On Equation Finance Calculator FCFE Two-Stage Model formula for calculating the FCFE Two-Stage Model

What is the Free Cashflow to Equity Two Stage Model?

The Free Cashflow to Equity Two Stage Model measures the value of equity of a firm that undergoes an erratic stage of unstable growth before settling into a stable growth period. It is from the Gordon Growth Model family of growth valuation formulas. Investors use the FCFE Two Stage model to evaluate the value today of a firm moving from the growth stage into the maturity stage of firm life.

Unlike dividends, FCFE can turn negative in years where a firm requires significant reinvestment needs. However, the implicit assumption is that FCFE will be withdrawn by shareholders in every period.


FCFE Two Stage Model Variables

Expected growth in FCFE will be the result of increasing operating income rather than income from marketable securities held by the firm. Essentially, we are assuming the FCFE will eventually be paid out to shareholders. FCFE for a firm undergoing a period of unstable growth can be calculated using the following variables.

Cost of Equity or Rate of Return to Firm (r)

The cost of equity to the firm. This can also be the rate of return of the investor or the discount rate.

Stable Growth Rate (g)

The final growth rate that the firm reaches once reaching a maturity stage in its growth cycle. This value of growth is assumed to apply to future FCFE payments after erratic growth has settled.

Free Cashflow to Equity for a Given Period (FCFEt)

Free cashflow to equity in period t. In this formula, the period “t” can be any number of periods before a firm reaches maturity, in which it is assumed that payments will grow by a stable growth rate indefinitely.

Number of Periods (t)

The number of periods is the number of unstable growth periods before a firm reaches maturity and achieves a stable state of growth.

Final Period Before Stable Growth Period (n)

This is the final period of unstable growth before stable growth is reached. For example, a firm that has 7 values for unstable FCFE before reaching a stable growth period would have an n value of 7, with the value of FCFE after this final period being the first value for stable growth, as explained below.

First Stable FCFE Value after Stable Growth (FCFEn+1)

The first value of stable growth after period “n”, “n” being the last period of unstable growth. This value is used to calculate the value of a firm indefinitely using the standard DDM calculation, as depicted in the formula above.

Estimated Value of FCFE at Time 0 (V0)

The present value of a firm’s equity to an investor, calculated with the Free Cashflow to Equity Two Stage Model. This value is used by investors to determine whether a firm is viable for investment and thus influences investor decisions. It can be used to compare to other firms within the industry as a form of valuation, or to compare a firm to previous years of its operation in order to measure performance.


How to Calculate the Free Cashflow to Equity Two Stage Model

The FCFE Two Stage Model is designed to value the equity in a firm with two stages of growth; an initial period of higher growth and a subsequent period of stable growth.

Assume a company is going through a growth stage lasting 5 periods. In order, the company makes cashflows of $500,000 in period 1, $650,000 in period 2, $475,000 in period 3, $600,000 in period 4, and $395,000 in period 5 which is the first period of stable growth. After the fourth period the company is assumed to reach maturity and achieve stable growth for every period thereafter, making the FCFE value in period 5 the first payment of stable growth FCFE value (FCFEn+1). The stable growth rate for the company is 5% and the return on equity is 12%. Using the FCFE Two Stage Model, the value for the company can be calculated as follows:

V = Σ(FCFEt / (1+r)t) + (FCFEn+1 / (r–g)) / (1+r)n

V = (500,000 / (1+0.12)1) + (650,000 / (1+0.12)2) + (475,000 / (1+0.12)3) + (600,000 / (1+0.12)4) + (395,000 / (0.12–0.05)) / (1+0.12)5

V = $5,270,148.78

Using the FCFE 2 Stage Model formula, the value of the company to shareholders today is $5,270,148.78.

Although the free cash flow to equity may calculate the amount available to shareholders, it does not necessarily equate to the amount that is paid out to shareholders.


On Equation Finance Calculator example of how to calculate FCFE Two-Stage Model with the On Equation Finance Calculator App

Advantages of the FCFE Two Stage Model

The FCFE Two Stage Model is useful to investors as it allows an investor to evaluate to value of equity that a company may pay out as dividends. This is useful to investors and companies as companies use dividends to signal prerogatives, demonstrate stability, take advantage of tax factors, and meet future investment needs. The FCFE Two Stage model, in contrast to the FCFE Single Stage Model, allows investors to calculate with more depth the value of Free Cashflows to Equity of a company by including factors such as lifecycle stage of the company and varying levels of growth demonstrated by the company.

Although the free cash flow to equity may calculate the amount available to shareholders, it does not necessarily equate to the amount that is paid out to shareholders.


FCFE Two Stage Model Summary

The FCFE Two Stage Model can be used to value companies where the first stage has an unstable initial growth rate and there is stable growth in the second stage, which lasts forever. The first stage may have a positive, negative, or volatile growth rate and will last for a finite period, whereas the second stage is assumed to have a stable growth rate for the rest of the life of the company. In this model, it is assumed that the dividend paid by a company also grows in the same way, i.e., in two stages.


On Equation Finance Calculator App Screen example of FCFE Two-Stage Model with no values loaded in calculator inputs

FCFE Two-Stage Model with On Equation Finance Calculator

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