Couldn’t the company keep the $100 left over after investing in projects, as reserve for investing in the working capital for the year? Considering there might be higher inflation rates coming into play (although not a part of this practice question) which would mean the company might need some additional funds to buy materials in the upcoming years within the 3 year life of the project?
Kindly let me know your thoughts.

Hi Sir,
Instead of calculating the NPV for all combinations of projects in case of non-infinitely divisible projects, can’t we simply rank the individual NPVs for the projects (similar to ranking used in the “infinitely divisible projects” case) and select the top 3 for adding up and getting the best possible combination?
I think it would save time of calculating the NPVs for all possible combinations. Please do let me know your thoughts.

No, you cannot rank by the profitability index if they are not divisible. There is no alternative but to look at each possible combination.
(If profitability index ever leads to the same result, then it is purely coincidence)

Apologies Sir.
I didn’t mean ranking by Profitability index, but, rather ranking the NPVs themselves, as they are already given and then total up the highest ranked NPVs, instead of calculating different possible combinations of total NPVs.

No – you cannot simply rank based on the NPV’s because the amount needed to be invested also matters.
There is no alternative but to calculate the total NPV’s of the possible investments and choose whichever give the highest total NPV.

I remember seeing a past question, cannot remember which year, where there were 5 projects to decide on investing and 3 of them were divisible and 2 were exclusively indivisible?
I am trying to recall what exclusively indivisible means. i think it means that if you produce one of the exclusive indivisible project you cannot produce the other?! I am not sure this is correct. Please clarify for me.

The term is not ‘exclusively indivisible’ – it is ‘mutually exclusive’ and that does mean that if you do one of the projects then you cannot do the other.

Thanks for the great lecture. I am wondering wouldn’t the company be better off to use the cash surplus to decrease overdraft or other uses we went over in Cash management lecture instead of paying dividends?

If the cash is being borrowed, then they will not borrow it if they have nowhere to invest it.

If, on the other hand, they already have the cash available, then presumably they have a cash balance and not an overdraft, in which case they should give the money to shareholders.

On part C – Not infinitely divisible, when explaining that the remaining $100 can be given back to the shareholders as dividends, why specifically as dividends and not simply give it back?

You can’t simply give money back to shareholders! The only way you give them money is by paying them a dividend.
Legally, you can only pay dividends out of profits that have been realised, but you need to have cash to pay it. The reason most companies do not pay out all their profits as dividends is because they retain and use the cash to expand the company. If they are not able to invest it profitably then they should pay more dividends.

I think your lectures are very clear and helpful. Thank you.

On the point regarding returning the $100 to the investors. If the money has not been borrowed to invest but is sitting in your bank, are you not still earning the cost of capital on that money? I understood that the cost of capital was either the cost of having that money you invested because you had to borrow it, or it was the money you could have made from it if it had just sat in the bank. In which case it would still be making some money?

The cost of capital is always the cost of raising money, and money is either raised from the shareholders (and we have the cost of equity) or borrowed from long-term bonds etc. (and we have the cost of debt) or both (and we have the WACC).

Hello john grt lecture, as usual.
However in part a when we had divisible projects the order of choosing them was D, C , A. This was before considering the divisibility.
So, the same can be considered as a rule for non divisibility projects as well right? Why do we consider total npv instead? And how does this make a difference?

No – the same rule cannot be used for non-divisible projects (and this is in fact explained in the lecture).

When they are divisible we are able to invest all of the capital available. However, when they are indivisible it is likely to not be possible to invest all of the capital and we have no choice but to simply look at the various combinations of projects available.

Hi John, just wanna say thank u for the lecture notes and the videos that go with them, I found them to be very useful. I feel more confident now approaching the F9 Dec 2015 exam.

