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CFA® Level I · Equities · free lesson
Discounted Cash Flow (DCF) and Growth Models
Present value models are the foundation of intrinsic valuation: a share is worth the discounted value of what it will deliver to its owners. This module compares the cash flow measures that different models discount, applies constant-growth and multistage models to dividends and free cash flow, examines where growth assumptions break down, and values preferred shares with and without contingent features.
What you will learn
1. Contrast the cash flows and discount rates used in dividend discount, free cash flow to equity, free cash flow to the firm and residual income models, and outline the steps in applying a present value model.
- DDM discounts dividends at r; FCFE discounts cash flow available to equity at r.
- FCFF is discounted at WACC to give firm value; subtract debt and other claims to reach equity.
- FCFE = CFO - FCInv + net borrowing; FCFF = CFO + Int(1 - t) - FCInv.
- Residual income = net income - r x beginning book value; value = book value + PV of RI.
- Always match the cash flow to the discount rate of the investors who receive it.
2. Calculate and interpret the intrinsic value of a share using constant-growth and multistage present value models, and infer the required return or growth rate implied by a market price.
- Gordon model: V0 = D1 / (r - g), valid only if g < r and growth is constant forever.
- Grow D0 by one period to get D1 when only the last dividend paid is given.
- Implied required return = D1 / P0 + g; implied growth = r - D1 / P0.
- Multistage: PV of explicit-stage cash flows + PV of terminal value at the end of the stage.
- Terminal value at year n uses D(n+1) and is discounted n periods.
3. Explain the limitations of constant-growth and multistage growth assumptions in present value models.
- Value is inversely proportional to r - g; small input changes cause large value changes when the spread is narrow.
- The model breaks down if g >= r; long-run g should not exceed long-run nominal GDP growth.
- Sustainable growth g = b x ROE ties growth to retention and profitability.
- Terminal values often supply most of a multistage valuation.
- Abrupt stage transitions and changing payout policies make growth paths stylized.
4. Calculate the intrinsic value of a non-callable, non-convertible preferred share and explain how call, put, conversion and other contingent features affect its value.
- Perpetual, non-callable, non-convertible preferred: V0 = Dp / rp.
- Use periodic dividends with the matching periodic rate (e.g. quarterly).
- Fixed-maturity preferred is valued like a bond: PV of dividends plus PV of par.
- Issuer options (call) reduce value; holder options (put, conversion) and cumulative dividends increase it.
- Contingent write-down or conversion features shift risk to investors and raise the required yield.
Module at a glance
- Match cash flows and rates: dividends and FCFE at the cost of equity; FCFF at WACC, then subtract debt.
- FCFE = CFO - FCInv + net borrowing; FCFF = CFO + Int(1 - t) - FCInv.
- Gordon model: V0 = D1 / (r - g); grow D0 by one period first.
- Implied r = D1 / P0 + g; implied g = r - D1 / P0.
- Multistage: discount explicit dividends plus a terminal value based on D(n+1), discounted n periods.
- Value is very sensitive to r - g; long-run g must be sustainable (g = b x ROE, no faster than the economy).
- Perpetual preferred: Dp / rp; calls reduce value, puts and conversion increase it.
This free module has 4 lessons, 12 practice questions with full explanations.