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Hello Tutor,
I would like to understand the logic of the calculation in example 7 chapter 15.
I understand the market value is the PV of all the future dividends.If the question were to say “ a constant growth of 4 percent” , then we would just have to use the Po formula and have a PV at time 0 of 189 cents.
However, since the question said that the first year ( time 1) and second year ( time 2) will have merely dividends of 20 cents. Then my understand is that the market value will only be slightly less than 189 cents with the difference is the difference between PV of 20 cents discounted at time 1 and time 2 AND the PV of 20×1.04x DF time 1 and 20×1.04xDF time 2.
My calculation would be as below:
(1) Po= 189 cents
(2) If 4% of growth started in year 1, then total PV of dividend of year 1 and divide of year 2 is: (20×1.04×0.87)+(20×1.04×1.04×0.756)= 34.45 cents
(3) PV of dividend of year 1 and year 2 if no growth is: (20×0.87)+(20×0.756)=32.52 cents
(4) therefore, the difference is 34.45-32.52= 1.93 cents
(5) Therefore, the market value is : 189- 1.93 cents= 187 centsI don’t understand why in the lecture you added up the whole 189 cents with the PV of dividends in year 1 and year 2. Since the 189 cents is already the PV of all future dividends ( including year 1 and year 2)
Please advise where has went wrong with my understanding on this question.
Thank you dear Tutor 🙂
If the first dividend was 20 x 1.04 in 1 years time and continuing to grow at 4% then the MV given from the formula would be 189 and would be the present value of the dividends at time 0.
However, the dividend is 20 x 1.04 in 3 years time, which is 2 years later than in 1 years time, and so the 189 is the present value in 2 years time (i.e. t years later than time 0).
So to get the PV now (i.e. at time 0) we need to discount the 189 for 2 years (which gives the PV at time 0 of the dividends from 3 to infinity) and in addition we need to add the PV of the dividends at time 1 and at time 2. So then we have the PV of all of the future dividends 🙂
The 189 is not the PV of all of the future dividends. It is the PV at time 2 of the dividends from time 3 to infinity (and does not include the dividends at time 1 and time 2).
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