CFA Level I Exam · Sources of Equity Returns

How to Decompose Equity Returns: Earnings Growth, P/E and Yield

Updated 7 October 2026 · Fact-checked

Equity return splits into three sources: dividend yield, earnings growth and change in the P/E multiple. Price return equals (1 + earnings growth) × (1 + P/E change) − 1, and you then add dividend yield. The Grinold-Kroner model extends this by splitting earnings growth into inflation, real growth and share count change.

Understand Decomposing Returns: Earnings Growth, P/E and Yield

A share price is a P/E multiple times earnings per share: P = (P/E) × EPS. So the price can only rise for two reasons. Earnings per share grow, or investors pay a higher multiple for each unit of earnings. The third source of return is cash paid out: the dividend yield.

That gives the basic decomposition: total return ≈ dividend yield + earnings growth + change in P/E. Earnings growth is the part driven by the business. The P/E change is the part driven by market sentiment, interest rates and risk appetite. It is often called multiple expansion (P/E rises) or multiple contraction (P/E falls), or repricing.

The pieces multiply, they do not simply add. If EPS grows 5% and P/E rises 6.67%, the price rises (1.05 × 1.0667) − 1 = 12%, not 11.67%. The additive version is a good approximation when the numbers are small. The gap is the cross-term, which is the growth rate times the P/E change.

The Grinold-Kroner model goes one level deeper. It splits earnings growth into expected inflation, real earnings growth and the change in shares outstanding. It also treats share repurchases as a yield alongside dividends. The approximate form is: E(Re) ≈ D/P − ΔS + i + g + ΔP/E. Over long horizons, analysts usually assume the P/E change is small, because a multiple cannot keep expanding forever.

The exam tests this in two ways. First, a numerical question gives you starting and ending P/E and EPS and asks for the return or one component. Second, a conceptual question asks which source is least sustainable (multiple expansion) or how a buyback changes the picture.

Key formulas to remember

Price identity: P = (P/E) × EPS; Any price change must come from a P/E change, an EPS change, or both.
Exact price return from components: Price return = (1 + earnings growth) × (1 + P/E change) − 1; Use this when the question asks for an exact figure. Equivalent to (P/E₁ × EPS₁) ÷ (P/E₀ × EPS₀) − 1.
Basic total return decomposition (approximate): Total return ≈ dividend yield + % change in EPS + % change in P/E; Ignores the cross-term. Dividend yield here is dividends ÷ starting price.
Grinold-Kroner expected equity return (approximate): E(Re) ≈ D/P − ΔS + i + g + ΔP/E; D/P = dividend yield, ΔS = % change in shares outstanding (negative for net buybacks), i = expected inflation, g = real total earnings growth, ΔP/E = % repricing. i + g is nominal earnings growth.
Net yield to shareholders: Dividend yield − ΔS; A net buyback (ΔS < 0) adds to the yield. Net issuance (ΔS > 0) subtracts from it.

How to solve Decomposing Returns: Earnings Growth, P/E and Yield questions

Use this order for any question that asks you to break equity return into its sources.

1Write down what you are given: starting and ending P/E, starting and ending EPS (or growth rates), and dividend yield or dividends per share.
2Decide whether the question wants an exact figure or an approximation. Words such as 'approximately', 'Grinold-Kroner' or 'sum of components' point to the additive form.
3Compute the P/E change as a percentage: P/E₁ ÷ P/E₀ − 1.
4Compute earnings growth as a percentage: EPS₁ ÷ EPS₀ − 1. In a Grinold-Kroner question, build it from inflation, real growth and the share count change.
5For price return, multiply the growth factors: (1 + earnings growth) × (1 + P/E change) − 1.
6Add dividend yield (dividends ÷ starting price) to get total return. In Grinold-Kroner, add the net buyback yield as well.
7Check the sign of every item, especially a falling P/E and net buybacks.
8Pick the option that matches your number. If two options differ by the cross-term, re-read whether the question asks for exact or approximate.

Quickest way: Factor-multiply, then add the yield

When to use it: Use it when you are given both P/E and EPS values or growth rates and need a total or price return under time pressure (about 90 seconds).

Turn each change into a factor. For example EPS +5% is 1.05, and P/E 15 to 16 is 16 ÷ 15.
Multiply the factors on your calculator: 1.05 × 16 ÷ 15 = 1.12 (the same keystrokes work on a TI BA II Plus or HP 12C in normal arithmetic mode, though the HP 12C needs ENTER between numbers: 1.05 ENTER 16 × 15 ÷).
Subtract 1 to get price return: 12%.
Add the dividend yield on the starting price.
Eliminate options: the answer must be larger than price return if dividends are positive, and an approximation that ignores the cross-term will be slightly off an exact answer.

