In the notes of this chapter, we have heading “The valuation of equity – non-constant dividends” but there is no example of non-constant dividend below the notes anywhere. There is only one example which is for constant dividend only.

Which chapter in the lecture notes are you talking about?
This lecture relates to Chapter 17 of the lecture notes and all of the examples (except for the first one) have growing dividends!!
There is no heading in this chapter saying “non-constant dividends”!!

I am quite confused sir,
in example 6 : part c (estimate the market value in 2 years time)
why not use the formula of Po=Do*(1+g)/re-g ????
i saw previous lectures with regards Po … and i thought its for the constant growth in the Dividends, while it is the same in here a constant growth of 0.0675 in the dividend !!
but you added it simply to the market value over 2 years ..
solution sir ??

Of course it is not correct – there is only one correct answer! (And how on earth can you expect the market value to increase from $2.80 to $2,989.00???

If you want to use the formula, then Do = 20 x (1.0675^2); g = 0.0675; Re = 0.14375.
If you put these in the formula you get $3.19

You need to watch the lectures on the valuation of securities – the lectures are supposed to be watched in order.
Since the MV is the PV of future expected dividends, as dividends increase then so will the MV increase.

for the problem i gave earlier i did not include 16m shares in issue($1 each),current share price at $3 and book value equity per share of $3.6 in 2013. so given this information would i be able to estimate cost of equity using earnings retention model(g=rb)? because the requirement is that part(i) i use Dividend growth model…which i have and part(ii) i use earnings retention model…which is a bit tricky for me?

You should calculate the retention rate (b) for each year and then find the average retention rate.

With regard to the return on investment (r), you would assume it to be equal to the cost of equity (in practice it may not be, but in theory it should be).

To use Gordons growth model (g = r b) you would need more information. From what you have given, we can calculate the average retention rate, but there is not enough information to calculate the rate of return on the retentions.

However, given that the most likely reason that you need the growth rate would be to use the dividend valuation formula to get the market value of shares, if you are given past dividends then you would calculate the dividend growth rate based on the past dividends (which for your example would be: (the fourth root of (21/11)) – 1 = 0.1755 (or 17.55%)

Hi sir, why is it when I try to divide the dividends by the required rate of return it does not give me the market value of 2.80? for instance I do 0.20 / 0.14375 it gives 1.39?

Because you have not brought in the growth rate – the formula is the first one on the formula sheet!
Go back to Chapter 15 in the Lecture Notes and watch the lecture that goes with it (you should work through the chapters in number order).

oh yeah! I have seen the lecture I just completely forgot about bringing the growth in as I tried to calculate it using a constant dividend ………..All good now thanks for clearing that up.

If you notice in my trend 31 is the latest year not 33 as per your lecture. I repeat the trend for your reference 28,29,30,33 & 31. Or would it be correct to solve as thus: 28(1+g)^4=31.

First of all many thanks for these excellent lectures!!!

I would like to ask a question re example 6 part (c) . You said that the market value of a share is the present value of future dividends discounted at the shareholders required rate of return. We didn’t discount the $3.19 , because we weren’t given the shareholders required rate of return or am I mixing things up ?

I have a question, here you said in theory the market value is the present value of future expected dividents.
If company is retaining all it’s earnigs then this means shareholders are not getting any dividends but the total capital in the company is increasing for which shareholders are owner of.
In theory, how does this case effects the market value of an equity.

Case:-Company A issue $100 shares

Earnings $10, Divident: $0 and Retained Earnings $10
Re (S/H req rate of return)=8%
M.V. =?

In theory, how does the market value is affected if we Company A pays all the earnings as dividends and zero retained earning?

A company cannot retain all its earning for ever!
Shareholders would not allow them to retain all their earnings for ever – the shareholders own the company and they appoint the directors.

They may well retain all their earnings for some years – this will lead to growth in profits, and ultimately dividends.

The market value remains the present value of the future dividends.

However the situation of your response is in real world…i’m wondering how all earnings as retainted earnings will effect the MV in theory.

I know the wealth of shareholders is increasing by that earned amount…will it last year cap + new retained earnings divide by no. of shareholders of the company?

Shareholders wealth is measured by the market value of their shares.

In theory this is determined by the present value of expected future dividends. What I said before is the theory!
‘g’ in the formula is not the actual growth rate – we have absolutely no idea what the actual growth rate will be! ‘g’ is the average rate of growth that shareholders expect.

In practice other factors affect the share price as well.

Of course you can! (Except, of course, you use D3 in the formula instead of D0 because we want a value at time 3)

But why waste time? It is automatic that if shareholders expect dividends to grow then they will be expecting the share price to grow at the same rate.

