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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.
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.
