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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 50.00% 1.125 1.125 1.09445 1.027913564
2 1.125 50.00% 1.6875 1.6875 1.197820803 1.408808393
3 1.6875 50.00% 2.53125 2.53125 1.310954977 1.930844342
4 2.53125 20.00% 3.0375 3.0375 1.434774675 2.117057161
5 3.0375 20.00% 3.645 3.645 1.570289143 2.321228556
6 3.645 20.00% 4.374 4.374 1.718602953 2.545090472
7 4.374 20.00% 5.2488 161.502 166.7508 1.880925001 88.65361451
Long term growth rate (given)= 6.00% 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 = Dividend Current 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 = 9.445%

100 = 0.75*(1+0.5)/(1+r)+0.75*(1+0.5)^2/(1+r)^2+0.75*(1+0.5)^3/(1+r)^3+0.75*(1+0.2)*(1+0.5)^3/(1+r)^4+0.75*(1+0.2)^2*(1+0.5)^3/(1+r)^5+0.75*(1+0.2)^3*(1+0.5)^3/(1+r)^6+0.75*(1+0.2)^4*(1+0.5)^3/(1+r)^7+0.75*(1+0.2)^4*(1+0.5)^3*((1+0.06)/(r-0.06))/(1+r)^7

jeff jeffy answered 1 year ago
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