thank you sir for the lecture. Sir in example 4, if we calculate using the formula the the average growth comes out to 4.19% and if we use the average out the annual growths we get 4.31%, so there is a slight difference in the result. Therefore, will the examiner grant us the marks equally for both methods or does he prioritize one method over another?

Hi Sir, I am struggling to understand WHY the formula for cost of equity with growth in dividends works. I have understood how to apply the formula. I do not understand the rationale behind it.

I am aware that knowing how the formula is derived is not required in the exam. However, understanding its derivation would make it very easy for me to both remember and comprehensively understand it.

I have searched on google to find a mathematical proof or derivation of the formula with no luck. If you could help me out it would be much appreciated.

Will make a note though for future readers of this comment thread and would appreciate you signing off on this, the denominator is (r-g) and not (1-r) on the right hand side of the formula

adnanhustle says

thank you sir for the lecture.

Sir in example 4, if we calculate using the formula the the average growth comes out to 4.19% and if we use the average out the annual growths we get 4.31%, so there is a slight difference in the result.

Therefore, will the examiner grant us the marks equally for both methods or does he prioritize one method over another?

John Moffat says

The formula does give the average. It is the geometric mean and you cannot use the arithmetic mean on growth rates.

Having said that, the examiner probably would allow it or if not then only deduct 0.5 marks 馃檪

Aslan says

Hi Sir, I am struggling to understand WHY the formula for cost of equity with growth in dividends works. I have understood how to apply the formula. I do not understand the rationale behind it.

I am aware that knowing how the formula is derived is not required in the exam. However, understanding its derivation would make it very easy for me to both remember and comprehensively understand it.

I have searched on google to find a mathematical proof or derivation of the formula with no luck. If you could help me out it would be much appreciated.

John Moffat says

Po = PV of future dividends = Do(1+g)/(1+r) + Do (1+g)^2/(1+r)^2 + Do(1+g)^3/(1+r)^3 + …………

Multiply everything by (1+g)/(1+r):

Po(1+g)/(1+r) =Do(1+g)^2/(1+r)^2 + Do(1+g)^3/(1+r)^3 + …………

Subtract everything in this last equation from everything in the equation in the first line:

Po – Po(1+g)/(1+r) = Do(1+g)/(1+r)

Multiply everything by (1+r):

Po(1+r) – Po(1+g) = Do(1+g)

Po = Do(1+g)/(r-g)

There you go 馃檪

If you are happy with the algebra then fine, if not then just learn how to use the formula (this is the only way of proving it).

Aslan says

Very well understood and thank you Mr Moffat. I should have realised it is just a geometric series.

Aslan says

Will make a note though for future readers of this comment thread and would appreciate you signing off on this, the denominator is (r-g) and not (1-r) on the right hand side of the formula

John Moffat says

Thank you – I have corrected my typing mistake 馃檪