hi, i would like to clarify for me this”500,000 10% irredeemable debentures” mean. beacause i thought it was 500,000 *10%=50000 then divide 0.08 to get market value of debt. instead ur using 100 *10%=10. is it assumption that ur using 100 instead of 500000 issued debentures

I make it clear in the earlier lectures that debt is always quoted on the stock exchange in units of $100 nominal (unless specifically told otherwise in the exam). The $125 is the market value of one unit ($125 p.c.). The total market value of all the debt is therefore $500,000 x 125/100 = $625,000 (which is the same as what you are doing).

Exam questions will make it clear whether they want the total market value of all the debt, or whether they want the market value that will be quoted on the stock exchange i.e. the value per $100 nominal.

please confirm if i am correct in my understanding ?

1) A market value higher than the nominal value would mean that a lower interest rate would be paid to the investor as because a higher market value is a compensation for the lower rate and vice versa ??

2) let suppose that i initially bought a debenture for a nominal value of $ 100 from a company last year . Currently the market value of the same debenture is worth $ 120 which would mean that the company would offer a lower return rate as the market value is greater than the nominal value . my question is that why would a person buy that debenture on the stock exchange from me when he has nothing to gain by purchasing it ??

firstly he would buy that debenture from me for $ 120 and secondly he would be paid a lower rate of interest . both of these are financially not in his favor …

1. Correct – assuming you are referring to the return to the investor (as opposed to the coupon rate, which would stay unchanged).

2. Firstly, the interest paid by the company (the coupon rate) is not changing. Whatone investor chooses to pay to another investor to take over the debenture is nothing to do with the company. As far as it not being financially in the investors favour – why not? If I have $120 to invest I will look to see what returns I can get on the money. If banks are paying (say) 1% a year interest, then I will be quite happy to pay $120 for the debenture is I end up getting a return of more than 1%! As I explain in the lecture, it is investors who determine the market value – not the company – and it depends on the interest they will get each year and the rate of return that they require.

At 16.25 in the video, (example 12) you take the discount factors for only years 1-3 thereby treating it as it was redeemable by 2010. However, in the lecture notes in example 12 it says they’ll be redeemable by 2020. Please correct me if I’m wrong.

please donot amend the year 2007 to 2017 . change 2020 to 2010 because as per your words in the video u have used 2010 as the maturity year . so altering the maturity year would get the lecture in line with the notes 🙂

Sir, in example 12 (chapter 15) it was better as of today to convert it to shares and therefore we calculated current m.v and parity value based on it but say if today it was better to take money at maturity would we calculate m.v based on $100 nominal in 3 years time. Also will parity value be $100 ? Please help

In example 12 your answer says investors are looking for a return of 10%. This isn’t stated in the question. Where do you get this assumed required rate of return or have I missed it?

We have certain assumptions and limitations in dividend valuation model, do the same applies to i.e., irredeemable debt as well?

Dividend valuation model formula = D/Re if there is no growth Irredeemable debt formula = Interest/kd

1. We assume that dividends/interest are paid once in a year and there is not interim dividend or semi annual interest 2. We assume that we have constant dividends or interest payments till infinity.

I have done some further work on question # 9. The investor required rate of return is 12%.

The interest rate that the investor will be getting is 8%. If we add the discount % and the premium % on this interest rate then it will also be around 12% which is equal to investor required rate of return.

Breakup: Interest rate getting 8% Discount (100-91.21)/5 years 1.76% Premium 10/5 years 2% TOTAL 11.76%

My question is: If the investor can easily get 12% bank interest then why he would buy traded debts which has the same fixed interest (even lower 11.76% in this question than 12%)? I think the risk is almost the same.

Can you please correct me if I am wrong? and provide explanations to understand the main ideas.

Firstly, your calculation (of 11.76%) is only an approximation. The correct return the investor is getting is the IRR, which is exactly 12%. (Although this is explained in a later chapter – the cost of capital – if you think about it, the return must be the IRR because that is the rate of interest that gives a NPV of zero).

Secondly, if bank interest is 12% then an investor in bonds will almost certainly want more than 12% and therefore the market value will end up being lower. The interest given by the bank may well be a starting point, but the exact return required by investors will depend on the level of risk, and again this is dealt with in a later chapter. It is impossible to explain everything at once – this chapter is dealing with the fact that in theory the market value will be the present value of future expected receipts discounted at the investor required rate of return. What determines the rate of return they require is a separate issue.

