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Example 1
Cant Co has a cost of equity of 10% and has forecast its future dividends as follows:
Current year: No dividend
Year 1: No dividend
Year 2 $0·25 per share
Year 3: $0·50 per share and increasing by 3% per year in subsequent years
What is the current share price of Cant Co using the dividend valuation model?
A $7·35
B $5·57
C $6·11
D $6·28The answer is C,
Would you be able to explain why?
Many thanksSurely there is are workings in the same book in which you found the question? You should ask which bit of the workings you are not clear about!
The market value is the PV of the future expected dividends. So the year 2 dividend needs discounting for 2 years at 10%, which gives 0.25 x 0.826 = 0.2065
For the growing dividend, we use the dividend growth formula.
Usually in the formula we have on the top Do(1+g) which is the dividend in 1 years time, and the answer from the formula is the PV now.
However the first growing dividend here is the dividend in 3 years time, and so we use that instead of Do(1+g) and since it is 2 years later than the normal 1 years time, the answer from the formula is a PV in two years time which then needs discount for 2 years at 10% to get a PV now.
So from the formula we get 0.50 / (0.10 – 0.03) = 7.1429.
Discount for 2 years gives 7.1429 x 0.826 = 5.9So the total PV = 0.2065 + 5.9 = $6.1065 (6.11)
The point is that the Do(1+g) in the normal formula is actually the dividend in 1 years time, and then the formula gives the PV now.
If you imagine you are at time 2, the the dividend in one more years time is an actual 50c (not 50c x (1+g), and so putting just 50c in the formula will give a PV at time 2.
Yes but we want to know the dividend not for only time 2, but for years after?
The formula gives the PV (which is the MV) for the years after! That is why we have the formula.
I am sorry, but you really need to watch my free lectures on the valuation of securities.
I have watched it already but i dont understand this point.
If the formula gives the market value for the years after, why do we ever then include (1+g) in any question.
Basically my question is why this time do we not include (1+g)?As I wrote before, Do(1+g) is the dividend in 1 years time and the formula gives a value at time 0 (i.e now).
If we already know the dividend in 1 years time, then we don’t need to take the current dividend and then grow it.
Here we already know the dividend in 3 years time, and so using it (instead of growing it) will give the value in 2 years time.
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