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Lesson 7 of 7 11–14% of the exam

Where DCF and growth models break down

Discounted cash flow (DCF) growth models rest on one cash flow measure, one base year and fixed growth and discount rates. Company-specific (bottom-up) problems distort the cash flow; market-wide (top-down) problems distort the cost of capital. They fit stable, mature firms best, so analysts also use scenarios and other models.

5 min cram, 24 min full read. Based on the 2027 CFA® Program Level I curriculum, Equities, Learning Module 6.

Tailor this to you: take the self-assessment

Before this: Discount rates and terminal values

On the exam

  • Explain the shortcomings of constant and multistage cash flow growth assumptions in present value models

Explain the shortcomings of constant and multistage growth assumptions. Expect why dividend and free cash flow to equity (FCFE) values diverge (buybacks, payout, share count), base-year effects, transformation and decline that growth rates cannot capture, a probability-weighted value when the firm may fail, how a change in the risk-free rate moves the weighted average cost of capital (WACC) and value, and which rate to use when rates are changing.

How deeply to learn each part
Know the idea
Understand it in general. It frames other topics, but you will not calculate with it.
Use it
Understand it well enough to solve a question with it. Recognize when it applies.
Memorize
Learn it by heart. The exam will not give it to you.

You know this one. The full lesson is folded away. The takeaways, formulas and checkpoint below are your quick refresher, and the checkpoint is a fair test of whether you still do.

You tested strong here. The full lesson is folded away. The takeaways, formulas and checkpoint below are your quick refresher, and the checkpoint is a fair test of whether you still know it.

Cram mode: the one-screen version of this lesson. Switch to Full for the explanations, worked examples and interactives.

What can go wrong?

Two kinds of problem. Bottom-up (company-specific) limitations hit the cash flow: the cash flow measure itself, wrong assumptions or models, and company changes the model cannot capture. Top-down (macroeconomic and market) limitations hit the inputs to the cost of capital in the denominator (the weighted average cost of capital, WACC, and the required return on equity, rer_e), which move with the economy.

The earlier lessons already built in some cautions:

  • Growth gg must be below the required return and should not beat the economy forever (lesson 3).
  • Constant growth from one year’s cash flow is a simplification.
  • The shorter the horizon, the more the terminal value weighs (lesson 5).
  • The gap between the required return and gg drives the value.
Why a growth model can mislead
Limitations of DCF growth models
  • Bottom-up (company-specific) Memorize the numerator
    • Incomplete measure dividends miss buybacks; payout and share-count shifts
    • Base year one-off years bias growth and forecasts
    • Static assumptions transformation, decline, sudden distress
  • Top-down (macro and market) Memorize the denominator
    • Changing risk-free rate moves r_d, r_e and WACC
    • Developing markets no truly risk-free or long-term rate

When the cash flow measure tells only part of the story

Any single measure can bias the value if it misses how the company returns or uses cash. This is the incomplete cash flow metric problem.

Dividends ignore buybacks. A company that keeps a steady payout but returns more and more through buybacks will look too cheap in a dividend model compared with a model based on free cash flow to equity (FCFE). This is the dividend versus FCFE valuation gap .

The gap can also run the other way. Dividends per share can rise quickly while earnings are flat, because the payout ratio is rising or buybacks are shrinking the share count. Growing total dividends at that per-share rate can make a dividend value higher than an FCFE value; the gap comes from the payout ratio, the share count, or both.

An FCFE forecast at a constant debt ratio inherits any oddity in the base year. Operating profit, margins and investment in long-term assets and working capital can be hard to define for both FCFE and free cash flow to the firm (FCFF). These base-year effects also bias historical growth rates of volatile measures (lesson 3).

When the company does not stand still

Growth-rate models suit mature firms whose base-year cash flow is a fair starting point. Two stages allow change within set limits, but not reinvention. These are static growth assumptions .

Kestrel Mowers made petrol lawnmowers for decades. Then it poured its cash and heavy new borrowing into home batteries and a rooftop solar installation business, cut its dividend and sold its old factories. No base-year cash flow and growth rate could describe what it was turning into. That is transformational growth .

Present value models also rest on the going concern assumption . A negative growth rate can model a slow decline (lesson 5), but financial distress (bankruptcy, restructuring, liquidation) often arrives suddenly. It is better modeled as an explicit scenario with a probability. The result is a probability-weighted scenario value .

Probability-weighted value with financial distress Use it
IVt=p×IVgoing concern+(1−p)×Value in distressIV_t = p \times IV_{\text{going concern}} + (1 - p) \times \text{Value in distress}

Here pp is the probability the firm survives.