For the purposes of the exam will MV of Debt = MV of ALL debentures? I just want to ensure that I don’t stop at the working that gives the nominal pv and miss any points.

Dear John, Is it possible to be asked to calculate the share price at a given point in time in the future, using the dividend growth model? I get the idea that the dividends being discounted are full year dividends. So is it okay to apportion the dividend growth half way through? Say for 6 months, as in (D_0 (1+g)^(6/12))/(K_e-g)^(6/12) .

These are two separate questions (and in future they are better asked in the Ask the Tutor Forum rather than as a comment on a lecture).

First – if you know the market value now, and you want an estimate of the share price in the future, then you multiply the current share price by (1+g)^n (where n is the number of years in the future).

Second – you will not be asked to deal with 6 monthly dividends. In practice some companies certainly do pay dividends twice a year, but the interim dividend is usually much smaller that the final dividend, which means you would have to use the formula twice (once on the interim dividends and then on the final dividends).

Hi, In example 10 it says issued $1000,000 , 7% debentures are redeemable in four years time at par?invester required rate ov return is 10 %. Calculate the m.v ov the debt? in last question it says on premium is there any difference in par and premium if yeah how to solve this example .?

Have you watched all of our lectures? Debentures (and bonds and loan stock) are usually (in the exam) redeemed at a premium and the premium is always by reference to the nominal value. In which case the redemption amount is higher than the nominal (or par – which means the same thing) value.

In the case of Example 7 the debentures are already paying an interest of 10% annually so prospective investors would only be prepared to invest if they can at least earn interest of at least 10% or even better higher so why would they settle for a lower interest of 8%?

The market value is the price at which existing holders will sell it to other investors, and the price the people are prepared to pay to buy if from existing holders.

If investors are happy with a return of 8% (because maybe general bank interest rates are 8%) then they will be prepared to pay $125 (and existing holders would demand $125). The 10% is the interest on the nominal value. Investors buying now will get $10 a year on an investment of $125 which is a return of 8% and that is what they are currently happy with.

Hello sir with reference to example 9, is it sth like the investors would have liked an int. of $12/$100 nominal but have agreed for $8 because they are buying the loan notes at a discount and will also receive a premium on redemption? Also I get the computation behind why the MV rises the closer it gets to the redemption date. But does the loan notes being issued at a higher price has anything to do with the co. having borrowed the money for a shorter period of time?

I have got a question regarding redeemable debts. Why do we calculate the present value of the par instead of calculating the whole debt. Example 9. You calculated the repayment in 5 years time to be 110. Why should it not be 440?

Usually we calculate the market value of one unit (units have a nominal value of $100).

If the question wants the market value of all the debt then you either multiply the value of 1 unit by 400,000/100 to get the total market value. Or alternatively you could do as you suggest and calculate the present value of the interest on the 400,000 each year, and the repayment of 440,000.

Hi Sir, when we calculate the mv of loan note/debenture then formula is, the interest p.a on £100 nominal/ require rate of return. eg; interest is 10 on per unit of 100, nd rate of return is 8%, so now when we put the figure in the formula, why we put this like 10/.08, why not like .10/.08 or 10/8, as both are on 100.?

There is only one formula in all cases: Po = Do (1 + g) / (Re – g)

If the rate of growth in dividends is zero, then g = 0 and the same formula therefore automatically becomes Po = Do/Re !! (but only if there is zero growth)

The formula is given on the formula sheet. If you want the proof of it (which is certainly not required) I typed it out last year in reply to the post below this one.

Hi. In the lecture, you said that the dividend growth formula is easy to prove. I’ve got a very elementary understanding of maths, having only done GCSE maths to C level about 25 years ago! But I’m curious, why do we minus the growth figure in the bottom line of the fraction? Thanks.

Thanks for that! I’ll have a think about all that, and let you know when I can make head or tail of it! Don’t worry though, I won’t study this proof to the exclusion of the exam!

I was just thinking about your proof, and I’ve come to a realization! Would I be correct in saying that the (optional) growth figure in the top of the equation is merely there to calculate the dividend payable in one year’s time? Is it the growth figure in the bottom of the equation (the one you minus from the cost of capital) which is more relevant, and it is only this figure which incorporates growth into the equation? I probably haven’t explained myself very well, but am I on the right lines?

