Sources of Equity Returns: formula sheet

Key formulas

Price return

Price return = (P1 − P0) ÷ P0

P0 is the beginning price and P1 the ending price. Dividends are ignored.

Dividend yield (over the holding period)

Dividend yield = D1 ÷ P0

Use dividends received during the period divided by the beginning price.

Total return / holding period return

HPR = (P1 − P0 + D1) ÷ P0 = Price return + Dividend yield

Valid when dividends are received but not reinvested during the period.

HPR with multiple dividends

HPR = (P1 − P0 + D1 + D2 + … + Dn) ÷ P0

Add all cash dividends received in the period. This simple form ignores reinvestment income.

HPR from ending value

HPR = (Ending value ÷ Beginning value) − 1

Ending value includes the final price plus any dividends or reinvested proceeds.

Dividend yield

Dividend yield = D ÷ P₀

D is the dividend per share received in the period. P₀ is the price at the start of the period.

Capital gains yield (price return)

Capital gains yield = (P₁ − P₀) ÷ P₀

Negative if the price falls. Uses the beginning price as the base.

Single-period total return

Total return = (P₁ − P₀ + D) ÷ P₀ = capital gains yield + dividend yield

Assumes the dividend is received at the end of the period and is not reinvested within it.

Cumulative total return with reinvestment

(1 + R₁)(1 + R₂)...(1 + Rₙ) − 1

Each Rₜ is the total return for period t, with dividends reinvested at that period's end price.

Shares from reinvestment

New shares = D × shares held ÷ price at reinvestment date

Use the price on the date the dividend is reinvested, not the starting price.

Dividend payout ratio

Payout ratio = DPS ÷ EPS = dividends ÷ net income

A company measure. It is not the same as dividend yield.

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.

Quick revision

• Total return = price return + dividend yield (for one period, with dividends received at period end).
• Price return = (P1 − P0) ÷ P0.
• Dividend yield = D1 ÷ P0, using the starting price unless the question says otherwise.
• Reinvesting dividends raises ending wealth compared with spending them, so compare total return, not price return.
• Price = EPS × P/E, so price change comes from EPS growth and P/E change.
• Return sources: earnings growth, change in P/E, and dividend yield.
• If the P/E is unchanged, price return equals EPS growth.
• A rising P/E adds to return, but it cannot be assumed to continue indefinitely.
• Equity risk premium = expected equity return − risk-free rate.
• Expected return builds up from income, growth and valuation change.
• Always check whether a question asks for price return or total return before calculating.
• Never leave an MCQ blank, as wrong answers carry no penalty.

Common mistakes

• Dividing by the ending price instead of the beginning price. Fix: Return is always gain ÷ amount invested at the start. Use P0 as the denominator.
• Forgetting dividends when asked for total return. Fix: Underline 'total return' in the stem and add D before dividing. A wrong option often equals the price return.
• Dividing the price change by the ending price. Fix: Capital gains yield and dividend yield both use the beginning price P₀.
• Confusing dividend yield with the payout ratio. Fix: Yield has price in the denominator. Payout ratio has earnings in the denominator. Ask yourself whether the question is about investor return or company policy.
• Adding growth and P/E change when the question wants an exact price return 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 Fix: Buybacks shrink the share count, so ΔS is negative and −ΔS is a positive contribution. Issuance does the reverse.

Exam tips

• Options are in ascending order. Compute your answer first, then match it. Do not guess from the position.
• The trap option is usually the price return only, or the gain divided by the ending price. Compute both so you can reject them.
• If a stem says 'reinvested', slow down and compute ending value, not just the simple sum.
• A negative price return can still give a positive total return if dividends are large enough. Check the sign before choosing.
• With 90 seconds per question, this calculation should take under a minute. Move on once you have checked the denominator.
• Questions are three-option MCQs with numbers listed smallest to largest. Compute the answer first, then match. Do not guess from the order.
• The base for yield is almost always the beginning price. Check this first when two options differ slightly.
• If a question gives period total returns, go straight to multiplying growth factors. It is faster than tracking shares.