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Shares, dividends and yield for HSC Maths Standard 2

Syllabus dot point

“Calculate dividend yield, dividend payout, capital gain and total return on share investments”

HSCMaths Standard 2Year 12: Financial Mathematics10 min read

Quick answer

Dividend yield is dividend per share divided by share price; total return adds capital gain to dividend income and is usually expressed as a percentage of the original investment.

Jump to a section
  1. What this dot point is asking
  2. The answer
  3. Exam-style questions
  4. Practice questions

What this dot point is asking

NESA (the body that sets the HSC exam) wants you to work out the return on a share investment in two parts. The first part is income from dividends. The second is capital gain or loss, which is the money made or lost when the share price changes. You also need to find related ratios, such as the dividend yield and the price-earnings ratio.

The answer

Every shares question rests on one idea: an investor earns in two separate ways, and the marks come from keeping them apart until the final step. Income is the dividends a company pays out of profit, measured by the dividend yield. Capital growth is the share price rising (or falling) between buying and selling, measured by the capital gain. Total return adds the two. The figure below splits a real Telstra holding into exactly these two slices so the relationship is concrete.

The two sources of total return on a share investmentA horizontal bar showing that the 120 dollar total return on a 950 dollar Telstra investment splits into two parts: a 75 dollar capital gain from the share price rising from 3.80 to 4.10, drawn in the accent colour, and 45 dollars of dividend income, drawn in the muted colour. Together they give a total return of 120 dollars, or 12.63 percent of the original 950 dollars invested.Total return = capital gain + dividend income250 Telstra shares bought for $950capital gain$75dividends$45total$1207.89% capital growth4.74% yieldtotal return = 12.63%\$120 of return on \$950 invested. Yield is only the dividend slice; total return adds the capital gain.

Dividend per share

A dividend is a cash payment a company pays to shareholders out of its profit. It is usually quoted per share, in dollars and cents.

If a company pays a total dividend of DD across nsharesn_{\text{shares}} shares on issue:

dividend per share=Dnshares.\text{dividend per share} = \frac{D}{n_{\text{shares}}}.

For an investor holding kk shares, the dividend received is k×k \times (dividend per share).

Dividend yield

Dividend yield expresses the dividend as a percentage of the share price:

yield=dividend per shareshare price×100%.\text{yield} = \frac{\text{dividend per share}}{\text{share price}} \times 100\%.

Higher yields tend to come from mature companies (banks, telcos, utilities); growth companies often pay low or no dividends because they reinvest profits.

Key fact

Returns on shares come from two sources, and each has its own formula. Income: dividend yield=dividend per shareshare price×100%\text{dividend yield} = \dfrac{\text{dividend per share}}{\text{share price}} \times 100\%. Capital growth: capital gain=shares×(sell price−buy price)\text{capital gain} = \text{shares} \times (\text{sell price} - \text{buy price}). Total return combines them: in dollars, dividends plus capital gain; as a percentage, dividends+capital gainoriginal investment×100%\dfrac{\text{dividends} + \text{capital gain}}{\text{original investment}} \times 100\%. Name which one you are computing at each step, and put the original investment in the denominator unless told otherwise.

Capital gain or loss

Capital gain is the increase in share price over the holding period.

capital gain=shares held×(selling price−purchase price).\text{capital gain} = \text{shares held} \times (\text{selling price} - \text{purchase price}).

Negative result is a capital loss.

Total return

Total return combines income (dividends received) and capital gain or loss:

total return (dollars)=total dividends+capital gain.\text{total return (dollars)} = \text{total dividends} + \text{capital gain}.

As a percentage of the original investment:

total return (%)=total dividends+capital gainoriginal investment×100%.\text{total return (\%)} = \frac{\text{total dividends} + \text{capital gain}}{\text{original investment}} \times 100\%.

The figure at the top of the page is exactly this calculation: a $75 capital gain plus $45 of dividends gives a $120 total return, which is 12.63%12.63\% of the $950 invested. The dividend slice alone (the 4.74%4.74\% yield) understates the return; the capital growth slice (7.89%7.89\%) makes up the rest.