Question 4 from the June 2010 exam makes more sense to me now when I think of it this way.

Sir, like as you said market value represents the pv of the futer cash inflow, after a year time we may loose a cash inflow and so the market value shall be lower than as to previous year, how does it give rise to it?

The market value is always the PV of future expected receipts. If in a years time the expected receipts are lower, then in a years time the market value will be lower.

The nominal value of one unit of debenture is $100 .If the company has in issue $1000 6%debentures.Is it correct to say that the company has issued 10 debentures? The question “what will be the value of the debt “,does it mean the price of one unit of debenture?

The nominal value of one unit is usually $100, but it doesn’t have to be (it could for example, be $1000). In the exam, he does usually tell you the nominal value and it is usually $100. (If he doesn’t tell you, then assume it to be $100).

The reason I mention this is that to only have in issue $1000 in total would be unusual. If you are quoting from a question then check you have read it correctly and that it wasn’t just telling you that the nominal value of each unit was $1000.

If you are asked for the market value of the debt, then I would always calculate the value of one unit, but I would also (to be safe) show the total market value of all the units as well. (That only takes a second to multiply by the total number of units)

In example 5, you stated the MV cum div as 2.84 + 0.30= 3.14.

Since dividends are growing at the rate of 4 % p.a, in one year, the dividend to be received should be 0.30 *1.04 = 0.31. If my assumption is correct, MV cum div should be 2.84 + 0.31 = 3.15 dollars.

The current dividend is 0.30. Ex div is the situation when the current dividend has just been paid. Cum div is when the current dividend is about to be paid.

My Qn is on past exam paper dec 2007 Qn 1b(i).Using the approach that you used on this video lecture i would not agree with answer given by examiner(Market value of each convertible bond = (9 x 4·100) + (122 x 0·713) = $123·89) This is wrong because the nominal value is not 9% but 100 I am right to calculate it: 100*4.1=410 100*0.713=71.3 market value gives 410+71.3=481.3 compared to 121.98

The market value is the present value of the future receipts. The receipts are the interest each year (9% of nominal value = $9) and the redemption (122).

Hi john , can you please tell what if the dividend growth rate is abnormal in the early years and then after it becomes with a constant rate of growth , how to calculate the ex.div price in this case . thanks

The market value is the present value of the future expected dividends discounted at the shareholders required rate of return. So for the years where the dividend is ‘abnormal’, these dividends will have to be discounted individually. Once is becomes a constant rate of grown you can use the dividend growth formula, but since the constant growth starts ‘late’ (lets say it starts in 3 years time instead of in 1 years time) you then have to discount the answer by the extra years (in this case an extra 2 years).

(Although you could be required to do this, it is much less likely – simply because shareholders are usually unlikely to expect precise future dividends – they are more likely to be expecting average growth – be it 1% a year or 10% a year or whatever, in which case we do not have the problem above.)

Dear Jhon, Two companies A and B have same default risk. 1) An investment (lending money) for one year to company A and a debenture for 10 year to company B, should the investor require higher rate of return from company B since investing in B means giving up opportunity to invest elsewhere after one year if a better opportunity arises. I do know debentures are traded but are not as liquid as 1 year loan. 2) Principal amount is returned without adjusting it for inflation. If debentures are not convertible or investors do not expect to profit from conversion from debt to ordinary stock, there is a massive difference between the actual value of principal amount. Suppose inflation is constant at 5% after one year when Company A returns the nominal principal of 100 it will value 95 but when the company B returns the principal it will value at 60. Are investors not supposed to require additional return i.e. market return +premium for the lost of value in currency. 3) With time default risk increases, even if year to year default risk between two companies are constant but with since company B is paying after 10 years it has more default risk, should investor not require higher return to compensate for this as well?

Remember one general thing – it is not one single investor who will determine the returns required, but investors in general. One single investor simply has to decide whether the return is good enough for him/her and therefore whether or not they are prepared to invest.

All of the factors you mention will have a bearing on the return that investors will require – certainly the time to repayment; certainly the riskiness of the companies (even though your A and B supposedly have the same default risk); certainly the general interest rates (which are likely to tie in to a degree with the expected rate of inflation).

