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).

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