Hi john
I’ve got the point that we would get the same NPV whether we discount real cash flows by the real cost of capital or the inflated cash flows by the inflated cost of capital, but in the example there is no scrap & tax savings, if there had been any of these in the question, then the NPV we would get by discounting at the real cost of capital would be higher than the NPV calculated using the nominal or inflated cost of capital.
My question is that how will it affect our decision & should we discount the tax savings & scrap value at the rate of inflation, before including them in cash flows, while discounting at the real cost of capital(because both of them are future values), to get the same NPV?

Secondly, as you said that in theory, the change in inflation rate doesn’t makes a difference to our decision as the cost of capital will change accordingly, resulting in same npv, but you focused that it is only in theory, why not its always the case
practically?

The answer to both your points is that discounting the real cash flows at the real cost of capital only ‘works’ if all of the cash flows are inflating at the same general rate of inflation.

In real life and in most exam questions, different cash flows are subject to different inflation rates and therefore we need to inflate the cash flows to get the actual/nominal cash flows and then discount at the actual/nominal cost of capital.

As in your example, a general rate of inflation is applied to all cash flows, for example:
If there were tax payments & tax savings in the same question & we are required to calculate the NPV in real & nominal terms, in this case, applying tax rate on the real cash flows will result in lower tax payments than applying the tax rate on the nominal flows, but if we calculate tax savings due to capital allowances, they will be the same in both cases.
My question is that why don’t we deflate the figures for tax savings, before including them in the calculation of NPV, using real rate?
The reason i’m asking this, is that there is one such question in December 2013 exam.

The December 2013 question was a slightly silly question for the reasons you have stated. However the examiner did allow you to deflate the tax savings which is what effectively he did in the alternative approach that he showed in his answer.

It is 6 per unit certainly, but the net operating flow is 60,000 which is what I have in the lecture (as usual in the exam, and as I say in the lecture, all of the figures are in thousands).

Wonderful lecture Sir. Just a small observation. If you just calculate 1.05/1.15 you get 9.13%, rounded to 9%. Then you discount at 2.531 and the NPV is +31.86 which is much closer to the initial +32.

Please I don’t get the comments here or they are probably misleading. 1/1.0952=0.913075=91.3% and not 9.13%. I think its just mere coincidence because discounting 1000 at 9.52% (df =1/1.0952) is never the same as discounting the same thousand at 9.13% (df=1.0913). I hope am clear.

Hi Mr. Moffat, do we ever round down instead of up? For example, 9.52% becomes 10%, had it been 9.22 would it still round up to 10% or would we round down to 9%?

what will happen to the cash flows if they are different in each of the five years and these cash flows are before taken account of general inflation.
eg yr 1=10000, yr2=15000, yr 3 17000 and so on. inflation is at the rate of 6.2%.
Thanks

Yes – he could have prices falling, but the approach would be exactly the same.

(In fact F9 is not a topical exam and never has been. Also, apart from two tiny blips there has never been deflation in the Eurozone as a whole – low inflation certainly in recent years but not deflation (apart from the two blips) 🙂 )

You are kindly requested to response in my query below in regards to the question 5b of the inflation – effective rates:

We have discounted the operating profit of $60 x 2.487 annuity rate ( but the cost of capital is 15% so 2.283 annuity) and then again, we discounted the NPV by the effective rate which includes both rates of inflation and cost of capital.

I did not understand the logic and I have somehow stuck on this.

I think maybe it would be helpful for you to watch the lecture again.

Usually, we discount the actual (nominal) cash flows (i.e. after inflating them) by the actual (i.e. nominal) cost of capital.

The alternative (which is very rarely relevant in the exam) is to discount the real cash flows (i.e. the current price flows, ignoring any inflation) at the real cost of capital (the effective rate, the cost of capital with inflation ‘removed’).

In part (b) of the example, the real/effective cost of capital is 10% and therefore the 3 year annuity factor at 10% is correct at 2.487.

However, it is very rarely in the exam that this is relevant (because, as I state in the lecture) it only works if all the cash flows inflate at the same general rate of inflation).

Usually in the exam, you need to inflate the flows (to get the actual/nominal cash flows) and then discount them at the actual/nominal cost of capital.

Thank you so much for the easy to follow lecturers. I am however, worried that you do not seem to meantion the fishers equation in all your lectures relating to inflation yet nominal and real interest rates are a CONSTANT FEATURE of the exam. Can l assume that your formula on page 52 of the lecture notes(1+e=1+m/1+i) is the same as the Fisher equation. l have a textbook from BPP but would rather stick to Open Tuition(especially at this 11th hour) so please advise on this.

