Discounted Cash Flow Problem [Archive]

Snoopy

01-07-2004, 05:45 PM

quote:Originally posted by Dimebag

A bond generally doesn't pay "10% interest compound"

It may pay a 10% coupon which can then be 'compounded' by the owner simply by reinvesting the coupon in further bonds.

(It is, of course, possible for Bonds to be pure discount bonds, in which case the 'implied' released return on face value may be 10% compound, but no coupons are actually 'paid'. However, it is impossible to have a discount bond that is of an infinite term).

So Trader100 must be correct.

In a realistic example I agree with you Dimebag. However this example is one I pulled out of a book. The bond doesn't have to be 'real' in the sense that you describe. Like I said before, its not a trick question.

But I am interested in what people 'assume' given the somewhat scanty description of the problem the book provides. So thanks for your reply.

SNOOPY

madmike

01-07-2004, 05:50 PM

I must have it wrong!!!!
I calculate $100.70.
Please tell us who's right....and why you ask this little "teaser"!!!!
regards

Snoopy

01-07-2004, 06:04 PM

quote:Originally posted by Trader_100

Snoopy,
Based on the assumption that you receive the first $10 payment one year from today <snip>

Based on the assumption that you receive the first $10 payment now
<snip>

Excellent Trader100. So I am not alone in seeing that there are two ways to look at this. Do you discount the cash flow of year one or not?

Of course, in a real example you would tend to be comparing one cash flow with another so as long as you used the same assumptions in both of the cash flows you are comparing it shouldn't matter.

But let's say you wanted to work out this cash flow as a 'standard' for comparing other cash flows with. You then ask someone else to work out the discounted value of a completely different cash flow over ten years and using an appropriate discount rate so that you can compare it with this one. How do you know which of the two assumptions the other person is using?

Is there a 'standard' way to interpret this problem?

SNOOPY

CAM

01-07-2004, 06:14 PM

standard way??...not sure, but when I was doing some finance/economics stuff unless otherwise stated we always assumed the payment was received at the end of the first period not the start of it

brother coy

01-07-2004, 07:34 PM

a stop comfusing us poor suckers hahhaa with ya supposed bond valuation when in da fact ya was meaning cashflow valuations hahhaa

da snoop ya dont know what da other person is using hahhaaa:D

skinny

01-07-2004, 08:11 PM

Quite right brother coy - the '$100 bond' is irrelevant in the question. Also, if we were to be realistic about this as a DCF exercise we shouldn't forget the tax collector ;)

Trader_100

01-07-2004, 08:13 PM

Snoopy,

It is standard to assume that the first cashflow occurs 1 year from now (ie at the end of this year) unless it is otherwise stated.

Elfer,

As Dimebag pointed out, a bond never compounds the coupon payment but if it did you answer still isn't correct. The correct way to answer the question based on this assumption is:

10/1.08 + 10*1.1 /(1.08)^2 + 10*1.1^2 / (1.08)^3 + 10*1.1^3 / (1.08)^3

The answer is 100.70

Coaster

02-07-2004, 12:13 AM

Trader 100,

I disagree with your logic. What you appear to be doing is taking a payment, compounding it foward n periods and then discounting it back n periods.

All this results is a PV for each payment at the time it was issued, not at n=0.

For instance, the payment at n=1 needs to be compounded foward 9 periods (to n=10) and then discounted back 10 periods (back to n=0). The payment at n=2 needs to be compounded foward 8 periods (to n=10) and then discounted back 10 period (to n=0).

It should look something like this:

10 x (1.10)^9/(1.08)^10 + 10 x (1.10)^8 /(1.08)^10 + ... + 10 x (1.10)^0 / (1.08)^10

or more simply:

10 x (1.10^9 + 1.10^8 + ... + 1.10^0) / (1.08)^10

or

PVIF8%,10 x ( 10 x FVIFA 10%,10)

or

0.4632 x 10 x 15.9374 = $73.82

I'll have to agree with elfer on this one.

Coaster

Trader_100

02-07-2004, 07:31 AM

Coaster,

I stand by my answer.

To work out this problem you need to:
1. Calculate the payment received at the end of each period. For period 1 the payment is 10, for period 2 the payment is 10*1.1, for period 3 the payment is 10*1.1^2.
2. Discount these payments back to the present. The period one payment should be divided by 1.08, the period 2 payment should be divided by 1.08^2 etc.

Your method works out the future value of the income stream at the end of 10 years and discounts this future value back to the present in one go. This is incorrect as you are receiving the payments yearly not all at once at the end.

Perhaps you would like to adjuticate Snoopy!

T100.

