51e Gordon Growth Model

Assuming the growth rate of a stock and the growth rate of its dividends are constant,

Value  = (Dividend) /(stock growth rate – dividend growth rate)

1. how did they get that simplified formula? I was trying to add each individual year out to infinity to get an idea. Any mathematicians know how to do a proof real fast?

2. How does this formula even make sense if we lower the value of the stock growth rate and its dividend growth rate in unison?

Take for example a stock with a D = $2.10. K= 12% and G =5%

V =2.1/(0.12-0.05)= 2.1/0.07= $30 per share. Makes sense  so far.but what if we lower K and G? With lower growth rates, then certainly the present day value of the shares would be reduced right? Substitute the new K as 0.08 and G as 0.01. You still get

V =2.1/(0.08-0.01)= 2.1/0.07= $30 per share. That makes no sense. Shouldnt the value have gone down?

In corporate finance now, looking to get my CFA and possibly an MBA.

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If I understand your example correctly: if you lower your required rate of return and the dividend growth rate to have the same difference between the 2 than the value stays the same.

I dont understand the question here

For the question of the formula being so simplified, I believe it is simply the algebraic rearrangement of the original formula by Gordon which he gave for calculating the cost of equity (Ke) and it went something like Ke = (D1/P0) + g where P0 = stock price D1 is the next expected dividend. Say if youre calculating Ke for FY 13-14, D1 would be dividend for the fy 12-13 as increased by Growth % g.

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As for your 2nd question, Id say the the formula makes sense in both the conditions. The reason being K is the expectations of shareholders from the stock and if growth rate falls, lets say, the shareholders expectations also decline accordingly thereby maintaining the stock price. This formula is based on various assumptions and if well try to apply this in practical scenario, there are numerous factors that act upon in deciding the stock price which, perhaps, cannot be summed up in a formula.

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The general formula for the sum of an infinite geometric series whose first term isaand whose common ratio is R is:

In the Gordon Growth model, the first term is the present value of D1,

Putting this into the standard formula, we get:

= [D1/(1 + r)] / (1 [(1 + g)/(1 + r)])

= [D1/(1 + r)] / [(1 + r) (1 + g)] / (1 + r)

Once again, youre confusing the growth rate of the stock with the investors required rate of return.  If the required rate of return decreases, the value of the stock rises.  If the rate of dividend growth decreases, the value of the stock falls.  These two effects cancel each other, leaving the value of the stock unchanged.

Simplify the complicated side; dont complify the simplicated side.

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The general formula for the sum of an infinite geometric series whose first term isaand whose common ratio is R is:

In the Gordon Growth model, the first term is the present value of D1,

Putting this into the standard formula, we get:

= [D1/(1 + r)] / (1 [(1 + g)/(1 + r)])

= [D1/(1 + r)] / [(1 + r) (1 + g)] / (1 + r)

Once again, youre confusing the growth rate of the stock with the investors required rate of return.  If the required rate of return decreases, the value of the stock rises.  If the rate of dividend growth decreases, the value of the stock falls.  These two effects cancel each other, leaving the value of the stock unchanged.

In corporate finance now, looking to get my CFA and possibly an MBA.

For the question of the formula being so simplified, I believe it is simply the algebraic rearrangement of the original formula by Gordon which he gave for calculating the cost of equity (Ke) and it went something like Ke = (D1/P0) + g where P0 = stock price D1 is the next expected dividend. Say if youre calculating Ke for FY 13-14, D1 would be dividend for the fy 12-13 as increased by Growth % g.

Right, and my algebra/calculus isnt good enough to do that anymore:

I found this paper but I didnt understand all of it.

In corporate finance now, looking to get my CFA and possibly an MBA.

. The reason being K is the expectations of shareholders from the stock and if growth rate falls, lets say, the shareholders expectations also decline accordingly thereby maintaining the stock price.

Im perhaps misreading your comment, but if not, theres an error.  K is not the shareholders EXPECTATIONs its their required rate of return.   So, its unlikely that both their expectations of growth (g) and their required rate of return will change by the same amount.  Its more likely that the growth expectation changes and their requiered rate of does not.  In this case, the stock becomes less attractive (i.e. the intrinsic value goes down).

You keep using that word.  I do not think it means what you think it means.

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