CFA Level II Exam · Free Cash Flow Valuation

Sensitivity Analysis and Practical Issues in FCF Valuation

Updated 7 October 2026 · Fact-checked

Sensitivity analysis shows how FCFF or FCFE value changes when one input, such as the discount rate or growth rate, changes. Practical issues include negative FCF, non-operating assets, and choosing between FCF models and the dividend discount model. Rebuild the value with the changed input, then compare results.

Understand Sensitivity Analysis and Practical Issues in FCF Valuation

A free cash flow model gives one value from a set of forecasts. But the inputs are estimates. Sensitivity analysis changes one input at a time, such as the growth rate, the discount rate, or the operating margin, and recomputes the value. It shows which assumptions matter most and how wide the range of value is.

In a constant-growth model, value = FCF1 ÷ (r − g). The value is very sensitive to the gap r − g. When g is close to r, a small change in either one moves value a lot. A one-point rise in the discount rate cuts value more when the spread is small. For a multistage model, the terminal value often carries most of the total value, so the terminal growth rate and the exit multiple drive the answer.

Some practical issues come up often. Negative FCF is common in young or fast-growing firms because capital spending and working capital investment exceed operating cash flow. You cannot apply the constant-growth formula to a negative FCF. Instead, forecast FCF until it turns positive and stable, then value the terminal point. Alternatively, use another model, such as a multiple-based or residual income approach. Also check why FCF is negative. Negative FCFF from heavy investment may be fine. Negative FCFF from poor operations is not.

Non-operating assets matter in FCFF valuation. FCFF captures cash flow from operations, so the firm value from discounting FCFF at WACC covers only operating assets. Add the value of excess cash, marketable securities and non-operating investments, then subtract debt and preferred stock to reach equity value. Do not double count: do not add the cash flows from these assets into FCFF as well.

Choosing a model: use the dividend discount model when dividends are stable and tied to earnings and the investor holds a minority stake. Use FCFE when dividends differ from the firm's capacity to pay, when the firm pays no dividends, or when you take a control perspective. FCFE equals dividends only when the firm pays out all FCFE. Otherwise, retained FCFE makes the FCFE and DDM values differ. FCFF suits firms with changing leverage or negative FCFE, since FCFF is not affected by debt flows and uses WACC.

Key formulas to remember

Constant-growth FCFF firm value: Firm value = FCFF1 ÷ (WACC − g); Requires WACC > g and a stable growth, stable capital structure.
Constant-growth FCFE equity value: Equity value = FCFE1 ÷ (r − g); r is the required return on equity.
Equity value from FCFF: Equity = Firm value (operating) + non-operating assets − debt − preferred stock; Use market or fair values of the claims. Do not include non-operating asset income in FCFF.
Multistage terminal value: TV at n = FCF(n+1) ÷ (r − g), or TV = multiple × metric at n; Discount TV back n periods along with the explicit-period flows.
Sensitivity method: Change one input, hold others constant, recompute value; Compare percentage change in value across inputs to rank importance.

How to solve Sensitivity Analysis and Practical Issues in FCF Valuation questions

Use this order for any vignette question on sensitivity or practical issues in FCF valuation.

1Identify the cash flow in the exhibit (FCFF or FCFE) and the matching discount rate (WACC or cost of equity).
2Check the sign and stability of FCF. If negative or erratic, do not apply the single-stage formula to it.
3Find any non-operating assets, debt and preferred stock in the balance sheet exhibit.
4Compute the base value, or take it from the vignette if given.
5Change only the input the question names. Recompute, or reason using r − g.
6Convert firm value to equity value if the question asks about per-share value.
7Compare the result with the base case and state the direction and size of change.
8If the question asks which model fits, match the firm's facts to the model conditions (dividends, control, leverage, FCF sign).

Quickest way: Spread shortcut for r − g

When to use it: When a question asks how value changes after a change in the discount rate or growth rate in a constant-growth model.

Value is proportional to 1 ÷ (r − g), so compare old and new spreads.
New value ÷ old value = old spread ÷ new spread.
Multiply the base value by that ratio. Do not recompute FCF1 unless g changes it.
Note that a change in g also changes FCF1 if FCF0 is given, so recompute FCF1 = FCF0 × (1 + g).

Common mistakes in Sensitivity Analysis and Practical Issues in FCF Valuation

Applying the Gordon growth formula to a negative FCF.
Students plug numbers in without checking the sign, which gives a negative value.
Fix: Forecast FCF until it turns positive and stable, then use the terminal formula at that point.
Adding non-operating assets to FCFF and also counting their income in FCFF.
Students want to be thorough and include both.
Fix: Keep FCFF operating only. Add the asset value once at the equity bridge.
Forgetting to subtract debt and preferred stock after discounting FCFF.
Students treat the WACC-based value as equity value.
Fix: Discounting FCFF at WACC gives firm value. Subtract debt and preferred to get equity.
Using WACC to discount FCFE or the cost of equity to discount FCFF.
Both rates are in the exhibit and look similar.
Fix: Match: FCFF with WACC, FCFE with the required return on equity.
Changing several inputs at once in a sensitivity test.
Students try to model a scenario rather than one factor.
Fix: Sensitivity changes one input and holds the rest constant. Scenario analysis changes several.
Assuming FCFE value always equals DDM value.
Both value equity, so they seem equivalent.
Fix: They agree only if all FCFE is paid out. Retained cash that is not reinvested well makes the values differ.