MeNoBatty

02-07-2004, 08:32 AM

Snoopy, did you get this question from a first or second year text book? From memory, they dont tend to deal with real world examples in these, instead focusing on the math.

The simple answer is as per Coaster and Elfer. The word compounding is the key, real world or not, you have to read the whole question and why it is being asked.

If, instead, this is from a later year text book, you would have to list your assumptions such as payments at the end of the period, no taxes etc....

Coaster

02-07-2004, 09:02 AM

quote:Originally posted by Trader_100

Your method works out the future value of the income stream at the end of 10 years and discounts this future value back to the present in one go.

That's right.

quote:This is incorrect as you are receiving the payments yearly not all at once at the end.

I don't believe so, because if the interest payment are not received, they are reinvested.

Because they are reinvested, you only end up with a notional amount at the end of your 10 year timeframe. As I understand your calculation, you have discounted each payment (which is reinvested) to n=0 and at the same time reinvested it to get the n+1 interest amount. I don't believe you can do this.

I liken it to a DCF valuation: you need to subtract capex as part of the calculations even though capex produces fcf in future periods. You can't discount both capex and the cash flows that it produces to reach a DCF because this is akin to 'double-dipping'.

Snoopy, you better call this one.

Regards
Coaster

Trader_100

02-07-2004, 09:17 AM

Hi Coaster,

I can see your logic now. You are certainly correct based on that assumption. I was assuming that the coupon payment had a growth component that saw it increase by 10% per year, but that you still received the payment each year.

Different assumptions = different results aye.

Regards,

T100.

madmike

02-07-2004, 09:32 AM

yes $100.70 is right trader100.

coaster - if you had various investments at various interest rates at various maturity dates how will you compare each one with each other or get an overall view of the portfolio. using your method you must take all investments out to 10 years and discount them. using my and trader100 formula you can compare npv's after any given year!!!
you would probably only use your method if the investment is for a definite fixed term with a substantial break fee that would severlly impact on total interest earnt over the period (ie break after 5 years and all interest will be recalculated at 5%)

What made me wonder is the 10% compounding but discount at 8%. Is the 8% the cost of capital or the average rate of investment???

It is very difficult to factor in the taxman for these questions and I beleive if you try and to do it often distorts thr figures to such an extent that they are meaningless. (its a bit like the $99 dollar fares to aust. you still have the $45 surcharge to add on. that $45 surcharge looks meaningless compared to the full fare but against the discounted fare it is substantial!!!)

And hey, if you are paying 38c in the dollar you're a mug!!!!or you should shoot your accountant and/or lawyer!!!

Snoopy

02-07-2004, 10:10 AM

quote:Originally posted by Trader_100

Coaster,
Your method works out the future value of the income stream at the end of 10 years and discounts this future value back to the present in one go. This is incorrect as you are receiving the payments yearly not all at once at the end.

Perhaps you would like to adjuticate Snoopy!

T100.

I'm not sure if I can give you a 'definitive' answer Trader 100, which is of course the reason I started this thread and didn't just do the problem on my calculator at home!

The first point to come out of your two efforts at solving the problem is the rather large difference between the present value of the interest of same investment 'compounded' ( $100.70 ) verses 'uncompounded ' ( $67.10 ). That clearly demonstrates the extra value that can be rung out of an investment by allowing it to compound - or does it?

On my first assessment of the problem my logic was the same as yours Trader 100. The compound interest is paid annually and because the interest is paid 'up front' annually it should be discounted annually. So my answer to the problem was $100.70.

However, I reflected that this was quite a long calculation to perform when in real terms the money although undoubtedly paid out, had not been taken out of the investment. I reasoned there should be a 'short cut' method of arriving at the same answer. I noted that in order to receive the full discounted value of $100.70 in interest you had to wait until year 10. So why not treat the whole calculation as a single investment maturing in year 10? So I took the initial $100 investment and proceeded this way.

100(1+i)^10= Future value of Investment

i , the interest rate is 10% so this gave me a future value of the investment of $259.37. $100 of this is the original capital, so that makes the interest component of this future value $159.37. But this interest earned only exists ten compounding periods out in the future.
We need to calculate the 'present value' of this interest and that means discounting it back using our discount rate of 8%.

PV(1+0.08)^10= $159.37

Solving that for the present value of the interest I get $73.81, which looks remarkably close to the answer put forward by both Elfer and Coaster! Initially this result shocked me as $73.81 is much less than $100.70 and I began thinking that I must have made a mistake. However, I could not find one in either calculation. Then it dawned on me that the reason that your final answer was higher Trader 100, was that the interest received, while exactly the same in each case, had been discounted less in your calculation.