Hi Mr Moffat,,just wanted small clarification,,if in a certain scenario we were given both return on capital employed or return on equity,,which one should we use in relation to Gordons growth model?

This is rather hypothetical – the examiner has never given both for these purposes!
(In fact I can only remember two times – both of them a very long time ago – when Gordons growth model was even relevant!)

However, what we need is the rate of return that the company gets on reinvestment. In theory it would be the return on equity, but if he did give both then you would get credit for using either (provided you stated your assumption).

Hi,John.In example 6 question C , Shouldn’t the answer to be 280(1.0675)^3?According to the share price with constant growth rate model,the numerator should be D0(1+g) and I think D0 is 20(1.0675)^2 so D1is 20(1.0675)^3.Therefore the price in 2 years time should be 280(1.0675)^3.Is it my opinion correct? Thanks

No – the answer in the notes and the lecture is correct. The share price will be 280 (.0675)^2

Although the numerator will indeed be 20(1.0675)^3, you are forgetting that the numerator for the current share price will be 20(1.0675). So…..the numerator will be (1.0675)^2 times the current numerator.

Always (in theory) the share price will increase at the same growth rate p.a. as the dividend growth rate.

Here, the shareholders are requiring a return of 14.375% (as calculated in part (b) – this is why they are prepared to pay $2.80 per share on the stock exchange). As a result the company needs to give them 14.375% and so the cost of equity is 14.375% (and here also the cost of the capital is 14.375% because there is no debt borrowing – this is dealt with in the next lecture).

The company therefore needs to make sure that they invest the money to get a return of at least 14.375% – if they can earn more then great, if they earn less from any investment then they should not invest.
In this case they are earning 18% from investing the money which is great.

(In the long term it is the case that if the company is always managing to earn 18% on investments, then shareholders will eventually want a return of 18% themselves (this is due to risk and is covered in a later chapter), but from year to year this certainly need not be the case.)

You will have to be a bit more specific as to what you mean.
For cost of capital we always want the cost to the company. Because debt interest is tax allowable, the cost to the company is the cost after tax relief (so we take the after tax interest when calculating the cost of debt).

Hi John:
I have a much better understanding of “after-tax” cost of capital now.

Can you clarify a few things for me;-
1. how do you calculate the cost of preference share, dec. 2010 question # 4c? I’m not sure if I grasp the concept from the answer.
2. Dec 2012 # 2a, is it a error that current receivables days should be 60 and not 30?
3. Dec 2012 # 2b, i note in the answer the holding cost was not discounted. why wasn’t it?
4. Dec 2009 # 1a, (ASOP Co) tax benefit was applied to the licencing fee. Why so? The question asked for “financing” cash flow, what is different about a financing cash flow?

The cost of preference share is simply the dividend/market value. They pay a constant dividend, and there is no tax relief on the dividends. The dividend is quoted as a percentage of the nominal value.

The answer does not mention the current receivables days. It is not necessary to calculate them because we know what current receivables are from the balance sheet. (our current terms of sales are payment within 30 days, but that does not mean that everyone does pay within 30 days.)

We never discount the holding cost in the exam. (Maybe in real life, we should, but it would be a big problem because the cost is spread day-by-day over the year and we normally only discount for whole years.)

It is reasonable to assume (from F6) that the licencing fee is tax allowable. The reason it is needed when we are considering the cost of financing, is that although it is not relevant if we lease, it is relevant if we buy. So if we are comparing the cost of leasing with that of buying we need to take it into account.

The market value increases at the same rate dividend increases.(refer to the eg on pg94).
In part a, you had calculated it and its 6.75%. Hence,
market value of share in 2yrs time
= 2.80(1+0.0675)^2
=$3.19

both comments are right but i see the driving factor is the interet rate because this seems to be the determing factor in the sense that an increase in interest rate will automatically increase SH/H reguired return but a decrease will also decrease share holders return though a decrease is more demotivating to investors, since they expect their money to be worthy investing hence will bring conflict here.

You are quit right – in practice the growth in the share price is unlikely to be the same as the dividend growth rate,

The main reason for this is that the shareholders required rate of return is likely to change – partly because general interest rates change (if interest rates in general go up then shareholders will require a higher rate of return, and vice versa), and also because the riskiness of the business might change (if the company becomes more risky then shareholders required rate of return will increase, and vice versa).

However, if we are trying to predict the future share price, then we cannot predict what will happen to the interest rates or to the riskiness and therefore all we can do is assume that the remain the same – in which case the share price should increase at the same rate as the growth in dividends.

