Suppose a dividend of $1.25 was paid. The stock has a required rate of return of
ID: 2706432 • Letter: S
Question
Suppose a dividend of $1.25 was paid. The stock has a required rate of return of 11.2% and investors expect the dividend to grow at a constant rate of 10%. Complete parts (a) through (e) below.
a) Compute D0, D1, D2, D3 and D7.
b)Compute the present value of the dividends for t = 3 years.
c) Compute the current market price.
d) Assume that the constant growth rate is actually 0%. What is the current market price?
Describe the behavior of the present value of each future dividend (i.e. the behavior as t increases to maturity of 10%.
Explanation / Answer
a) D0=$1.25
D1= D0(1+g)1
= $1.25(1+0.10)1
= $1.25*1.10
= $1.375
D2= D0(1+g)2
=$1.25(1+0.10)2
= $1.25*1.21
= $1.5125
D3= D0(1+g)3
=$1.25(1+0.10)3
= $1.25* 1.331
= $1.6637
D7 =D0(1+g)7
=$1.25(1+0.10)7
= $1.25* 1.9487
= $2.4358
b) Present value of dividends:
Present value of dividend till year3=D1/(1+0.112)1+ D2/(1+0.112)2+ D3(1+0.112)3
= $1.375/(1.112)+$1.5125/( 1.2365)+$1.6697/( 1.375)
= 1.2365+ 1.2232+ 1.2143
= 3.674
c) The formula for current market price is:
P0=Dividend1/(Required rate of return-growth rate)
Substitute the values in the formula:
P0=$1.375/(0.112-0.10)
= $1.375/ 0.012
= $114.58
P1=$1.5125/(0.112-0.10)
= $1.5125/ 0.012
= $126.04
P2=$1.6637/(0.112-0.10)
= $1.6637/ 0.012
= $138.64
P6=$2.4358/(0.112-0.10)
= $2.4358/ 0.012
= $202.98
d) If the constant growth rate is 0% then,
P0=Dividend1/(Required rate of return)
Substitute the values in the formula:
P0=$1.375/(0.112)
= $12.27
P1=$1.5125/(0.112)
= $13.50
P2=$1.6637/(0.112)
= $14.85
P6=$2.4358/(0.112)
= $ 21.74
The Present value of dividend keeps increasing as the value of t increases
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