Worked examples

Example 1

Vignette: An analyst values Lumen Corp using the constant-growth FCFE model. FCFE1 is $60 million, the cost of equity is 10% and the growth rate is 4%. She asks: (1) What is the equity value? (2) If the cost of equity rises to 11%, what is the equity value? (3) Is the value more sensitive to a 1-point rise in r or a 1-point fall in g? Answer first with FCFE1 held at $60 million, then with FCFE1 = FCFE0 × (1 + g), where FCFE0 is implied by the base case.

Show the solution

Base value = 60 ÷ (0.10 − 0.04) = 60 ÷ 0.06 = $1,000 million.
With r = 11%: 60 ÷ (0.11 − 0.04) = 60 ÷ 0.07 = $857.14 million.
With g = 3% and FCFE1 held at 60: 60 ÷ (0.10 − 0.03) = 60 ÷ 0.07 = $857.14 million. Each change narrows the spread by one point, so with FCFE1 fixed the effects are identical.
Now assume FCFE1 = FCFE0 × (1 + g). FCFE0 is implied by the base case: 60 ÷ 1.04 = 57.69, and it stays the same in every scenario. At g = 3%, FCFE1 = 57.69 × 1.03 = 59.42 and value = 59.42 ÷ 0.07 = $848.9 million.
A rise in r leaves g at 4%, so FCFE1 stays at 60 and value is $857.14 million under either assumption. The fall in g also lowers FCFE1 when FCFE1 = FCFE0 × (1 + g), giving $848.9 million. The conclusion depends on the assumption: with FCFE1 fixed, the two effects are equal; with FCFE1 = FCFE0 × (1 + g), the fall in g has the larger impact ($848.9 million versus $857.14 million).

Answer: (1) $1,000 million. (2) About $857.14 million. (3) It depends on the assumption. With FCFE1 fixed at $60 million, the two effects are equal: both give $857.14 million. With FCFE1 = FCFE0 × (1 + g), a fall in g also lowers FCFE1, so value drops to about $848.9 million versus $857.14 million for the rise in r. Value is then more sensitive to g.

Example 2

Vignette: Orion Ltd. has FCFF1 of $90 million growing at 5% forever. WACC is 9%. It holds $120 million of excess cash and marketable securities that generate no income in FCFF. Debt is $400 million and there are 50 million shares. Questions: (1) What is the value of operating assets? (2) What is equity value per share? (3) Why can FCFF be preferred to FCFE here if Orion plans to raise its debt ratio?

Show the solution

Operating value = 90 ÷ (0.09 − 0.05) = 90 ÷ 0.04 = $2,250 million.
Equity value = 2,250 + 120 − 400 = $1,970 million.
Per share = 1,970 ÷ 50 = $39.40.
FCFE depends on net borrowing, which changes as leverage changes, so it is hard to forecast. FCFF is not affected by debt flows.

Answer: (1) $2,250 million. (2) $39.40 per share. (3) FCFF is unaffected by changes in debt, and WACC can be kept stable more easily than FCFE can be forecast when leverage is changing.

Exam tips

Read which cash flow the vignette gives, then pick the rate. This avoids the most common mismatch.
Always scan the balance sheet exhibit for excess cash, investments and debt before finalizing equity value.
When the spread r − g is small, value is highly sensitive to both r and g. To find which input has the largest effect, compare the percentage change in value for each input.
For negative FCF, expect answers that forecast to a positive stable year or use a different model, not a direct formula.
For model choice questions, tie each answer to a fact in the vignette: dividend policy, control, leverage change or FCF sign.

Sensitivity Analysis and Practical Issues in FCF Valuation in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Sensitivity Analysis and Practical Issues in FCF Valuation: frequently asked questions

What is sensitivity analysis in FCFF valuation?

It changes one input, such as WACC or growth, and recomputes the value while holding the others constant. It shows which assumptions drive value most. It does not give probabilities.

How do you value a firm with negative free cash flow?

Do not use the constant-growth formula on a negative flow. Forecast FCF until it becomes positive and stable, then compute a terminal value at that point and discount everything back. You can also use a different model if the forecast is too uncertain.

When should you use FCFE instead of the dividend discount model?

Use FCFE when dividends do not reflect the firm's ability to pay, when the firm pays no dividends, or when you take a control perspective. The DDM suits minority holders of firms with stable, earnings-linked dividends.

How do non-operating assets affect FCFF valuation?

FCFF values only operating assets. Add the value of excess cash and non-operating investments separately, then subtract debt and preferred stock to reach equity value. Do not include their income in FCFF.