Although the examiner often (but certainly not always) refers to nominal and real costs of capital, it is overdoing it to regard it as a constant feature (or to regard it as a major part of the question)!

I make it clear in the lecture that we always discount the actual/nominal cash flows at the actual/nominal cost of capital unless specifically told to do otherwise. (On only one occasion ever have you also been told as a separate part of the question, to also discount the real cash flows at the real cost of capital.)

Otherwise the only relevance has been that on one or two occasions you have been given the real cost of capital and therefore needed to calculate the nominal cost of capital.
Again, in the lecture I explain the reasoning and how to do this, and what to watch out for.

(It is the Fisher formula, but you are right – I will update to use his symbols. He did not used to give the formula (and I think the symbols he uses are very odd 🙂 ) but it would be better if I used his symbols.)

Please I require some explanation on cash conversion cycle and the calculation of the ratios. I listened to your F9 lectures but I am still struggling to understand these.

Inventory days = 15
Receivable days =10
Payable days = 14

Cash conversion cycle is 11 days.

This is how I interpret this, in 25 days I get cash, however the first 14 days out of the 25 days I have to pay out cash, so I still need to wait 11 days to get cash back? but I really still need to wait the whole 25 days to get back cash regardless of the fact that the first 14 days I pay out cash. Please help as I am really confused!

Also for the ratios, say receivables days 24,000/50,000 (Receivables/Sales)This just tells me that receivables is 48% of total sales. when I multiply it by 365 days then what does that mean? I don’t see how it means it takes 175.2 days to collect sales. Rather, I interpret this as receivables are outstanding for 175.2 days out of the whole year.

Please help explain from different angles, I’m sure I will get it once you explain vividly to me John M.

In future please post questions either under the relevant lecture, or (if you want me to answer) in the Ask ACCA Tutor forum for F9. This question has nothing to do with relevant cash flows for DCF.

The operating cycle is the time that you are without the cash – i.e. the time between receiving the cash and paying out the cash.
Our bank balance only falls when we pay out to buy the materials, which is in 14 days. The bank balance goes up again when we receive the cash from our customers from selling the goods, which is in 25 days. So we are without the cash for 11 days.

If we have sales of 50,000, the the sales per day are 50,000/365.
If the receivables are 24,000 at the end of the year, then it means we are owed for sales for 24,000 / sales per day. That comes to 175.2 days. So it means that we are allowing customers to take 175.2 days to pay us.

Fixed costs are only relevant if the total will change as a result of doing the project.
Just absorbing or charging some of the costs to the new project (for profit purposes) is not relevant because it does not mean that the total is changing – it is just being shared differently.

Thanks alot! I learnt this in class, but I had no idea what it was. Even during the revision, I was just wondering what was going on :/
And, now it’s so clear…. Brilliant lecture! 🙂

Hi ?john.I have a question about nominal rate of interest.It seems that the cost of capital given in the NPV question is the nominal rate of interest (is it?),then why the cost of capital given in the question doesn’t increase as the rate of inflation increase every year? THX John.

The cash flow keeps increasing, but the rate of inflation stays the same.

The cost of capital will only change if the general rate of inflation changes. (Look at the Fisher formula – the cost of capital depends on the rate of inflation. If the rate of inflation is constant then the cost of capital is constant)

in investment appraisal , we have to give tax payment on cashflows which are sales less variable cost less fixed cost , my question is , the scrap value should be added in the final year after the tax payment ? scrap value and working capital adjustments should be included after we made the tax payment ? kindly guide me , what would be the EXACT FORMAT of net present value /investment appraisal ?

The lecture on Relevant cash flows for tax gives the EXACT format.

First we list the operating cash flows (sales less variable costs less incremental (extra) fixed costs)
Then we calculate the tax on the operating flows.
Then we list the capital flows (cost and scrap proceeds)
Then we calculate the tax saving on the capital allowances (or ‘tax allowable depreciation’)
Then we bring in the working capital flows (at the end, because they have no tax effect)

Thanks its really helpful , my another question is when calculating ROCE/ARR , we make operating cashflows (sales less variable cost less extra fixed cost) into accounting profit i.e operating cashflows less accumulated depreciation divided by projests life equals to accounting profit , right? my question is that whether to include scrap value in the operating cashflows too ?

the discount rate /cost of capital given in the investment appraisal (in which we discount cashflows for present values) is a Nominal rate (money term) ? what basically it is ? nominal ? and is this a before tax or after tax cost of capital ? n my other question is if we r given general inflation so we have to convert Real into Nominal rate ? kindly make it clear . with exaples , it confuses me so much .

