Hope you are doing well…..
I am having provlem in part (b).
It has asked to calculate the value of the company by using dividend valuation model by using the cost of equity that has been calculated using CAPM menthod.
Value of company using the dividend valuation model
The current cost of equity using the capital asset pricing model = 4 + (1·6 x 5) = 12%
Since a dividend will not be paid in Year 1, the dividend growth model cannot be applied straight away. However, dividends after Year 3 are expected to grow at a constant annual rate of 3% per year and so the dividend growth model can be applied to these dividends. The present value of these dividends is a Year 3 present value, which will need discounting back to year 0. The market value of the company can then be found by adding this to the present value of the forecast dividends in Years 2 and 3.
PV of year 2 dividend = 500,000/1·122 = $398,597
PV of year 3 dividend = 1,000,000/1·123 = $711,780
Year 3 PV of dividends after year 3 = (1,000,000 x 1·03)/(0·12 – 0·03) = $11,444,444
Year 0 PV of these dividends = 11,444,444/1·123 = $8,145,929
Market value from dividend valuation model = 398,597 + 711,780 + 8,145,929 = $9,256,306 or approximately $9·3 million
Alternative calculation of dividend valuation method market value
The year 3 dividend of $1m can be treated as D1 from the perspective of year 2
The year 2 value of future dividends using the dividend growth model will then be:
$1,000,000/(0·12 – 0·03) = $11,111,111
Year 0 PV of these dividends = 11,111,111/1·122 = $8,857,710
Adding the PV of the year 2 dividend gives a market value of 8,857,710 + 398,597 = $9,256,308 which, allowing for rounding, is the same as the earlier calculated value.
In method 1: we calculated the Present value of year 2 and 3, then why did they calculate the value by putting year 3 dividend value in the dividend growth formula, and then discounted it back to 0 and then adding up all values?
I’d be grateful to you if you can explain this bit to me.
The market value is always the present value of future expected dividends.
The dividend growth formula give the present value (i.e. the market value) of growing dividends where the first dividend receipt is in one years time, and the Do in the formula is the current dividend.
However, if the dividend is only growing after year 3, then you can still use the same value but it will give a present value (i.e. a market value) in 3 years time (instead of now), is assuming the next dividend is in 4 years time (instead of in 1 years time), and that Do is the dividend in three years time (instead of the dividend now) – everything in the formula is three years later than usual.
Because it gives a present value in three years time, we then need to discount it for three years to get the present value now.
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