It cannot be disputed that the interest is being paid annually, and by that logic your answer of $100.70 must be correct Trader 100. However if any interest, as paid annually, is withdrawn from the investment before the bond hits tens years old, that means the compounding effect of that interest will be lost. Any withdrawal before bond maturity time will see the total interest projected to be earned ( $159.37 ) not realised. That means that although $10 interest is earned after year one you absolutely cannot touch that interest if you are to achieve your compounding interest goal. If you cannot touch it after year one, and indeed have to leave it in there until after year ten, how can you justifty discounting the $10 interest earned by 8% only once? If the interest has to remain in the investment for ten years does that not mean that *all* the interest earned has to be discounted over ten years? If that is what one believes the inescapable conclusion is that the answer to this problem is $73.81, as proposed by Coaster and Elfer.

If we accept Coaster and Elfers solution we can see that the oft touted benefits of 'compounding' are still present but have been severely reduced ($73.81 vs $67.10).

elfer

02-07-2004, 11:03 AM

Snoopy

As you say, the answer is $73.82 - the $10es can't compound if it is paid out. The original question stated it is accrued.

Its a strange question because it doesn't really bear any relevance to a real-world instrument. It would be better to ask the value of a 10 year bond **paying** (not accruing) interest quarterly at 10% per annum, if the expected yield (ie discount rate) is:

a) 10% ---> I reckon $102.26
b) drops to 8% ---> I reckon $115.40

Geeez, I feel like teacher.

You say that the benefits of compounding are low. This might be a wee bit hard to explain, but basically the benefits of compounding are irrelevant to present values - in the example you have the difference between $74 and $67 which equates to the benefits of earning 10% on reinvestment when you expect 8% (implicit in an 8% discount rate). In other words, using a discount rate of 8% assumes that your expected investment is at 8% compounding.

Finally, if the tax dept takes an interest in the investment, then you need to adjust the discount rate in an equivalent manner (ie both need to be after-tax rates).

willy_wonker

02-07-2004, 11:58 AM

Wow, no wonder Willy failed prob & stats and calculas at university.

The coffee tasted good at the cafe while the maths lecturer was talking.

Willy only knows how to BUY and SELL.

zyreon

02-07-2004, 12:23 PM

PV/FV etc is FINC
you're talking about QUAN (yeech, I be doing that next semester!)
must continue flicking through the QUAN101 text, that way I may walk in to class with atleast -some- understanding!

OldRider

02-07-2004, 12:44 PM

There is a PV formula within Excel, I haven't used it myself but it is used in a calculator I have. May be of some use.

Snoopy

02-07-2004, 01:19 PM

quote:Originally posted by skinny

If we were to be realistic about this as a DCF exercise we shouldn't forget the tax collector ;)

I saw the smilie, but if you must think about tax let's say the 'net' rate of return from the bond is 10%. We are paying tax at 33% in this example and the gross return is 14.925%.

so 14.925% x (1-0.33) = 10%

Satisfied?

While on the subject of 'realism' I would like you to substitute for the word 'bond' , 'an investment that exhibits the characteristic of a bond'. I know that 'bond' has a specific meaning in the investment world, but that is not why I am using that word here.

What I am looking at here is an investment in a much more general sense. An investment with a forecast future cashflow and a capital trading value that relates to its income producing capacity. I know that the value of any particular share you select will not behave in such a simply computed way over time. (Although I would argue that 'long term' the value of a share does fluctuate around a price that can calculated using 'discounted income flow'.) For want of a better word to use, I suggest to you that a share with forecastable cash flows and a residual value that is ultimately determined by the sum of those future profit flows may be thought of as a 'bond' for the purpose of evaluating it as an investment. Hopefully those comments put this 'problem' more in context.

SNOOPY

maxine

02-07-2004, 01:52 PM

Unless you seek unimplied complications there is only one way of doing this calculation.

Elfer is correct.

The question again states: "A $100 bond is issued for an indefinite period, and pays 10% interest annually compounding. What is the present value of the first ten years of interest accrued by the bond? Discount the interest back at 8% per annum to get the present value."

Key points are:
1. "Annual"
2. "Compounding"
3. "First 10 years" (think about this as 10 intervals between 11 dates from yr = 0 to yr = 10 if it is not self evident to you)
4. "Accrued"
5. 10% interest
6. Discount back at 8%

Therefore the interest is not paid out annually.
Further, the problem does not contemplate tax.

Given the above the $100 at yr 0 compounds to 1.1^10 x 100 = 259.375 after 10 years, of which $100 is principal and therefore $159.375 is accrued interest. Discount this at 8% to get a yr 0 NPV (like the problem says...and it is not a silly combination of numbers), and you get 159.375/(1.08^10) = $73.82.

