Equity Question, Please Help!

I Don’t understand the answer: A stock has a steady 5% growth rate in dividends. The Require rate of return for stocks of this risk class is 15%. The stock is expected to pay a $1 dividend this coming year. The expected value of the stock at the end of the fourth year is : My Logic: The end of the fourth year is the beginning of the fifth year. In order to find the value of the stock at beginning of T=5, I have to find the dividend at T=6 to discount it back to T=5. 1(1.05)^6 = $1.3401 $1.3401 / .15-.10 = 13.40 (WRONG ANSWER) WHERE AM I GOING WRONG?

your growth rate should be .05 or 5%

Sorry YES, I made a mistake G=5% still… you still get $13.40

It would be helpful if you would post the choices. I am getting $10. It’s a wierd question though because normally it would give you an intermediate growth rate before the constant 5%. Since it didn’t, i used 5% for 1-3 and then year 4 applied the constant growth formula with the same 5% growth. *shrug*

A) 12.16 B) 14.21 C) 16.32 My logic is wrong in thinking that by asking to find the value at the end of the 4th year (begining of the 5th year), I must find the dividend at the beginning of the 6th year to discount back to PV beg5th year (to get the Pv @end of 4th). If someone could help me see the light, i would be very greatful.

got your problem Time 0 1 2 3 4 5 Dividend - 1 1.05 1.1025 1.157625 1.215506 To find price at the end of year 4 you need to discount year 5 dividend using DDM with constant growth. In shortcut it is (1*(1.05)^4)/(0.15-.05)=12.16

But they are expecting a $1.00 dividend, so wouldn’t D1 actually be just that $1.00? You typically only multiply the growth rate if it is “just paid” or “previously”…

Man, I am still confuse… Ok so. D1 =1 D2 = 1.05 D3 = 1.1025 D4 = 1.1576 D5 = 1.2155 D6 = 1.2763 If we want to find the Price of the stock at the end of the 4th year (BEGINNIG OF THE 5TH year), why don’t we discount the dividend in the “6TH” year to find the price at the BEGINNING of the 5th year (end of the 4th)??? This is were my flaw lays.

I wanted to draw the timeline but the forum did not support that. D0=unknown D1=1 D2=1.05 D3=1.1025 D4=1.1576 D5=1.2155 To find the price at D4 we used the next periods (D5) dividend, that is 1.2155. This is the rule. Think of what you would do to find price at Time 0. Would you use D1 or D2? I think you got confused with the end of year thing. Consider end of year 4 as year 4.

Kh.Asif, Yes, “the end of the fourth year” makes me think, the beginning of the 5th year, which makes me think, find D6.

i dont see why you dont discount the dividends in yr 1-4…

markCFAIL Wrote: ------------------------------------------------------- > i dont see why you dont discount the dividends in > yr 1-4… Because you are trying to find the price at end of year 4 which makes past data obsolete. If Year 4 is 2009 and you want to find the price of a stock in 2009 would you use the dividends of 2005-2008? You would only see those if you want to make a reasonable estimate of the dividend growth rate using past data. However the constant growth rate of dividends is already given in the question, so no need to do that.

calc value now: P0 = D1 / (RR - GR) = 1 / (.15 - .05) = 10 calc value in 4 years: growth rate = 5 stock should grow at this rate for 4 years: P4 = P0 x (1 + GR)^4 = 10 x 1.05 ^4 = 12.16 ok?