Common mistakes in Decomposing Returns: Earnings Growth, P/E and Yield

Adding growth and P/E change when the question wants an exact price return
The additive formula is the one students remember, so they apply it everywhere.
Fix: Read the wording. If exact figures are given for P/E and EPS, compute the prices and the return directly, or multiply the factors.
Treating a net share buyback as a negative
The term −ΔS looks like a subtraction, so students subtract the 1% instead of entering ΔS = −1% and getting +1%.
Fix: Buybacks shrink the share count, so ΔS is negative and −ΔS is a positive contribution. Issuance does the reverse.
Computing dividend yield on the ending price
Students divide dividends by the price at the end because it is the last number they used.
Fix: Return is measured on what you paid. Use dividends ÷ starting price.
Forgetting that a falling P/E reduces return
Students focus on earnings growth and assume the multiple is stable.
Fix: Always compute P/E₁ ÷ P/E₀ − 1 and keep its sign. Earnings can grow 8% while a P/E drop makes price return near zero.
Treating earnings growth as the same as real earnings growth in Grinold-Kroner
The g in the model sounds like total growth.
Fix: Nominal earnings growth is roughly i + g. Add inflation to the real growth rate. Check whether the question already gave nominal growth.
Assuming multiple expansion is a reliable long-run return source
Past bull markets with rising P/Es make it look permanent.
Fix: Over long horizons the P/E tends to stay in a range, so long-run return comes mainly from yield and earnings growth. Treat expansion as temporary.

Worked examples

Example 1

A share has a starting P/E of 15 and EPS of 4.00. At the end of the year the P/E is 16 and EPS is 4.20. The share paid a dividend equal to 2% of its starting price. What is the total return? A) 12.0% B) 14.0% C) 16.0%

Show the solution

Starting price = 15 × 4.00 = 60.00.
Ending price = 16 × 4.20 = 67.20.
Dividend = 2% × 60.00 = 1.20.
Total return = (67.20 + 1.20) ÷ 60.00 − 1 = 68.40 ÷ 60.00 − 1 = 14.0%.
Cross-check by components: EPS growth = 5%, P/E change = 16 ÷ 15 − 1 = 6.67%. Price return = 1.05 × 1.0667 − 1 = 12.0%. Adding 2% yield gives 14.0%.
Option A is price return only, so it leaves out the dividend. Option C overstates the return and does not match the computed 14.0%. It could come from counting the 2% dividend twice (12.0 + 2.0 + 2.0).

Answer: B) 14.0%

Example 2

An analyst uses the Grinold-Kroner model. Dividend yield is 2.5%, expected inflation is 2.0%, real total earnings growth is 3.0%, the change in shares outstanding is −1.0% because of net buybacks, and the P/E is expected to fall by 0.5%. What is the approximate expected equity return? A) 6.0% B) 8.0% C) 9.0%

Show the solution

Use E(Re) ≈ D/P − ΔS + i + g + ΔP/E.
Net yield = D/P − ΔS = 2.5% − (−1.0%) = 3.5%.
Nominal earnings growth = i + g = 2.0% + 3.0% = 5.0%.
Repricing = −0.5%.
E(Re) ≈ 3.5% + 5.0% − 0.5% = 8.0%.
Option A comes from subtracting the buyback (2.5 − 1.0 + 5.0 − 0.5 = 6.0). Option C comes from adding the P/E change instead of subtracting it (3.5 + 5.0 + 0.5 = 9.0). Ignoring the P/E change altogether would give 8.5%.

Answer: B) 8.0%

Exam tips

Check the question for 'exact' versus 'approximate'. The cross-term decides between two close options.
Dividend yield always sits on the starting price. Mark this before you calculate.
In Grinold-Kroner questions, write each symbol with its sign (ΔS = −1.0%) before you put it into the formula.
For conceptual items, remember that earnings growth and yield reflect fundamentals, while P/E change reflects sentiment and discount rates, so it is the least dependable source over long horizons.
With no penalty for wrong answers, always answer. If you are short of time, a quick sign check usually eliminates one option.

Practice questions from Sources of Equity Returns

Decomposing Returns: Earnings Growth, P/E and Yield in other exams

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

CMA FinalYield and Earnings-Based Methods

Decomposing Returns: Earnings Growth, P/E and Yield: frequently asked questions

What are the three sources of equity return?

They are dividend yield, earnings growth and change in the P/E multiple. Price return comes from earnings growth and P/E change combined. Total return adds the dividend yield.

What is the Grinold-Kroner model in simple terms?

It is an approximate model for expected equity return: dividend yield minus the change in share count, plus inflation, plus real earnings growth, plus the change in P/E. It treats net buybacks as part of the shareholder yield. It is a build-up of the basic yield, growth and multiple decomposition.

Is multiple expansion a good source of long-term return?

Usually not. A P/E cannot rise indefinitely, so over long horizons return depends mainly on yield and earnings growth. Over shorter periods, P/E changes can dominate the result.

Do I add or multiply earnings growth and P/E change?

Exactly, you multiply the factors: (1 + g) × (1 + ΔP/E) − 1. The additive form is an approximation that works well for small changes. Use the exact form when the question gives full values and offers close options.