Brokerage

Buying and selling shares through a broker costs a fee called brokerage, quoted either as a flat amount (for example $10 a trade with an online broker) or as a percentage of the trade value. Brokerage is paid on the way in and on the way out, so a round trip incurs it twice. When a question mentions brokerage, fold it in:

  • The true cost of buying is shares×buy price+brokerage\text{shares} \times \text{buy price} + \text{brokerage}.
  • The net proceeds of selling are shares×sell price−brokerage\text{shares} \times \text{sell price} - \text{brokerage}.

A net return after costs subtracts both brokerage charges. If a question gives no brokerage, assume there is none.

Price-earnings ratio

The price-earnings ratio compares the share price to the company's earnings per share:

P/E=share priceearnings per share.\text{P/E} = \frac{\text{share price}}{\text{earnings per share}}.

A higher P/E suggests the market is paying more for each dollar of current earnings, often because it expects strong growth. The ASX market average P/E typically sits between 1414 and 2020.

Franking credits

In Australia, dividends are often franked (or partly franked), meaning the company has already paid corporate tax on the profit being distributed. This is examinable only in worded form (the question will tell you the cash amount); you do not need to compute the gross-up.

Two sources of return

The key idea behind every shares question is that an investor earns in two separate ways. Most questions want you to keep these two apart, then combine them at the end. Income comes from dividends, the regular cash a company pays out of profit. You measure income with the dividend yield. Capital growth comes from the share price rising (or falling) between when you buy and when you sell. You measure it with the capital gain. Total return adds the two together. Mixing them up is the most common error. For example, do not quote a dividend yield when the question asks for total return, so name which part you are working out at each step.

Choosing the right denominator

Every percentage in this topic is a percentage "of" some base amount, and the care needed is in choosing that base. The base is the denominator, the number you divide by. Dividend yield is the dividend as a percentage of the current share price (or the original investment, depending on the wording). Total return percentage is the dollar return as a percentage of the original investment, unless the question clearly says otherwise. Read each question carefully. Check whether a percentage is per share or for the whole holding, and whether it uses the purchase price or the current price. Writing down which denominator you used protects the method marks even if your arithmetic slips.

How exam questions ask about shares

The wording tells you which of the two sources, or which ratio, is wanted:

  • "Find the dividend yield." Dividend per share over share price, times 100%100\%. If only a total dividend and a number of shares are given, find the dividend per share first.
  • "How much does the investor receive in dividends?" Shares held times dividend per share (or just the stated total dividend).
  • "Find the capital gain / loss." Shares times (sell price minus buy price). A negative answer is a loss; keep the sign.
  • "Find the total return (in dollars and as a percentage)." Add dividends and capital gain for the dollar figure, then divide by the original investment for the percentage. State the denominator.
  • "Including brokerage of $X each way..." Add brokerage to the buy cost and subtract it from the sell proceeds before computing the net return.
  • "Find the price-earnings (P/E) ratio." Share price over earnings per share. Do not confuse earnings per share with dividend per share.
  • "Which investment gives the better return?" Compute the total-return percentage of each on the same basis and compare.
Dividend yield, total return, capital loss, and P/E ratio

Calculate dividend yield for a single share, total return on a Telstra holding, total return including a capital loss on a mining holding, and the P/E ratio for a share trading at $60.

Dividend yield of a single share

Dividend yield expresses the annual dividend as a percentage of the current share price. It tells an investor how much income they earn per dollar invested, ignoring any price movement.

A share trades at $32.50 and pays an annual dividend of $1.95.

Yield=1.9532.50×100%=6.00%\text{Yield} = \frac{1.95}{32.50} \times 100\% = 6.00\%

Final answer (Part 1): Dividend yield =6.00%= 6.00\%.

Total return on a Telstra holding

Calculate total cost of the Telstra purchase: Before finding any return, we need the amount of money at risk. Multiplying the number of shares by the purchase price gives the total capital invested, which is the denominator for the percentage return.

Purchase cost=250×3.80=950\text{Purchase cost} = 250 \times 3.80 = 950

i.e. $950.

Find the capital gain and total dollar return: Total return has two components: the change in share price (capital gain or loss) and dividends received. Both must be included to measure how much the investment actually earned. An investor buys 250250 Telstra shares at $3.80 each in 2024; by the end of the year the price is $4.10 and total dividends of $45 were paid.