In F9 we always discount the actual (nominal) cash flows at the actual (nominal) after tax cost of capital.

If the cash flows are given in real (current price) terms the we need to inflate them to get the actual (nominal ) cash flows.

If the cost of capital is given in real terms ( the ‘real’ cost of capital) we need to use the formula (with the inflation rate) to get the actual (nominal) cost of capital.

We always use the after tax cost of capital.

For examples watch the lecture again and see the course notes.

if v have to inflate the discount rate (to make in money terms) we will use Fishers formula right ? and we will do this if we have General inflation given in the question and clearly stated right ? and the inflation rates given for other elements like sales 5%, material 2% labour 2.5% are called Spefic inflation rates ?

Hi John:
Thanks for your lecture with such clarity. As it relates to inflation, June 2012 question # 1, how are the inflated selling and variable costs arrived at from years 2 to 4? we are given selling prices from years 1 to 4 being $25, $24, $23 & $23 with 4% inflation the answers given are $26 (ok), $25.96, $25.87, & $26.91. Variable cost given for years 1 to 4 are $10, $11, $12 & $12.50 at 2.5% inflation. answers given are $10.25 (ok), $11.56, 12.92 & $13.80.

I agree with what my dear brother says. I am from pakistan and even here the teachers are not very talented if i may compare them with John! thank you John for such wonderful lectures.

i study at india where there is a great lack for good teachers and i have just(4days) come to know of your videos and already am gonna complete watching all the sessions-they are so addictive which also means you are still to do a lot of marketing about these lectures but i can tell you they ll be more than just a soaring hit……………………!!!!!!!!!!!
kudos u guys rock…………………
the part when you said about bringing

1.05/1.15 = 1/1.15/1.05 …..it hit the penultimate part of my understanding of the fischer’s formula…………

zee says

Thanks Super man…:) all your F9 lectures are so wonderful to brushup the basics for P4 exams.God bless you

John Moffat says

Thank you for the comment 🙂

Mahrukh says

Hi john

I’ve got the point that we would get the same NPV whether we discount real cash flows by the real cost of capital or the inflated cash flows by the inflated cost of capital, but in the example there is no scrap & tax savings, if there had been any of these in the question, then the NPV we would get by discounting at the real cost of capital would be higher than the NPV calculated using the nominal or inflated cost of capital.

My question is that how will it affect our decision & should we discount the tax savings & scrap value at the rate of inflation, before including them in cash flows, while discounting at the real cost of capital(because both of them are future values), to get the same NPV?

Secondly, as you said that in theory, the change in inflation rate doesn’t makes a difference to our decision as the cost of capital will change accordingly, resulting in same npv, but you focused that it is only in theory, why not its always the case

practically?

John Moffat says

The answer to both your points is that discounting the real cash flows at the real cost of capital only ‘works’ if all of the cash flows are inflating at the same general rate of inflation.

In real life and in most exam questions, different cash flows are subject to different inflation rates and therefore we need to inflate the cash flows to get the actual/nominal cash flows and then discount at the actual/nominal cost of capital.

Mahrukh says

As in your example, a general rate of inflation is applied to all cash flows, for example:

If there were tax payments & tax savings in the same question & we are required to calculate the NPV in real & nominal terms, in this case, applying tax rate on the real cash flows will result in lower tax payments than applying the tax rate on the nominal flows, but if we calculate tax savings due to capital allowances, they will be the same in both cases.

My question is that why don’t we deflate the figures for tax savings, before including them in the calculation of NPV, using real rate?

The reason i’m asking this, is that there is one such question in December 2013 exam.

John Moffat says

The December 2013 question was a slightly silly question for the reasons you have stated. However the examiner did allow you to deflate the tax savings which is what effectively he did in the alternative approach that he showed in his answer.

Mahrukh says

Thanks 🙂

John Moffat says

You are welcome 🙂

Arun says

In the alternative method isn’t the net operating flow 6 (20-16) instead of 60?

John Moffat says

No – it is 200 – 140 = 60

Arun says

I looked at the solution in the notes and it’s taken as 60,000 which means the net operating flow is 6 per unit (60000/10000).

