Shares & Dividends
Learn shares and dividends for NSW Year 12 Mathematics Standard 2. A dividend is the profit a company pays per share, and the dividend yield writes it as a percentage of the share price — the percentage return your investment earns each year.
You will calculate the total dividend on a parcel of shares, find the dividend yield, add brokerage to work out the total cost of a purchase, and compare shares by their yield — core investment skills for Standard 2 financial mathematics.
Theory
Shares and dividends are part of the investment topic in Year 12 Standard 2 (NSW). A dividend is profit paid per share; the dividend yield writes it as a percentage of the share price, giving the percentage return. This guide shows how to find the total dividend, calculate the yield, add brokerage, and compare shares.
A dividend is the portion of a company's profit paid out to each shareholder, usually quoted as an amount per share (often in cents). The total dividend you receive is the dividend per share multiplied by the number of shares you own.
The dividend yield writes that dividend as a percentage of the share's market price: \(\text{yield}=\dfrac{\text{dividend per share}}{\text{market price}}\times100\%\). It is the annual percentage return the shares pay in dividends.
Because the yield is measured against the price, it lets you compare shares that cost different amounts. In this Year 12 Standard 2 (NSW) topic you also add brokerage to a purchase (total cost \(=\) value of shares \(+\) brokerage) and read share value over time off a graph.
With dividend per share \(d\), market price \(P\) and \(n\) shares held:
Rearranged, the dividend for a given yield is \(d = \text{yield}\times P\). When you buy, the total cost adds brokerage:
How to work with shares and dividends
- Identify the dividend per share \(d\), the market price \(P\) and the number of shares \(n\). Convert a dividend in cents to dollars first.
- Total dividend: multiply \(d\times n\).
- Dividend yield: divide \(d\) by \(P\), then \(\times100\%\).
- Compare or interpret: use the yield (percentage return) to compare shares, and add brokerage when you need the total cost of a purchase.
Convert the dividend to dollars, then multiply by the number of shares.
| \(\text{dividend per share}\) | \(=\) | \(45\text{c} = \$0.45\) |
| \(\text{total dividend}\) | \(=\) | \(\$0.45 \times 1200\) |
| \(\) | \(=\) | \(\$540\) |
Leon receives a total dividend of \(\$540\).
Divide the dividend per share by the market price, then multiply by \(100\%\).
| \(\text{yield}\) | \(=\) | \(\dfrac{1.15}{18.40}\times100\%\) |
| \(\) | \(=\) | \(0.0625\times100\%\) |
| \(\) | \(=\) | \(6.25\%\) |
The dividend yield is \(6.25\%\).
Compare the yields, not the raw dividends.
| \(\text{yield}_P\) | \(=\) | \(\dfrac{0.66}{12.00}\times100\% = 5.5\%\) |
| \(\text{yield}_Q\) | \(=\) | \(\dfrac{1.50}{25.00}\times100\% = 6.0\%\) |
| \(6.0\%\) | \(>\) | \(5.5\%\) |
Share Q has the higher yield, so Share Q gives the better dividend return \((6.0\%)\).
Value of shares \(=\) price \(\times\) number; add brokerage for the cost.
| \(\text{value of shares}\) | \(=\) | \(500 \times \$9.60 = \$4800\) |
| \(\text{(i) total cost}\) | \(=\) | \(\$4800 + \$19.95 = \$4819.95\) |
| \(\text{(ii) total dividend}\) | \(=\) | \(\$0.38 \times 500 = \$190\) |
| \(\text{(iii) yield}\) | \(=\) | \(\dfrac{0.38}{9.60}\times100\% \approx 3.96\%\) |
Total cost \(\$4819.95\), dividend \(\$190\), yield \(3.96\%\).
Common pitfalls
Frequently asked questions
What is a dividend?
A dividend is a share of a company's profit paid to its shareholders, usually quoted as an amount per share, often in cents. Your total dividend is the dividend per share multiplied by the number of shares you own.
How do you calculate dividend yield?
Divide the dividend per share by the share's market price and multiply by 100 percent. For example, a $1.15 dividend on a share priced at $18.40 gives a yield of 1.15 divided by 18.40, which is 6.25 percent.
Is dividend yield the same as percentage return?
Yes, the dividend yield is the annual percentage return you earn from dividends for each dollar invested. It does not include any gain or loss from the share price changing, only the dividend income.
How do you compare two shares using dividend yield?
Work out each share's yield by dividing its dividend by its price, then compare the percentages. The share with the higher yield gives the better dividend return, even if it pays fewer cents per share.
What is brokerage?
Brokerage is the fee a broker charges to buy or sell shares. The total cost of a purchase is the value of the shares (price times number of shares) plus the brokerage fee.
Does a higher share price mean a bigger dividend yield?
No. Yield depends on both the dividend and the price. A share that costs more can pay a larger dividend in cents but still have a lower yield, because the dividend is spread over a larger price.