CFA Level II Exam · Free Cash Flow Valuation

Multistage Free Cash Flow Valuation and Terminal Value

Q: What is the difference between a two-stage and a three-stage FCF model?

A two-stage model has one high-growth period followed by a stable growth period. A three-stage model adds a transition period in which growth declines toward the stable rate. The three-stage version suits firms whose growth fades gradually.

Q: How do you calculate terminal value for FCFF?

Using Gordon growth, TV = FCFF(n+1) ÷ (WACC − g), where g is the stable long-run growth rate. Then discount TV back n years at WACC. The result is a firm value that still needs debt subtracted to reach equity value.

Q: How do you calculate terminal value using multiples?

Multiply the year-n metric by the chosen multiple. For example, EV/EBITDA times year-n EBITDA gives firm terminal value, and P/E times year-n EPS gives equity terminal value. Discount the result n years at the appropriate rate.

Q: Why must the terminal growth rate be less than the discount rate?

The Gordon formula divides by (r − g). If g equals or exceeds r, the result is undefined or negative, which has no meaning. In practice g should also be sustainable, close to long-run economic growth.

Updated 7 October 2026 · Fact-checked

A multistage FCF model values a firm when growth will change over time. You forecast free cash flow for a high-growth period, estimate a terminal value at the end of it using Gordon growth or a market multiple, then discount everything. FCFF uses WACC and gives firm value. FCFE uses the cost of equity and gives equity value.

Understand Multistage Free Cash Flow Valuation and Terminal Value

A single-stage model assumes cash flow grows at one constant rate forever. That fits mature firms. It fails for a firm growing fast today that will slow down later. Multistage models fix this by splitting the future into phases.

In a two-stage model, the firm grows at a high rate for n years, then at a stable long-run rate g forever. In a three-stage model, there is a high-growth phase, a transition phase where growth declines (often linearly), and a mature phase. You can also forecast each year explicitly and only then switch to a constant growth rate.

The value has two parts: the present value of explicit forecast cash flows, plus the present value of the terminal value (TV). TV is the value at the end of the forecast horizon of all later cash flows. It is often the largest part of total value, so small changes in g or the discount rate move the answer a lot.

There are two ways to estimate TV. The Gordon growth method assumes cash flow grows at a constant rate g after year n: TV = FCF(n+1) ÷ (r − g). The market multiple method applies a multiple, such as EV/EBITDA or P/E, to the year-n metric. The multiple method is only as sound as the multiple chosen, and it brings current market pricing into the model.

Match cash flow and discount rate. FCFF is discounted at WACC and gives firm value; subtract market value of debt (and preferred stock) to get equity value. FCFE is discounted at the required return on equity and gives equity value directly. Discounting FCFE at WACC is a classic error.

Key formulas to remember

Multistage firm value (FCFF): Firm value = Σ FCFF(t) ÷ (1 + WACC)^t for t = 1 to n + TV(n) ÷ (1 + WACC)^n; Equity value = firm value − market value of debt − preferred stock (plus non-operating assets if not already included).
Multistage equity value (FCFE): Equity value = Σ FCFE(t) ÷ (1 + r)^t for t = 1 to n + TV(n) ÷ (1 + r)^n; r is the required return on equity.
Terminal value, Gordon growth (FCFF): TV(n) = FCFF(n+1) ÷ (WACC − g) = FCFF(n) × (1 + g) ÷ (WACC − g); Requires g < WACC. Use the long-run sustainable g, not the high-stage rate.
Terminal value, Gordon growth (FCFE): TV(n) = FCFE(n+1) ÷ (r − g) = FCFE(n) × (1 + g) ÷ (r − g); Requires g < r.
Terminal value, multiples: TV(n) = multiple × metric(n); For example EV/EBITDA × EBITDA(n) gives firm TV; P/E × EPS(n) gives equity TV. Match the multiple to firm or equity value.
Multiple implied by Gordon growth: Implied TV/FCFF(n) = (1 + g) ÷ (WACC − g); Use it to cross-check a multiple-based TV against a growth-based TV.

How to solve Multistage Free Cash Flow Valuation and Terminal Value questions

Use this order for any multistage FCF question in a vignette.

1Decide FCFF or FCFE from the question: firm value or equity value. Pick the matching discount rate (WACC or cost of equity).
2Pull the data from the vignette and exhibits: current or forecast cash flows, growth rates by stage, length of each stage, and discount rate. Ignore unrelated figures.
3Build the explicit cash flows. Grow each year by that stage's growth rate. For a three-stage model, step growth down through the transition years.
4Find the terminal value at the end of the last explicit year. Use FCF(n+1) ÷ (r − g) with the stable growth rate, or the multiple times the year-n metric.
5Discount the terminal value back n years, and discount each explicit cash flow by its own year.
6Add the present values. For FCFF, subtract debt and preferred stock to get equity value; divide by shares for value per share.
7Sanity check: g below the discount rate, TV share of value plausible, and the answer in the right units.

