While there’s much to cover in chapter 14 of Anurag Sharma’s book, “Book of Value: The Fine Art of Investing Wisely”, I’d like to focus on just one aspect of it: finding appropriate discount and growth rates.
The discount rate matters because it is one of the key parameters used in a discounted cash flow calculator. Sharma has used Walmart (WMT, Financial) as an example company in his discussions, so we will look at its DCF valuation using the GuruFocus calculator, as of the close of trading on March 25:
The red arrow on the image points to the area where the discount rate is entered. And the value of the discount rate is critical.
- With a discount rate of 12%, the fair, or intrinsic, value is $55.54, well below the current market price of $109.50 and, hence, the negative (red) margin of safety.
- If we cut the rate to 11%, the intrinsic value jumps to $59.90 and the margin of safety improves.
- Increase the rate to 13% and the picture worsens. The intrinsic value drops to $51.66 and the negative margin of safety is even worse.
The point is that the discount rate matters when analyzing a stock using discounted cash flow. Where to set the rate has always been a thorny problem, and one that Sharma addressed.
He began by observing there is a market-based indicator of uncertainties about earnings in the future—the perceived risk in a company’s bonds. More specifically, the average yield on a company’s bonds is derived from both interest rates and the company’s financial state. So he proposed that bond yields should be the baseline for the discount rate on companies that have actively trading bonds.
Now stockholders don’t enjoy the same benefits as bondholders; in the event of bankruptcy, the owners of bonds get priority access to the company’s remaining cash and assets. What’s more, shareholders are not guaranteed a positive return; in many cases, they earn less than they could earn by putting their money into 10-year corporate or Treasury bonds. In some cases, they get nothing at all or even lose money.
Therefore, there needs to be an equity premium (a higher return than bonds because of the extra risk or uncertainty), which is added to the average 10-year bond yield. Sharma noted the amount of that premium will vary according to operating situations. It can be estimated by considering the average bond yield; bonds with higher yields imply greater uncertainty and that means higher equity premiums and higher discount rates.
He thought that a discount rate should be a multiple of two to three times the average 10-year bond yield. That would be closer to two for strong companies with a history of consistent and robust fundamentals, and closer to three for companies with a shorter history and bumpy fundamentals.
The other parameters that may be adjusted in a discounted cash flow calculator are the growth rates, first for regular growth (usually the first 10 years) and terminal growth (in perpetuity, after 10 years):
This image shows Walmart's DCF values at the close of trading on March 25. Repeating the exercise from above, we see the growth rate can also make a significant difference:
- At a 4% annual growth rate, the intrinsic value is $52.24.
- At a 5% annual growth rate, the intrinsic value is $55.54.
- At a 6% annual growth rate, the intrinsic value is $59.18.
Just a 2% difference in the growth rate makes an 11.9% difference in intrinsic values.
Terminal growth rates are estimated independently and often are based at or near historical gross domestic product rates. In 2019, the rate of growth was 2.3%, so when the default is set at 4%, it implies that Walmart is expected to grow faster than GDP in the years beyond 2030.
How do we find the right growth rate for the next 10 years? Sharma told us it varies with the discount rate, and as you’ll recall the discount rate is long-term bond yield plus an equity premium. He offered the following formula to connect the growth rate to the discount rate, where "g" equals the future growth rate, "r" equals the discount rate and "EY" equals the earnings yield:
g = (r – EY) / (1 + EY)
He wrote, “We now have a theoretical estimate of future growth (g) that appears to be embedded in the price. We then try to refute the investment thesis by comparing the estimates of g with the company’s historical performance and, as we will see in later chapters, in light of our subjective understanding of the company’s medium- to long-term prospects.”
Trying to refute that estimate of growth is what the author earlier referred to as negating a case, an idea that goes back to Karl Popper’s concept of falsification.
Finally, Sharma reminded us again that valuations from discounted cash flow analysis are appropriate for stable companies with long histories. This approach is less appropriate for companies with short or unstable histories.
Conclusion
Among advocates of academic finance, discount and growth rates are based on standard deviation (volatility) or beta. Yet as Sharma showed in chapter 13, these two methods have serious flaws.
Thus, he has provided an alternative approach to getting to intrinsic value through discounted flow analysis. Discount rates are based on the average of a company’s 10-year bonds plus an equity premium. Growth rates can be then be calculated using the discount rate and a company’s earnings yield.
Once the DCF analysis has been completed and a valuation has been reached, the investor can then test it by trying to refute the case.
Disclaimer: This review is based on the book, “Book of Value: The Fine Art of Investing Wisely,” by Anurag Sharma, which was published in 2016 by Columbia Business School Publishing. Unless otherwise noted, all ideas and opinions in this review are those of the author.
Read more here:
- Book of Value: Flaws in the Academic Approach to Risk and Uncertainty
- Book of Value: 2 Ways to Value a Business
- Book of Value: Sharma’s Valuation Ideas and the Current Market
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