Thanks.

John Moffat says

It is 6 per unit certainly, but the net operating flow is 60,000 which is what I have in the lecture (as usual in the exam, and as I say in the lecture, all of the figures are in thousands).

Kelly says

Wonderful lecture Sir. Just a small observation. If you just calculate 1.05/1.15 you get 9.13%, rounded to 9%. Then you discount at 2.531 and the NPV is +31.86 which is much closer to the initial +32.

Kelly says

Never mind. its clarified when we use the fomula

annonymous says

Hi John.

Regarding the above comment, is it not better to discount at 9% rather than 10% if you do not wish to use the Fisher formula?

1/1.0952 = 9.13 rounded to 9% DOES give a more accurate answer than 9.52 rounded to 10%

And if i’m correct, can the same logic be used for other questions, or was this just a coincidence?

Thanks for the wonderful lectures…they have been very helpful 🙂

John Moffat says

Its not a coincidence (and thanks for the comment) 🙂

Ernest says

Please I don’t get the comments here or they are probably misleading. 1/1.0952=0.913075=91.3% and not 9.13%. I think its just mere coincidence because discounting 1000 at 9.52% (df =1/1.0952) is never the same as discounting the same thousand at 9.13% (df=1.0913). I hope am clear.

John Moffat says

Sorry – I misread the earlier comment. You are correct 🙂

Ernest says

Thank you.

ahlaamzk says

Hi Mr. Moffat, do we ever round down instead of up? For example, 9.52% becomes 10%, had it been 9.22 would it still round up to 10% or would we round down to 9%?

John Moffat says

You round to the nearest – so 9.22 would be rounded to 9%

rabiatu says

what will happen to the cash flows if they are different in each of the five years and these cash flows are before taken account of general inflation.

eg yr 1=10000, yr2=15000, yr 3 17000 and so on. inflation is at the rate of 6.2%.

Thanks

John Moffat says

You use the same logic.

The actual cash flow at time 1 is 10,000 x 1.062

The actual cash flow at time 2 is 15,000 x 1.062^2

The actual cash flow at time 3 is 17,000 x 1.062^3

charlottemaomao says

this is amazing

John Moffat says

Thank you 🙂

Philip says

Hi John,

Just a quick question regarding inflation. Could he ever ask the question were prices are falling – i.e. deflation?

just wondering because it is topical in Eurozone over the last couple of years and I know from other papers he does like to bring in current topics.

Cheers.

John Moffat says

Yes – he could have prices falling, but the approach would be exactly the same.

(In fact F9 is not a topical exam and never has been. Also, apart from two tiny blips there has never been deflation in the Eurozone as a whole – low inflation certainly in recent years but not deflation (apart from the two blips) 🙂 )

Philip says

Thanks John. I might give a question with prices falling a bash, just so I’m not seeing it for the first time in the exam.

Thanks again

KeepWalking says

Dear Sir,

You are kindly requested to response in my query below in regards to the question 5b of the inflation – effective rates:

We have discounted the operating profit of $60 x 2.487 annuity rate ( but the cost of capital is 15% so 2.283 annuity) and then again, we discounted the NPV by the effective rate which includes both rates of inflation and cost of capital.

I did not understand the logic and I have somehow stuck on this.

Looking forward for your helpful reply.

John Moffat says

I think maybe it would be helpful for you to watch the lecture again.

Usually, we discount the actual (nominal) cash flows (i.e. after inflating them) by the actual (i.e. nominal) cost of capital.

The alternative (which is very rarely relevant in the exam) is to discount the real cash flows (i.e. the current price flows, ignoring any inflation) at the real cost of capital (the effective rate, the cost of capital with inflation ‘removed’).

In part (b) of the example, the real/effective cost of capital is 10% and therefore the 3 year annuity factor at 10% is correct at 2.487.

However, it is very rarely in the exam that this is relevant (because, as I state in the lecture) it only works if all the cash flows inflate at the same general rate of inflation).

Usually in the exam, you need to inflate the flows (to get the actual/nominal cash flows) and then discount them at the actual/nominal cost of capital.

George says

Hi John,

Thank you so much for the easy to follow lecturers. I am however, worried that you do not seem to meantion the fishers equation in all your lectures relating to inflation yet nominal and real interest rates are a CONSTANT FEATURE of the exam. Can l assume that your formula on page 52 of the lecture notes(1+e=1+m/1+i) is the same as the Fisher equation. l have a textbook from BPP but would rather stick to Open Tuition(especially at this 11th hour) so please advise on this.

