1. The last dividend CompU paid was $0.80. The historical growth rate in dividen
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Question
1. The last dividend CompU paid was $0.80. The historical growth rate in dividends has been 6%, and analysts expect it to remain constant for the foreseeable future. Investors require a 14 percent rate of return.
a. What is the current value or price of CompU’s stock?
=.80 * (1+.06) / (.14-.06) = $10.60
b. What is the expected dividend yield?
= .80 / 10.60 = .0755 0r 7.55%
c. If the growth rate was 8 instead of 6 percent, what would be the value of CompU’s stock?
=.80 * (1+.08) / (.14 -.08) = $14.40
d. If the growth rate was as originally stated (6 percent) but the required rate of return increased from 14 to 16 percent, what would be the value of CompU’s stock?
= .80 * (1+.06) / (.16-.06) = $8.48
e. Based on the answers for c. and d., what is the relationship between growth rates and stock price and required return and stock price?
A higher growth rate will increase the price of the stock overall. An increase in the required return will decrease the price of the stock overall.
2. Instead of the information in question 1, what if analysts expect CompU’s dividend to grow by 25 percent for the next 3 years, but increased competition is expected to force their growth rate to a constant 6 percent thereafter. CompU just paid a dividend of $0.80, and investors’ rate of return is 14%. What is the value of CompU’s stock today?
Explanation / Answer
Solution for question 2:
Dividend (Do) = $0.80, Rate of return (Ke) = 14%, Growth rate1 (g1) = 25%, Growth rate2 (g2) = 6%,
Now in this case, for the next 3 years, dividend will grow by 25% and after that it will grow by 6% , so for 3 years, it is a constant growth model and after that it is a perpetual growth model.
So Value of CompU's stock today will be = Present value due to constant growth for 3 years + Present value due to perpetual growth after 3 years
Constant growth case
Do = $0.80, g1= 25%, Ke=14%
Hence, present value of stock due to constant growth for first 3 years = $2.89 ------ (1)
Perpetual growth case
After 3 years, the stock dividend will grow by 6% , g2=6%, Ke=14%
So, value of stock after 3 years = D3*(1+g2)/(Ke-g2)
= 1.56*(1+6%)/(14%-6%)
= $20.70
Present value of stock would be = Value of stock after 3 years * Discounting factor for 3 years
= 20.70 * 0.67 (from above table)
= $13.97
Hence, present value of stock due to perpetual growth after 3 years = $13.97 ------ (2)
Adding (1) & (2)
$13.97 + $2.89 = $16.87
Hence, Value of CompU's stock today will be = $16.87
Year 1 2 3 Dividend (Do*(1+g1)) 1.00 1.25 1.56 Discounting factor (1/(1+Ke)^n) 1/(1+14%)^1 1/(1+14%)^2 1/(1+14%)^3 0.88 0.77 0.67 Present values (Dividend * Discounting factor) 0.88 0.96 1.05 Sum of present values 2.89Related Questions
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