Capital gain=250×(4.10−3.80)=250×0.30=75\text{Capital gain} = 250 \times (4.10 - 3.80) = 250 \times 0.30 = 75

i.e. a capital gain of $75.

Total return in dollars=75+45=120\text{Total return in dollars} = 75 + 45 = 120

i.e. $120.

Express total return as a percentage: Dividing the dollar return by the original investment and multiplying by 100%100\% puts the return on a comparable basis with other investments and with the dividend yield calculated above. This is the calculation drawn in the figure at the top of the page.

Total return (%)=120950×100%≈12.63%\text{Total return (\%)} = \frac{120}{950} \times 100\% \approx 12.63\%

Final answer (Part 2): Total return ≈12.63%\approx 12.63\%.

Total return with a capital loss

When the share price falls, the capital gain is negative. The same method applies: add the capital component (now negative) and the dividend component. An investor buys 10001000 shares of a mining company at $8.20; a year later the price is $6.40 and dividends total $200.

Capital component=1000×(6.40−8.20)=−1800\text{Capital component} = 1000 \times (6.40 - 8.20) = -1800

i.e. a capital loss of $1800.

Total return in dollars=200+(−1800)=−1600\text{Total return in dollars} = 200 + (-1800) = -1600

i.e. a loss of $1600.

Total return (%)=−16008200×100%≈−19.5%\text{Total return (\%)} = \frac{-1600}{8200} \times 100\% \approx -19.5\%

Final answer (Part 3): Net loss for the year is $1600 (a return of −1600-1600), or approximately −19.5%-19.5\%.

Price-to-earnings (P/E) ratio

The price-to-earnings (P/E) ratio compares the market price to annual earnings per share. A higher P/E means investors are paying more for each dollar of current earnings, often because they expect strong future growth. A share trades at $60 and reports earnings per share of $3.

P/E=603=20\text{P/E} = \frac{60}{3} = 20

The market is paying $20 for each $1 of current annual earnings.

Final answer (Part 4): P/E ratio =20= 20.

Edge case: total return after brokerage

Suppose the Telstra investor above paid $10 brokerage to buy and $10 to sell. The true cost is 950+10=960950 + 10 = 960, i.e. $960; the net sale proceeds are 250×4.10−10=1025−10=1015250 \times 4.10 - 10 = 1025 - 10 = 1015, i.e. $1015; and with $45 of dividends the net dollar return is 1015+45−960=1001015 + 45 - 960 = 100, i.e. $100, not $120. As a percentage of the $960 outlay that is 100960×100%≈10.42%\frac{100}{960} \times 100\% \approx 10.42\%. Brokerage of $20 on a small parcel has shaved more than two percentage points off the return, which is why it matters for small trades.

Exam technique

Name the component you are computing at each step (dividend, capital gain, or total return) so a marker can follow which formula you are using. Quote dividend yield and total-return percentages to two decimal places with the percent sign. Use the original investment as the denominator for total return unless the question explicitly says the current value, and state which you used. Keep the sign on a capital loss and carry it into the total. If brokerage is mentioned, apply it on both the buy and the sell before finding the net return. Do not mix earnings per share (for P/E) with dividend per share (for yield).

Common traps
Mixing up dividend yield and total return
Yield is just the dividend component. Total return includes capital gain.
Computing the return on the closing price
Use the original investment in the denominator for the total return percentage, unless the question explicitly says otherwise.
Forgetting to multiply by number of shares
Dividend per share times number of shares gives total dividend received.
Negative capital gain is a loss
Include the sign in the total-return calculation.
Confusing P/E with yield
P/E uses earnings per share. Yield uses dividend per share. Earnings is the company's profit; dividend is the cash paid out to shareholders (usually less than earnings).
Note

A share is a small piece of a company that you can own. Owning shares can pay you back in two ways. First, the company can hand out some of its profit as cash, and your slice of that cash is called a dividend. Second, the price of the share can go up, so it is worth more than you paid, and that extra value is called a capital gain (if the price drops instead, it is a loss). Add the cash you got and the change in value together and you have your total return for the year. Most questions just ask you to find one of these parts, or both, so the trick is to keep them separate as you work.