Rearrange itProbability-weighted value with financial distress: solve for any input
The question asks for
Analysts value a company's equity at 895.59 if it survives. They give a 75.00% probability to survival and 25.00% to a distress outcome in which shareholders would receive 60.00. The probability-weighted value of the equity is closest to:

0.75 × 895.59 + 0.25 × 60.00 = 686.69

Probability-weighted value686.69

On your calculator
  1. 0.75×895.59=STO1
  2. 0.25×60+RCL1=686.6925

STO store · RCL recall a stored number

  1. 0.75ENTER895.59×0.25ENTER60×+686.6925

ENTER enter (on the HP, puts the number on the stack)

Learning Module 8 builds full probability-weighted scenarios.

When interest rates move

The risk-free rate sits inside both the cost of debt and the cost of equity, so when it changes, WACC, rer_e and the value all move, often as much as any company-specific factor. This is the changing risk-free rate problem.

What analysts do: the practice of matching the risk-free rate to the forecast horizon uses a long-run average rather than today’s short-term rate. Developing markets add a problem: government debt may not be risk-free, and long-term government bond yields may not exist (developing market discount rates ).

So what do analysts do?

Use present value growth models where they fit best: stable firms with consistent dividends and cash flows. Be wary with non-payers, firms with negative cash flow and firms at an early or late turning point in their life cycle. Remember that technology and competition can break static growth assumptions. And practice using more than one model and approach.

InteractiveGoing concern or not: a probability-weighted value

Try this 0 of 3

  • Going concern: lower the survival probability until the value falls below 500
  • What moves the value: pick the input with the widest bar
  • Rates move: raise the risk-free rate by 2 points
Dunmore Retail (EUR millions)

Going concern 895.59 with probability 75%, liquidation 60.00 with probability 25%: probability-weighted value EUR 686.69 million.

Dunmore Retail equity686.69probability-weightedGoing concern895.5975 × 1.015 ÷ 8.5%!Liquidation60.00to shareholders
  • Dunmore Retail equity, 686.69, probability-weighted, (matches)
    • 75% (survives): Going concern, 895.59, 75 × 1.015 ÷ 8.5%
    • 25% (distress): Liquidation, 60.00, to shareholders, (warning)

Hover over or tap a box to follow its path.

Probability-weighted value (EUR m)686.69
Going-concern value895.59
Trap: distress ignored895.59
Trap: nothing recovered671.69
Show working

Going concern = FCFEₜ × (1 + g) ÷ (rₑ − g) = 75 × 1.015 ÷ (0.1 − 0.015) = 895.59

IVₜ = p × going concern + (1 − p) × value in distress = 0.75 × 895.59 + 0.25 × 60.00 = 671.69 + 15.00 = 686.69

Present value models assume a going concern. Sudden distress is better modeled as an explicit scenario with a probability than as a small negative growth rate.

Probability-weighted value on your calculator
  1. 75×1.015÷(0.1−0.015)=895.59, going concern
  2. ×0.75+(0.25×60)=686.69
  1. 75ENTER1.015×0.1ENTER0.015−÷895.59
  2. 0.75×0.25ENTER60×+686.69

ENTER enter (on the HP, puts the number on the stack)

Display: 686.69

A growth model is only as good as its base year, its growth path and its discount rate.

Memorize this

MemorizeTwo kinds of limitation

KindHitsExamples
Bottom-upthe cash flow (numerator)dividends miss buybacks; base-year effects; hard-to-define margins and investment; transformation; sudden distress
Top-downthe cost of capital (denominator)changing risk-free rate; developing markets without a risk-free or long-term rate

Memory hook Bottom-up breaks the top of the fraction; top-down breaks the bottom.

Know it cold Best for stable firms with steady dividends and cash flows; weakest for non-payers, negative cash flow and life-cycle turning points.

MemorizeWhat to do about it

ProblemResponse
Possible failureprobability-weighted scenario, not just a negative g
Slow declinea negative long-run growth rate
Rates changinglong-run average risk-free rate matched to the horizon
Rising buybacksFCFE or FCFF, not dividends
Any single modeluse more than one

Memory hook Scenario, negative g, long-run rate, broader cash flow, second model.

Know it cold IVt=p×IVgoing concern+(1−p)×value in distressIV_t = p \times IV_{\text{going concern}} + (1 - p) \times \text{value in distress}.

Why a growth model can mislead
Limitations of DCF growth models
  • Bottom-up (company-specific) Memorize the numerator
    • Incomplete measure dividends miss buybacks; payout and share-count shifts
    • Base year one-off years bias growth and forecasts
    • Static assumptions transformation, decline, sudden distress
  • Top-down (macro and market) Memorize the denominator
    • Changing risk-free rate moves r_d, r_e and WACC
    • Developing markets no truly risk-free or long-term rate
Probability-weighted value with financial distress Use it
IVt=p×IVgoing concern+(1−p)×Value in distressIV_t = p \times IV_{\text{going concern}} + (1 - p) \times \text{Value in distress}
Quick example

80% chance of a going-concern value of 50, 20% chance of 5 in distress: 0.80 × 50 + 0.20 × 5 = 41.00.

