CFA Level II Exam · Discounted Dividend Valuation

Estimating Required Return and Implied Return in DDM

Q: How do I find the implied required return from a DDM?

Set the market price equal to the model's present value of dividends and terminal value, then solve for the discount rate. For constant growth use r = D1 ÷ P0 + g. For multistage models use IRR or trial and error.

Q: What is the build-up method for cost of equity?

It starts with a risk-free rate and adds premiums for risk, such as an equity risk premium, a size premium and a company-specific premium. It is mainly used for private companies where a reliable beta is not available.

Q: Can I use CAPM to estimate required return for equity valuation?

Yes. CAPM gives required return as the risk-free rate plus beta times the equity risk premium. It is the default method unless the vignette provides a multifactor model or build-up components.

Q: Why does the implied return depend on my forecasts?

The implied return is the IRR on your forecast dividends and terminal value. If the growth or dividend forecasts are too high, the implied return will be too high, so the undervalued signal may be false.

Updated 7 October 2026 · Fact-checked

Required return is the return investors demand for an equity's risk, often estimated with CAPM or a build-up method. Implied return is the discount rate that makes a dividend model's present value equal today's market price. You solve it by setting price equal to the model value and finding the rate, using the Gordon formula or trial and error for multistage models.

Understand Estimating Required Return and Implied Return

A dividend discount model turns forecast dividends into a value using a required return. Usually you know the inputs and compute value. This topic reverses the question in two ways: where does the required return come from, and what return does today's price imply?

Required return is the minimum expected return investors need to hold the stock, given its risk. The most common estimate is CAPM: risk-free rate plus beta times the equity risk premium. Alternatives are multifactor models (such as Fama-French, which add size and value factors), and the build-up method, mainly used for private companies where beta is hard to observe. Build-up starts with a risk-free rate and adds premiums, such as an equity risk premium, a size premium and a specific-company premium.

Implied return is the internal rate of return (IRR) on buying the stock at the market price and receiving the forecast dividends and a terminal value. If price is P0, you find r such that P0 equals the present value of the forecast cash flows. In the Gordon growth model this is easy: r = D1 ÷ P0 + g.

The comparison is the point. If the implied return is above your CAPM required return, the stock looks undervalued, because the market price offers more than you need. If it is below, the stock looks overvalued. Implied return is also a way to back out the market's expected return, but it depends on your growth and dividend forecasts being sensible.

For multistage models there is no closed form. You solve by trial and error, or with the financial calculator's cash flow and IRR function. The cash flows are the high-growth dividends, then the terminal value at the end of the high-growth period, which itself depends on r when the Gordon formula is used.

Key formulas to remember

CAPM required return: r = Rf + β × (E(Rm) − Rf); (E(Rm) − Rf) is the equity risk premium. Use the beta and premium given in the vignette.
Build-up method: r = Rf + equity risk premium + size premium + specific-company premium; Premiums are added. Some versions use a beta on the equity risk premium. Follow the vignette's stated components.
Multifactor (Fama-French style): r = Rf + β(mkt) × λ(mkt) + β(size) × λ(size) + β(value) × λ(value); Each λ is a factor risk premium. Multiply each factor beta by its premium and add.
Implied return, Gordon growth: r = D1 ÷ P0 + g; Valid for a constant growth rate g below r. D1 is next year's dividend, not D0.
Implied return, multistage: P0 = Σ Dt ÷ (1 + r)^t + Vn ÷ (1 + r)^n, solve for r; Vn = Dn+1 ÷ (r − gL) if terminal value uses Gordon growth. Set P0 to market price and find r by IRR or trial and error.
Decision rule: Implied r > required r: undervalued. Implied r < required r: overvalued; Assumes the dividend forecasts are reasonable.

How to solve Estimating Required Return and Implied Return questions

Use this sequence for any question on required or implied return in a dividend model.

1Read the vignette and decide what is asked: a required return estimate, or an implied return from a price.
2For required return, pick the model named or implied by the data: CAPM if beta and a risk premium are given, build-up if premiums are listed, multifactor if factor betas appear.
3Compute the required return by adding the pieces. Convert percentages to decimals carefully.
4For implied return, list the forecast dividends by year and identify when the stable growth phase starts.
5Write the equation: market price equals PV of dividends plus PV of terminal value. Check that the terminal value uses Dn+1 and the long-run growth rate.
6If the model is single-stage, use r = D1 ÷ P0 + g. Otherwise test rates or use the calculator IRR.
7Compare implied return with the required return and state whether the stock is under- or overvalued.
8Sanity check: the answer should be above the long-run growth rate and plausible for equity.

Quickest way: Bracket and interpolate the multistage IRR

When to use it: Use when a multistage model asks for the implied return and the answer options are spread out, as in a three-option item.

Guess a first rate near D1 ÷ P0 + long-run growth, or a rate close to the required return.
Compute the model value at that rate. If value is above price, the true r is higher. If below, the true r is lower.
Try one more rate on the other side, typically 1% away.
Interpolate between the two values to estimate r.
Match to the closest option. With options several tenths of a percent apart you rarely need a third trial.
If the terminal value is a Gordon formula, remember it changes with each trial rate.

