Learning Module 4 of Equities 11–14% of the exam

Sources of Equity Returns

2 lessons. About 15 minutes in cram mode, 68 minutes in full.

Start with lesson 1 Learn with Sensei Read the module summary Practice this module

Lessons

1
Dividends, share repurchases, stock splits and the dividend timetable
describe 7 min cram, 32 min full
2
Price return, total return and the price of a share
calculate 8 min cram, 36 min full

What the exam expects you to do

Describe features and uses of dividends, share repurchases, stock splits, and reverse stock splits.Dividends, share repurchases, stock splits and the dividend timetable
Describe dividend payment chronology.Dividends, share repurchases, stock splits and the dividend timetable
Calculate price and total return for equity securities.Price return, total return and the price of a share

Module summary

The whole module on one sheet, organised by lesson: what to memorize, how the ideas fit together, the formulas and the key terms. No paragraphs, just what you need to revise.

Hide what I know

How deeply to learn each part

Know the idea: Understand it in general. It frames other topics, but you will not calculate with it.
Use it: Understand it well enough to solve a question with it. Recognize when it applies.
Memorize: Learn it by heart. The exam will not give it to you.

Dividends, share repurchases, stock splits and the dividend timetable

Known

MemorizePayouts: effect on shareholder wealth

Event	Shares	Price	Total value
Cash dividend	same	falls by about D	cash received offsets
Special or liquidating dividend	same	falls by about D	cash received offsets; liquidating = return of capital
Stock dividend, split	up	down in proportion	unchanged
Reverse split	down	up in proportion	unchanged
Share repurchase	down	about the same	same as a dividend of equal size; cash only to sellers

Memory hook Cutting the pie into more slices does not make more pie.

Know it cold Stock dividends and splits are not relevant for valuation. New price = old price ÷ (new shares per old share).

MemorizeDividend dates in order

Order	Date	What matters
1	Declaration	amount and dates announced
2	Ex-dividend	buy before this date to receive the dividend
3	Record	registered owners are entitled; usually one business day after the ex-date
4	Payment	cash arrives

Memory hook Declare, Ex, Record, Pay. Ex comes first so every earlier trade has settled by Record.

Know it cold Buy BEFORE the ex-date to get the dividend. On the ex-date the price falls by about the dividend.

MemorizeWhy companies repurchase shares

Reason	Meaning
Signal or support	undervalued shares, price support, debt-to-equity
Issuer flexibility	pay less when there is more to invest in
Investor flexibility and tax	sell or not; gains taxed less than dividends; no double tax
Option dilution	absorb shares from employee options, manage earnings per share (EPS)
Raise EPS	fewer shares in the period

Memory hook Five reasons: Signal, Flex for the firm, Flex and tax for the investor, Options, EPS.

Know it cold Repurchased shares get no dividends, no votes and are left out of EPS. Cash goes only to sellers.

MemorizeTaking apart an ex-date move

Part	How to get it
Total	(ex-date close − prior close) ÷ prior close
Dividend	−D ÷ prior close
Market	broad index change that day
Company-specific	total − dividend part − market part

Memory hook Total = Dividend + Market + Company. Solve for the one they ask.

Know it cold Divide the dividend by the close the day BEFORE the ex-date.

Key terms

regular cash dividend Memorize
dividend signaling Know the idea
dividend withholding tax Know the idea
extraordinary or special cash dividend Memorize
liquidating dividend Use it
share repurchase Memorize
buyback Know the idea
reasons for share repurchases Memorize
stock dividend Memorize
bonus issue of shares Know the idea
spin-off Know the idea
stock split Memorize
forward split Know the idea
optimal trading range Know the idea
reverse stock split Memorize
share consolidation Know the idea
declaration date Memorize
ex-dividend date Memorize
record date Memorize
settlement Know the idea
payment date Memorize
ex-date price change Use it
company-specific price change Use it
dividend capture Know the idea