On your calculator
  1. 0.8×50=STO1
  2. 0.2×5+RCL1= 41

STO store · RCL recall a stored number

  1. 0.8ENTER50×0.2ENTER5×+ 41

ENTER enter (on the HP, puts the number on the stack)

How it is asked

  1. Dividend versus FCFE gap

    Payout steady, buybacks rising. Which model gives the lower value?

    The dividend model; it misses the buybacks. Trap: the FCFE model.

  2. Distress scenario

    Going concern 895.59; 25% chance of liquidation worth 60 to shareholders.

    0.75 × 895.59 + 15 = 686.69. Traps: 895.59 (ignored), 671.69 (nothing recovered).

  3. Rate shift

    Risk-free rate +2 points; 25% debt at r_d 8%, tax 25%; r_e 12%.

    New WACC 12.375%, up 1.875 points. Traps: 12.5%, 12.0%.

  4. Slow decline

    A firm expected to shrink slowly for decades.

    Use a negative long-run growth rate. Trap: a finite horizon or no present value model.

Exam traps

  • Expecting a dividend model to capture buybacks; with rising buybacks it gives the lower value.
  • Explaining a dividend-versus-FCFE gap by only one cause; payout changes, share-count changes or both can drive it.
  • Modeling sudden distress with a small negative growth rate instead of a probability-weighted scenario.
  • Adding a risk-free rate change straight to WACC; recompute WACC with the new costs of debt and equity.
  • Reporting a firm value as an equity value after a rate change; subtract the market value of debt.
  • Using today's short-term rate for cash flows far in the future; use a long-run average matched to the horizon.

Checkpoint

3 exam-style questions. About 90 seconds each.

  1. 1A company keeps its dividend payout ratio steady but spends more on share repurchases every year. Compared with a valuation based on free cash flow to equity, a valuation based on dividends will most likely be:

  2. 2A retailer's free cash flow to equity for the year just ended was GBP 40 million. If it survives, FCFE should grow 2% a year indefinitely; the required return on equity is 9%. Analysts give a 30% probability to a liquidation in which shareholders would receive nothing. The intrinsic value of its equity is closest to:

  3. 3A company finances itself with 30% debt and 70% equity at market values. Its pre-tax cost of debt is 5%, its tax rate is 20% and its required return on equity is 10%. If the risk-free rate rises by 1.5 percentage points and both the cost of debt and the cost of equity rise by the same amount, the new weighted average cost of capital is closest to:

Key takeaways

  • Bottom-up limits hit the cash flow: incomplete measures (dividends miss buybacks), base years, hard-to-define margins and investment, transformation and decline.
  • Present value models assume a going concern; sudden distress is better handled with a probability-weighted scenario.
  • Top-down limits hit the cost of capital: a changing risk-free rate moves r_d, r_e and WACC; use long-run averages matched to the horizon.
  • Growth models fit stable, mature firms best, so analysts use more than one model.
Probability-weighted value with financial distress Use it
IVt=p×IVgoing concern+(1−p)×Value in distressIV_t = p \times IV_{\text{going concern}} + (1 - p) \times \text{Value in distress}
Quick example

80% chance of a going-concern value of 50, 20% chance of 5 in distress: 0.80 × 50 + 0.20 × 5 = 41.00.

On your calculator
  1. 0.8×50=STO1
  2. 0.2×5+RCL1= 41

STO store · RCL recall a stored number

  1. 0.8ENTER50×0.2ENTER5×+ 41

ENTER enter (on the HP, puts the number on the stack)

All Equities formulas, every lesson

Practice exam-style questions on Discounted Cash Flow and Growth Models

Questions about this lesson?

Where this comes back

Questions candidates ask

What are the limitations of DCF growth models in CFA Level 1?

Company-specific problems with the cash flow measure, the base year and static growth assumptions, and market-wide problems estimating the cost of capital as rates change. The models fit stable, mature firms best and are weakest for non-payers, firms with negative cash flow and firms at life-cycle turning points.

Why can a dividend model undervalue a company?

Dividends leave out share repurchases and cash the company keeps. A firm that returns more and more through buybacks while holding its payout steady looks cheaper in a dividend model than in an FCFE model.

How do analysts value a company that might fail?

Value it as a going concern, value what shareholders would get in distress, and weight the two by their probabilities. A 75% chance of an 895.59 going-concern value and a 25% chance of 60 give 686.69.

How do changing interest rates affect a DCF valuation?

The risk-free rate is part of both the cost of debt and the cost of equity, so a rise lifts WACC and r_e and lowers value. Analysts use long-run average rates matched to the forecast horizon.

Spotted an error? Tell us and we will fix it.

  1. Dividend discount and free-cash-flow-to-equity models
  2. Dividends, FCFE, FCFF or residual income: which cash flow, which discount rate
  3. Constant growth models, implied growth and the sustainable growth rate
  4. Two-stage (multistage) growth models
  5. Discount rates and terminal values
  6. Valuing preferred stock, and how call, put and conversion features change value
  7. Where DCF and growth models break down

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