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Dear Mr Moffat,
Could you please explain how the Average growth rate of earnings per share calculation?
Q1b – December 2008
Dartig Co is a stock-market listed company that manufactures consumer products and it is planning to expand its existing business. The investment cost of $5 million will be met by a 1 for 4 rights issue. The current share price of Dartig Co is $2·50 per share and the rights issue price will be at a 20% discount to this.
The finance director of Dartig Co expects that the expansion of existing business will allow the average growth rate of earnings per share over the last four years to be maintained into the foreseeable future.
The earnings per share and dividends paid by Dartig over the last four years are as follows:
2003 2004 2005 2006 2007
earnings per share (cents) 27.7 29.0 29.0 30.2 32.4
dividend per share (cents) 12.8 13.5 13.5 14.5 15.0
Dartig Co has a cost of equity of 10%. The price/earnings ratio of Dartig Co has been approximately constant in recent years. Ignore issue costs.
Required:
Calculate the expected share price following the proposed business expansion using the price/earnings ratio method.Solution
Current price/earnings ratio = 250/32·4 = 7·7 times
Average growth rate of earnings per share = 100 x ((32·4/27·7)0·25 – 1) = 4·0%
Earnings per share following expansion = 32·4 x 1·04 = 33·7 cents per share
Share price predicted by price/earnings ratio method = 33·7 x 7·7 = $2·60Thanks
Gabriella
There have been 4 years for growth in earnings.
To get the average rate of growth we do exactly the same as we do when calculating the average growth rate for dividends.
i.e. g = (fourth root (latest/earliest)) – 1
So here, g = fourth root (32.4/27.7) – 1 = 0.03995 (or 4%)
( x^0.25 is another way of writing ‘fourth root of x’)
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