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Consider a stock that most recently paid a dividend of $0.75. The company plans to increase...

Consider a stock that most recently paid a dividend of $0.75. The company plans to increase dividends by 50% each year for the next 3 years, then by 20% each year for 4 years, and then level off to a permanent growth rate in dividends of 6%. If the actual stock price today is $100, what is the implied required rate of return

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Expert Solution

Required rate= 9.45%
Year Previous year dividend Dividend growth rate Dividend current year Horizon value Total Value Discount factor Discounted value
1 0.75 50% 1.125 1.125 1.094 1.0283
2 1.125 50% 1.6875 1.6875 1.198 1.4086
3 1.6875 50% 2.53125 2.53125 1.311 1.93078
4 2.53125 20% 3.0375 3.0375 1.435 2.11672
5 3.0375 20% 3.645 3.645 1.57 2.32166
6 3.645 20% 4.374 4.374 1.719 2.5445
7 4.374 20% 5.2488 161.497 166.7458 1.881 88.64742
Long term growth rate (given)= 6% Value of Stock = Sum of discounted value = 100
Where
Current dividend = Previous year dividend*(1+growth rate)^corresponding year
Unless dividend for the year provided
Total value = Dividend + horizon value (only for last year)
Horizon value = current Dividend year 7 *(1+long term growth rate)/( required rate-long term growth rate)
Discount factor= (1+ required rate)^corresponding period
Discounted value= total value/discount factor

implied rate = 9.45%

jeff jeffy answered 1 year ago
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