By the way, to answer to the 6 c I have actually used the modified version of dividend growth model.

ie if p0 = d0(1+g)/ Ke – g , then p2 should be equal to d2(1+g)/Ke-g OR the same as saying p2= d3/Ke-g.

As d3 is equal to d0(1+g)^3, we can get the answer to p2 which is the market value of share in two years time.

But your explanation about market value is the present value of future dividends discounted at shareholder’s expected return and if dividends are growing at a certain growth rate and the market value should be growing at the same growth rate, says it all.

But in practise, I believe market value and dividends are not growing exactly at the same growth rate.

Can I please have your comments about this Mr John.

marlenadouglas says

should it be a formula in order to find the retention rate (eg, 6) we divide the eps by the retained earnings?

John Moffat says

That is what the retention rate is.

Laiq Hussain says

Hi Mr. Moffat,

In the notes of this chapter, we have heading “The valuation of equity – non-constant dividends” but there is no example of non-constant dividend below the notes anywhere. There is only one example which is for constant dividend only.

Thanks,

John Moffat says

Which chapter in the lecture notes are you talking about?

This lecture relates to Chapter 17 of the lecture notes and all of the examples (except for the first one) have growing dividends!!

There is no heading in this chapter saying “non-constant dividends”!!

Fardeen Samim says

I am quite confused sir,

in example 6 : part c (estimate the market value in 2 years time)

why not use the formula of Po=Do*(1+g)/re-g ????

i saw previous lectures with regards Po … and i thought its for the constant growth in the Dividends, while it is the same in here a constant growth of 0.0675 in the dividend !!

but you added it simply to the market value over 2 years ..

solution sir ??

John Moffat says

By all means use the formula and you will arrive at the same answer.

The market value will grow at the same rate as dividends (and I explain why in the lecture).

Nelson says

Hi John,

Sorry but using this formula Po=Do*(1+g)/re-g I found a different Market value 2,989. Is this correct?

John Moffat says

Of course it is not correct – there is only one correct answer! (And how on earth can you expect the market value to increase from $2.80 to $2,989.00???

If you want to use the formula, then Do = 20 x (1.0675^2); g = 0.0675; Re = 0.14375.

If you put these in the formula you get $3.19

Arun says

Hi John,

Could you please explain to me the logic as to why the market value will increase at the same rate as the dividend?

Thanks.

John Moffat says

You need to watch the lectures on the valuation of securities – the lectures are supposed to be watched in order.

Since the MV is the PV of future expected dividends, as dividends increase then so will the MV increase.

Gary says

Sorry – please ignore. I got the dividend and retentions the wrong way around.

Greenson says

Thank you sir for your help!!!!!!

John Moffat says

You are welcome 🙂

Greenson says

Thank you sir,

for the problem i gave earlier i did not include 16m shares in issue($1 each),current share price at $3 and book value equity per share of $3.6 in 2013. so given this information would i be able to estimate cost of equity using earnings retention model(g=rb)? because the requirement is that part(i) i use Dividend growth model…which i have and part(ii) i use earnings retention model…which is a bit tricky for me?

John Moffat says

You should calculate the retention rate (b) for each year and then find the average retention rate.

With regard to the return on investment (r), you would assume it to be equal to the cost of equity (in practice it may not be, but in theory it should be).

Greenson says

Thank Sir,

however i have a similar problem on how to estimate cost of equity using earnings retention model given this situation:

year EPS(cents) Dividend per share(cents)

2009 15 11

2010 27 12

2011 33 13

2012 45 17

2013 57 21

How can i approach this problem if am to use gordon’s growth model?

John Moffat says

To use Gordons growth model (g = r b) you would need more information. From what you have given, we can calculate the average retention rate, but there is not enough information to calculate the rate of return on the retentions.

However, given that the most likely reason that you need the growth rate would be to use the dividend valuation formula to get the market value of shares, if you are given past dividends then you would calculate the dividend growth rate based on the past dividends (which for your example would be: (the fourth root of (21/11)) – 1 = 0.1755 (or 17.55%)

fahim231 says

Hi sir, why is it when I try to divide the dividends by the required rate of return it does not give me the market value of 2.80? for instance I do 0.20 / 0.14375 it gives 1.39?

John Moffat says

Because you have not brought in the growth rate – the formula is the first one on the formula sheet!

Go back to Chapter 15 in the Lecture Notes and watch the lecture that goes with it (you should work through the chapters in number order).

fahim231 says

oh yeah! I have seen the lecture I just completely forgot about bringing the growth in as I tried to calculate it using a constant dividend ………..All good now thanks for clearing that up.

rabiu says

If you notice in my trend 31 is the latest year not 33 as per your lecture. I repeat the trend for your reference 28,29,30,33 & 31. Or would it be correct to solve as thus: 28(1+g)^4=31.

