Question

Consider two stocks. For each, the expected dividend next
year is $100, and the expected growth rate of dividends is 3 percent. The risk
premium is 3 percent for one stock and 8 percent for the other. The economy’s safe
interest rate is 5 percent.

a). Use the Gordon growth model to compute the price of each stock.
Why is one price higher than the other? What does the difference in risk premiums
tell us about the dividends from each stock? Please note, to get full points, you
need to show all your steps and explain your answer.
b). Suppose the expected growth rate of dividends rises to 5 percent for
both stocks. Compute the new price of each. Which stock’s price changes by a
larger percentage?

Explain your answer. Please note, to get full points, you need to
show all your steps and explain your answer.

Answer 1

a) Dividend Year 1 =100
g=3%
Required rate for stock 1 =Risk Premium +Safe Interest Rate =3%+5% =8%
Price of Stock 1=Dividend Year 1/(Required Rate-growth) =100/(8%-3%) =2000
Required rate for stock 2 =Risk Premium +Safe Interest Rate =8%+5% =13%
Price of Stock 2=Dividend Year 1/(Required Rate-growth) =100/(13%-3%) =1000
On price is higher due to lower risk or lower risk premium.

The difference in risk premium shows the variance in dividend payout. Higher the risk premium higher is the variability of dividend payout.

b) Dividend Year 1 =100
g=5%
Required rate for stock 1 =Risk Premium +Safe Interest Rate =3%+5% =8%
Price of Stock 1=Dividend Year 1/(Required Rate-growth) =100/(8%-5%) =3333.33
Required rate for stock 2 =Risk Premium +Safe Interest Rate =8%+5% =13%
Price of Stock 2=Dividend Year 1/(Required Rate-growth) =100/(13%-5%) =1250

Stock 1 shows higher percentage increase in stock price.