If you are in the habit of doing these calculations you will see them as follows:

100 x [(1.1^10-1)-1.08^10]= 73.82

....which is a pretty simple calculation and IS the answer to the question as stated unless you are determined to infer complexities that are really not implied.

At the risk of sounding like a stroppy cow this thread has stunned me....it's like those threads where someone argues that returns or risks are inherently different in $18 stocks versus $1.80 stocks....just goes to show you never can be sure how others see the world I guess.

Maxine

Snoopy

02-07-2004, 01:56 PM

quote:Originally posted by CAM

standard way??...not sure, but when I was doing some finance/economics stuff unless otherwise stated we always assumed the payment was received at the end of the first period not the start of it

Righto, not having come up through the ranks of finance school I wasn't sure what the convention was.

I know that if I went into a bank and asked to take out a one year term deposit and they quoted me 14.925% ( I'm choosing this figure for convenience for all the realists out there. I don't actually expect to be able to march into a bank and get a term deposit with a net return of 10% )

THEN I wouldn't do any sudden calculation as to what the 'present value' was of the interest I was going to get in a years time.

I'm also betting that if you rounded up a 'rich' old pensioner on the street and asked them what interest rate they were getting on their term deposit they could tell you, and they could probably give you a good idea in dollar terms what their expected income is to be from it. But I would virtually guarantee that 99% of them would not have worked out the 'present value' of the interest they expected to receive from their one year term deposit.

With term deposits of less than a years duration, the present value becomes much less relevant because the discounting period is so short.

With longer rated term deposits, then the issue of compunding interest and discounting cash flows becomes more of an issue.

So I kind of had the impression that when 'Average Joe' looks at an investment they take a one year return at 'face value' (even though they know they won't be getting the income for a year, so they know the interest is discounted by the time they get it) and all subsequent returns are discounted to that benchmark.

That means a two year term deposit would have the first years interest not discounted, while the second years interest should be discounted by one year only (even though the actual payout is two years away).

I fully accept that this is not the way a 'finance guy' would do things. But if you adopt a 'don't discount the first years interest/dividends policy' when comparing investments it shouldn't matter PROVIDED all of your investment alternatives receive equal treatment and are evaluated using the same benchmark.

SNOOPY

Halebop

02-07-2004, 02:03 PM

quote:Originally posted by maxine

...At the risk of sounding like a stroppy cow this thread has stunned me....it's like those threads where someone argues that returns or risks are inherently different in $18 stocks versus $1.80 stocks....just goes to show you never can be sure how others see the world I guess...

LOL :D Thanks Maxine!

Dimebag

02-07-2004, 02:20 PM

Snoopy

I think I understand what you are intimating.

However, your description "pays 10% interest annually compounding" is still inherently ambiguous. You may mean:

(1) Has an initial yield of 10%pa on face value paid annually, and can therefore be compounded by reinvestment
(2) Has an initial yield of 10%pa which will grow at a compound rate of 10%pa
(3) Has an initial yield of 10%pa which will grow at a compound rate of x%pa (i.e. anything - the rate isn't stated)
(4) Has an initial yield of x% (i.e. isn't stated), which will then grow at a compound rate of 10%pa.

You simply haven't quoted enough information to give an unambiguous answer.

However, I do suspect you mean (2) above, in which case the value of the first 10 years of "dividends" is unambiguously $100.70.

(I suspect you are refering to an instrument more likely to be a stock than a bond. The value of a perpetual bond with coupons growing at 10%pa would be infinity with a discount rate of 8%).

Dimebag

MeNoBatty

02-07-2004, 03:03 PM

Dimey, hands off the joystick, mate. I hope you dont answer exam questions like that.

As maxine rightly points out, the ambiguity of the first sentence is clarified somewhat by the second. The use of the word 'accrued' would suggest that interest has not been paid out and compounds with the priciple. The 3rd sentence then asks for this interest to be discounted back at 8%. Pretty simple really.

The correct answer is therefore $73.82

elfer

02-07-2004, 04:48 PM

$73.82 - you can't compound AND receive interest - only one or the other.

Snoopy - "But I would virtually guarantee that 99% of them would not have worked out the 'present value' of the interest they expected to receive from their one year term deposit."

The thing is, what they get from the bank (lets call it 6% pre tax) on short term deposits is also the rate at which they should discount the returns --> the discount rate for present value purposes should be risk adjusted and 6% pre tax, ie what the banks pay, is about right for an essentially risk-free investment.

So the present value of their $100 in the bank paying 6% is ....... $100.