(I am not sure why you say the debentures are not as liquid as a loan – an investor can sell the debentures on the stock exchange at any time they want, whereas with a one year loan they have no choice (they cannot get their money back sooner, nor can they (normally) extend the loan at the same interest rate).

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hadi245 says

hi,

i would like to clarify for me this”500,000 10% irredeemable debentures” mean. beacause

i thought it was 500,000 *10%=50000 then divide 0.08 to get market value of debt.

instead ur using 100 *10%=10. is it assumption that ur using 100 instead of 500000 issued debentures

John Moffat says

I make it clear in the earlier lectures that debt is always quoted on the stock exchange in units of $100 nominal (unless specifically told otherwise in the exam). The $125 is the market value of one unit ($125 p.c.). The total market value of all the debt is therefore $500,000 x 125/100 = $625,000 (which is the same as what you are doing).

Exam questions will make it clear whether they want the total market value of all the debt, or whether they want the market value that will be quoted on the stock exchange i.e. the value per $100 nominal.

ahonanuga says

Hi John

In the example 12 where you cal the PV of the interest payments for 3 year…

You say $8 * 2.487 = 18.90

this is not correct as 8* 2.487 =19.896 or am I missing something.

John Moffat says

You are correct – it was a silly mistake and I should have said 19.90.

I will rerecord the lecture at some stage. However the answer in the lecture notes is correct 🙂

kirill009 says

Great lecture, thank you!

John Moffat says

Thank you for your comment 🙂

kellykhan99 says

In example 12 how did you know to use the df of 10%. It does not state what investors require of return should be.

kellykhan99 says

just read the comments i can see it was just not added!!!

John Moffat says

🙂

fola94 says

In Example 12, how did you get to know it is 1-3 years? The questions says nothing about three years, so I do not seem to understand. Thank you.

John Moffat says

Please read the comment from mracca11 below, and my reply.

usama93 says

please confirm if i am correct in my understanding ?

1) A market value higher than the nominal value would mean that a lower interest rate would be paid to the investor as because a higher market value is a compensation for the lower rate and vice versa ??

2) let suppose that i initially bought a debenture for a nominal value of $ 100 from a company last year . Currently the market value of the same debenture is worth $ 120 which would mean that the company would offer a lower return rate as the market value is greater than the nominal value . my question is that why would a person buy that debenture on the stock exchange from me when he has nothing to gain by purchasing it ??

firstly he would buy that debenture from me for $ 120 and secondly he would be paid a lower rate of interest . both of these are financially not in his favor …

kindly guide me in that please !

John Moffat says

1. Correct – assuming you are referring to the return to the investor (as opposed to the coupon rate, which would stay unchanged).

2. Firstly, the interest paid by the company (the coupon rate) is not changing. Whatone investor chooses to pay to another investor to take over the debenture is nothing to do with the company.

As far as it not being financially in the investors favour – why not? If I have $120 to invest I will look to see what returns I can get on the money. If banks are paying (say) 1% a year interest, then I will be quite happy to pay $120 for the debenture is I end up getting a return of more than 1%!

As I explain in the lecture, it is investors who determine the market value – not the company – and it depends on the interest they will get each year and the rate of return that they require.

mracca11 says

Hello Sir,

At 16.25 in the video, (example 12) you take the discount factors for only years 1-3 thereby treating it as it was redeemable by 2010. However, in the lecture notes in example 12 it says they’ll be redeemable by 2020. Please correct me if I’m wrong.

Thankyou 🙂

John Moffat says

Oops! It is a typing mistake – it should say that ‘now’ is 2017.

Thank you for spotting it. I will have it corrected 🙂

usama93 says

please donot amend the year 2007 to 2017 . change 2020 to 2010 because as per your words in the video u have used 2010 as the maturity year . so altering the maturity year would get the lecture in line with the notes 🙂

John Moffat says

Good point – thanks 🙂

rakhi2rakhi says

Sir, in example 12 (chapter 15) it was better as of today to convert it to shares and therefore we calculated current m.v and parity value based on it but say if today it was better to take money at maturity would we calculate m.v based on $100 nominal in 3 years time. Also will parity value be $100 ? Please help

John Moffat says

Yes to both questions 🙂

tree38 says

HI

In example 12 your answer says investors are looking for a return of 10%. This isn’t stated in the question. Where do you get this assumed required rate of return or have I missed it?

