There is a direct relationship between the return on equity of a stock and its price to book value. Understanding this relationship can give you insight into whether a stock is undervalued. Here’s the way valuation expert Aswath Damodaran of the Stern School of Business at NYU illustrates this relationship:
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This makes sense if you follow Buffett and look at a stock as an equity bond. The primary difference between an equity bond and an actual bond is that the equity bond does not have a fixed coupon – it’s up to the business analyst to estimate it – and an equity bond frequently has a growing coupon, owing to the reinvestment of earnings back into the business, just as would happen if you reinvested interest back into a savings account.
It follows that there is a general relationship between the return on equity of a business and the price to book ratio at which it trades. For example, you can expect a decent business that generates an ROE of 6-8% to trade around 1x book. On the other hand, a business that is able to generate an ROE of 24% should trade around 4x book, especially if the business enjoys a durable competitive advantage and its long-term prospects are promising.
We can see this mathematically if we consider the following formula:
PV (present value) = initial earnings x 1/(R – G) where R is the cost of capital and G is the growth rate of earnings. In this case, following Buffett, we will assume that the cost of capital is the risk free rate of return on long-term government bonds. Buffett does not look for safety in using a higher discount rate because he thinks it is a poor substitute for the certainty he demands in an equity investment.
For the first business earning an ROE of 6% and assuming equity of $100 million, the PV is $100 million. This assumes long-term government bonds are paying 6%.
$100 million = $6 million x 1/(6% – 0)
For the second business earning an ROE of 24% and assuming equity of $100 million, the PV is $400 million.
$400 million = $24 million x 1/(6% – 0)
It follows that the second asset will sell for four times the price of the first asset. If the equity base is growing the difference in value is even more pronounced. Consider a $100,000 15-year bond that is paying 24% with a payout ratio of 60% that lets you reinvest the balance at 24%. The invested capital will grow by 9.6% annually. [G (growth) = (1 – Payout ratio) * Interest rate]
Such a bond would have a NPV of $584,130. Here’s the data.
A business with similar economics could be expected to trade at as much as 6x book value. Consider American Express which has had an average ROE in the mid to high twenties over the past decade and a payout ratio (dividends and share repurchases) of 60-70%. It has generally traded at 3x to 7x book value over the past decade.
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Obviously, the relationship between price-to-book ratio and return on equity is not fixed and can vary greatly depending on the business and its prospects. Investing can never be reduced to a simple one-variable formula. However, this relationship can give you insight into whether a business is over or undervalued.
It also underscores the tremendous value of a business that can earn a high return on equity and reinvest most or all of it back into the business at a high ROE. These types of businesses are rare. It is not widely appreciated that a large part of Berkshire Hathaway’s stellar track record owes itself to Buffett being able to do precisely this for four decades.