Regarding your example on part c (non-infinitely divisible) if we calculate NPV per invested $:
ABC NPV – 143 Total cost – 1400 NPV per $ – 0.102
ABD NPV – 157 Total cost – 1500 NPV per $ – 0.10466
ACD NPV – 143 Total cost – 1200 NPV per $ – 0.119
BCD NPV – 136 Total cost – 1300 NPV per $ – 0.10461
We should chose fraction ACD with highest NPV per $ at the same time we save (no borrow thereby less cost of capital) $400

My question is can I get on exam the same marks for this type of answer or is it better your answer ABD higher NPV?

No – your answer would not get the marks.
We always want the highest total NPV, and the only correct answer is ABD.
Remember that the NPV is the surplus after repaying the borrowing (together with interest).

To explain, here is a very very basic illustration.
Suppose you could borrow $10 and get back $20 – a surplus of $10 ignoring interest.
Alternatively, you could borrow $100 and get back $120 – a surplus of $20 ignoring interest.
Which would you prefer? The first one gives surplus of $1 per $1 (10/10) and the second one only gives a surplus of $0.20 per $. (20/100).
However, surely you would prefer the second and end up with a surplus (cash profit) of $20 after repaying the borrowing as opposed to a surplus of only $10.

The only problem (and this is only relevant for a written part of a question) is that we are assuming that the returns are certain. If there is uncertainty then by choosing the second one we are taking more risk. However for the numbers part of questions we would always assume certainty.

Hi Mr Moffat
Thanks to yourself and Open Tuition for the lectures.
A question regarding the answer to example 1(c) if I may (this question was asked by louise06111 back in Feb-12 but, and no disrespect to tameablebunchy, I’m not convinced by the answer given at that time, but I may be missing something).
The answer given to 1(c) in the lecture, is to choose the projects giving the greatest NPV, being A, B and D. However, A, C and D give the highest return per $ invested ($0.113 per $ invested compared to £0.105 per $ invested, if my maths are correct).
Using the same sort of logic, take this example (a spurious one but it’s simply to make the point):
A – cost $10000, NPV $1000
B – cost $2000, NPV $999
Assuming a capital restriction of $11000, and the projects are not infinitely divisible, A has the greater NPV, but B has much better return on investment. Surely B would be the better choice?
What am I missing?
Thanks again for the assistance you provide.

The NPV is the cash surplus we end up with (after accounting for interest).

To take your examples, if you invest in project A then you end up with a cash surplus of $1000 (the amount not invested earns nothing.
If you take project B, then you end up with a cash surplus of $999 (the remaining $9,000 of the cash available earns nothing).

I would prefer to end up with a surplus of $1000 than a surplus of $999 🙂

(If we could invest all our money in B (i.e. 9.5 B’s) then certainly B would be better – we would end up with a much bigger cash surplus. However, that is not the case – we either invest in just one A or just one B)

Mr Moffat, thanks for replying.
Of course, the interest on the source of the capital in the first place (cost of capital) is already being accounted for in coming to the NPV, so choosing to ‘borrow’ the additional capital in the first place is the better option as it gives a greater NPV.
Knew I was missing something.
Thanks again.
Regards

If the projects were all mutually exclusive, it would mean that you could only do one of them – then you would simply select the project with the higher NPV.

If just 2 of them were mutually exclusive then you need to do the exercise twice. (If, for example, A and B were mutually exclusive, then you would do as normal first as though only A, C and D were available, and then as though only B, C and D were available. Whichever of the two solutions gave the higher NPV would be the best.

There is no such term as mutually inclusive. If they are all available, then it is the normal solution. I suppose what you could have (although extremely unlikely indeed for the exam) was that if, for example, we were to do A then we would be forced to do B. If that did happen, then you would treat A and B as being one project (simply adding them together) and then continue as normal. However, I do not think there is any chance at all of that being relevant for the exam.

Could we in the exam say that the amount of 100$ leftover can be used as working capital in the projects so as to avoid the trap of fast expansion and working capital cash management?

I have a question regarding investment appraisal,
When do I add Working Capital Recovery in DCF?.
I have noticed that some times it is added and sometimes it is just ignored.?

