# Expected Return from Stock Investments

Expected Returns From Investing in Stocks

This article provides calculations and insight as to what return you can logically expect from investing in stocks in general or in a particular stock.

Firstly, it must be recognized and acknowledged that we can never know in advance the return that will result from investing in a stock. Actual returns will be affected by whether the economy grows or shrinks. Various company-specific developments can dramatically affect a company’s cash flows (for example BP and its gulf oil spill). Interest rates and the mood of investors can dramatically affect the price at which a company’s shares sell for even if its expected cash flows are unchanged.

Still estimates of the expected return from investing in a given stock or bond can be made. Mathematically the expected return depends on estimates of key variables including growth in earnings per share and dividends and the P/E ratio or multiple of earnings that a stock is expected to sell for in “X” years. The uncertainty of such estimates will depend on whether they are applied to a single stock as opposed to the overall market index of equities, and if applied to a single stock will depend greatly on the nature of the particular company. The earnings of some companies are relatively predictable while the earnings of other companies are inherently unpredictable.

When calculating the expected return from stocks we would be wise to consider certain mathematical relationships. Given all the uncertainties in investing in stocks we can’t expect mathematics to provide all the answers, but it can certainly point us in the right direction. In order to use mathematics to estimate the expected return from stocks, certain assumptions must be made.

In the calculations that follow we will assume that a company making a given return on equity or ROE will continue to make that same ROE in future. In real life such an assumption may be valid for some companies but is certainly not valid for all companies. This constant ROE assumption means that we can calculate the earnings per share growth rate of a company as simply its ROE minus its dividend pay out ratio. A company earning a constant 10% ROE will grow its earnings at exactly 10% per year if it retains all of its earnings and it will grow its earnings at 5% per year if it pays out half of its earnings as a dividend. That is a mathematical fact once we assume a constant ROE of 10%. The scenarios below implicitly assume that the number of shares in the company remains constant.

Input Initial Share Price Input Initial Earnings Constant Pay-out Ratio Scenario Input Constant ROE Assumed Selling P/E after 5 years Calculated Buying P/E Calculated Buying P/B Calculated Initial Dividend Calculated Initial Dividend Yield Calculated Initial Earnings Yield Growth based on ROE times earnings retention ratio Expected Return per year 5 year holding period
100 10 100% 7.00% 10 10 0.7 10 10.00% 10% 0.00% 10.00%
100 10 50% 7.00% 10 10 0.7 5 5.00% 10% 3.50% 8.70%
100 10 30% 7.00% 10 10 0.7 3 3.00% 10% 4.90% 8.00%
100 10 0% 7.00% 10 10 0.7 0 0.00% 10% 7.00% 7.00%

In the above table we pay \$100 for a share of a company earning an initial \$10 per share and we assume that this arises from a constant 7.0% ROE. We examine the expected annual return if we sell it after five years at the same P/E ratio that we paid and assuming different earnings pay-out ratios. It’s interesting to note that this share purchased at a P/E of 10 mathematically has a Price to Book Value ratio of 0.7 or 70%. In reality stocks of companies earning even just 7% ROE do not today often sell below book value. Therefore it would actually be rare to find such a company selling at a P/E as low as 10.

The first row of the table shows our expected return if the company pays out all of its earnings. In fact this would mathematically be not only our expected but our actual return if all of assumptions turned out to be precisely correct – which would never happen in the real world. This first row scenario is more like a bond than a stock. The share has zero growth and pays out all of its earnings. Our expected return is 10.0% even though the underlying company is only earning 7.0%. The extra return comes from the fact that we bought the share below book value. 7.0% on book value turns into 10.0% on the price we paid. In this scenario we also sell the share at a P/E of 10 which will equate to a P/B of 0.7 and still we earn 10% on a company that is itself only earning 7% due to the bargain price we paid for the share.

The bottom row of the table shows what happens if the company pays no dividend but instead re-invests all of its earnings at the 7.0% ROE. In this case our expected return is precisely 7.0%. Our bargain P/E purchase does not increase our return because of our assumption that we sell the shares at the same P/E ratio as we paid. The company earns 7.0% and we earn 7.0%.
The above table shows that if we can buy a share at a P/E ratio that represents an initial earnings yield (in this case 10%) that is higher than the company’s current and expected ROE (in this case 7%), then we would strongly prefer that such a company dividend out as much of its earnings as possible.

Input Initial Share Price Input Initial Earnings Constant Pay-out Ratio Scenario Input Constant ROE Assumed Selling P/E after 5 years Calculated Buying P/E Calculated Buying P/B Calculated Initial Dividend Calculated Initial Dividend Yield Calculated Initial Earnings Yield Growth based on ROE times earnings retention ratio Expected Return per year 5 year holding period
100 10 100% 7.00% 12 10 0.7 10 10.00% 10% 0.00% 13.10%
100 10 50% 7.00% 12 10 0.7 5 5.00% 10% 3.50% 12.20%
100 10 30% 7.00% 12 10 0.7 3 3.00% 10% 4.90% 11.70%
100 10 0% 7.00% 12 10 0.7 0 0.00% 10% 7.00% 11.00%

This next scenario is identical to the one above except that in this case the investment is sold at a P/E of 12, rather than the 10 that paid. Equivalently the price to book value ratio recovers to 0.84 from the 0.70 paid. The expected returns from each row in the table are therefore higher. In each case the investor earns more than the 7% return that the company is earning due to buying the shares at less than book value and due to selling them at a multiple of book value that recovers somewhat.

