The simple maths of share ownership

When you buy a share the amount of money that you will ultimately make or lose is determined by two - and only two - things:

• The change in the share price between when you buy and sell the share.
• The amount of dividends that are paid to you whilst you own it.

Added together these two things make up your total return from owning a share. Try not to forget this.

Total return from a share = Change in share price + total dividends received

Let's say you buy a share for 100p. You own it for five years and then sell it for 120p. During that time you have also been paid an annual dividend of 5p per share giving you 25p of dividends in total. Your total return from owning the share is:

• The change in share price of 20p (The 120p you get from selling less the 100p you paid for it)
• 25p of dividends - five years of 5p per share paid.
• A total gain of 45p (20p + 25p) or 45% (45p/100p).

When you are investing you should always keep coming back to this simple sum. Every bit of research that you do on a company should boil down to two very basic questions:

• What does it mean for the value of the company? (This will eventually be reflected in the share price)
• Will it change the size of dividends that a shareholder will receive?

Anything you do that isn't helping to answer these questions is essentially time wasted. So let's have a look at these two bits separately.

How share prices are determined

Share prices are no different to any other prices. They are determined by the forces of demand and supply. When a company is very popular with investors its share price tends to go up. It tends to fall when it is out of favour and struggling.

The famous investor Benjamin Graham summed up the workings of the stock market very well. He said in the short run it was a voting machine based on popularity but in the long run it was a weighing machine where share prices would ultimately reflect the real value of a business. In the meantime share prices can drift a long way from their true or intrinsic value - i.e. they can be undervalued or overvalued.

In reality, the market value of a company and its share price are determined by two things:

• Its profits and cash flows.
• The value attached to those profits or cash flows. This is often expressed as a multiple of them such as the price to earnings (PE) ratio.

So share prices change if:

• profits or cash flows change.
• stock market valuations change.

Now let's look at the dividend part of the total return from a share.

Total return and investment risks

Focusing on total returns really helps to focus your thinking when you are researching a company. What it forces you to do is direct your attention on the only two things that really matter:

• The outlook for future profits. These will determine both the share price and dividend payments.
• The valuation of the shares. What you pay for them will have a large bearing on how much money you will ultimately make or lose.

This approach also gets you to think a lot about the risks you are potentially exposing yourself to. These are:

• Business risks - whether a company can grow and hang on to its profits. This depends on things such as how good its products are and how much competition it faces.
• Share price risk - whether you are paying too much for the shares. Buying shares with high valuations (such as a high PE ratio) can be more risky than buying shares with lower valuations.

If a company's profits stand a good chance of growing in the years ahead then you can begin to see how you might end up making money from owning the shares. Higher profits could cause the share price to go up and see you being paid a growing stream of dividend payments. But, if those shares are too highly priced and the company fails to live up to lofty expectations then even if profits and dividends increase you could still end up losing money - sometimes a lot of money - if the share price falls.

So how on earth can you try and work out whether the maths of share ownership are going to work in your favour? You can never be certain but like lots of things with investing, you can get a good feel of what the future might bring by studying what has happened in the past.

By working out what has made up the total return of a share in the past, you can start to weigh up whether you might make or lose money by buying the shares today. As with lots of things in life, the best way to understand something is to look at some real world examples.

Whitbread - returns driven by profits growth

If you have owned shares in Whitbread - known for its Costa Coffee and Premier Inn hotels - for the last ten years you will probably be very happy with your investment as it has increased more than fourfold.

The breakdown of its total returns is shown below with an explanation afterwards:

Associated British Foods - returns driven by valuation increases

Investors in Associated British Foods have tripled their money during the last ten years. But the bulk of the gains have been driven by valuation increases - an expanding PE ratio. This is due to the fact that the share price has gone up a lot faster than the profits of the company.

However, the shares now trade on a very demanding valuation of 32 times EPS - the kind of valuation that needs strong profits growth to justify - but profits growth has stalled. The big potential risk with a share like this is that the PE multiple could collapse if profits don't start growing again. Dividends don't look big enough to offset this. Can shareholders bank on holding on to the big share price gains?

Aggreko - how paying high prices can really hurt your wealth

Not that long ago, Aggreko was a hot share to own. The provider of temporary power generators had been growing its profits at a rapid rate and investors were prepared to pay nearly 26 times earnings for the shares back in 2010. For a while the shares continued to do very well but they have come crashing down as profits growth has become a lot more difficult to achieve.

Investors have lost faith in this company and the PE ratio has more than halved. Shareholders have lost money even though profits have gone up.

This highlights a very important lesson for all investors: The price you pay for a share has a big impact on the returns that you get from it. Pay too much and you can lose money.

To sum up:

• Focus on total returns (share prices + dividends) not just share prices when you are investing.
• Study risks as well as returns.
• You are exposed to business and share price risks when you own a share.
• Knowing what has driven shareholder returns in the past is important.
• Past share price gains can disappear, dividends paid can't.
• Be wary of shares with high valuations and where share prices have increased faster than profits.
• Dividend shares can be less risky.
• Buying cheaper shares is usually better than buying more expensive ones