CFA Level I Exam · Discounted Cash Flow (DCF) and Growth Models

Dividend Discount Model (DDM) Basics for CFA Level I

Updated 7 October 2026 · Fact-checked

The dividend discount model values a share as the present value of all expected future dividends, discounted at the required return on equity. For a finite holding period, you discount each dividend and the expected sale price. Find the cash flows, pick r, discount, and add.

Understand Dividend Discount Model (DDM) Basics

A share is a claim on the cash a company pays out to its owners. If you buy it and hold it, the cash you receive is dividends, plus the sale price if you sell. The dividend discount model (DDM) says the value of the share today is the present value of those expected cash flows.

The discount rate is the required rate of return on equity (r). It reflects the risk of the shares. A riskier stock has a higher r and a lower value, because the same dividends are worth less today.

Start with a one-year holder. You receive a dividend D1 at the end of the year and sell at price P1. Value today is V0 = D1 ÷ (1 + r) + P1 ÷ (1 + r). Now P1 is itself the present value, at time 1, of the dividends after year 1. Substitute that in and repeat, and the sale price disappears. You are left with the present value of dividends forever.

This is why a stock that pays no dividend today can still have value under the DDM. The model counts expected future dividends, and the sale price stands in for the dividends beyond your holding period. For a multi-period holder, the sale price at the end of the holding period is the terminal value.

On the exam, the basic DDM is mostly arithmetic with the time value of money. The skill is to match each cash flow to the right date and to use r, not a growth rate or a bond yield, as the discount rate.

Key formulas to remember

Single-period DDM: V0 = D1 ÷ (1 + r) + P1 ÷ (1 + r); D1 and P1 both arrive at the end of year 1. Equivalent to (D1 + P1) ÷ (1 + r).
Finite-horizon (multi-period) DDM: V0 = Σ [Dt ÷ (1 + r)^t] for t = 1 to n + Pn ÷ (1 + r)^n; Pn is the expected sale price at the end of year n. Discount it n periods.
General DDM (infinite horizon): V0 = Σ [Dt ÷ (1 + r)^t] for t = 1 to ∞; Value is the present value of all future dividends. Needs a dividend forecast or a growth assumption.
Required return from a one-year price: r = (D1 + P1) ÷ V0 − 1; If V0 is the current market price, this gives the expected return, a holding period return.

How to solve Dividend Discount Model (DDM) Basics questions

Use this method for any basic DDM question, single-period or multi-period.

1Read the stem and list each expected dividend with its timing. Dividends are usually at the end of each year.
2Find the required return on equity r. Convert from a percentage to a decimal.
3Check whether a sale price is given. If the holder sells at the end of year n, include Pn as a cash flow at time n.
4Discount each cash flow by (1 + r)^t, where t is the year it arrives.
5Add the present values. This is the value V0.
6If the question asks for the return instead, use the cash flows and the price and solve for the rate, with the calculator's cash flow keys if there is more than one year.
7Sense-check: V0 should be below the undiscounted sum of the cash flows, and a higher r should give a lower value.

Quickest way: Calculator shortcut for uneven dividends

When to use it: Use when there are two or more yearly dividends plus a sale price, so that discounting each by hand is slow.

BA II Plus: press CF, then 2ND CLR WRK to clear. Enter CF0 = 0, then C01 = D1, C02 = D2, and so on. Add the sale price to the final year's cash flow, for example C03 = D3 + P3.
Press NPV, enter I = r as a percentage, press ↓ then CPT. The result is V0.
HP 12C: enter 0 g CF0, then D1 g CFj, D2 g CFj, and so on, with the final dividend plus price as the last CFj. Enter r i, then f NPV.
For one period, skip the cash flow keys: V0 = (D1 + P1) ÷ (1 + r).

