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D0=1.00 Dividend is expected to grow at 8% for 10 years, then 5% indefinitely. R=8% for...

D0=1.00

Dividend is expected to grow at 8% for 10 years, then 5% indefinitely. R=8% for the next 4 years, R=7% for the following 3 years, then 6% indefinitely.

What is today's expected stock price?

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Expert Solution

As pe dividend discount model, current price of stock is the present value of future dividends.
Step-1:Calculation of present value of dividends for first 10 years
Year Dividend Discount factor Present value
a b c=a*b
1 $       1.08 0.925926 $       1.00
2 $       1.17 0.857339 $       1.00
3 $       1.26 0.793832 $       1.00
4 $       1.36 0.73503 $       1.00
5 $       1.47 0.686944 $       1.01
6 $       1.59 0.642004 $       1.02
7 $       1.71 0.600003 $       1.03
8 $       1.85 0.566041 $       1.05
9 $       2.00 0.534001 $       1.07
10 $       2.16 0.503774 $       1.09
Total $    10.26
Working:
Dividend of year:
1 = $       1.00 * 1.08 = $       1.08
2 = $       1.08 * 1.08 = $       1.17
3 = $       1.17 * 1.08 = $       1.26
4 = $       1.26 * 1.08 = $       1.36
5 = $       1.36 * 1.08 = $       1.47
6 = $       1.47 * 1.08 = $       1.59
7 = $       1.59 * 1.08 = $       1.71
8 = $       1.71 * 1.08 = $       1.85
9 = $       1.85 * 1.08 = $       2.00
10 = $       2.00 * 1.08 = $       2.16
Discount factor of year:
1 = 1.08^-1 = 0.925926
2 = 1.08^-2 = 0.857339
3 = 1.08^-3 = 0.793832
4 = 1.08^-4 = 0.73503
5 = 1.07^-1 * 1.08^-4 = 0.686944
6 = 1.07^-2 * 1.08^-4 = 0.642004
7 = 1.07^-3 * 1.08^-4 = 0.600003
8 = 1.06^-1 * 1.07^-3 * 1.08^-4 = 0.566041
9 = 1.06^-2 * 1.07^-3 * 1.08^-4 = 0.534001
10 = 1.06^-3 * 1.07^-3 * 1.08^-4 = 0.503774
Step-2:Calculation of present value of dividend after year 10
Present value of dividends = D10*(1+g)/(Ke-g)*DF10 Where.
= $ 114.20 D10 $       2.16
g 5%
Ke 6%
DF10 0.503774
Step-3:Calculation of value of stock today
Value of stock today = Sum of present value of future dividends
= $    10.26 + $ 114.20
= $ 124.46

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