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Consider a firm that has just paid a dividend of $2. An analyst expects dividends to...

Consider a firm that has just paid a dividend of $2. An analyst expects dividends to grow at a rate of 8% per year for the next five years. After that dividends are expected to grow at a normal rate of 5% per year. Assume that the appropriate discount rate is 7%. What is the price of the stock today (P0)?

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Expert Solution

Required rate= 7.00%
Year Previous year dividend Dividend growth rate Dividend current year Horizon value Total Value Discount factor Discounted value
1 2 8.00% 2.16 2.16 1.07 2.0187
2 2.16 8.00% 2.3328 2.3328 1.1449 2.03756
3 2.3328 8.00% 2.519424 2.519424 1.225043 2.0566
4 2.519424 8.00% 2.72097792 2.72097792 1.31079601 2.07582
5 2.72097792 8.00% 2.938656154 154.279 157.2176562 1.402551731 112.09402
Long term growth rate (given)= 5.00% Value of Stock = Sum of discounted value = 120.28
Where
Current dividend =Previous year dividend*(1+growth rate)^corresponding year
Total value = Dividend + horizon value (only for last year)
Horizon value = Dividend Current year 5 *(1+long term growth rate)/( Required rate-long term growth rate)
Discount factor=(1+ Required rate)^corresponding period
Discounted value=total value/discount factor

jeff jeffy answered 5 months ago
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