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hscscience Maths Std · Y12
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MST-12-S2-02 ~45 min ⚡ +75 XP available

Shares: Value, Dividends and Dividend Yield

A share pays you in two separate ways, and they move independently. The price can rise while the income falls. Reading a share table means telling those two apart, and the yield column is the one that catches people out.

Today's hook, A company keeps paying exactly the same dividend, cent for cent, two years running. Over the same two years its share price climbs by a quarter. The dividend yield printed in the paper falls. Nothing has gone wrong, and every holder is better off. Why does the number go down?
0/4QUESTS

Get oriented

Meet the two returns a share pays and settle the key terms.

Worksheets

Practise this lesson

Three printable worksheets that build from foundations to mastery, or build your own from any question in this focus area.

Build Foundations & guided practice Apply Application practice Master Mastery challenge Build custom Build your own from any question
01
Recall, your gut answer first
+5 XP warm-up

You own $500$ shares in a company. It announces a dividend of $20$ cents per share, and on the same day the share price moves from $\$4.00$ to $\$5.00$.

Without calculating write down which of those two events puts money in your bank account this month, and which one only changes what your holding is worth on paper.

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02
Two returns, and they move independently
+5 XP to read

Owning shares pays you in two ways that have almost nothing to do with each other. Capital growth is the price going up, and you only receive it if you sell. Dividends are cash the company pays you for holding the share, whatever the price is doing.

Dividends are quoted per share, in cents. A dividend of $24$ cents per share means every single share you hold pays you $\$0.24$. Multiply by how many you own to get the cash.

The yield is a rate, so it needs a price. The dividend yield expresses the cash payment as a percentage of what one share currently costs. It lets you compare a $24$ cent dividend on a $\$6$ share against a $\$1.62$ dividend on a $\$45$ share.

$\text{yield} = \dfrac{\text{dividend per share}}{\text{market price per share}} \times 100\%$
DIVIDEND PAID
Cash in your account. Number of shares $\times$ dividend per share. The only place the size of your parcel matters.
DIVIDEND YIELD
A percentage, per share. How many shares you own makes no difference at all to the yield.
CENTS AND DOLLARS
Dividends are quoted in cents, prices in dollars. Convert before dividing: $162\text{c} = \$1.62$.
03
What you'll master
Know

Key facts

  • Dividend paid $=$ number of shares $\times$ dividend per share
  • Dividend yield $=$ dividend per share $\div$ market price, as a percentage
  • The yield uses the price now, not the price you paid
  • Share table columns: Last, Change, High, Low, Div, Yield
Understand

Concepts

  • Why capital growth and dividend income are separate returns
  • Why a rising price pushes the yield down when the dividend is unchanged
  • Why the number of shares never appears in a yield
  • What the shape of a price graph says beyond its two endpoints
Can do

Skills

  • Read any row of a share table and reproduce its yield column
  • Find the dividend paid on a parcel of any size
  • Find a price from a yield, the reverse direction
  • Interpret a share price graph over time, including a fall inside a rise
04
Key terms
ShareOne unit of ownership in a company. Like this: holding $500$ of a company's shares makes you a part-owner, entitled to your share of any dividend it declares.
DividendA cash payment made to shareholders, quoted in cents per share. Like this: a declared dividend of $24$ cents pays the holder of $850$ shares $850 \times \$0.24 = \$204$.
Dividend yieldThe dividend expressed as a percentage of the current share price. Like this: a $24$ cent dividend on a $\$6.40$ share is a yield of $0.24 \div 6.40 = 3.75\%$, and that figure is the same whether you own $10$ shares or $10\,000$.
Capital growthThe rise in the price of a share, measured against what you paid. Like this: a share bought at $\$4.00$ and now worth $\$4.60$ has grown $0.60 \div 4.00 = 15\%$, which you only bank if you sell.
LastThe most recent traded price, the column a share table leads with. Like this: a row reading Last $\$44.60$ means the last completed trade was at $\$44.60$, and that is the price the yield column is built from.

Read a share table

Find price, dividend and yield, and see why the yield moves on its own.

05
Reading a share table, and why the yield moves on its own
core concept

A share table prints six columns, and the last one is calculated from two of the others. That is the single most useful thing to know about it:

dividend paid: $\quad D = n \times d$   ($n$ shares, $d$ dollars per share)
dividend yield: $\quad y = \dfrac{d}{P} \times 100\%$   ($P$ the current price)
capital growth: $\quad g = \dfrac{P_{\text{now}} - P_{\text{paid}}}{P_{\text{paid}}} \times 100\%$

Look at what is not in the yield formula: $n$. The number of shares you own cannot change a percentage, and a great many marks are lost by multiplying a yield by the size of the parcel.

