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# Stock Valuation

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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)

#### Solution Preview

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?

Po= Div1/ (r-g)

1 g= -5%
Div0 = \$2
Dividend for next year= Div1 = 1.90 =(1+(-5.%)) *2
Cost of equity= r= 15%
growth rate of dividends/earnings= g= -5%
Current stock price= Po=
Plugging in the values:
Po= \$9.50 =\$1.9/ (15.% - (-5.%))

2 g= 0%
Div0 = \$2
Dividend for next year= Div1 = 2.00 =(1+(.%)) *2
Cost of equity= r= 15%
growth rate of dividends/earnings= g= 0%
Current stock price= Po=
Plugging in the values:
Po= \$13.33 =\$2./ (15.% - (.%))

3 g= 5%
Div0 = \$2
Dividend for next year= Div1 = 2.10 =(1+(5.%)) *2
Cost of equity= r= 15%
growth rate of dividends/earnings= g= 5%
Current stock price= Po=
Plugging in the values:
Po= \$21.00 =\$2.1/ (15.% - (5.%))

4 g= 10%
Div0 = \$2
Dividend for next year= Div1 = 2.20 =(1+(10.%)) *2
Cost of equity= r= 15%
growth rate of dividends/earnings= g= 10%
Current stock price= Po=
Plugging in the values:
Po= \$44.00 =\$2.2/ (15.% - (10.%))

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?

1 g= 15%
Div0 = \$2
Dividend for next year= Div1 = 2.30 =(1+(15.%)) *2
...

#### Solution Summary

The solution calculates the value of stocks using CAPM and Gordon (constant growth) model.

\$2.19