# Estimate of the Risk-Free Rate Pf Interest ("U.S. 10-Year Treasury" Bond Rate

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• Published : December 8, 2006

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1. Estimate of the risk-free rate pf interest ("U.S. 10-year Treasury" bond rate = 4.78%. Assumed Market Risk Premium = 7.5%.

2. IBM Stock Information
a.IBM's Beta = 1.64
b.IBM's current annual dividend = \$0.80
c.IBM's 3-year dividend growth rate (g) = 8.2%
d.Industry P/E = 23.2
e.IBM's EPS = \$4.87

3. With the information you have, use the CAPM to calculate IBM's required rate of return or ks.

CAPM: ks = RF +{ (kM  Krf) x Beta} =

ks = 4.78% + {7.5% x 1.64) = 17.08%

ks = 17.08%

4. Use the GCM to find the current stock price for IBM. We will call this the theoretical price or Po.

D1 = D0 x (1 + g) = \$0.80 x (1 + 8.2%) = \$7.36

CGM: P0 = D1/(ks  g) =

P0 = \$7.36/(17.08%  8.2%) = \$82.88

5. Now use appropriate Web resources to find IBM's current stock quote, or P. Compare Po and P. Do you see any differences? Can you explain what factors may be at work for such a difference in the two prices?

a. P = \$76.28
P0 = \$82.88

b. Due to the Constant Growth Model's sensitivity to the discount rate, dividend growth rate and the expected dividend value, any error in estimating these values may give us values for share price, which is very different from the actual share price. Moreover, Assuming that the stock's present performance will continue in the future can result in overestimating the value of the stock.

6. Now assume the market risk premium has increased from 7.5% to 10%; and this increase is due only to the increased risk in the market. In other words, assume krf and stock's beta remains the same for this exercise. What will the new price be? Explain what happened.

a. CAPM: ks = RF +{ (kM  Krf) x Beta} =

ks = 4.78% + {10% x 1.64) = 21.18%

ks = 21.18%

P0 = \$82.88/(21.8% - 8.2%) = \$6.10

b. An increase in the market risk premium from 7.5 to 10% suggests that investors must take more risk to own the market portfolio of assets. This increase in risk contributes to a...