Estimating the Cost of Equity  313
subsequent recession unfolded, the yield on ten-year government bonds began 
a long and volatile decline, reaching an all-time low of 1.5 percent in July 2016. 
(Just prior to this book going to press, the U.S. Federal Reserve reduced interest 
rates in response to the global Coronavirus outbreak. As a result, in March 2020, 
the 10-year government bond fell below 1 percent for the first time.)
In the period following July 2016, many practitioners realized that valua-
tion models based on these historically low interest rates didn’t lead to sen-
sible results. With government bonds at 1.5 percent, a 5 percent market risk 
premium implies an expected market return of just 6.5 percent. Compared 
with pre-crisis expected returns, this should have caused a dramatic rise in the 
market’s price relative to earnings. Mathematically, every 1 percent decrease 
in the cost of equity for the S&P 500 index should increase the P/E of the index 
by roughly 20 to 25 percent. So a 3 percent drop in cost of equity would have 
increased the P/E from a typical trading range of 15 times to over 25 times. 
Yet no rise occurred. Instead, the P/E for the S&P 500 index has recovered to 
pre-crisis levels of approximately 20 times.
To overcome the inconsistency between low interest rates and the market 
values of equities, we recommend using a synthetic risk-free rate in both the 
estimate of the expected market return and for use in the CAPM. To build a 
synthetic risk-free rate, add the expected inflation rate of 1.7 to 2.3 percent pre-
sented in the previous section to the long-run average real interest rate of 2 per-
cent, which leads to a synthetic risk-free rate of between 3.7 and 4.3 percent.13
Adding the 5 percent market risk premium estimated earlier leads to an 
expected market return of 8.7 to 9.3 percent. If market prices eventually rise 
to incorporate ultralow interest rates (or if interest rates rise to better match 
market prices), make sure to reevaluate your perspective.
Matching Cash Flow Duration  In the preceding analysis, we focused on re-
turns from ten-year bonds. But why ten years and not something longer or 
shorter? The most theoretically sound approach is to discount a given year’s 
cash flow at a cost of capital that matches the maturity of the cash flow. In 
other words, year 1 cash flows would be discounted at a cost of capital based 
on a one-year risk-free rate, while year 10 cash flows would be discounted at 
a cost of capital based on a ten-year discount rate. To do this, use zero-coupon 
bonds (known as STRIPS),14 rather than Treasury bonds that make interim 
13 For ease of implementation, we use a single cost of equity to discount all cash flows. More advanced 
models split cash flows into two periods: an explicit forecast period and a continuing value. When us-
ing two periods, discount the first set of cash flows at observed yields, and create the perpetuity using 
a synthetic risk-free rate. Although a two-period model uses short-term market data more effectively, 
the valuation differences between one- and two-period models are relatively small, especially for short 
forecast windows.
14 Introduced by the U.S. Treasury in 1985, STRIPS stands for “separate trading of registered interest 
and principal of securities.” The STRIPS program enables investors to hold and trade the individual 
components of Treasury notes and bonds as separate securities.