# Single Stage FCFF Model to Equity Valuation

Just like we have the single stage Free Cash Flow to the Firm (FCFF) model, we also have the Free Cash Flow to Equity model. This model also is not used by analysts in advanced calculations. Rather it is used for the most rudimentary back of the envelope calculations for deriving the equity valuation of a given firm. However, this model also forms the basis on which more complex equity valuation models are built. Hence, it is important that we have a good understanding of the working of this model. We will make an attempt to gain the required understanding through this article.

### When Used?

The free cash flow to equity model is primarily used in the case of international valuations. The model becomes even more effective when the multinational company also conducts business is some countries which are prone to high inflation.

In this case, the inputs being used by the free cash flow to equity formula i.e. the cost of equity and free cash flow to equity are much easier to predict than compared to inputs used by other formulas.

### Similarity to Gordon Growth and Single Stage FCFF Models:

The Gordon model, the single stage free cash flow to the firm (FCFF) growth model as well as the single stage free cash flow to equity (FCFE) model all look deceptively similar. The advantage of their similarity is that once you understand one of these models you understand all three. The disadvantage is that it is possible to get confused amongst the subtle differences that these models have.

The thumb rule is to remember that the relevant cash flow metric has to be discounted at the relevant discount rate. Let’s see how this works.

**Differences in Cash Flow:**The Gordon model uses dividends as a measure of cash flow. We have already established that in the previous module. The free cash flow to the firm uses the free cash flow to the firm as an input. It therefore ends up deriving the value of the entire firm as an output. Free cash flow to equity, on the other hand only considers the free cash flow that is due to equity shareholders. The value thus derived is therefore the value of the equity shares of the firm and not the firm itself!**Differences in Discount Rate:**Now since different measures of cash flows are being used, different discount rates also need to be used, isn’t it! Hence in case of free cash flow to the firm, we are using the weighted average cost of capital (WACC) whereas in case of both Gordon model as well as free cash flow to equity model, we are using the Cost of Equity.**Differences in Growth Rate Assumptions:**The rates at which dividends grow is dependent on the firm’s dividend policy. Dividends, therefore do not fluctuate wildly as they are 100% percent within the control of the firm. Free cash flows, both to the firm and equity are not within the control of the company. They are dependent on external factors and may significantly vary from year to year. Hence, while calculating the growth rate for free cash flow to equity, we need to be aware that it could significantly different from the free cash flow to the firm.

Notice that even though Gordon model and free cash flow to equity use different measures of cash flow, they use the same discount rate to discount them. Hence, we have three different measures of cash flow but only two different measures of discount rates. This maybe a possible source of confusion and students may want to pay attention here.

For instance, if a firm takes on a lot of debt, the free cash flow to the firm may not be affected that much. However, once you consider the interest payments and debt repayments that will accrue, the free cash flow to equity may exhibit a very different growth rate as a result of the leverage.

**Formula:**

The formula for calculating terminal value of a firm using free cash flow to equity is as follows:

*Terminal Value of the Firm = FCFE (1) / ROE – g*

Where

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

ROE is the return on equity that accrues to the equity shareholders

G is the long term growth rate

- Once again, for the formula to give a valid answer, the ROE number must be greater than the g number which depicts the growth rate
- Secondly, future assumptions regarding the change in cost of equity may be used to arrive at the return on equity since the cash flows being discounted are also assumptions regarding the future.

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