Thanks

John Moffat says

Although the examiner often (but certainly not always) refers to nominal and real costs of capital, it is overdoing it to regard it as a constant feature (or to regard it as a major part of the question)!

I make it clear in the lecture that we always discount the actual/nominal cash flows at the actual/nominal cost of capital unless specifically told to do otherwise. (On only one occasion ever have you also been told as a separate part of the question, to also discount the real cash flows at the real cost of capital.)

Otherwise the only relevance has been that on one or two occasions you have been given the real cost of capital and therefore needed to calculate the nominal cost of capital.

Again, in the lecture I explain the reasoning and how to do this, and what to watch out for.

(It is the Fisher formula, but you are right – I will update to use his symbols. He did not used to give the formula (and I think the symbols he uses are very odd 🙂 ) but it would be better if I used his symbols.)

George says

Thanks, John l guess its just the 11th hour panick, your videos clearly address the issue l was raised. Thanks a lot.

Maria says

Dear John,

Please I require some explanation on cash conversion cycle and the calculation of the ratios. I listened to your F9 lectures but I am still struggling to understand these.

Inventory days = 15

Receivable days =10

Payable days = 14

Cash conversion cycle is 11 days.

This is how I interpret this, in 25 days I get cash, however the first 14 days out of the 25 days I have to pay out cash, so I still need to wait 11 days to get cash back? but I really still need to wait the whole 25 days to get back cash regardless of the fact that the first 14 days I pay out cash. Please help as I am really confused!

Also for the ratios, say receivables days 24,000/50,000 (Receivables/Sales)This just tells me that receivables is 48% of total sales. when I multiply it by 365 days then what does that mean? I don’t see how it means it takes 175.2 days to collect sales. Rather, I interpret this as receivables are outstanding for 175.2 days out of the whole year.

Please help explain from different angles, I’m sure I will get it once you explain vividly to me John M.

Thank you for your assistance.

John Moffat says

In future please post questions either under the relevant lecture, or (if you want me to answer) in the Ask ACCA Tutor forum for F9. This question has nothing to do with relevant cash flows for DCF.

The operating cycle is the time that you are without the cash – i.e. the time between receiving the cash and paying out the cash.

Our bank balance only falls when we pay out to buy the materials, which is in 14 days. The bank balance goes up again when we receive the cash from our customers from selling the goods, which is in 25 days. So we are without the cash for 11 days.

If we have sales of 50,000, the the sales per day are 50,000/365.

If the receivables are 24,000 at the end of the year, then it means we are owed for sales for 24,000 / sales per day. That comes to 175.2 days. So it means that we are allowing customers to take 175.2 days to pay us.

Maria says

Thanks. Well i tried to, but it kept logging me off. And i have to be logged on to post a comment. This was the only page that didn’t log me off.

opentuition_team says

try another browser.. we can’t replicate the problem about getting logged off.. maybe some security settings on your PC do it.. not sure

arad says

When to ignore fixed costs.Thanks your lectures are really helping me.

John Moffat says

Fixed costs are only relevant if the total will change as a result of doing the project.

Just absorbing or charging some of the costs to the new project (for profit purposes) is not relevant because it does not mean that the total is changing – it is just being shared differently.

henna says

brilliant lecture…thanks a lot 🙂

sdmaalex says

Thanks alot! I learnt this in class, but I had no idea what it was. Even during the revision, I was just wondering what was going on :/

And, now it’s so clear…. Brilliant lecture! 🙂

jewel086 says

Not working on iPad …plz fix it ASAP ….thanks

John Moffat says

Have you looked at the technical support page?

The lecture is working fine and does not need fixing.

massivecodedake says

Hi ?john.I have a question about nominal rate of interest.It seems that the cost of capital given in the NPV question is the nominal rate of interest (is it?),then why the cost of capital given in the question doesn’t increase as the rate of inflation increase every year? THX John.

John Moffat says

But the rate of inflation is not increasing each year – the rate is staying constant 🙂

massivecodedake says

Er…Actually I mean we have to multiply contribution by (1+inflation rate) every year.Why doesn’t the cost of capital do so ?

John Moffat says

The cash flow keeps increasing, but the rate of inflation stays the same.