Now the hook. Hold $d$ fixed and let $P$ rise. The fraction $d/P$ has a constant numerator and a growing denominator, so the yield falls. Nothing has gone wrong: the company still pays exactly the same cash, but each share now costs more to buy, so each dollar invested buys less income.

Which return matters is a question about the investor, not the share. Someone living on the income cares about the yield. Someone building wealth over decades cares about capital growth. A share can be the best choice on one measure and the worst on the other, which is why an exam question asking you to compare two shares almost always wants both numbers and a reason.

Dividend paid $=$ number of shares $\times$ dividend per share. Dividend yield $=$ (dividend per share $\div$ current market price) $\times 100\%$, and the number of shares never appears in it. Because the price is the denominator, a rising price lowers the yield when the dividend is unchanged. Capital growth is measured against the price you paid, the yield against the price today.

Pause, copy both formulas, and write one line explaining why the yield falls when the price rises and the dividend does not, into your book.

Quick check: A share trades at $\$8.00$ and pays a dividend of $32$ cents per share. What is the dividend yield?

Work the share examples

Follow dividend, yield and share-value calculations from the table.

Worked examples · 3 in a row, reveal as you go

PROBLEM 1 · READING THE TABLE

A share table prints this row. Show that the Yield column is consistent with the other columns.

CompanyLastChangeHighLowDivYield
Brindle Ltd$\$44.60$+0.35$\$48.20$$\$37.15$162c3.63%
1
$d = 162\text{c} = \$1.62, \qquad P = \$44.60$
Convert the dividend out of cents first. Dividing $162$ by $44.60$ would give a number a hundred times too large, and it is the most common slip in this topic.
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PROBLEM 2 · DIVIDEND PAID AND DIVIDEND YIELD

Kalina holds $850$ shares in a company that declares a dividend of $24$ cents per share. The shares currently trade at $\$6.40$. Find the dividend she receives and the dividend yield.

1
$D = n \times d = 850 \times \$0.24 = \mathbf{\$204.00}$
This is the cash paid into her account. The share price plays no part in it at all.
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PROBLEM 3 · THE VALUE OF A SHARE OVER TIME

A share's closing price is recorded at the end of each month for six months: $\$3.20$, $\$3.55$, $\$3.40$, $\$3.90$, $\$4.15$, $\$3.95$. Describe what the graph shows, and find the overall percentage change.

1
$3.20 \to 3.55 \to 3.40 \to 3.90 \to 4.15 \to 3.95$
Plot month on the horizontal axis and price on the vertical, then join the points. A share price graph is a line graph, because the price exists continuously between the readings.
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Avoid the yield traps

Stop dividing cents by dollars and fix the per-share slips.

Common errors · the 3 traps that cost marks

Trap 01
Dividing cents by dollars
A dividend of $162$c against a price of $\$44.60$ is $1.62 \div 44.60$, not $162 \div 44.60$. The second gives $3.63$ where the answer is $3.63\%$, and because the digits look right it survives a glance. Convert to dollars before you divide, every time.
Trap 02
Putting the number of shares into the yield
The yield is a property of the share, not of your holding. Owning $850$ of them does not make your yield $850$ times larger. If $n$ appears anywhere in a yield calculation, it is wrong.
Trap 03
Using the price you paid instead of the price now
Dividend yield uses the current market price. Capital growth uses the price you paid. The two formulas take different prices from the same question, and swapping them produces two wrong answers from one mistake.

True or false: If a company holds its dividend steady and the share price rises, the dividend yield falls.

Drill it and revisit

Run the drill, then return to your opening answer and name what has changed.

Quick-fire practice · 5 calculations

1

A holding of $1200$ shares pays a dividend of $18$ cents per share. Find the dividend paid.

2

A share trades at $\$9.50$ and pays a dividend of $38$ cents. Find the dividend yield, to 2 decimal places.

3

A share trades at $\$2.50$ and pays a dividend of $9$ cents. Find the dividend yield, to 2 decimal places.

4

A share pays a dividend of $26$ cents and has a dividend yield of $5.2\%$. Find its market price.

5

Marcus holds $640$ shares trading at $\$12.80$, each paying a dividend of $45$ cents. Find the dividend paid and the dividend yield.

Match each quantity to what it is measured against:

  • Dividend paid
  • Dividend yield
  • Capital growth
  • Last
  • The price you originally paid
  • The number of shares you hold
  • The most recent traded price
  • The current market price of one share
10
Revisit your thinking

Back to the hook. The company pays $30$ cents per share two years running, and the price climbs from $\$6.00$ to $\$7.50$.

Year 1 yield: $\dfrac{0.30}{6.00} \times 100\% = 5.00\%$.   Year 2 yield: $\dfrac{0.30}{7.50} \times 100\% = 4.00\%$.

The yield fell by a fifth while every holder gained $\$1.50$ a share in capital growth and lost not a cent of income. The yield went down because the denominator went up, and that is the only thing that changed.