Exam-style questions

Questions in the style of NESA exam questions on this dot point, each with a worked answer. They are written by ExamExplained unless tagged "Past paper"; the year shows the paper a question is modelled on.

2022 HSC-style2 marks
A share is bought at $25.40. The company pays a dividend of $1.27 per share. Find the dividend yield correct to two decimal places.
Show worked answer →

Dividend yield = dividend per shareshare price×100%\frac{\text{dividend per share}}{\text{share price}} \times 100\%.

Yield =1.2725.40×100%≈5.00%= \frac{1.27}{25.40} \times 100\% \approx 5.00\%.

Markers reward the formula, substitution, and the answer to two decimal places with the percent sign.

2023 HSC-style4 marks
An investor buys 400400 Commonwealth Bank shares at $98.50 each. After a year the share price is $104.20 and a total dividend of $1680 has been paid. Find the capital gain, dividend yield, and total return for the year.
Show worked answer →

Purchase: 400×98.50=39400400 \times 98.50 = 39400, i.e. $39400.

Capital gain: 400×(104.20−98.50)=400×5.70=2280400 \times (104.20 - 98.50) = 400 \times 5.70 = 2280, i.e. $2280.

Dividend yield: 168039400×100%≈4.26%\frac{1680}{39400} \times 100\% \approx 4.26\%.

Total return in dollars: 2280+1680=39602280 + 1680 = 3960, i.e. $3960.

Total return (%): 396039400×100%≈10.05%\frac{3960}{39400} \times 100\% \approx 10.05\%.

Markers reward the capital gain calculation, dividend yield based on the original investment, and the total-return percentage. Some marking guides accept total return based on either the original or the closing investment value, but be explicit about which.

Practice questions

Original practice questions graded from foundation to exam level, each with a full worked solution. Try them before revealing the solution.

foundation1 mark
An investor holds 12001200 ANZ shares. The company pays an annual dividend of $0.81 per share. Calculate the total dividend the investor receives.
Show worked solution →

Choose the calculation. The total dividend received is the number of shares held multiplied by the dividend per share.

Substitute and evaluate. The investor holds 12001200 shares at $0.81 each.

dividend received=1200×0.81=972.\text{dividend received} = 1200 \times 0.81 = 972.

State the answer. The investor receives $972.00 in dividends. As a check, 972÷1200=0.81972 \div 1200 = 0.81, i.e. $0.81 per share, which matches the stated dividend.

foundation2 marks
A Westpac share trades at $46.00 and pays an annual dividend of $2.07 per share. Calculate the dividend yield, correct to two decimal places.
Show worked solution →

Write the formula. Dividend yield is the dividend per share as a percentage of the share price, yield=dividend per shareshare price×100%\text{yield} = \dfrac{\text{dividend per share}}{\text{share price}} \times 100\%.

Substitute and evaluate. The dividend per share is $2.07 and the price is $46.00.

yield=2.0746.00×100%=4.50%.\text{yield} = \frac{2.07}{46.00} \times 100\% = 4.50\%.

State the answer. The dividend yield is 4.50%4.50\%. As a check, 4.50%4.50\% of the $46.00 price is 0.045×46.00=2.070.045 \times 46.00 = 2.07, i.e. $2.07, which is the dividend, so the yield is correct. The share price is the divisor, not the dividend.

foundation2 marks
Priya owns 850850 shares in an electricity company that pays a dividend of $0.84 per share for the year. Calculate the total dividend she receives.
Show worked solution →

Choose the calculation. The total dividend received is the number of shares held multiplied by the dividend per share.

Substitute and evaluate. Priya holds 850850 shares at $0.84 each.

dividend received=850×0.84=714.\text{dividend received} = 850 \times 0.84 = 714.

State the answer. Priya receives $714.00 in dividends. As a check, 714÷850=0.84714 \div 850 = 0.84, i.e. $0.84 per share, which matches the stated dividend. Multiply by the number of shares; do not stop at the per-share figure.

foundation2 marks
A BHP share trades at $44.00 and pays an annual dividend of $2.42 per share. Calculate the dividend yield, correct to two decimal places.
Show worked solution →

Write the formula. Dividend yield is the dividend per share as a percentage of the share price, yield=dividend per shareshare price×100%\text{yield} = \dfrac{\text{dividend per share}}{\text{share price}} \times 100\%.

