In this article, we will be using a powerful formula to determine the expected returns of an investment. I use this formula in combination with my preferred valuation method the reverse DCF model.

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Although the formula is easy to apply to past data, it can be quite challenging to create a forward-looking estimate of annual returns. This is because we are not using historical figures and returns after the fact. Instead, we are estimating based on a forecasted assumption. This makes stock valuation a complex process.

There are numerous formulas, tools, and resources available that can be used to provide guidance, but they should never be used in isolation. Returns are just assumptions and estimates, which can provide an idea that can guide decisions. It is essential to remember that the final number is not a done deal or a locked-away return.

Why try to estimate expected returns?

Estimating expected returns is a crucial aspect of valuation. After using one of the valuation models, I calculate the estimated yearly return by running a simple formula.

This helps me determine if the return meets my benchmark and if it’s worth investing in. However, it’s important to note that this is not a guarantee. This is just an estimate to ensure that the investment meets my minimum required returns.

Just like the Earnings Yield is used to determine the probable return, I want to make sure that the return justifies the investment. Opportunity cost is a critical factor to consider for every investment.

The Earnings Yield is a simple calculation of the P/E ratio that indicates the estimated return on the business. For instance, if a company has a P/E ratio of 20x, then its Earnings Yield would be 5% (1/20 = 0.05 x 100 = 5%). I evaluate whether this return is sufficient to justify the investment or if there are better investment opportunities available.

One of the benefits of this formula is it is quite simple once you’ve done it a few dozen times. This can be a good way to vet investment ideas before running them through the rigorous Investment Process. You can run an estimated look at the likely returns. If it meets your minimum threshold then you can proceed with the most viable ideas. If the returns don’t stack up, then don’t waste your time. Remember, “Sometimes what you don’t do is just as important as what you do.”

What is the formula?

The Expected Yearly Return OR Future Value is based on a 3-part formula. There are quite a few ways it can be done. However, I have found these two to be the best when estimating returns.

I have replaced Dividend Yield with Shareholder Yield in the formula. Shareholder Yield is a more comprehensive way to evaluate how management is delivering returns to shareholders. There are two methods to use the formula: Free Cash Flow per share growth or Earnings Growth Rate.

I use the Free Cash Flow formula for companies that have consistent Free Cash Flow, which indicates they are high-quality and established. On the other hand, the Earnings Growth model is based on companies that are growing earnings while not generating FCF. These companies usually reinvest aggressively in growth to increase revenue and earnings.

You can use whatever multiple you prefer, whether P/E, P/S, EV/EBITDA, or any other. The most challenging part of estimating the formula is the multiple components, which is a forward-looking estimate. You should aim for an annualised and nominal % over a 5–10-year period in line with your holding period. If your holding period is shorter, say 2-3 years, you can calculate the forward multiple from this period.

The earnings growth rate or Free Cash Flow growth rate is similar to your anticipated growth in a DCF. Let’s walk through each of these prior to going through examples.

Shareholder Yield

The Shareholder Yield is a metric that measures how a company rewards its shareholders through three ways. Issuing dividends, conducting share buybacks, or reducing the company’s debt. Learn more here ➡️ Shareholder Yield.

The formula for this is Shareholder Yield = (Cash Dividends + Net Share Repurchases + Net Debt Paydown) ÷ Market Capitalisation

If you are a dividend investor and primarily focused in income then replace shareholder yield with the Dividend Yield. The dividends received will make up a bigger portion of the Investment returns. To determine which one is a better fit, understand what management have been doing with free cash flow and how they reward shareholders.

Earnings Growth Rate OR FCF Growth

To calculate the growth rate of a company, you can either use the earnings growth rate or the free cash flow per share growth. However, it’s important to determine the fundamentals of the business to know which one to use. If the company has positive free cash flow and is generating a lot of it, then use the free cash flow growth rate. On the other hand, if the company is growing and focused on increasing revenue, which drives earnings growth, then use the earnings growth rate.

To calculate the growth rate, you need to make forward-looking estimates based on historical data to ensure that what you extrapolate into the future is not absurd. For instance, if you expect the earnings growth for the next 10 years to be 8% annually, then that is the growth rate you should use. The same goes for free cash flow. You can take this number from your own modelling work, from the discounted cash flow model, or from other trusted sources like Tikr or Yahoo finance.

To determine the growth rate, you can go back over the last 5-10 years of either earnings growth or free cash flow growth, take the average, and then look at a few trusted resources to determine what their forward projections are. Once you have done that, take the average again. If it’s a smaller company or hyper-growth business, you can attempt to model future revenue and earnings based on a range of assumptions.

Multiple Expansion or Contraction

This particular part of the formula is considered to be the most challenging one. It all depends on the multiple used, we are going to stick to the Price-to-Earnings Multiple. To calculate it, you need to look at the current P/E multiple and examine how it is likely to evolve over the next 5-10 years. Then, you will calculate the average over the years you have used to get an annualized percentage.

Before estimating this, it is essential to understand Multiple Expansion and Contraction. The multiple can change dramatically over long periods because we have no idea what value the market will place on the company. To determine this, we can use a combination of averages of the industry, other comparative companies, and the company itself. We want to look at a range of possibilities over time.

If we are considering an undervalued company, we will think about what the P/E will grow to leading to an expansion. On the other hand, if we are evaluating a high-growth company with an expensive-looking P/E, we will be considering how much it compresses over those 5-10 years.

