E(r) = 3.5 + 0.90(7) = 9.8%
Cost of Equity using Gordon Growth Model...
P0 = D1 / (r - g)
$47 = $1.80(1.05) / (r - 0.05)
1.89 / 47 = r - 0.05
0.04021 + 0.05 = r
r = 0.09021, or 9.02% < this is the rate at which the Market is valuing CDB's equity but you would expect it to move toward the CAPM rate
Since the market value rate plots below the SML (less than the CAPM rate) the stock would be considered overpriced. I'm not sure how you are taught to determine which of these is the better estimate, but I would choose the CAPM rate because CAPM (via Beta) gives you an historic view of volatility.
At the CAPM rate, the stock would be valued at:
P0 = 1.89 / (0.098 - 0.05)
= $39.38
Stock in CDB Industries has a beta of .90. The market risk premium is 7 percent, and T-bills are currently yielding 3.5 percent. CDB’s most recent dividend was $1.80 per share, and dividends are expected to grow at a 5 percent annual rate indefinitely.
Required:
If the stock sells for $47 per share, what is your best estimate of CDB’s cost of equity?
