Our clients are well aware of the importance and emphasis we place on valuation and why it is important not to risk overpaying for an investment in any company.

This article attempts to put the risk of overpaying into perspective by using the Constant Growth Gordon Dividend Discount Model (DDM)* to assess the long-term growth (g) and Return on Equity (ROE) that is required by a company in order to justify the price or value that you pay (the value in this case is determined by the price-to-earnings multiple, or PE ratio, that you’ve paid for the company). We will reference a few practical examples in this analysis by using an example of a South African stock that we own (Lewis) and one that we don’t own (Truworths).

*Constant Gordon Growth DDM model: P = [d*(1+g)]/ (k-g) where P = price of a stock, d = current dividend, g = long term growth, k = discount rate (required return).

The Constant Growth Gordon model

By using the constant growth Gordon model formula, you’re able to back out an enormous amount of information that is implicit in the “price that you’re willing to pay” for a company. In the analysis, we back out the implied long-term growth (annual growth in dividends expected to justify the price you’ve paid), discount rates (this is the annual rate of return that you would expect from your investment to justify owning it), PE ratios, and implied Return on Equity (a measure of the profitability of the company) to justify the price you’re paying. In the table below, we put this into perspective:

Note: Long term growth (g) is the expected growth rate in dividends, Payout Ratio is the % of a company’s earnings that is paid out as dividends.

The table above highlights the required long-term growth in dividends and ROE that justifies the PE ratio. By referencing the highlighted row, for example, if you pay an 8 times PE ratio, assuming a 14% required return and a dividend payout ratio of 45%, the company needs to grow its dividends at an annualised rate of 8% (in nominal terms) a year into perpetuity and generate an ROE of 15% to justify its current price (valuation). Assuming inflation of 5.5% and real growth of 2.5%, this is reasonable. On the other hand, if you were willing to pay a 16.7 times PE ratio for a company, this would imply that the business would need to grow its dividends at an annualised rate of 11% (in nominal terms) a year into perpetuity and generate a ROE of 20% to justify its current PE ratio. This implies that a 16.7 times PE ratio company needs to grow at a rate of 37.5% faster (annually into perpetuity) relative to an 8 times PE ratio company to justify its relative valuation (PE ratio). The margin of safety in this case is marginal (at best) for the 16.7 times PE ratio business, but very high for the 8 times PE ratio company. To look at it differently, if you assume inflation of 5.5%, it implies that the business would have to grow at a real rate of 5.5% annually to justify the price you’ve paid!

To look at this graphically, refer to the chart below that highlights the relative annual growth rate in dividends required (y-axis) to justify the PE ratio that you pay (the relative growth rate is referenced relative to a PE ratio of 8 times). This simply means that a low PE ratio company needs to grow its dividends at a rate much lower than a high PE ratio company in order to justify its current valuation; hence it will have a larger margin of safety and a lower probability of disappointment. The “risk” of potential loss of capital is lower.

In summary, the cheaper the company, the higher the margin of safety and the less you need to rely on this “promise of future growth” that often does not transpire when you invest in overvalued companies. There are, obviously exceptions. These are generally companies that are still in the early stages of a high growth phase (like MTN was five to ten years ago). In addition, there may be companies that are trading on high multiples today because their earnings are on a highly depressed base, so when earnings “normalise”, the rating (i.e. PE multiple) looks more attractive. This is generally the case for more cyclical businesses (e.g. resource companies).

In order to demonstrate this practically, let’s consider two companies: Lewis** and Truworths***. Lewis is a conservatively managed business with reasonable ROE’s that is cheap (its PE ratio is 9.5 times and its dividend yield is 5%). Truworths, on the other hand, is expensive and is trading on a PE ratio of 16.5 times and a dividend yield of 3.5%. Using the constant growth Gordon Model, this implies that Truworths needs to grow its dividends at an annual rate of 22% a year faster than Lewis to justify the difference in the valuation. There is little margin of safety in the Truworths valuation relative to Lewis. This is especially evident when you consider that Truworths margins and returns are significantly above “normalised” (sustainable) levels. This can be referenced in the chart below showing how the group’s margins have grown rapidly over the past number of years making it one of the most profitable retailers in the world (earnings before interest and tax (EBIT) margins have more than doubled to 37%). We believe that the risks are now to the downside!
**Lewis share price at 7300 cps (27th September 2011)
***Truworths share price at 7148 cps (27th September 2011)

In contrast, Lewis has had fairly stable margins and ROE’s over time. It is neither at peak levels, nor at depressed levels – in fact it is close to its long-term average.

In conclusion, the risk when buying expensive companies (like Truworths), especially when margins and returns are at peak levels, is that the margin of safety is non-existent. The risk of a loss of capital over time is significantly greater than when you buy cheap companies (with a high margin of safety) that are well managed (like Lewis). We’re not saying that Truworths is a poor company. To the contrary, it is an exceptionally well managed retailer. However, even a great business can be a poor investment if the price that you pay is not fair!

Claude van Cuyck and Ricco Friedrich are portfolio managers at Sanlam Investment Management