The formula for this is to use the annualised formula as opposed to just the average formula.

What is the difference between Annualised return vs. Average return? The main difference is the impact of compounding. Annualised returns include the effect of compounding while average returns do not.

To find the annualised number we use the following formula.

(Ending Value ÷ Beginning Value) ^(1÷n) – 1

• End Value = Use the P/E Multiple at the end of the time period.
• Beginning Value = Use the current P/E Multiple.
• n = The time period in years. So if it is 10 years use 10 as the denominator.

An example of Multiple Expansion

An undervalued business has a P/E of 10x. We plan to hold this investment for 5 years and expect it to revert to a mean with a P/E of 18x in line with the industry average. The formula will look like this.

Annualised Multiple Expansion = (18÷10)^(1÷5) – 1 = 0.1247 x 100 = 12.47%

This is what we would put into the end of our expected returns formula. As the number is POSITIVE we add the number.

An example of Multiple Contraction

A quality high-growth business has a P/E of 35x. We plan to hold this investment for 10 years and expect it to compress as it matures to a P/E of 21.5x in line with its peers The formula will look like this.

Annualised Multiple Contraction = (21.5÷35)^(1÷10) – 1 = -0.04756 x 100 = -4.75%

This is what we would put into the end of our expected returns formula. As the number is NEGATIVE we must ensure we minus it.

Putting the expected returns formula together.

Let’s put all of this together to look at a hypothetical return on a business that we want to hold for 10 years. We are trying to predict the expected annual returns to see if it is in line with our minimum return of 10% annually.

We will go slowly through each of the stages to illustrate how it can come together and use the Earnings Growth rate over the FCF for this example.

Expected Returns on Stoic Incorporated

We will be using the following details after evaluating the company.

Item	Number
Current P/E Multiple:	20x
Share Buybacks:	$9.7 million
Shares Issued via Cap Raise:	$1.02 million
Debt Reduction:	$8.66 million
Outstanding Shares:	100,000,000
Current Share Price:	$6.32
Earnings Growth % p/a	4%

Starting with the Shareholder Yield and based on analysing the financials of the business we have pulled out the following details. Using our Shareholder Yield formula we put all the inputs together and get:

Shareholder Yield = $7.5m + ($9.7m – $1.02m) + $8.66m ÷ $632m x 100

Shareholder’s Yield = 3.93%

Then we assess Earnings Growth and forecast the growth to be 4% annually. We work this out by evaluating the average over the past 10 years and determining the growth falls between 3% and 5% and average it out.

The last part of the formula is the Multiple. We have a current P/E of 20x and we believe the company is currently undervalued. We believe over the next few years the company will move up in line with its historical average which has been trading around P/E 28x.

Multiple Expansion Annualised = (28÷20)^(1÷10) – 1 = -0.03422 x 100 = 3.42%

Now that we have worked out each of the inputs we can put it all together into the final formula.

The estimated annual expected returns will be:

3.93% + 4% + 3.42%

Expected Returns = 11.35%

This is above our required 10% per annum return requirement. Then you decide whether this return is worth it to you.

This is purely hypothetical. It is an assumption and not a realised return. You will only know what the return is looking back after the years have passed to compare how far you were off.

What happens if the multiple contracts?

If we were to use the same inputs, but anticipate a multiple contraction, let’s see how this reversal of the P/E ratio brings down the overall return (the speculative aspect).

Let’s assume the same shareholder yield and growth rate as before, but with a higher P/E ratio of 35x and a reversion back to a historical average of, say, 19.5x over 10 years. Using our formula for annualising the multiple, the result would be a P/E compression annualized to -5.92%. Now, let’s throw this negative into the expected returns formula.

3.93% + 4% -5.92% = 2.01%

By adding up the shareholder yield, growth rate, and P/E compression, we get the expected annual return, which would be 2.01%. This shows us how sensitive the formula is to the impact of the P/E ratio on the estimated returns on share prices.

This is also a great example of Mr Market at play. A company can be growing and doing all the right things, rewarding shareholders, creating a profit and reinvesting in itself. However, the market may still be valuing the business differently. Value and Quality are always recognised eventually but in the meantime, a shrinking P/E still damages overall returns as it brings the share price down.

In Summary…

Although the formula assumes returns only if all the inputs align, it can still help guide investment decisions. However, it is important to remember that like everything else in investing and evaluation, it is only a guide and not a guarantee. Use this in combination with a DCF or Reverse DCF model and a multiples valuation. It is good practice to run sensitivity tests on all our valuations and assumptions.

The formula is useful for companies with a lot of historical data, and consistency, and that have moved past the early and hyper-growth stages. These companies may have crossed an inflection point, achieved operating leverage, and moved into mature company territory.

It’s important to note that the formula requires a high degree of consistency in the inputs. For example, a small-cap high-growth business with lumpy earnings, no shareholder yield, and wildly fluctuating multiples may make it difficult for the formula to provide an estimate with any degree of confidence.

The Investment Return is a lot more accurate to determine than the multiple expansion or contraction. One component is determined by the fundamentals of the business and a tangible source of valuation. The multiple is the value the market places on the business and your guess is as good as mine where it can be in 10 years.

I rely on this formula when looking at businesses of all sizes whether small or big. The one common characteristic is they are all quality businesses. They are consistent in their growth, they reward shareholders intelligently and there is a lot of data around the multiples enough to make a few forward-looking assumptions.