## Bbsdingdicom

Estimating Intrinsic Value 553

To demonstrate the estimate of the required rate of return equation for Walgreens, we make several assumptions regarding components of the security market line (SML) discussed in Chapter 8. First, the prevailing nominal risk-free rate (RFR) is estimated at about 5.0 percent— the current yield to maturity for the intermediate-term government bond. The expected equity market rate of return (RM) depends on the expected market risk premium on stocks. As noted earlier, there is substantial controversy on the appropriate estimate for the equity market risk premium—that is, the estimates range from a high of about 8 percent (the arithmetic mean of the actual risk premium since 1926) to a low of about 3 percent, which is the risk premium suggested in several recent academic studies. The authors reject both of these extreme values and will use a 4.5 percent risk premium (0.045). The final estimate is the firm's systematic risk value (beta), which is typically derived based upon the following regression model (the characteristic line) noted in Chapter 8.

where:

rwag = monthly rate of return for Walgreens a = constant term PWAG = beta coefficient for Walgreens

RM = monthly rates of return for a market proxy—typically the S&P 500 Index

When this regression was run using monthly rates of return during the five-year period 1997-2001 (60 observations), the beta coefficient was estimated at 0.90.

Putting together the RFR of 0.050 and the market risk premium of 0.045 implies an expected market return (RM) of 0.095. This combined with the Walgreens beta of 0.90 indicates the following expected rate of return for Walgreens:

= 0.050 + 0.90 (0.095 - 0.050) = 0.050 + 0.90 (0.045) = 0.050 + 0.040 = 0.090 = 9.0%

Present Value At this point, the analyst would face a problem: the intent was to use the basic DDM, which of Dividends assumed a constant growth rate for an infinite period. You will recall that the model also required Model (DDM) that k > g (the required rate of return is larger than the expected growth rate), which is not true in this case because k = 9.0 percent and g = 13 percent (as computed earlier). Therefore, the analyst must employ a two- or three-stage growth model. Because of the fairly large difference between the current growth rate of 13 percent and the long-run constant growth rate of 8 percent, it seems reasonable to use a three-stage growth model, which includes a gradual transition period. We assume that the growth periods are as follows:

g1 = 7 years (growing at 13 percent a year)

g2 = 5 years (during this period it is assumed that the growth rate declines 1 percent per year for 5 years)

g3 = constant perpetual growth of 8 percent Therefore, beginning with 2002 when dividends were expected to be \$0.15, the future dividend payments will be as follows (the growth rate is in parentheses):

 Year High-Growth Period Year Declining-Growth Period 