Introducing Gordon's Growth formula

When it comes to dividend shares there is a relatively simple bit of maths that you can use to work out a share's value. It was devised by Professor Gordon of Toronto University and is commonly known in the investing world as Gordon's Growth formula.

To work out the value of a dividend paying share you need three key inputs:

1. A forecast for next year's dividend per share (DPS +1)
2. A constant rate of dividend growth forever (g)
3. A minimum interest rate or required rate of return demanded by shareholders (r) - sometimes called a discount rate.

The value of a share is worked out as follows:

Share Price = (DPS + 1) / (r-g)

Say you have a share with a forecast dividend per share of 10p. Investors reckon it can constantly grow its dividends at 4% forever and want a minimum return to own the shares of 8% per year. The value of the share would be:

10p / (8% - 4%) = 250p

This simple approach is one of the Investor tools in SharePad. Alternatively you can use a calculator or a spreadsheet.

The views on what returns investors should want and what the future growth will be is what professional investors spend hours trying to work out. Unsurprisingly, different investors have different views on these key issues. One person may think the shares are cheap whilst another might think they are expensive.

Implied rates of dividend growth from high-yielding shares

Let's have a look at some of the current high-yielding shares in the FTSE 350 index. What I will do here is compare the implied rate of dividend growth with the growth being forecasted by City analysts.

I've prepared a table in SharePad which gives me forecast dividend yields and forecast dividend growth. I've asked SharePad to calculate dividend growth by comparing the forecast dividend per share in two year's time with next year's forecast dividend.

To avoid complicating matters, I have also excluded shares where dividend growth is being boosted by one off special dividends.

After exporting the table to a spreadsheet, I've then worked out the implied rates of dividend growth at different rates of interest. The thing to remember here is that the higher the rate of interest/return the investor wants, the bigger the rate of growth is required to justify the current share price and vice versa.

Are utility shares overpriced?

The shares of National Grid, United Utilities and Severn Trent all have implied constant dividend growth rates that are higher than forecast dividend growth rates. Could this be a sign that these shares are looking expensive?

Maybe not.

The bulls of these shares would argue that they are very similar in makeup to bonds. They have predictable cash flows that can grow in line with inflation. Some would argue that they are inflation-linked bond proxies.

Given that index-linked gilts have negative yields, the yields offered by these shares could be very attractive.

But maybe they are overpriced.

These companies are mature, regulated utilities where the prices they can charge their customers are regularly reviewed by regulators. Once a price control has been set then companies know with reasonable certainty how much they can pay out in dividends for the next few years.

These three companies have told investors that they expect to grow their dividends by the rate of inflation until the next price review. On that basis, the forecast growth of dividends of around 2% seems sensible.

But what happens when the regulator looks at prices at the next regulatory review? A key determinant of prices is the allowed rate of return that companies can earn on their assets. This is a function of interest rates.

With interest rates on bonds falling, the regulators might argue that electricity grids and water companies can get by with lower returns in future and tell them to cut prices. This might lead to lower profits and lower dividends. If this happens then the current rates of implied dividend growth might be too high.

I'll leave you to work this out for yourselves.