Input Initial Share Price Input Initial Earnings Constant Pay-out Ratio Scenario Input Constant ROE Assumed Selling P/E after 5 years Calculated Buying P/E Calculated Buying P/B Calculated Initial Dividend Calculated Initial Dividend Yield Calculated Initial Earnings Yield Growth based on ROE times earnings retention ratio Expected Return per year 5 year holding period
100 7 100% 7.00% 14.3 14.3 1 7 7.00% 7% 0.00% 7.00%
100 7 50% 7.00% 14.3 14.3 1 3.5 3.50% 7% 3.50% 7.10%
100 7 30% 7.00% 14.3 14.3 1 2.1 2.10% 7% 4.90% 7.10%
100 7 0% 7.00% 14.3 14.3 1 0 0.00% 7% 7.00% 7.00%

In this scenario we buy shares at a price equal to book value. With an ROE of 7.0% this equates to a P/E ratio of 14.3. In this case if we also sell the shares at book value after a five year holding period. (The P/E at sale is the same 14.3 as at the purchase). In this case the company makes 7% and we make 7%. The dividend policy does no matter. We earn what the company earns.

Input Initial Share Price Input Initial Earnings Constant Pay-out Ratio Scenario Input Constant ROE Assumed Selling P/E after 5 years Calculated Buying P/E Calculated Buying P/B Calculated Initial Dividend Calculated Initial Dividend Yield Calculated Initial Earnings Yield Growth based on ROE times earnings retention ratio Expected Return per year 5 year holding period
100 7 100% 14.00% 14.3 14.3 2 7 7.00% 7% 0.00% 7.00%
100 7 50% 14.00% 14.3 14.3 2 3.5 3.50% 7% 7.00% 10.70%
100 7 30% 14.00% 14.3 14.3 2 2.1 2.10% 7% 9.80% 12.10%
100 7 0% 14.00% 14.3 14.3 2 0 0.00% 7% 14.00% 14.00%

This next scenario is perhaps most representative of what investors face in the real world. The shares are selling at twice book value, but have an attractive ROE of 14%. The initial earnings yield is 7%. In the first row the company pays out all of its earnings as a dividend and as a result does not grow its earnings. The Investor earns 7% despite the company earning 14%. This is because the investor has paid twice book value. In the fourth row, the company retains all of the earnings and is able to earn the same 14% ROE on the retained earnings. The earnings therefore grow at 14% per year. The investor can earn 14% as long as the selling P/E (or equivalently P/B) remain at the same level as the investor paid. It is interesting to note that due to the high ROE the investor is better off if the company retains all of its earnings. The investor who pays twice book value to acquire a high ROE stock should do so only if the company is expected to grow (which gnerally means it will retain its earnings rather than pay much if any dividend). The investor has to hope that the ROE will remain high and that this will lead to the market P/E and P/B remaining high.

Input Initial Share Price Input Initial Earnings Constant Pay-out Ratio Scenario Input Constant ROE Assumed Selling P/E after 5 years Calculated Buying P/E Calculated Buying P/B Calculated Initial Dividend Calculated Initial Dividend Yield Calculated Initial Earnings Yield Growth based on ROE times earnings retention ratio Expected Return per year 5 year holding period
100 5.00 100% 18.0% 15.0 20.0 3.60 5.00 5.0% 5% 0.0% 0.0%
100 5.00 50% 18.0% 15.0 20.0 3.60 2.50 2.5% 5% 9.0% 6.0%
100 5.00 30% 18.0% 15.0 20.0 3.60 1.50 1.5% 5% 12.6% 8.2%
100 5.00 0% 18.0% 15.0 20.0 3.60 0.00 0.0% 5% 18.0% 11.4%

This next scenario shows the danger of paying too much even when the ROE is high. In the first row the investor has paid a P/E of 20 for a stock with a very attractive ROE of 18. This equates to a price to book value ratio of 3.6. The company dividends out all of its 18% earnings. But due to the high price paid, the investor gets a yield of just 5%. If after five years the P/E has declined to 15 (perhaps due to the expectation that the high 18% ROE is going to decline) then the investor earns nothing. Five years of dividends at 5% are wiped out by the 25% fall in the P/E.

In the fourth row the company retains all of its earnings and so its earnings growth at 18% per year. In this case despite the 25% drop in the P/E ratio, the investor still makes an average return of 11.4% per year due to the rise in the value of the shares triggered by the huge 18% per year gains in earnings.

END
Shawn C. Allen, CFA, CMA, MBA, P.Eng.
InvestorsFriend Inc.
August 1, 2010