Ways a company pays shareholders or reshapes its shares

Payouts and share-count changesonly the first group moves cash to shareholders

Cash returned Memorize cash leaves the company
- Regular cash dividend known intervals; quarterly in the United States and Canada, usually semiannual in Europe and Japan, usually annual in Scandinavia and China
- Special (extraordinary) cash dividend one-off or on top of the regular one; surprise earnings or sale proceeds
- Liquidating dividend return of capital, not earnings; can exceed retained earnings
- Share repurchase (buyback) cash only to sellers; same total wealth effect as an equal dividend
Share count changed, no cash Memorize value of the pie is unchanged
- Stock dividend (bonus issue) new shares instead of cash, or shares of a spun-off division
- Stock split forward split: more shares, lower price
- Reverse stock split share consolidation: fewer shares, higher price

The dividend timetable, in order

Dividend payment chronologyset in motion when the board (and shareholders, where required) votes to pay

1. Declaration date Memorize board announces amount and dates
2. Ex-dividend date Memorize first day shares trade without the dividend; price drops by about D
3. Record date Memorize registered owners are paid; usually one business day after the ex-date
4. Payment date Memorize cash is sent

Formulas

Price after a split or stock dividend Use it

P_1 = \dfrac{P_0}{k}, \quad k = \dfrac{\text{new shares}}{\text{old shares}}

Quick example

A 4-for-3 split (k = 1.3333) of a share at 80.00 gives 80.00 ÷ 1.3333 = 60.00. A 20% stock dividend is k = 1.20, and a 1-for-5 reverse split is k = 0.20.

On your calculator

80÷4×3= 60

80ENTER4÷3× 60

ENTER enter (on the HP, puts the number on the stack)

Shares repurchased Use it

N_{repurchased} = \dfrac{\text{cash distributed}}{P}

Quick example

A company with 40 million shares at INR 250 spends INR 1,000 million on a buyback: 1,000 ÷ 250 = 4 million shares, leaving 36 million. As a dividend it would be INR 25 a share, a realized return of 25 ÷ 250 = 10%.

On your calculator

1000÷250= 4 million shares
25÷250= 0.10

1000ENTER250÷ 4
25ENTER250÷ 0.10

ENTER enter (on the HP, puts the number on the stack)

Ex-dividend price Use it

P_{ex} \approx P_{t-1} - D

Quick example

A share closes at 36.00 the day before its ex-dividend date and the dividend is 0.60. The price should open near 36.00 − 0.60 = 35.40.

On your calculator

36−0.6= 35.4

36ENTER0.6− 35.4

ENTER enter (on the HP, puts the number on the stack)

Ex-date price change Use it

\dfrac{P_{ex} - P_{t-1}}{P_{t-1}} = -\dfrac{D}{P_{t-1}} + r_{market} + r_{company}

Quick example

Prior close 30.00, dividend 0.45, ex-date close 29.37, index −0.80%: −2.10% = −1.50% − 0.80% + company-specific, so company-specific = +0.20%.

On your calculator

29.37−30=÷30= −0.021 total
0.45÷30= 0.015 dividend, so −2.10% + 1.50% + 0.80% = +0.20%

29.37ENTER30−30÷ −0.021
0.45ENTER30÷ 0.015

ENTER enter (on the HP, puts the number on the stack)

Price return, total return and the price of a share

Known

MemorizeEquity return and price formulas

Case	Formula
No dividend	$r_E = \frac{P_{t+1} - P_t}{P_t}$
Dividend at the end	$r_E = \frac{P_{t+1} - P_t + D_{t+1}}{P_t}$
Dividend reinvested in shares	$r_E = \frac{P_{t+1}(1 + D/P_{PD}) - P_t}{P_t}$
Several periods	$(1 + r_1)(1 + r_2)\cdots - 1$
Price, one year	$P_t = \frac{E(P_{t+1}) + E(D_{t+1})}{1 + r_e}$
Price, n years	$P_t = \sum \frac{D}{(1 + r_e)^i} + \frac{E(P_{t+n})}{(1 + r_e)^n}$

Memory hook Return looks back from the price paid; price looks forward from what you expect. Same pieces, opposite direction.

Know it cold Across a split, adjust the purchase price (or scale end price and dividend together). Last period's dividend is added, not reinvested.

