of the whole exercise.

The FCFF metric can be used in various ways to derive the valuation for a firm. One of the most basic ways is called the single stage FCFF model.

In this article we will have a look at this model. It is very basic and is usually not used by analysts. However, it helps in forming a strong base on which the concepts related to slightly complicated models can be built. So let’s begin.

### Similarity with Gordon Growth Model

The best way to introduce this model will be to highlight its similarities with the Gordon Growth model. FCFF valuation is almost analogous to the Gordon model except that it uses other components as inputs to the calculation.

Like the Gordon model, **the single stage FCFF model calculates the value of the firm in two parts**. The first part is called the horizon period. This is the period for which the analyst explicitly forecasts the value of the firm by explicitly forecasting the growth rates. Obviously this can only be done for a short period of time let’s say 5 to 7 years.

However, the firm has a perpetual life and its value can only be calculated by using a perpetuity. This is accomplished by using a terminal value. Once again, the assumptions of the Gordon growth rate model are followed. The long term growth rate that the firm is expected to achieve is always less than the long term discount rate which is being used. Only if this assumption is used, can a finite value be reached.

### Differences with Gordon Growth Model:

There are some differences between the single stage FCFF model and the Gordon growth model. These differences stem from the different inputs that are used by the models:

- the single stage FCFF model uses Free cash flow to the firm as an input whereas the Gordon growth model uses dividends as an input to calculate the value of the firm
- the single stage FCFF model uses Weighted average cost of capital (WACC) at which the value of the firm is discounted whereas the Gordon model uses return on equity as the input
- Lastly, the single stage FCFF model has to make adjustments to include the after tax cost of debt while calculating the weighted average cost of capital.

### Assumptions

There are certain assumptions implicit in this model.

- First is the assumptions that the cash flows of the firm will not change much over the years. They are explicitly forecasted for some years and then a constant growth pattern is assumed.
This model is therefore only useful for very mature companies who have extremely stable cash flows. Since these companies are few and far off, the usage of the single stage FCFF model in the real world is very limited

- Secondly, there is this assumption that the long term growth rate will be less than the long term discount rate. This is the problem with all valuation models since the value of a firm would be infinite is its long term growth rate is more than its long term cost of capital.

**Formula**

Lastly, the formula for calculating the value of the firm using the single stage FCFF model is as follows:

*Terminal Value of the Firm = FCFF (1) / WACC – g *

Where

FCFF (1) is the cash flow that accrues to the firm in the first year post the horizon period

WACC is the weighted average cost of capital

G is the long term growth rate

*WACC itself is calculated as follows:*

*WACC = (w (E) * r (E) ) + (w (D) * r (D) *(1-tax rate) )*

### Using Target Capital Structure

The intention behind conducting this analysis is to ensure that the future valuation of the company is known. Also, we are using the cash flows which will accrue in the future to arrive at the valuation. Hence, it only makes sense that the discount rate being used also depicts the future.

In many cases, the present capital structure as well as the target capital structure for the future may be mentioned in the question paper. Students are expected to use the target capital structure for calculation of the WACC.

This may sound counter-intuitive as present capital structure is a fact and the future capital structure is only a target which may or may not be used by the firm. However, it would still be advisable that the future target structure is used since even the cash flows being discounted are only an assumption!

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