John Moffat says

You are quite right – thank you for spotting it.

I will have it added to the example in the notes immediately.

Libin Jacob ACCA says

hi John Sir, 10% is not in the question so can you kindly tell me how did you get that 10 %.Many thanks 🙂

John Moffat says

Have you not read the previous post here? It is a mistake – it should be in the question.

mktaguba says

Hi John,

In example 12 of the new lecture notes, is the “8% debentures 2020” suppose to say its repayable in 2010 and why is did we discount at 10%?

Thanks

madihakhan18 says

Hi,

are these lectures still valid??

John Moffat says

Of course they are otherwise they would not be here 🙂

salman7 says

Dear sir,

We have certain assumptions and limitations in dividend valuation model, do the same applies to i.e., irredeemable debt as well?

Dividend valuation model formula = D/Re if there is no growth

Irredeemable debt formula = Interest/kd

1. We assume that dividends/interest are paid once in a year and there is not interim dividend or semi annual interest

2. We assume that we have constant dividends or interest payments till infinity.

You comment needed pls. Thanks,

John Moffat says

We assume that interest is paid annually.

Interest payments are constant, but that is not an assumption – it is a fact. If the coupon rate is (say 8%) then it is fixed at 8% per year.

salman7 says

Hi Mr. John,

I have done some further work on question # 9. The investor required rate of return is 12%.

The interest rate that the investor will be getting is 8%. If we add the discount % and the premium % on this interest rate then it will also be around 12% which is equal to investor required rate of return.

Breakup:

Interest rate getting 8%

Discount (100-91.21)/5 years 1.76%

Premium 10/5 years 2%

TOTAL 11.76%

My question is: If the investor can easily get 12% bank interest then why he would buy traded debts which has the same fixed interest (even lower 11.76% in this question than 12%)? I think the risk is almost the same.

Can you please correct me if I am wrong? and provide explanations to understand the main ideas.

John Moffat says

Firstly, your calculation (of 11.76%) is only an approximation. The correct return the investor is getting is the IRR, which is exactly 12%. (Although this is explained in a later chapter – the cost of capital – if you think about it, the return must be the IRR because that is the rate of interest that gives a NPV of zero).

Secondly, if bank interest is 12% then an investor in bonds will almost certainly want more than 12% and therefore the market value will end up being lower. The interest given by the bank may well be a starting point, but the exact return required by investors will depend on the level of risk, and again this is dealt with in a later chapter. It is impossible to explain everything at once – this chapter is dealing with the fact that in theory the market value will be the present value of future expected receipts discounted at the investor required rate of return. What determines the rate of return they require is a separate issue.

matekane1113 says

OMG! these lectures are so overwhelming, thank you so much sir John

kc09 says

For the purposes of the exam will MV of Debt = MV of ALL debentures? I just want to ensure that I don’t stop at the working that gives the nominal pv and miss any points.

John Moffat says

Yes 🙂

sophierayner says

Is the answer to LE10, $90.49?

$7 x 3.170 (DF @ 10% for T1-T4) = $22.19

$100 x 0.683 (DF @ 10% for T4) = $68.30

$22.19 + $68.30 = $90.49?

sophierayner says

Oops, just seen your answer at the start of the next lecture.. I got it right, yay! 🙂

John Moffat says

Great 🙂

samson says

Dear John,

Is it possible to be asked to calculate the share price at a given point in time in the future, using the dividend growth model? I get the idea that the dividends being discounted are full year dividends. So is it okay to apportion the dividend growth half way through? Say for 6 months, as in

(D_0 (1+g)^(6/12))/(K_e-g)^(6/12) .

Kind regards

John Moffat says

These are two separate questions (and in future they are better asked in the Ask the Tutor Forum rather than as a comment on a lecture).

First – if you know the market value now, and you want an estimate of the share price in the future, then you multiply the current share price by (1+g)^n (where n is the number of years in the future).

Second – you will not be asked to deal with 6 monthly dividends. In practice some companies certainly do pay dividends twice a year, but the interim dividend is usually much smaller that the final dividend, which means you would have to use the formula twice (once on the interim dividends and then on the final dividends).

samson says

Dear John,

Thank you very much for the clarification.