However, if prevailing interest rates were to fall (but their fixed interest rate did not), the PV would go up (because their risk adjusted discount rate, being the rate epplicable to the equivalent investment, would fall). If that is what you mena then I agree - the average pensioner would be unaware of the change in the value of their fixed term investment.

madmike

02-07-2004, 07:46 PM

as with maxine i'm quite stunned by some of these answers.

what is the interest npv of
1) $100 at 10% compounded annually for 10 years
vs
2) $100 at 10% compounded annually for 5 years
then the $161.05 reinvested at 10% compounded annually for 5 years

you have exactly the same amount for both options at the end of the 10 years.

the people who say $100.70 for snoopy's original scenario will have the same answer ($100.70) for both of my scenarios.

the people who say $73.82 for snoopy's original scenario will have $73.82 for the first and $87.09 for the second of my scenarios

buttttttt, you have the same $ value in your hand after the 10 years!!!!

ps - lets not get into the agrument that 10% may not be the interest rate in 5 years or that to buy the bond maybe a different capital outlay.

hence if you break your investment more often you will get a higher npv!!!!

Coaster

02-07-2004, 09:42 PM

Madmike, you are doing the same thing as the others. You can't discount the value of the first 5 years worth of interest payments back to n=0 and then continue to use that interest past n=5 to generate further interest - you will get too high a NPV, which you did. It's double dipping.

Consider this question:

I have two investments, the first is a $100 bond-type instrument that annually pays 10% compounding interest for 10 years. At the end of year 10 my investment has accumulated $159.37 of interest ($100 x 1.1^10 -$100).

The second investment's total value at the end of n=10 equals $159.37, but this investment only compounds at 8% annually. What is today's value of this investment.

It is $159.37/1.08^10 = $73.82

What does this mean? It means that a rational person would be indifferent between receiving the interest from the bond in investment 1 (interest at n=10 = $159.37) or receiving $73.82 today and being able to invest it at 8% (value at n=10 = $159.37).

It leads on that if there is indifference then PV of the interest payments in investment 1 = the PV of the investment 2.

Coaster

Snoopy

03-07-2004, 09:44 AM

quote:Originally posted by MeNoBatty

Snoopy, did you get this question from a first or second year text book? From memory, they dont tend to deal with real world examples in these, instead focusing on the maths.

If, instead, this is from a later year text book, you would have to list your assumptions such as payments at the end of the period, no taxes etc....

No not from a text book, but from a book by Brian McNiven entitled

'A Wonderful Company at a Fair Price'

subtitled, 'A guide for serious investors on the Australian Sharemarket.'

I think it is time I put the whole problem in context rather than quote the one line summary version that I did. So here goes:

quote
------------

"In determining the the PV of a bond that accumulates and compounds interest rather that disbursing interest annually, we cannot, when assessing yield or value, include both the compounding annual interest not received by bondholders and the value of that accumulated interest at a future date. The future value in 10 years of a bond issued at $100 with compounding interest at 10% annually is $259.37. By capitalising year 11 earnings of $25.94 at 8%, the FV of $324.25 ($25.94/8%), discounted back at a required return rate of 8% gives a PV of $150.19. If the annual compounding non distributed interest that caused the capital value to increase is also discounted back at 8%, its PV is (THE ANSWER) ......"

------------

end quote

The problem is that the answer that Brian gives is $120.14, which is quite different to the answer that anyone has given so far. Anyone like to comment?

SNOOPY

Coaster

03-07-2004, 12:06 PM

Snoopy, the question you give above is different from the question in your first post.

The question above is asking for the PV of the investment, not just the interest payments.

The value of the investment at n=10 is $259.37 (as stated in the question), and this comprises of the capital of $100 and compounded interest of $159.37 (as worked out previously).

Now all we have to do is discount back to n=0:
$259.37 / (1.08)^10
= $259.37 / 2.158925
= $120.14

You can also see that if you break the investment value up at n=10 into capital ($100) and compounded interest ($159.37) and discount them back to n=0 seperately, you get:

Capital: $100 / (1.08)^10 = $46.32
Compounded interest: $159.37 / (1.08)^10 = $73.82 (note this is the answer to the previous, interest-only question)

Add togeather: $46.32 + $73.82 = $120.14

Simple as...

Coaster

OldRider

03-07-2004, 12:12 PM

SNOOPY: I have heard about McNivens book,but not read it.Have you found it a worthwhile purchase? He sells a program called Stockval,calling it "A guide to Value Investing," he has a NZ agent for this. I have a 24 page booklet about the program, but not the program,it contains his thinking, and as well some of the formulae it uses.I am still wading my way through them gaining understanding very slowly.