Common mistakes in Dividend Discount Model (DDM) Basics

Leaving out the sale price in a finite holding period question
The model is called the dividend discount model, so students discount only dividends.
Fix: If the stem gives an end-of-holding-period price, add it as a cash flow in the final year. It stands for the later dividends.
Discounting the final price by one period fewer or more than needed
Students treat the price as arriving at a different time to the last dividend.
Fix: The year-n price is discounted n periods, the same as the year-n dividend.
Using the wrong discount rate, such as a bond yield or the dividend growth rate
Several rates appear in the stem and they all look like percentages.
Fix: Dividends to shareholders are discounted at the required return on equity. Ignore other rates unless the stem says to use them.
Entering r as 8 instead of 0.08 in a formula
Calculator I/Y takes percentages, but the formula needs decimals.
Fix: Use 8 in the NPV key I field and 0.08 when you type the formula, then check the answer is below the sum of cash flows.
Concluding that a non-dividend-paying stock is worth zero
Students read the model as needing dividends today.
Fix: Value depends on expected future dividends and the eventual sale price. A firm paying nothing now can still have positive value.

Worked examples

Example 1

An investor expects a share to pay a dividend of $2.00 at the end of the year and to be sold for $52.00 then. The required return on equity is 8%. What is the value of the share today? A) $48.15 B) $50.00 C) $54.00

Show the solution

Cash flows at time 1: dividend $2.00 plus sale price $52.00 = $54.00.
Discount one period at 8%: V0 = 54.00 ÷ 1.08.
54.00 ÷ 1.08 = 50.00.
Option C ($54.00) is the undiscounted sum of D1 and P1, so it ignores the time value of money. Option A ($48.15) is $52.00 ÷ 1.08, which discounts the sale price but omits the dividend.

Answer: B) $50.00

Example 2

An investor will hold a share for two years. Expected dividends are €1.50 at the end of year 1 and €1.60 at the end of year 2. The share is expected to sell for €30.00 at the end of year 2. The required return is 10%. What is the value today? A) €26.12 B) €27.48 C) €33.10

Show the solution

Year 1: 1.50 ÷ 1.10 = 1.3636.
Year 2 cash flow: 1.60 + 30.00 = 31.60.
Discount 31.60 by 1.10² = 1.21: 31.60 ÷ 1.21 = 26.1157.
Add: 1.3636 + 26.1157 = 27.4793, which is about €27.48.
Option C (€33.10) equals the undiscounted sum of the cash flows (1.50 + 1.60 + 30.00), so it ignores discounting. Option A (€26.12) is 31.60 ÷ 1.21, which leaves out the present value of the year 1 dividend.

Answer: B) €27.48

Exam tips

Look for the timing words: end of year, at the end of the holding period. They set the exponent on (1 + r).
If the stem gives a sale price, it is almost always meant to be included. Check that you have added it to the final dividend before discounting.
With three options, remove any answer that equals the plain sum of cash flows. A present value must be lower for positive r.
For two or more years, use the cash flow keys rather than discounting by hand. It saves time and avoids rounding slips.
Expect the DDM to be a stepping stone. Questions often build on it with a constant growth or multistage assumption.

Practice questions from Discounted Cash Flow (DCF) and Growth Models

Dividend Discount Model (DDM) Basics in other exams

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

Dividend Discount Model (DDM) Basics: frequently asked questions

What is the dividend discount model formula?

The general form is V0 = Σ Dt ÷ (1 + r)^t, summed over all future periods. For a finite holding period, add the expected sale price discounted from the sale date. For one year it is V0 = (D1 + P1) ÷ (1 + r).

Why do we discount dividends and not earnings?

Dividends are the cash that actually reaches the shareholder. Discounting earnings would double count retained cash that is meant to produce future dividends. Other models, such as free cash flow models, use different cash flows.

Can the DDM value a stock that pays no dividend?

Yes. The model uses expected future dividends, not current ones. A firm that pays nothing now can be valued on dividends expected later or on the price at which you can sell.

Which discount rate do I use in the DDM?

Use the required rate of return on equity, r. It compensates the shareholder for the risk of owning the shares. It can be estimated using a model such as the CAPM.