The comment is well noted as well.

Regards

John Moffat says

You are welcome 🙂

uzma1111 says

Hi,

In example 10 it says issued $1000,000 , 7% debentures are redeemable in four years time at par?invester required rate ov return is 10 %.

Calculate the m.v ov the debt?

in last question it says on premium is there any difference in par and premium if yeah how to solve this example .?

John Moffat says

Have you watched all of our lectures?

Debentures (and bonds and loan stock) are usually (in the exam) redeemed at a premium and the premium is always by reference to the nominal value. In which case the redemption amount is higher than the nominal (or par – which means the same thing) value.

uzma1111 says

yes i did but after this lecture

thank u so much 🙂

John Moffat says

You are welcome 🙂

mansoor says

the required rate of return … are we assuming its pre tax rate of return?

John Moffat says

It is not an assumption, it is a fact.

It is only the company that gets tax relief on the interest payments, not the investor.

You really should watch our free lectures because this is all explained in detail – I cannot (and will not) simply type out the lectures here 🙂

mansoor says

thank u

… with 20 things to consider i tend to ask the stupidest questions..:) .. thank u again …

John Moffat says

No problem 🙂

Arun says

Hi John,

In the case of Example 7 the debentures are already paying an interest of 10% annually so prospective investors would only be prepared to invest if they can at least earn interest of at least 10% or even better higher so why would they settle for a lower interest of 8%?

Thanks.

John Moffat says

The market value is the price at which existing holders will sell it to other investors, and the price the people are prepared to pay to buy if from existing holders.

If investors are happy with a return of 8% (because maybe general bank interest rates are 8%) then they will be prepared to pay $125 (and existing holders would demand $125). The 10% is the interest on the nominal value. Investors buying now will get $10 a year on an investment of $125 which is a return of 8% and that is what they are currently happy with.

sayma says

Hello sir

with reference to example 9, is it sth like the investors would have liked an int. of $12/$100 nominal but have agreed for $8 because they are buying the loan notes at a discount and will also receive a premium on redemption?

Also I get the computation behind why the MV rises the closer it gets to the redemption date. But does the loan notes being issued at a higher price has anything to do with the co. having borrowed the money for a shorter period of time?

John Moffat says

Yes to your first question 🙂

Not really is the answer to your second question.

sayma says

Thanks!!!

Got to say this..its a wonder how you make me start liking every paper you teach.

I frankly dreaded f9 a few days back:p

John Moffat says

You are welcome and I am pleased that the lectures are helping you 🙂

marsibejko says

Hi John,

I have got a question regarding redeemable debts. Why do we calculate the present value of the par instead of calculating the whole debt.

Example 9.

You calculated the repayment in 5 years time to be 110. Why should it not be 440?

Many thanks for the videos.

John Moffat says

Usually we calculate the market value of one unit (units have a nominal value of $100).

If the question wants the market value of all the debt then you either multiply the value of 1 unit by 400,000/100 to get the total market value.

Or alternatively you could do as you suggest and calculate the present value of the interest on the 400,000 each year, and the repayment of 440,000.

Both approaches will give the same answer 🙂

shahz20 says

did I hear right that the examiner is a bastard? I had to pause and comment and LOL

John Moffat says

No – you must have heard wrong. I wouldn’t have said that 🙂 🙂

shahz20 says

xD

rushdi says

sir can you explain what is the difference between the term Re[shareholders required rate of return]and Ke[cost of capital]

John Moffat says

They are the same figure (except that Ke is not the cost of capital – it is the cost of equity)

It is the return that shareholders require that determines the rate the the company pays.

The free lectures on the valuation of securities and on the cost of capital will help you.

Na54 says

Thankyou Mr. Moffat for another great lecture.

arman90fy says

Hi Sir,

when we calculate the mv of loan note/debenture then formula is, the interest p.a

on £100 nominal/ require rate of return. eg; interest is 10 on per unit of 100, nd rate of return is 8%, so now when we put the figure in the formula, why we put this like 10/.08, why not like .10/.08 or 10/8, as both are on 100.?

