# Constant growth valuation formula for stocks

You are given the following information about three stocks:

Chapman Tech is expected to pay a $ 1.20 dividend at the end of the year. The required return on Chapman Tech's stock is 11% and its dividend is expected to grow at a constant rate of 7% per year.

Rust Petroleum is expected to pay a $ 1.50 dividend at the end of the year. Rust Petroleum's dividend yield and capital gains yield both equal 6%.

Schubert Fabric's current stock price is $15 per share, its required return is 13%, and its dividend yield is 8%.

Use the constant growth valuation formula to evaluate each stock's next dividend , current price, required return, expected dividend growth rate, and dividend yield. Assume the market is in equilibrium. In the table below, indicate which stock has the highest value for each of these metrics.

Which stock has the highest Chapman Tech Rust Petroleum Schubert Fabric

Expected Dividend (D1)=

Current stock Price (P0)=

Required return (rs) =

Expected Dividend growth rate (g)=

Dividend yield (Dy) =

Capital gains yield=

https://brainmass.com/business/dividend-yield/260310

#### Solution Preview

Please see the attached file:

Note: Required return = Dividend yield + Capital gains yield

Capital gains yield= Expected dividend growth rate (for constant growth model)

Expected Dividend (D1)= $1.20 (Given)

Current stock Price (P0)= $30.00 (see calculations below)

Required return (rs) = 11% (Given)

Expected Dividend growth rate (g)= 7% (Given)

Dividend yield (Dy) = 4% = 11%-7% ; required return = dividend yield + capital gains yield; therefore, dividend yield = required return - capital gains yield

Capital gains yield= 7% Capital gains yield= Expected dividend growth rate (for constant growth model)

Using the Dividend Discount (Constant Growth) Model

Po= D1/ (rs-g)

Dividend for next year= D1 = $1.20

Cost ...

#### Solution Summary

Using the constant growth valuation formula, evaluates for each of the three stocks, next dividend , current price, required return, expected dividend growth rate, and dividend yield.

Stock and Investment Problems

1.. Investors require a 15 percent rate of return on Levine Company's stock (rs = 15%).

a. What will be Levine's stock value if the previous dividend was D0 = $2 and if investors expect dividend to grow at a constant compound annual rate of (1) -5 percent, (2) 0 percent, (3) 5 percent, and (4) 10 percent?

b. Using data from part a, what is the Gordon (constant growth) model value for Levine's stock if the required rate of return is 15 percent and the expected growth rate is (1) 15 percent or (2) 20 percent? Are these reasonable results? Explain? c. Is it reasonable to expect that a constant growth stock would have g > rs?

2. The risk-free rate of return, rRF, is 11 percent; the required rate of return on the market, rM, 14 percent; and Upton Company stock has a beta coefficient of 1.5.

a. If the dividend expected on the coming year, D1, is $2.25, and if g = a constant 5 percent, at what price should Upton's stock sell?

b. Now, suppose that the Federal Reserve Board increases the money supply, causing the risk-free rate to drop to 9 percent and rM to fall to 12 percent. What would this do to the price of the stock?

c. In addition to the change in part bm suppose that investor's risk aversion declines; this fact, combined with the decline in rRF, cause rM to fall to 11 percent. At what price would Upton's stock sell?

d. Now, suppose Upton has a change in management. The new group institutes policies that increase the expected constant growth rate to 6 percent. Also, the new management stabilizes sales and profits, and this causes the beta coefficient to decline from 1.5 to 1.3. Assume that rRF and rM are equal to the values in part c. After all these changes, what is Upton's new equilibrium price? (Note D1 goes to$2.27)

View Full Posting Details