Presumably this is in the book also.Interestingly the calculator I mentioned in an earlier post came from a poster on an Australian forum who has attended some of McNivens seminars on the Gold Coast,where McNiven now lives,he follows McNivens ideas,and has written this small calculator, he calls it an intrinsic value calulator,intrinsic is a term McNiven use I think, I use it as part of the process to value companies.I ran your question through it and got an answer of $113-42.

brother coy

03-07-2004, 04:06 PM

hahaha ya all indas weal world we takes account of inflation and taxs to work outsd cashflow so da return da old ladys get in da bank is more like 1% a year hahahhaaa

stephen

03-07-2004, 04:32 PM

I am reading this book right now - it's in the Auckland Public Library, or will be when I return it tomorrow. I enjoyed it, and I'm taking notes on his valuation method.

The author is more than somewhat cynical about the directors of ASX companies. He has some interesting notes on the effects of new issues etc. He also disputes the methods used in so-called "Buffet-style" valuations, and I think he's right. More accurately, he criticises the mathematics, not the philosophy; in fact he frequently refers to Buffet as a model, and uniquely in my reading of FA books so far, actually wrote to the man to verify claims made about his practise.

Snoopy

03-07-2004, 06:23 PM

quote:Originally posted by Coaster

Snoopy, the question you give above is different from the question in your first post.

The question above is asking for the PV of the investment, not just the interest payments.

Yes. I dissected the original question and only talked about the valuation of the interest earned first. I didn't want to throw too many ideas into the discussion at once and didn't want to complicate things by talking about the PV of the asset ('bond') as well.

quote:
The value of the investment at n=10 is $259.37 (as stated in the question), and this comprises of the capital of $100 and compounded interest of $159.37 (as worked out previously).

Now all we have to do is discount back to n=0:
$259.37 / (1.08)^10
= $259.37 / 2.158925
= $120.14

You can also see that if you break the investment value up at n=10 into capital ($100) and compounded interest ($159.37) and discount them back to n=0 seperately, you get:

Capital: $100 / (1.08)^10 = $46.32
Compounded interest: $159.37 / (1.08)^10 = $73.82 (note this is the answer to the previous, interest-only question)

Add together: $46.32 + $73.82 = $120.14

Thankyou very much Coaster, you have shown very nicely how all the figures tie up.

McNiven wrote:
"If the annual compounding non-distributed interest that caused the capital value to increase is also discounted back at 8%, its PV is $120.14."

Because McNiven had just done another PV calculation in the previous sentence, and goes on to add these two PVs to demonstrate a point, I read that as

"If the annual compounding non-distributed interest that caused the capital value to increase (considered alone) is also discounted back at 8%, its PV is $120.14."

whereas McNiven meant

"If the annual compounding non-distributed interest that caused the capital value to increase (together with the capital) is also discounted back at 8%, its PV is $120.14."

A little comprehension error on my part, reinforced by the fact that if you take the interest only and sum the first *11* payments of interest only discounting after year two and not year one you also get $120.14
(actually $120.78, but near enough within rounding error - or so I convinced myself).

quote:
Simple as...

Thanks Coaster
These things always look simpler, once you know the answer!
What I couldn't figure out was why I had to consider the first eleven interest payments to make my figures work, and why my weird assumption gave me the right answer. It was all co-incidence as it turns out.

SNOOPY

Snoopy

03-07-2004, 06:59 PM

quote:Originally posted by OldRider

SNOOPY: I have heard about McNivens book,but not read it.Have you found it a worthwhile purchase?

I've had the book for about a year.

ISBN 0-7016-3655-6

I couldn't find it on the bookshelves here, even though it was only printed in 2002, so had to order it specially from Australia. It wasn't even that expensive IIRC - around $40.

I would say that if you were only allowed to own one book on Buffett style investing, this is the one to have. Not least of its advantages is that it is written from a 'down under' perspective.

It is possibly a little dauntingly mathematical to plunge into for the complete beginner (I like 'The Buffetology Workbook' as a better introduction to investing like Buffett for that), but overall I can't speak highly enough of McNiven's book. It is written in short snappy chapters so is the sort of book that is good to have on the shelf to refer back to.

quote:
He sells a program called Stockval,calling it "A guide to Value Investing," he has a NZ agent for this. I have a 24 page booklet about the program, but not the program,it contains his thinking, and as well some of the formulae it uses.I am still wading my way through them gaining understanding very slowly.

Presumably this is in the book also.

Stockval is mentioned in the book, but the book stands on its own merits as a stand alone work. McNiven mentions how some of the ideas in the book are incorporated in 'Stockval', yes.

quote:
Interestingly the calculator I mentioned in an earlier post came from a poster on an Australian forum who has attended some of McNivens seminars on the Gold Coast,where McNiven now lives,he follows McNivens ideas,and has written this small calculator, he calls it an intrinsic value calulator,intrinsic is a term McNiven use I think, I use it as part of the process to value companies.I ran your question through it and got an answer of $113-42.