Substitute and evaluate. The dividend per share is $2.42 and the price is $44.00.

yield=2.4244.00×100%=5.50%.\text{yield} = \frac{2.42}{44.00} \times 100\% = 5.50\%.

State the answer. The dividend yield is 5.50%5.50\%. As a check, 5.50%5.50\% of the $44.00 price is 0.055×44.00=2.420.055 \times 44.00 = 2.42, i.e. $2.42, which is the dividend, so the yield is correct. The share price is the divisor, not the dividend.

core3 marks
A company declares a total dividend of $5\,400\,000, paid equally across the 9 000 0009\,000\,000 shares on issue. Its shares trade at $24.00. Calculate the dividend per share and the dividend yield.
Show worked solution →

Find the dividend per share. Divide the total dividend by the number of shares on issue.

dividend per share=5 400 0009 000 000=0.60,\text{dividend per share} = \frac{5\,400\,000}{9\,000\,000} = 0.60,

i.e. $0.60 per share.

Find the dividend yield. Express the dividend per share as a percentage of the $24.00 share price.

yield=0.6024.00×100%=2.50%.\text{yield} = \frac{0.60}{24.00} \times 100\% = 2.50\%.

State the answer. The dividend per share is $0.60 and the yield is 2.50%2.50\%. As a check, 2.50%2.50\% of $24.00 is 0.025×24.00=0.600.025 \times 24.00 = 0.60, i.e. $0.60, the dividend per share, so the yield is correct. Find the per-share dividend first, then divide by the price, not by the number of shares.

core2 marks
A share trades at $73.50 and the company reports earnings per share of $4.20. Calculate the price-earnings (P/E) ratio.
Show worked solution →

Write the formula. The price-earnings ratio is the share price divided by the earnings per share, P/E=share priceearnings per share\text{P/E} = \dfrac{\text{share price}}{\text{earnings per share}}.

Substitute and evaluate. The price is $73.50 and the earnings per share is $4.20.

P/E=73.504.20=17.5.\text{P/E} = \frac{73.50}{4.20} = 17.5.

State the answer. The P/E ratio is 17.517.5, meaning the market is paying $17.50 for each $1 of current annual earnings. As a check, 17.5×4.20=73.5017.5 \times 4.20 = 73.50, the share price, so the ratio is correct. The P/E uses earnings per share, not the dividend per share.

core3 marks
Liam buys 750750 Woolworths shares at $33.20 each through an online broker that charges $29.50 brokerage on the trade. Calculate the total cost of the purchase, including brokerage.
Show worked solution →

Find the value of the shares. Multiply the number of shares by the price per share.

share value=750×33.20=24 900,\text{share value} = 750 \times 33.20 = 24\,900,

i.e. $24,900.

Add the brokerage. The broker charges $29.50 on the way in, so add it to the share value to get the true cost.

total cost=24 900+29.50=24 929.50.\text{total cost} = 24\,900 + 29.50 = 24\,929.50.

State the answer. The total cost of the purchase is $24,929.50. As a check, this is $29.50 more than the $24,900 value of the shares, the brokerage fee, so the cost is correct. Brokerage is added when buying; it is not part of the share value itself.

core4 marks
Daniel buys 600600 shares in a retailer at $18.50 each. A year later the price has risen to $21.20 and total dividends of $540 have been paid. Calculate the capital gain, the total return in dollars, and the total return as a percentage of his original investment, to two decimal places.
Show worked solution →

Find the original investment. Multiply the number of shares by the purchase price; this is the denominator for the percentage return.

cost=600×18.50=11 100,\text{cost} = 600 \times 18.50 = 11\,100,

i.e. $11,100.

Find the capital gain. Multiply the number of shares by the rise in price.

capital gain=600×(21.20−18.50)=600×2.70=1620,\text{capital gain} = 600 \times (21.20 - 18.50) = 600 \times 2.70 = 1620,

i.e. $1620.

Find the total dollar return. Add the dividends to the capital gain.

total return=1620+540=2160,\text{total return} = 1620 + 540 = 2160,

i.e. $2160.