The cost of capital will only change if the general rate of inflation changes. (Look at the Fisher formula – the cost of capital depends on the rate of inflation. If the rate of inflation is constant then the cost of capital is constant)

massivecodedake says

Understood. THX !

saulat says

in investment appraisal , we have to give tax payment on cashflows which are sales less variable cost less fixed cost , my question is , the scrap value should be added in the final year after the tax payment ? scrap value and working capital adjustments should be included after we made the tax payment ? kindly guide me , what would be the EXACT FORMAT of net present value /investment appraisal ?

John Moffat says

The lecture on Relevant cash flows for tax gives the EXACT format.

First we list the operating cash flows (sales less variable costs less incremental (extra) fixed costs)

Then we calculate the tax on the operating flows.

Then we list the capital flows (cost and scrap proceeds)

Then we calculate the tax saving on the capital allowances (or ‘tax allowable depreciation’)

Then we bring in the working capital flows (at the end, because they have no tax effect)

saulat says

Thanks its really helpful , my another question is when calculating ROCE/ARR , we make operating cashflows (sales less variable cost less extra fixed cost) into accounting profit i.e operating cashflows less accumulated depreciation divided by projests life equals to accounting profit , right? my question is that whether to include scrap value in the operating cashflows too ?

John Moffat says

Scap proceeds is not an operating flow, but it is taken into account when calculating the depreciation.

saulat says

the discount rate /cost of capital given in the investment appraisal (in which we discount cashflows for present values) is a Nominal rate (money term) ? what basically it is ? nominal ? and is this a before tax or after tax cost of capital ? n my other question is if we r given general inflation so we have to convert Real into Nominal rate ? kindly make it clear . with exaples , it confuses me so much .

John Moffat says

In F9 we always discount the actual (nominal) cash flows at the actual (nominal) after tax cost of capital.

If the cash flows are given in real (current price) terms the we need to inflate them to get the actual (nominal ) cash flows.

If the cost of capital is given in real terms ( the ‘real’ cost of capital) we need to use the formula (with the inflation rate) to get the actual (nominal) cost of capital.

We always use the after tax cost of capital.

For examples watch the lecture again and see the course notes.

saulat says

if v have to inflate the discount rate (to make in money terms) we will use Fishers formula right ? and we will do this if we have General inflation given in the question and clearly stated right ? and the inflation rates given for other elements like sales 5%, material 2% labour 2.5% are called Spefic inflation rates ?

John Moffat says

Yes – everything you have written is correct 🙂

saulat says

Thanx 🙂 it made me clear .

eadinnu says

Seemingly complex things made ordinary. You are a great teacher. It flows like a beautiful poem!

Thank you ver much OT team.

morren says

Hi John:

Thanks for your lecture with such clarity. As it relates to inflation, June 2012 question # 1, how are the inflated selling and variable costs arrived at from years 2 to 4? we are given selling prices from years 1 to 4 being $25, $24, $23 & $23 with 4% inflation the answers given are $26 (ok), $25.96, $25.87, & $26.91. Variable cost given for years 1 to 4 are $10, $11, $12 & $12.50 at 2.5% inflation. answers given are $10.25 (ok), $11.56, 12.92 & $13.80.

Thank you

John Moffat says

Inflation on selling prices is 4% per year.

So the selling price in year 2 is 24 x 1.04^2 and in year 3 is 23 x 1.04^3 and so on.

morren says

Thank you. I did ” x 1.04″ only and not “1.04^2” etc. Is there a time when you use only “x 1.04” for each year?

Greatful for your timely response.

John Moffat says

No – you multiply by 1.04 for each year of inflation.

morren says

Thank you

rolake says

You are wonderful.

laeeq says

Excellent ! Very understandable

sarahso says

Great Lecture!

Saad Bin Aziz says

I agree with what my dear brother says. I am from pakistan and even here the teachers are not very talented if i may compare them with John! thank you John for such wonderful lectures.

barzakh says

@Saad Bin Aziz, actually there ARE pretty good teachers here in karachi 🙂

arjunudayp91 says

i study at india where there is a great lack for good teachers and i have just(4days) come to know of your videos and already am gonna complete watching all the sessions-they are so addictive which also means you are still to do a lot of marketing about these lectures but i can tell you they ll be more than just a soaring hit……………………!!!!!!!!!!!

kudos u guys rock…………………

the part when you said about bringing

1.05/1.15 = 1/1.15/1.05 …..it hit the penultimate part of my understanding of the fischer’s formula…………

arjunudayp91 says

i am speechless…