John Moffat says

Yes – 28(1+g)^4 = 31.

You always would take the earliest dividend and the latest dividend.

rabiu says

Thank you.

rabiu says

How would i estimate dividend growth (g) in this trend 28,29,30,33 & 31.

John Moffat says

In exactly the same way as I do in the lecture when I go through example 4 in the chapter!!

Annalise says

Hi Sir,

First of all many thanks for these excellent lectures!!!

I would like to ask a question re example 6 part (c) . You said that the market value of a share is the present value of future dividends discounted at the shareholders required rate of return. We didn’t discount the $3.19 , because we weren’t given the shareholders required rate of return or am I mixing things up ?

Thanks

John Moffat says

Part (c) asked what the value will be in 2 years time. We know the current market value and we know the growth rate, so we can calculate from that.

Annalise says

I understand now .. its because he asked for the value in 2 years time. Thanks again Sir, really appreciated, very good lecturer!!

John Moffat says

It is not the actual growth rate in dividends that is relevant – it is the growth that shareholders expect that matters.

Shareholders will expect dividends to grow at the same rate as the profits (and in the long term they will anyway 🙂 )

Kawal says

Hi..

I have a question, here you said in theory the market value is the present value of future expected dividents.

If company is retaining all it’s earnigs then this means shareholders are not getting any dividends but the total capital in the company is increasing for which shareholders are owner of.

In theory, how does this case effects the market value of an equity.

Case:-Company A issue $100 shares

Earnings $10, Divident: $0 and Retained Earnings $10

Re (S/H req rate of return)=8%

M.V. =?

In theory, how does the market value is affected if we Company A pays all the earnings as dividends and zero retained earning?

Thanks in advance for your valuable response.

John Moffat says

A company cannot retain all its earning for ever!

Shareholders would not allow them to retain all their earnings for ever – the shareholders own the company and they appoint the directors.

They may well retain all their earnings for some years – this will lead to growth in profits, and ultimately dividends.

The market value remains the present value of the future dividends.

Kawal says

Thanks for your response.

However the situation of your response is in real world…i’m wondering how all earnings as retainted earnings will effect the MV in theory.

I know the wealth of shareholders is increasing by that earned amount…will it last year cap + new retained earnings divide by no. of shareholders of the company?

John Moffat says

Shareholders wealth is measured by the market value of their shares.

In theory this is determined by the present value of expected future dividends. What I said before is the theory!

‘g’ in the formula is not the actual growth rate – we have absolutely no idea what the actual growth rate will be! ‘g’ is the average rate of growth that shareholders expect.

In practice other factors affect the share price as well.

absylum007 says

can’t we use mv = Do(1+g) / (ro – g) in example 6 part c ????

John Moffat says

Of course you can! (Except, of course, you use D3 in the formula instead of D0 because we want a value at time 3)

But why waste time? It is automatic that if shareholders expect dividends to grow then they will be expecting the share price to grow at the same rate.

SOUD SAEED says

Hi Mr Moffat,,just wanted small clarification,,if in a certain scenario we were given both return on capital employed or return on equity,,which one should we use in relation to Gordons growth model?

John Moffat says

This is rather hypothetical – the examiner has never given both for these purposes!

(In fact I can only remember two times – both of them a very long time ago – when Gordons growth model was even relevant!)

However, what we need is the rate of return that the company gets on reinvestment. In theory it would be the return on equity, but if he did give both then you would get credit for using either (provided you stated your assumption).

SOUD SAEED says

Really appreciate it, you have cleared my doubts.

massivecodedake says

Hi,John.In example 6 question C , Shouldn’t the answer to be 280(1.0675)^3?According to the share price with constant growth rate model,the numerator should be D0(1+g) and I think D0 is 20(1.0675)^2 so D1is 20(1.0675)^3.Therefore the price in 2 years time should be 280(1.0675)^3.Is it my opinion correct? Thanks

John Moffat says

No – the answer in the notes and the lecture is correct. The share price will be 280 (.0675)^2

Although the numerator will indeed be 20(1.0675)^3, you are forgetting that the numerator for the current share price will be 20(1.0675). So…..the numerator will be (1.0675)^2 times the current numerator.

Always (in theory) the share price will increase at the same growth rate p.a. as the dividend growth rate.

davisyieh says

Sir John, for part b, why is the cost of capital not the return of 18% in the question? Isn’t required rate of return = cost of capital?

John Moffat says

I assume you are meaning part (b) of example 6.

