# One, Two, and Three Stage FCF Calculations

## Single Stage FCFE and International Valuation

• This approach is a variation on the Gordon Growth Method.
• Real cash flows, the real growth rate, and the real required rate of return will be applied to minimize potential distortion caused by inflation and other international differences.

International Stock: V0 = (FCFE0 * (1 + growth rate real)) / (r real - g real)

• Be mindful of the situation, to know if the question requires a total valuation or a per share valuation. If performing a per share valuation, then FCFE would need to be a per-share value to arrive at a stock price.

## Two Stage Valuation

• General Two Stage FCFF Valuation

Vfirm = Σ FCFFt / (1 + WACC)t + [(FCFF n+1 / (WACC - g) × 1/(1+WACC)n]

• General Two Stage FCFE Valuation

Vequity = Σ FCFEt / (1 + rce)t + [(FCFE n+1 / (rce - g) * 1/(1 + rce)n]

• Either the FCFE or FCFF general two stage model may be applied for situations where a high growth phase is expected to shift to a mature growth phase (or where a mature growth phase is expected to shift to a decline phase).

• The first segment of the expression is the present value of the shares in the high growth phase.

• Terminal Value: The second segment of the formula is terminal value of the company at maturity. It is a Gordon Growth Model like valuation performed at the year that stable growth is reached, which is then discounted back to a present value. Correctly calculating and then discounting the terminal value trips up many candidates either through misapplication or calculation errors.

• rce is commonly derived using CAPM for exam purposes.

• This model does not necessarily represent two years, but two stages.

• The first segment of the formula can be calculated for several years and then the terminal value is calculated at the end of the high growth phase.

• It is difficult to achieve full understanding of the two stage model without practice. Candidates must walk through numerous practice problems to be exam ready (and CFAI loves to test this material).

## Three Stage FCF Valuation

• As the name denotes, a three stage model can be applied to cover three phases of a company's growth life cycle (ex. high growth to slower growth to mature growth or high growth to mature growth to decline).
• Candidates are advised to spend time mastering problems for the two stage growth model before becoming overly concerned about the three stage growth model.

### Sensitivity Analysis and FCF Valuation

Because the value calculated in an FCF model is highly sensitive to the inputs; analysts are well served by testing a range of values for assumptions like the discount rate and growth rate.