John Moffat says

Because the interest on $100 nominal is 10% x $100 = $10, and because 8% = 8/100 = 0.08.

arman90fy says

got it .excellent sir…..thanks alot…….:)

Kawal says

Hi John,

My question is regarding the formula used in eg 5, Chapter 15.

Here you use the formula as Po= Do(1+G)/(Re-G)

Why do we subtract G (expected rate of growth in dividends p.a) from R (shareholder req. rate of return)?

In previous lecture (part a) we used another formula without expected growth rate of dividend which is :-

Po = Do/Re

Can this formula be used (in case of constant growth rate) as Po=Do(1+g)/Re

Obviously the ans will be different using this formula, but how this formula is not correct?

John Moffat says

No!

There is only one formula in all cases: Po = Do (1 + g) / (Re – g)

If the rate of growth in dividends is zero, then g = 0 and the same formula therefore automatically becomes Po = Do/Re !! (but only if there is zero growth)

The formula is given on the formula sheet. If you want the proof of it (which is certainly not required) I typed it out last year in reply to the post below this one.

Kawal says

No

Thats too long…I trust what you teach 🙂

neilsolaris says

Hi. In the lecture, you said that the dividend growth formula is easy to prove. I’ve got a very elementary understanding of maths, having only done GCSE maths to C level about 25 years ago! But I’m curious, why do we minus the growth figure in the bottom line of the fraction? Thanks.

John Moffat says

The only way to answer this is by giving you the proof (although I really think you should not waste your time on it!!!)

The MV is the present value of future dividends discounted at the shareholders required rate of return.

So: MV = Do(1+g)/(1+r) + Do(1+g)^2/(1+r)^2 + Do(1+g)^3/(1+r)^3+…….and so on for ever

Multiply this by (1+g)/(1+r) which gives:

MV(1+g)/(1+r)= Do(1+g)^2/(1+r)^2 + Do(1+g)^3/(1+r)^3+…….and so on for ever

Subtract the last equation from the first equation:

MV – MV(1+g)/(1+r) = Do(1+g)/(1+r)

Multiply both sides by (1+r)

MV(1+r) – MV(1+g) = Do(1+g)

Multiply through the brackets by MV

MV + MVr – MV – MVg = Do(1+g)

MV (r-g) = Do(1+g)

Divide by (r-g)

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

I bet you wish that you had not asked!!!!

neilsolaris says

Thanks for that! I’ll have a think about all that, and let you know when I can make head or tail of it! Don’t worry though, I won’t study this proof to the exclusion of the exam!

eadinnu says

Can’t stop laughing. The proof is for F10 to be introduced by ACCA

John Moffat says

🙂

neilsolaris says

I was just thinking about your proof, and I’ve come to a realization! Would I be correct in saying that the (optional) growth figure in the top of the equation is merely there to calculate the dividend payable in one year’s time? Is it the growth figure in the bottom of the equation (the one you minus from the cost of capital) which is more relevant, and it is only this figure which incorporates growth into the equation? I probably haven’t explained myself very well, but am I on the right lines?

Question 4 from the June 2010 exam makes more sense to me now when I think of it this way.

John Moffat says

Yes – sort of 🙂

hisaf says

Sir,

like as you said market value represents the pv of the futer cash inflow, after a year time we may loose a cash inflow and so the market value shall be lower than as to previous year, how does it give rise to it?

John Moffat says

The market value is always the PV of future expected receipts. If in a years time the expected receipts are lower, then in a years time the market value will be lower.

massivecodedake says

The nominal value of one unit of debenture is $100 .If the company has in issue $1000 6%debentures.Is it correct to say that the company has issued 10 debentures? The question “what will be the value of the debt “,does it mean the price of one unit of debenture?

John Moffat says

The nominal value of one unit is usually $100, but it doesn’t have to be (it could for example, be $1000). In the exam, he does usually tell you the nominal value and it is usually $100. (If he doesn’t tell you, then assume it to be $100).

The reason I mention this is that to only have in issue $1000 in total would be unusual. If you are quoting from a question then check you have read it correctly and that it wasn’t just telling you that the nominal value of each unit was $1000.

If you are asked for the market value of the debt, then I would always calculate the value of one unit, but I would also (to be safe) show the total market value of all the units as well. (That only takes a second to multiply by the total number of units)

massivecodedake says

Thanks!

eadinnu says

Dear prof,

In example 5, you stated the MV cum div as 2.84 + 0.30= 3.14.