Oh no, not another answer ;). Any idea why it is different to the answers that have been thrown up already?

SNOOPY

Snoopy

03-07-2004, 07:22 PM

quote:Originally posted by stephen

I am reading this book right now - it's in the Auckland Public Library, or will be when I return it tomorrow. I enjoyed it, and I'm taking notes on his valuation method.

There is a (single) copy in the Christchurch Public Library system as well.

quote:
He also disputes the methods used in so-called "Buffet-style" valuations, and I think he's right. More accurately, he criticises the mathematics, not the philosophy; in fact he frequently refers to Buffet as a model, and uniquely in my reading of FA books so far, actually wrote to the man to verify claims made about his practise.

Yes as it happens the problem I brought up on this thread that we have been discussing is from that very chapter 20:
'So called Buffett style valuations".

I agree with McNiven's criticisims too, - of the method outlined. However, there are many books and websites demonstrating the methods that Buffett supposedly uses. The one McNiven criticises is certainly *not* that used in the Buffetology Workbook. In fact nowhere in the McNiven book could I see where he pulled the method he criticises from. So while interesting, in my view those criticisims are of a straw man.

SNOOPY

OldRider

03-07-2004, 07:51 PM

I have rechecked the calculator,and find value is $120-14,messed up somehow initially.I have endeavoured to print the spreadsheet,not very successfully but will let it remain.

The query I have,is why on a 10 year term is the value at year 10 ,in fact year 11 as there is a year zero, used. It is obviously right as it gives the correct result. Can't see,must be getting too old.

A step by step calculation of Intrinsic Value using Discounted Cash Flows.

Assume:
Intend to hold for number of years 10
EPS in year 0 10
Expected GEPS over period period p.a. 0.10
Discount rate used 0.0800
Expected Dividend Payout ratio 0.00
Expected to sell at end of period at P.E. 10

Calculation:
Years: 0 1 2 3 4 5 6 7 8 9 10

EPS $10.00 $11.00 $12.10 $13.31 $14.64 $16.11 $17.72 $19.49 $21.44 $23.58 $25.94
(The EPS OF $10 in year 0 is grown at 10% p.a.)
Cash Flows:
Dividend received $- $- $- $- $- $- $- $- $- $-
No dividend received each year
Terminal Value Terminal Value $259.37
(Terminal Value is the cash expected to be received for the sale of the
share at end of year 10 =EPS $25-94*P.E. 10 = $259-37
Total Yearly Cash Flows $- $- $- $- $- $- $- $- $- $259.37
(In year 10 Terminal value is added to the Div received in that year)
Values discounted
back to present $- $- $- $- $- $- $- $- $- $120.14
(Each year total yearly cash flow is discounted back to the present at 8%)

Intrinsic Value = $120.14 (Intrinsic value is the sum of the present values in years 1 to 10)

stephen

03-07-2004, 08:32 PM

I think the method McNiven is criticising comes from the first books written by Mary Buffet, because I remember reading one and scratching my head at what appeared to be dodgy algebra.

OldRider

03-07-2004, 09:36 PM

The penny has just dropped, and has resulted in a new result for the query $109-22.I think this would be correct for a bond with interest compounded and paid at the term end.For a share $120-14 would be correct.

The calculator I used was designed to value shares, zero to eleven is required because with share earnings & dividend growth of 10% yearly,this gives a dividend payment of $11-00 at the end of year one.

A bond would be different,the first interest payment would only be $10-00,there is no appreciation of value until the payment is made,so the values at the end of year 9 are taken,not year 10 as for a share.

This has proved an interesting exercise, perhaps I will get that McNiven book,I can now see why I couldn't get results that agreed with examples in the article I have.

Snoopy

04-07-2004, 01:35 PM

quote:Originally posted by OldRider

There is a PV formula within Excel, I haven't used it myself but it is used in a calculator I have. May be of some use.

This is the response to one poster throwing their hands up in the air and complaining about the maths? I would say that looking for a black box calculator, like wahtever is built into Excel, that will do it all for you is not the answer for such a person.

I would like to point out that while the problem we are discussing can be formulated into an exercise in calculus, that was the furthest thing on my mind when I started this thread.

In fact all of the maths in this problem can be done on a simple four function calculator '+' '-' 'x' '/'. You can't get much more simple than that. This is not a high powered maths exercise.