Common mistakes in Estimating Required Return and Implied Return

Using D0 instead of D1 in r = D1 ÷ P0 + g.
The vignette gives the current dividend and it is quick to plug in.
Fix: Compute D1 = D0 × (1 + g) first, then divide by price.
Using the market return instead of the equity risk premium in CAPM.
The vignette gives a market return and a risk-free rate and students forget to subtract.
Fix: Always compute Rf + β × (Rm − Rf). Check whether the figure given is the premium or the full market return.
Holding the terminal value fixed while trying different rates.
Students compute the terminal value once at the first guessed rate.
Fix: If Vn = Dn+1 ÷ (r − gL), recompute it for every trial r. Alternatively the terminal value may be given as a fixed price, in which case keep it constant.
Reversing the undervalued and overvalued conclusion.
A higher implied return feels like a worse outcome.
Fix: A high implied return means the price is low relative to cash flows, so the stock is undervalued compared with your required return.
Discounting the terminal value by the wrong number of years.
Confusion about when the stable phase begins.
Fix: Vn is a value at the end of year n, using Dn+1. Discount it by (1 + r)^n, the same as the year n dividend.
Adding the size premium to a CAPM estimate when it is not given as part of the method.
Mixing build-up components with CAPM.
Fix: Use only the components the question describes. Build-up lists premiums to add; CAPM uses beta and the equity risk premium.

Worked examples

Example 1

A stock trades at ₹500. Its next dividend D1 is ₹20 and dividends are expected to grow at 6% indefinitely. The risk-free rate is 7%, the equity risk premium is 5% and the stock's beta is 1.2. (1) What is the CAPM required return? (2) What is the implied return? (3) Is the stock under- or overvalued relative to your required return?

Show the solution

CAPM: r = 7% + 1.2 × 5% = 7% + 6% = 13%.
Implied return: r = D1 ÷ P0 + g = 20 ÷ 500 + 6% = 4% + 6% = 10%.
Compare: implied return 10% is below the required return 13%.
The price offers less than investors need for the risk, so the stock is overvalued.

Answer: (1) 13%. (2) 10%. (3) Overvalued, because the implied return is below the required return.

Example 2

A stock is priced at ₹100 today. It will pay a dividend of ₹5 at the end of year 1 and ₹6 at the end of year 2. At the end of year 2, the analyst expects the stock to sell for ₹110. Which of the following is closest to the implied return: 9%, 10% or 12%? Also, is the stock undervalued if the required return is 10%?

Show the solution

Set up: 100 = 5 ÷ (1 + r) + (6 + 110) ÷ (1 + r)^2.
Try r = 11%: 5 ÷ 1.11 = 4.505. 116 ÷ 1.2321 = 94.15. Total = 98.65, below 100, so r is lower than 11%.
Try r = 10%: 5 ÷ 1.10 = 4.545. 116 ÷ 1.21 = 95.87. Total = 100.41, slightly above 100, so r is a little above 10%.
Interpolate: r ≈ 10% + (100.41 − 100) ÷ (100.41 − 98.65) × 1% = 10% + 0.41 ÷ 1.76 × 1% ≈ 10% + 0.23% ≈ 10.2%.
The implied return is about 10.2%, which is closest to the 10% option (9% and 12% are further away).
Implied return of about 10.2% is slightly above the 10% required return, so the stock is marginally undervalued.

Answer: Implied return is about 10.2%, closest to 10% among the options. Compared with a 10% required return, the stock is slightly undervalued.

Exam tips

Check whether a vignette gives the market return or the equity risk premium before using CAPM.
In multistage questions, mark the year when stable growth starts and use the dividend of the following year in the terminal value.
With three options, bracket the answer using two trial rates rather than solving exactly.
Always finish by comparing implied and required return if the question asks about valuation.
Use the calculator's cash flow worksheet if you are practised with it; otherwise trial and error is faster to get right under pressure.

Estimating Required Return and Implied Return in other exams

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

CFA Level IInterest Rates and Required Rate of Return

Estimating Required Return and Implied Return: frequently asked questions

How do I find the implied required return from a DDM?

Set the market price equal to the model's present value of dividends and terminal value, then solve for the discount rate. For constant growth use r = D1 ÷ P0 + g. For multistage models use IRR or trial and error.

What is the build-up method for cost of equity?

It starts with a risk-free rate and adds premiums for risk, such as an equity risk premium, a size premium and a company-specific premium. It is mainly used for private companies where a reliable beta is not available.

Can I use CAPM to estimate required return for equity valuation?

Yes. CAPM gives required return as the risk-free rate plus beta times the equity risk premium. It is the default method unless the vignette provides a multifactor model or build-up components.

Why does the implied return depend on my forecasts?

The implied return is the IRR on your forecast dividends and terminal value. If the growth or dividend forecasts are too high, the implied return will be too high, so the undervalued signal may be false.