Here, the shareholders are requiring a return of 14.375% (as calculated in part (b) – this is why they are prepared to pay $2.80 per share on the stock exchange). As a result the company needs to give them 14.375% and so the cost of equity is 14.375% (and here also the cost of the capital is 14.375% because there is no debt borrowing – this is dealt with in the next lecture).

The company therefore needs to make sure that they invest the money to get a return of at least 14.375% – if they can earn more then great, if they earn less from any investment then they should not invest.

In this case they are earning 18% from investing the money which is great.

(In the long term it is the case that if the company is always managing to earn 18% on investments, then shareholders will eventually want a return of 18% themselves (this is due to risk and is covered in a later chapter), but from year to year this certainly need not be the case.)

I hope that makes some sense 🙂

davisyieh says

Oh thank you very much! This really help! Your explanation is great, thanks Sir John.

morren says

Hi John:

Could you kindly clarify how you apply “before and after taxes”.

Do appreciate

John Moffat says

You will have to be a bit more specific as to what you mean.

For cost of capital we always want the cost to the company. Because debt interest is tax allowable, the cost to the company is the cost after tax relief (so we take the after tax interest when calculating the cost of debt).

morren says

Hi John:

I have a much better understanding of “after-tax” cost of capital now.

Can you clarify a few things for me;-

1. how do you calculate the cost of preference share, dec. 2010 question # 4c? I’m not sure if I grasp the concept from the answer.

2. Dec 2012 # 2a, is it a error that current receivables days should be 60 and not 30?

3. Dec 2012 # 2b, i note in the answer the holding cost was not discounted. why wasn’t it?

4. Dec 2009 # 1a, (ASOP Co) tax benefit was applied to the licencing fee. Why so? The question asked for “financing” cash flow, what is different about a financing cash flow?

Thank you

John Moffat says

The cost of preference share is simply the dividend/market value. They pay a constant dividend, and there is no tax relief on the dividends. The dividend is quoted as a percentage of the nominal value.

The answer does not mention the current receivables days. It is not necessary to calculate them because we know what current receivables are from the balance sheet. (our current terms of sales are payment within 30 days, but that does not mean that everyone does pay within 30 days.)

We never discount the holding cost in the exam. (Maybe in real life, we should, but it would be a big problem because the cost is spread day-by-day over the year and we normally only discount for whole years.)

It is reasonable to assume (from F6) that the licencing fee is tax allowable. The reason it is needed when we are considering the cost of financing, is that although it is not relevant if we lease, it is relevant if we buy. So if we are comparing the cost of leasing with that of buying we need to take it into account.

morren says

from the info provided the examiner said we should “assume” 60 days ……. Earlier when I downloaded the examiners reports, Dec 2012 was not accessible.

Thanks again

afridi420 says

sir i didnt get example 6 part c in chapter 17

manisha says

The market value increases at the same rate dividend increases.(refer to the eg on pg94).

In part a, you had calculated it and its 6.75%. Hence,

market value of share in 2yrs time

= 2.80(1+0.0675)^2

=$3.19

munthaliaunward says

both comments are right but i see the driving factor is the interet rate because this seems to be the determing factor in the sense that an increase in interest rate will automatically increase SH/H reguired return but a decrease will also decrease share holders return though a decrease is more demotivating to investors, since they expect their money to be worthy investing hence will bring conflict here.

John Moffat says

Thank you for your comments.

You are quit right – in practice the growth in the share price is unlikely to be the same as the dividend growth rate,

The main reason for this is that the shareholders required rate of return is likely to change – partly because general interest rates change (if interest rates in general go up then shareholders will require a higher rate of return, and vice versa), and also because the riskiness of the business might change (if the company becomes more risky then shareholders required rate of return will increase, and vice versa).

However, if we are trying to predict the future share price, then we cannot predict what will happen to the interest rates or to the riskiness and therefore all we can do is assume that the remain the same – in which case the share price should increase at the same rate as the growth in dividends.

funlover says

Absolutely awesome.

By the way, to answer to the 6 c I have actually used the modified version of dividend growth model.

ie if p0 = d0(1+g)/ Ke – g , then p2 should be equal to d2(1+g)/Ke-g OR the same as saying p2= d3/Ke-g.

As d3 is equal to d0(1+g)^3, we can get the answer to p2 which is the market value of share in two years time.

But your explanation about market value is the present value of future dividends discounted at shareholder’s expected return and if dividends are growing at a certain growth rate and the market value should be growing at the same growth rate, says it all.

But in practise, I believe market value and dividends are not growing exactly at the same growth rate.

Can I please have your comments about this Mr John.