It becomes easier with a scientific calculator that has a y to the power of x function, to be sure. But you certainly don't need any kind of high powered financial calculator to work through this exercise. I would urge anyone who thinks this kind of thing is beyond them to think again. I'm not saying it will all come to you instantly, but it is worth persevereing with.

SNOOPY

Snoopy

04-07-2004, 03:10 PM

quote:Originally posted by Dimebag

Your description "pays 10% interest annually compounding" is still inherently ambiguous. You may mean:

(1) Has an initial yield of 10%pa on face value paid annually, and can therefore be compounded by reinvestment{/quote]

Yes. Not only *can* the investment be compounded. It *is* compounded by reinvesting the interest at the end of each year. That is what I meant.

[quote]quote:
(2) Has an initial yield of 10%pa which will grow at a compound rate of 10%pa

If I draw up a table along those lines:

Year, Yield Rate , Interest Earned, Balance EOY .

0 N/A 0 100
1 x0.1 10 110
2 x0.1x1 12.1 122.1
3 x0.1x1.1^2 14.8 147.7
4 x0.1x1.1^3 19.7 167.4
5 x0.1x1.1^4 24.5 191.9
6 x0.1x1.1^5 30.9 222.8
7 x0.1x1.1^6 39.47 262.3
8 x0.1x1.1^7 51.11 313.4
9 x0.1x1.1^8 67.18 380.58
10 x0.1x1.1^9 89.74 470.32

Interest component of final total is 370.32.

So

PV(1+0.08)^10=370.32

Solving for PV gives the present value of the interest component based on an 8% discount rate as 171.53.

quote:
(3) Has an initial yield of 10%pa which will grow at a compound rate of x%pa (i.e. anything - the rate isn't stated)
(4) Has an initial yield of x% (i.e. isn't stated), which will then grow at a compound rate of 10%pa.

Too much lateral thinking with those two options Dimebag. I did mention it wasn't a trick question.

quote:
However, I do suspect you mean (2) above, in which case the value of the first 10 years of "dividends" is unambiguously $100.70.

If I had meant that, then the answer would have been 171.53, as explained above.

(I suspect you are refering to an instrument more likely to be a stock than a bond. The value of a perpetual bond with coupons growing at 10%pa would be infinity with a discount rate of 8%).

Stock? Bond? When it comes down to valuation purposes, what is the difference?

What you say is true Dimebag. But the value of a share with coupons growing at 10% pa would be infinite with a discount rate of 8% as well..

SNOOPY

OldRider

04-07-2004, 10:26 PM

SNOOPY: I see it now,what you have posted is correct,and your formula PV(1+0.08)^10=370.32
is correct,and there is no difference between a stock and a bond. However,it does seem to me the interest component($370.32) calculated in your table is incorrect,should it be $159.39?

This thread has indeed been thought provoking,and has increased my undertanding.Nonetheless,I much prefer to use the calculator in day to day work.

Snoopy

06-07-2004, 01:14 PM

quote:Originally posted by stephen

I think the method McNiven is criticising comes from the first books written by Mary Buffet, because I remember reading one and scratching my head at what appeared to be dodgy algebra.

Mary Buffett and David Clark published "The Buffetology Workbook" in 2001. I have that book. The examples in that book are laid out so that the dividend income is clearly separated from the retained earnings. The value of the retained earnings is only considered when looking at the residual value of the company. This I believe is the correct way to treat retained earnings and dividends.

It seems that whtever mistakes Mary Buffett had made in earlier books, she has now fixed them.

Anyone know what her earlier books were? I'll guess 'Buffettology' but were there any before that?

SNOOPY

Snoopy

06-07-2004, 01:30 PM

quote:Originally posted by OldRider

SNOOPY: I see it now,what you have posted is correct,and your formula PV(1+0.08)^10=370.32
is correct,and there is no difference between a stock and a bond. However,it does seem to me the interest component($370.32) calculated in your table is incorrect,should it be $159.39?

Yes the total interest question from the original question I asked works out to $159.39.

The $370.32 is what I figure is the answer to the second alternative interpretation of the question as proposed by Dimebag.

quote
-------------
(2) Has an initial yield of 10%pa which will grow at a compound rate of 10%pa
--------------
unquote

I read that as the growth rate in the first year being 10%. The growth rate in the next year being 10% plus "10% of 10%", which makes 10% plus 1% =11%. Similarly the 'growth rate' in the next year is

11% plus 10% of 11% = 11% +1.1%= 12.1%

And the growth rate just keeps on going up from there.

I don't believe there is a real world bond that would behave like this. Perhaps a high growth share might, but IMO investing on the basis of exponential growth for 10 years is just asking for trouble. There are too many wobbles in the development of an up and coming business that could derail such assumptions.

SNOOPY