Investors expect the following series of dividends from a particular stock:
Year one$1.10
Year two$1.25
Year three$1.45
Year four$1.60
Year five$1.75
After the fifth year, dividends will grow at a constant rate. If the required rate of return on this stock is $ 9% and the current market price is $45.64,What is the long term rate of dividend growth expected by the market ?
This is just a little bit of net present calculations. NPV of the first 5 years is the following:
1.1 /1.09 + 1.25/1.09^2 + 1.45/1.09^3 + 1.60/1.09^4 + 1.75/^1.75^5 = 5.451801.
This means the value of the dividend at constant growth after year 5 must now be 45.64 – 5.4518 = 40.1882. The formula to solve is:
1.75 x (1+g)
—————– / 1.09^5 = 40.1882
r-g
This can be rewritten as follows:
1.75 + 1.75g
—————————— = 40.1882
0.138476 -1.538624g
1.75g + 61.834529g = 5.565101 – 1.75
g = 3.815101 / 63.584529 = 0.06 = 6%
and that’s it……
This is just a little bit of net present calculations. NPV of the first 5 years is the following:
1.1 /1.09 + 1.25/1.09^2 + 1.45/1.09^3 + 1.60/1.09^4 + 1.75/^1.75^5 = 5.451801.
This means the value of the dividend at constant growth after year 5 must now be 45.64 – 5.4518 = 40.1882. The formula to solve is:
1.75 x (1+g)
—————– / 1.09^5 = 40.1882
r-g
This can be rewritten as follows:
1.75 + 1.75g
—————————— = 40.1882
0.138476 -1.538624g
1.75g + 61.834529g = 5.565101 – 1.75
g = 3.815101 / 63.584529 = 0.06 = 6%
and that’s it……
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