Since dividends are growing at the rate of 4 % p.a, in one year, the dividend to be received should be 0.30 *1.04 = 0.31.

If my assumption is correct, MV cum div should be 2.84 + 0.31 = 3.15 dollars.

Kindly throw more light if I am not correct.

Regards,

Ebele.

John Moffat says

The current dividend is 0.30.

Ex div is the situation when the current dividend has just been paid. Cum div is when the current dividend is about to be paid.

eadinnu says

Thanks a lot. We cannot thank you enough.

acnca says

My Qn is on past exam paper dec 2007 Qn 1b(i).Using the approach that you used on this video lecture i would not agree with answer given by examiner(Market value of each convertible bond = (9 x 4·100) + (122 x 0·713) = $123·89)

This is wrong because the nominal value is not 9% but 100

I am right to calculate it:

100*4.1=410

100*0.713=71.3

market value gives 410+71.3=481.3 compared to 121.98

John Moffat says

The answer is correct.

The market value is the present value of the future receipts.

The receipts are the interest each year (9% of nominal value = $9) and the redemption (122).

usman123usi says

Hi john ,

can you please tell what if the dividend growth rate is abnormal in the early years and then after it becomes with a constant rate of growth , how to calculate the ex.div price in this case .

thanks

John Moffat says

The market value is the present value of the future expected dividends discounted at the shareholders required rate of return.

So for the years where the dividend is ‘abnormal’, these dividends will have to be discounted individually. Once is becomes a constant rate of grown you can use the dividend growth formula, but since the constant growth starts ‘late’ (lets say it starts in 3 years time instead of in 1 years time) you then have to discount the answer by the extra years (in this case an extra 2 years).

(Although you could be required to do this, it is much less likely – simply because shareholders are usually unlikely to expect precise future dividends – they are more likely to be expecting average growth – be it 1% a year or 10% a year or whatever, in which case we do not have the problem above.)

usman123usi says

Dear John ,

Thank you very much for your concern .its all crystal clear now .cheers.

John Moffat says

You are welcome 🙂

sam420 says

Dear Jhon,

Two companies A and B have same default risk.

1) An investment (lending money) for one year to company A and a debenture for 10 year to company B, should the investor require higher rate of return from company B since investing in B means giving up opportunity to invest elsewhere after one year if a better opportunity arises. I do know debentures are traded but are not as liquid as 1 year loan.

2) Principal amount is returned without adjusting it for inflation. If debentures are not convertible or investors do not expect to profit from conversion from debt to ordinary stock, there is a massive difference between the actual value of principal amount. Suppose inflation is constant at 5% after one year when Company A returns the nominal principal of 100 it will value 95 but when the company B returns the principal it will value at 60. Are investors not supposed to require additional return i.e. market return +premium for the lost of value in currency.

3) With time default risk increases, even if year to year default risk between two companies are constant but with since company B is paying after 10 years it has more default risk, should investor not require higher return to compensate for this as well?

John Moffat says

Remember one general thing – it is not one single investor who will determine the returns required, but investors in general. One single investor simply has to decide whether the return is good enough for him/her and therefore whether or not they are prepared to invest.

All of the factors you mention will have a bearing on the return that investors will require – certainly the time to repayment; certainly the riskiness of the companies (even though your A and B supposedly have the same default risk); certainly the general interest rates (which are likely to tie in to a degree with the expected rate of inflation).

(I am not sure why you say the debentures are not as liquid as a loan – an investor can sell the debentures on the stock exchange at any time they want, whereas with a one year loan they have no choice (they cannot get their money back sooner, nor can they (normally) extend the loan at the same interest rate).

kayez1234 says

Thanks so much OT, this is so clear. Happy for such a lecture as I am doing self study. Thanks a billion!!!

Saad Bin Aziz says

yup:-)

estherpang87 says

I heard it too..HAHA

admin says

🙂

asadraza says

did he really said that or its just my ears =D

4:20 (the examiner is a *****)

panayiotis2002 says

@asadraza, yes he said it

barzakh says

@panayiotis2002, damn i missed it i guess .. lol lack of concentration 😛

rugalxx says

@asadraza, yes tht ws my quetion too hahahahah hilarious one hahhahaah cnt stop my self