Question 13.3: Assume the equity beta for Johnson & Johnson (ticker: JN...

Plan

The two ways to estimate J&J’s cost of equity are to use the CAPM and the CDGM.

1. The CAPM requires the risk-free rate, an estimate of the equity’s beta, and an estimate of the market risk premium. We can use the yield on 10-year Treasury notes as the risk-free rate.

2. The CDGM requires the current stock price, the expected dividend next year, and an estimate of the constant future growth rate for the dividend.

Risk-free rate: 3%                                Current price: $92.00
Equity beta: 0.55                                  Expected dividend: $2.81
Market risk premium: 6%                  Estimated future dividend growth rate: 4%

We can use the CAPM from Chapter 12 to estimate the cost of equity using the CAPM approach and Eq. 13.5 to estimate it using the CDGM approach.

Cost  of  Equity =\frac{Dividend  (in  one  year)}{Current  Price} + Dividend  Growth  Rate =\frac{Div_1}{P_E} +g             (13.5)

Execute

1. The CAPM says that

Cost of Equity = Risk-Free Rate + Equity Beta × Market Risk Premium

For J&J, this implies that its cost of equity is 3% + 0.55 × 6% = 6.3%.

2. The CDGM says

Evaluate

According to the CAPM, the cost of equity capital is 6.3%; the CDGM produces a result of 7.1%. Because of the different assumptions we make when using each method, the two methods do not have to produce the same answer—in fact, it would be highly unlikely that they would. When the two approaches produce

different answers, we must examine the assumptions we made for each approach and decide which set of assumptions is more realistic. We can also see what assumption about future dividend growth would be necessary to make the answers converge. By rearranging the CDGM and using the cost of equity we estimated from the CAPM, we have

Thus, if we believe that J&J’s dividends will grow at a rate of 3.2% per year, the two approaches would produce the same cost of equity estimate.