Quickest way: Value at the end of the high-growth stage, then discount once

When to use it: Use when the high-growth cash flows are few, or the question gives a single high-growth rate for a short period and then constant growth.

Write down each explicit cash flow for years 1 to n.
Compute TV at year n and add it to the year-n cash flow.
Discount that combined year-n amount once at (1 + r)^n, and discount earlier years separately.
Use a calculator cash-flow worksheet (CF, NPV) to avoid rounding errors across several years.
If the multiple method is asked, skip the Gordon step and multiply directly.

Common mistakes in Multistage Free Cash Flow Valuation and Terminal Value

Using the high-growth rate in the terminal value formula.
The vignette lists several growth rates and the first one is the most visible.
Fix: TV uses the stable growth rate that applies after year n. Label each rate by stage before calculating.
Computing TV with FCF(n) instead of FCF(n+1).
Students forget the formula needs next year's cash flow.
Fix: Multiply FCF(n) by (1 + g) first, or check whether the vignette already gives FCF(n+1).
Discounting TV by n − 1 or n + 1 years.
Confusion about when TV is measured.
Fix: TV is a value at time n, so discount it exactly n years.
Discounting FCFF at the cost of equity, or FCFE at WACC.
Both rates appear in the exhibits.
Fix: FCFF goes with WACC, FCFE with cost of equity. Subtract debt only after valuing FCFF.
Applying an EV multiple to get equity TV, or a P/E to get firm TV.
Multiple names are similar and the question is rushed.
Fix: EV-based multiples give firm value and need debt subtracted. P/E and P/B give equity value directly.
Ignoring that the terminal value dominates the result.
Students check only the arithmetic, not whether the assumptions are reasonable.
Fix: Look at the share of value from TV and at the sensitivity to g and the discount rate when a question asks for an evaluation.

Worked examples

Example 1

Vignette: An analyst values Corvane Ltd using FCFE. Last year's FCFE was 100 million. FCFE will grow 20% a year for 2 years, then 5% forever. The cost of equity is 11%. Corvane has 50 million shares. Q1: What is FCFE in year 2? Q2: What is the terminal value at the end of year 2? Q3: What is the value per share?

Show the solution

Year 1 FCFE = 100 × 1.20 = 120. Year 2 FCFE = 120 × 1.20 = 144.
FCFE in year 3 = 144 × 1.05 = 151.2.
TV at year 2 = 151.2 ÷ (0.11 − 0.05) = 151.2 ÷ 0.06 = 2,520.
PV of year 1 = 120 ÷ 1.11 = 108.108. PV of year 2 = 144 ÷ 1.2321 = 116.873.
PV of TV = 2,520 ÷ 1.2321 = 2,045.28.
Equity value = 108.108 + 116.873 + 2,045.28 = 2,270.26 million.
Value per share = 2,270.26 ÷ 50 = 45.41.

Answer: Q1: 144 million. Q2: 2,520 million. Q3: about 45.41 per share.

Example 2

Vignette: Delmar Corp is valued with FCFF. FCFF for the next 3 years is 80, 90 and 100 million. At the end of year 3, the analyst estimates terminal value using an EV/EBITDA multiple of 8.0 on year-3 EBITDA of 250 million. WACC is 10%. Market value of debt is 600 million and there are 40 million shares. Q1: What is the terminal value? Q2: What is the firm value? Q3: What is the equity value per share?

Show the solution

TV = 8.0 × 250 = 2,000 million. This is a firm-level value, so debt is subtracted later.
PV of FCFF: 80 ÷ 1.10 = 72.727; 90 ÷ 1.21 = 74.380; 100 ÷ 1.331 = 75.131. Sum = 222.238.
PV of TV = 2,000 ÷ 1.331 = 1,502.63.
Firm value = 222.238 + 1,502.63 = 1,724.87 million.
Equity value = 1,724.87 − 600 = 1,124.87 million.
Per share = 1,124.87 ÷ 40 = 28.12.

Answer: Q1: 2,000 million. Q2: about 1,724.9 million. Q3: about 28.12 per share.

Exam tips

Read each growth rate and label it by stage before calculating. Vignettes often include several rates, and only one belongs in the TV formula.
Check whether the vignette gives FCF(n) or FCF(n+1) before applying the Gordon formula.
If a question asks which approach is more reliable, note that TV is often most of the value and is sensitive to g and the discount rate.
With a multiple-based TV, confirm whether the multiple is an enterprise or an equity multiple, then decide whether to subtract debt.
There is no penalty for wrong answers, so never leave an item blank, but do the cash-flow worksheet on the calculator to save time.