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An investor is interested in purchasing shares of ABC company. The company pays annual dividends, and a dividend payment of 1.2 per share has just been made. Future dividends are expected to grow at the rate of 5% per annum comp ound.

(a) Calculate the maximum price per share that the investor should pay to give an effective return of 9% per annum.

(b) If the price of ABC’s share is being sold at the price found in part (a), find the Macaulay duration and the modified duration of the ABC’s share.

(c) If the effective return rate increases by 0.1%, estimate the new share price, based on the part (b)

Hi guys,I am having problems with understanding this question, in particular part a. How do i equate the Present value of the dividend cashflows to the price of the shares when i do not have information of the timeline. Could somebody provide a solution to this with an explanation please. thank you!

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  • $\begingroup$ I thought the problem assumes $5\%$ per annum - you can assume yearly dividends at $5\%$, no? $\endgroup$
    – gt6989b
    Nov 4, 2013 at 14:38

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Use the Gordon Growth Model (Dividend Discount Model): http://en.wikipedia.org/wiki/Dividend_discount_model http://www.investopedia.com/terms/g/gordongrowthmodel.asp

Remember that the numerator is the Dividend at TIME 1... so (1.05)*1.2

Then r is your required rate of return (9%) and g is the growth of your dividends (5%).

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