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.