Express the return as a percentage. Divide the dollar return by the original investment.

total return=216011 100×100%≈19.46%.\text{total return} = \frac{2160}{11\,100} \times 100\% \approx 19.46\%.

State the answer. The capital gain is $1620.00, the total return is $2160.00, and that is approximately 19.46%19.46\% of the $11,100 invested. As a check, 19.46%19.46\% of $11,100 is about 0.1946×11 100≈21600.1946 \times 11\,100 \approx 2160, i.e. $2160, matching the dollar return. Use the original investment as the denominator, not the closing value.

exam4 marks
An investor buys 15001500 shares in a mining company at $7.40 each. A year later the price has fallen to $5.90, but the company still pays total dividends of $360. Calculate the capital loss and the total return for the year, in dollars and as a percentage of the original investment, to two decimal places.
Show worked solution →

Find the original investment. Multiply the number of shares by the purchase price.

cost=1500×7.40=11 100,\text{cost} = 1500 \times 7.40 = 11\,100,

i.e. $11,100.

Find the capital component. Multiply the shares by the change in price; the price fell, so this is negative.

capital component=1500×(5.90−7.40)=1500×(−1.50)=−2250,\text{capital component} = 1500 \times (5.90 - 7.40) = 1500 \times (-1.50) = -2250,

a capital loss of $2250.

Find the total dollar return. Add the dividends to the (negative) capital component, keeping the sign.

total return=360+(−2250)=−1890,\text{total return} = 360 + (-2250) = -1890,

i.e. a loss of $1890.

Express the return as a percentage. Divide the dollar return by the original investment.

total return=−189011 100×100%≈−17.03%.\text{total return} = \frac{-1890}{11\,100} \times 100\% \approx -17.03\%.

State the answer. The capital loss is $2250.00 and the total return for the year is a loss of $1890.00, or about −17.03%-17.03\% of the $11,100 invested. The dividends soften the loss but do not erase it. As a check, 0.1703×11 100≈18900.1703 \times 11\,100 \approx 1890, i.e. $1890, matching the dollar loss. Carry the negative sign through; the loss is smaller than the price fall because the dividends are added back.

exam5 marks
Mei buys 400400 shares at $32.50 through an online broker that charges $19.95 brokerage on each trade. A year later she sells them at $35.80, and over the year the shares paid total dividends of $280. Calculate her net return for the year in dollars and as a percentage of her total outlay, to two decimal places.
Show worked solution →

Find the true cost of buying. Brokerage is added to the purchase value, since the broker charges it on the way in.

cost=400×32.50+19.95=13 000+19.95=13 019.95,\text{cost} = 400 \times 32.50 + 19.95 = 13\,000 + 19.95 = 13\,019.95,

i.e. $13,019.95.

Find the net sale proceeds. Brokerage is subtracted from the sale value, since it is charged again on the way out.

proceeds=400×35.80−19.95=14 320−19.95=14 300.05,\text{proceeds} = 400 \times 35.80 - 19.95 = 14\,320 - 19.95 = 14\,300.05,

i.e. $14,300.05.

Find the net dollar return. Add the dividends to the proceeds, then subtract the total cost.

net return=14 300.05+280−13 019.95=1560.10,\text{net return} = 14\,300.05 + 280 - 13\,019.95 = 1560.10,

i.e. $1560.10.

Express the return as a percentage of the outlay. Divide the net return by the true cost.

net return=1560.1013 019.95×100%≈11.98%.\text{net return} = \frac{1560.10}{13\,019.95} \times 100\% \approx 11.98\%.

State the answer. Mei's net return is $1560.10, or about 11.98%11.98\% of her $13,019.95 outlay. As a check, 0.1198×13 019.95≈15600.1198 \times 13\,019.95 \approx 1560, i.e. about $1560, matching the net return. Brokerage applies on both the buy and the sell, so the $39.90 of fees is deducted before the return is found.

exam5 marks
Two share parcels are held for a year. Parcel A is 10001000 shares bought at $12.00 each, sold at $12.90, with total dividends of $480. Parcel B is 800800 shares bought at $25.00 each, sold at $25.50, with total dividends of $1100. Using the total return as a percentage of the original investment, determine which parcel gave the better return.
Show worked solution →

Find the total return on Parcel A. The original investment is 1000×12.00=12 0001000 \times 12.00 = 12\,000, i.e. $12,000. The capital gain is 1000×(12.90−12.00)=9001000 \times (12.90 - 12.00) = 900, i.e. $900, and adding the $480 dividends gives a dollar return of 900+480=1380900 + 480 = 1380, i.e. $1380.

returnA=138012 000×100%=11.50%.\text{return}_A = \frac{1380}{12\,000} \times 100\% = 11.50\%.