Which matters more depends entirely on whether you are living on the income or building the holding, and that is the judgement an exam question is really asking for.

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Practise shares and dividends

Answer the question bank, then write full short-answer responses.

01
Multiple choice
+5 XP per correct · +25 XP all-correct

Pick your answer, then rate your confidence. That tells the system what to drill next.

Q1. A share table row shows Last $\$44.60$ and Div $162$c. The dividend yield is closest to:

Q2. Priya owns 1500 shares paying a dividend of 22 cents per share. The dividend she receives is:

Q3. A share priced at $\$2.50$ pays a dividend of $9$ cents. Its dividend yield is:

Q4. A company holds its dividend at 30 cents per share while the price rises from $\$6.00$ to $\$7.50$. The dividend yield:

Q5. A share bought at $\$8.00$ is now worth $\$9.60$. The capital growth is:

02
Short answer
ApplyBand 32 marks

SA 1. A share table row reads Last $\$18.40$ and Div $74$c. Calculate the dividend yield, correct to 2 decimal places. (2 marks)

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ApplyBand 44 marks

SA 2. Dev buys $2400$ shares at $\$5.60$ each. The company declares a dividend of $21$ cents per share.
(a) Find the dividend Dev receives. (1 mark)
(b) Find the dividend yield at the time of purchase. (1 mark)
(c) A year later the price has risen to $\$7.00$ and the dividend is unchanged. Find the new dividend yield, and explain why Dev is better off even though the yield has fallen. (2 marks)

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AnalyseBand 55 marks

SA 3. Two shares are compared after one year.
Share A: bought at $\$4.00$, now $\$4.60$, dividend $16$ cents.
Share B: bought at $\$9.00$, now $\$9.45$, dividend $45$ cents.
(a) Find the capital growth of each. (2 marks)
(b) Find the dividend yield of each, correct to 2 decimal places. (2 marks)
(c) State which share performed better, justifying your choice by reference to a stated investor goal. (1 mark)

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📖 Comprehensive answers (click to reveal)

MC 1, C: $162\text{c} = \$1.62$, so $y = 1.62 \div 44.60 = 3.63\%$. Option D, $27.53\%$, is the fraction inverted.

MC 2, A: $1500 \times \$0.22 = \$330.00$. Option D divides instead of multiplying.

MC 3, D: $y = 0.09 \div 2.50 = 0.036 = 3.60\%$. Option C is the ratio without multiplying by $100$; option A is inverted.

MC 4, B: $0.30 \div 6.00 = 5.00\%$ and $0.30 \div 7.50 = 4.00\%$. The dividend is unchanged, so the fall comes entirely from the larger denominator. Option D is the parcel-size error: the number of shares never enters a yield.

MC 5, C: $(9.60 - 8.00) \div 8.00 = 0.20 = 20.00\%$. Option B divides by the new price instead of the price paid.

SA 1 (2 marks): $74\text{c} = \$0.74$ [1]. $y = 0.74 \div 18.40 \times 100\% = \mathbf{4.02\%}$ [1]. Check: $0.0402 \times 18.40 = \$0.74$.

SA 2 (4 marks): (a) $D = 2400 \times \$0.21 = \mathbf{\$504.00}$ [1]. (b) $y = 0.21 \div 5.60 \times 100\% = \mathbf{3.75\%}$ [1]. (c) $y = 0.21 \div 7.00 \times 100\% = \mathbf{3.00\%}$ [1]. Dev is better off because he still receives the same $\$504$ of income and his $2400$ shares have gained $\$1.40$ each, a capital growth of $\$3360$. The yield fell only because the price, which is the denominator, rose; it measures income per dollar of current price, not Dev's return [1].

SA 3 (5 marks): (a) A: $(4.60 - 4.00) \div 4.00 = \mathbf{15.00\%}$ [1]. B: $(9.45 - 9.00) \div 9.00 = \mathbf{5.00\%}$ [1]. (b) A: $0.16 \div 4.60 = \mathbf{3.48\%}$ [1]. B: $0.45 \div 9.45 = \mathbf{4.76\%}$ [1]. (c) There is no single correct share, and the mark is for the justification. A is better for an investor seeking capital growth, tripling B's growth at $15\%$ against $5\%$. B is better for an investor living on the income, yielding $4.76\%$ against $3.48\%$. An answer naming a goal and matching the share to it earns the mark; an answer picking a share with no stated goal does not [1].

Drills: 1. $1200 \times \$0.18 = \$216.00$  ·  2. $0.38 \div 9.50 = 4.00\%$  ·  3. $0.09 \div 2.50 = 3.60\%$  ·  4. $P = 0.26 \div 0.052 = \$5.00$  ·  5. $D = 640 \times \$0.45 = \$288.00$ and $y = 0.45 \div 12.80 = 3.52\%$.