Key terms

capital gain or loss Know the idea
price return Memorize
total return Memorize
realized rate of return Know the idea
split-adjusted prices Use it
reinvested dividends Memorize
price on the dividend payment date Memorize
fractional share ownership Know the idea
reinvesting at the risk-free rate Use it
compounding periodic returns Use it
price index Know the idea
total return index Know the idea
required return on equity Use it
expected price Use it
price target Know the idea
present value of dividends and a future price Memorize
predictability of dividends Know the idea

Where an equity return comes from

Total returnprice change plus dividends, over the price paid

Price return Memorize capital gain or loss; the whole return of a non-payer
Dividends Memorize
- Paid at the end add D to the end price
- Reinvested in shares buy D ÷ payment-date price more shares
- Reinvested elsewhere use the dividend's value at period end

What today's price is made of

Price todaydiscounted at the required return

Present value (PV) of expected dividends Memorize the more predictable part
PV of the expected price at the end Memorize usually the larger part over a short horizon

Formulas

Price return Memorize

r_E = \dfrac{P_{t+1} - P_t}{P_t}

Quick example

A share bought at 36.00 that pays nothing and is sold at 38.70 returns (38.70 − 36.00) ÷ 36.00 = 7.50%.

On your calculator

38.7−36=÷36= 0.075

38.7ENTER36−36÷ 0.075

ENTER enter (on the HP, puts the number on the stack)

Total return Memorize

r_E = \dfrac{P_{t+1} - P_t + D_{t+1}}{P_t}

Quick example

Buy at 25.00, receive a dividend of 0.75 and sell at 26.50: (1.50 + 0.75) ÷ 25.00 = 9.00% (a price return of 6.00%).

On your calculator

26.5−25+0.75=÷25= 0.09

26.5ENTER25−0.75+25÷ 0.09

ENTER enter (on the HP, puts the number on the stack)

Return with the dividend reinvested in shares Memorize

r_E = \dfrac{P_{t+1}\left(1 + \dfrac{D}{P_{PD}}\right) - P_t}{P_t}

Quick example

Buy at 40.00. A dividend of 0.80 is reinvested at 42.00 and the share ends at 46.00. 46.00 × (1 + 0.80 ÷ 42.00) = 46.8762, so the return is (46.8762 − 40.00) ÷ 40.00 = 17.19%.

On your calculator

0.8÷42+1=×46= 46.8762
−40=÷40= 0.1719

0.8ENTER42÷1+46× 46.8762
40−40÷ 0.1719

ENTER enter (on the HP, puts the number on the stack)

Return over several periods Use it

r = (1 + r_1)(1 + r_2)\cdots(1 + r_n) - 1

Quick example

Yearly total returns of 6%, −2% and 9%: 1.06 × 0.98 × 1.09 − 1 = 13.23%. Adding them would give 13.00%.

On your calculator

1.06×0.98×1.09−1= 0.1323

1.06ENTER0.98×1.09×1− 0.1323

ENTER enter (on the HP, puts the number on the stack)

Price from next year's expected price Memorize

P_t = \dfrac{E(P_{t+1}) + E(D_{t+1})}{1 + r_e}

Quick example

An expected price of 30.00 and an expected dividend of 0.90 in a year, with a required return of 8%: (30.00 + 0.90) ÷ 1.08 = 28.61.

On your calculator

30+0.9=÷1.08= 28.6111

30ENTER0.9+1.08÷ 28.6111

ENTER enter (on the HP, puts the number on the stack)

Price from n years of dividends and a target Memorize

P_t = \sum_{i=1}^{n} \dfrac{D}{(1 + r_e)^i} + \dfrac{E(P_{t+n})}{(1 + r_e)^n}

Quick example

A dividend of 0.60 a year for 5 years, a target of 20.00 and a required return of 7%: 0.60 × 4.1002 + 20.00 ÷ 1.07⁵ = 2.46 + 14.26 = 16.72.

On your calculator

2NDCLR TVM
5N7I/Y0.6PMT20FV
CPTPV −16.72

2ND second function (the shifted label above a key) · CLR TVM clear the time value of money keys · N number of periods · I/Y interest rate per year (per period when P/Y is 1) · PMT payment · FV future value · CPT compute · PV present value

fCLEAR FIN
5n7i0.6PMT20FV
PV −16.72

f gold shift key · CLEAR FIN clear the financial registers · n number of periods · i interest rate per period · PMT payment · FV future value · PV present value