Find the total return on Parcel B. The original investment is 800×25.00=20 000800 \times 25.00 = 20\,000, i.e. $20,000. The capital gain is 800×(25.50−25.00)=400800 \times (25.50 - 25.00) = 400, i.e. $400, and adding the $1100 dividends gives a dollar return of 400+1100=1500400 + 1100 = 1500, i.e. $1500.

returnB=150020 000×100%=7.50%.\text{return}_B = \frac{1500}{20\,000} \times 100\% = 7.50\%.

Compare on the same basis. Both returns are measured as a percentage of the money invested, so they can be compared directly: 11.50%>7.50%11.50\% > 7.50\%.

State the answer. Parcel A gives the better return, 11.50%11.50\% against 7.50%7.50\%. As a check, Parcel B earns more in dollars ($1500 against $1380) but on a much larger $20,000 investment, so its percentage return is lower; comparing the dollar figures alone would be misleading, which is why the percentage is used.

exam6 marks
CSL shares trade at $285.00. The company reports earnings per share of $11.40 and pays an annual dividend of $2.85 per share. (a) Calculate the price-earnings (P/E) ratio and the dividend yield, the yield correct to two decimal places. (b) Sofia buys 5050 CSL shares at $285.00 through a broker charging $19.95 on each trade. She holds them for one year, receiving the dividend on every share, then sells at $312.00. Calculate her net return for the year in dollars and as a percentage of her total outlay, to two decimal places.
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(a) Find the P/E ratio. Divide the share price by the earnings per share.

P/E=285.0011.40=25.\text{P/E} = \frac{285.00}{11.40} = 25.

(a) Find the dividend yield. Express the dividend per share as a percentage of the share price.

yield=2.85285.00×100%=1.00%.\text{yield} = \frac{2.85}{285.00} \times 100\% = 1.00\%.

A P/E of 2525 with a yield of only 1.00%1.00\% is typical of a growth company that reinvests most of its profit rather than paying it out.

(b) Find the true cost of buying. Add the brokerage to the value of the shares, since the broker charges it on the way in.

cost=50×285.00+19.95=14 250+19.95=14 269.95,\text{cost} = 50 \times 285.00 + 19.95 = 14\,250 + 19.95 = 14\,269.95,

i.e. $14,269.95.

(b) Find the dividends and net sale proceeds. The dividend is paid on every share, so the income is 50×2.85=142.5050 \times 2.85 = 142.50, i.e. $142.50. Selling incurs brokerage again, so subtract it from the sale value.

proceeds=50×312.00−19.95=15 600−19.95=15 580.05,\text{proceeds} = 50 \times 312.00 - 19.95 = 15\,600 - 19.95 = 15\,580.05,

i.e. $15,580.05.

(b) Find the net dollar return. Add the dividends to the proceeds, then subtract the total cost.

net return=15 580.05+142.50−14 269.95=1452.60,\text{net return} = 15\,580.05 + 142.50 - 14\,269.95 = 1452.60,

i.e. $1452.60.

(b) Express the return as a percentage of the outlay. Divide the net return by the true cost.

net return=1452.6014 269.95×100%≈10.18%.\text{net return} = \frac{1452.60}{14\,269.95} \times 100\% \approx 10.18\%.

State the answer. The P/E ratio is 2525 and the yield is 1.00%1.00\%; Sofia's net return is $1452.60, or about 10.18%10.18\% of her $14,269.95 outlay. As a check, 0.1018×14 269.95≈14530.1018 \times 14\,269.95 \approx 1453, i.e. about $1453, matching the net return. Brokerage of $39.90 across the two trades is deducted before the return is found.

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