Please assist.. Dec 2009…Q 3. I wanna calculate part a TERP not the way it has been calculated in the answer somebody let me know the other optional method we have..

thanks f9 has been eased for me instead of calming things i real understand the concept open tuition is far better than these colleges were we pay heavily and get sub standard lectures with out you i don’t know how i would have made it thankes

Completely agree!!!! I have got no problem with paying money, in fact my study is half funded by my company, yet am so not gonna pay to have less quality lectures, that would be stupid! I can understand paying for a higher quality, but less quality! O.o! Opentuition is far better than the institute I was going to, it feels bad to be paying and then come to a free resource to understand everything you did not understand in the classes you have been paying for!!

Dear tutor,
Regarding part(c) of Eg1, I am confused.
We choose ABD combination which gives the highest total NPV, but why don’t we analyse the efficiency as we do in part(b)?
ABC: 1400 input, we get 143 output, the efficiency is 10.21%;
ABD: 1500 input, 157 output, 10.46%;
ACD: 1200 input, 136 output, 11.33%;
BCD: 1300 input, 143 output, 11.00%.
(OMG, I hope I’ve made it clear~)
From my view I may think ACD is the most efficient investment combinations and I am wondering whether I got something wrong. Can you please help check my thought? Thx a lot.

part B is infinitely divisible, this means you can do a fraction of a project, therefore you start with the highest NPV first and so forth what capital is left is invested into a fraction of the project B which 66.6666%.

With part C, capital is restricted to 1600 so you choose the best option that will return highest NPV per project because these projects are non infinitely divisible you have to choose the best option so you only have to borrow or use the amount of cash that is needed.

The key is to find the highest return/NPV for investment

Chetan says

Hi Sir Moffat,

Couldn’t the company keep the $100 left over after investing in projects, as reserve for investing in the working capital for the year? Considering there might be higher inflation rates coming into play (although not a part of this practice question) which would mean the company might need some additional funds to buy materials in the upcoming years within the 3 year life of the project?

Kindly let me know your thoughts.

John Moffat says

If that were the case then you would need to be told, and then it would effectively be an extra investment opportunity.

Chetan says

Hi Sir,

Instead of calculating the NPV for all combinations of projects in case of non-infinitely divisible projects, can’t we simply rank the individual NPVs for the projects (similar to ranking used in the “infinitely divisible projects” case) and select the top 3 for adding up and getting the best possible combination?

I think it would save time of calculating the NPVs for all possible combinations. Please do let me know your thoughts.

John Moffat says

No, you cannot rank by the profitability index if they are not divisible. There is no alternative but to look at each possible combination.

(If profitability index ever leads to the same result, then it is purely coincidence)

Chetan says

Apologies Sir.

I didn’t mean ranking by Profitability index, but, rather ranking the NPVs themselves, as they are already given and then total up the highest ranked NPVs, instead of calculating different possible combinations of total NPVs.

John Moffat says

No – you cannot simply rank based on the NPV’s because the amount needed to be invested also matters.

There is no alternative but to calculate the total NPV’s of the possible investments and choose whichever give the highest total NPV.

cecel says

Thanks for clarifying that for me John.

John Moffat says

You are welcome 🙂

cecel says

Hi John,

I remember seeing a past question, cannot remember which year, where there were 5 projects to decide on investing and 3 of them were divisible and 2 were exclusively indivisible?

I am trying to recall what exclusively indivisible means. i think it means that if you produce one of the exclusive indivisible project you cannot produce the other?! I am not sure this is correct. Please clarify for me.

John Moffat says

The term is not ‘exclusively indivisible’ – it is ‘mutually exclusive’ and that does mean that if you do one of the projects then you cannot do the other.

Farid says

Hi John

Thanks for the great lecture. I am wondering wouldn’t the company be better off to use the cash surplus to decrease overdraft or other uses we went over in Cash management lecture instead of paying dividends?

John Moffat says

If the cash is being borrowed, then they will not borrow it if they have nowhere to invest it.

If, on the other hand, they already have the cash available, then presumably they have a cash balance and not an overdraft, in which case they should give the money to shareholders.

Uber says

Hello John,

On part C – Not infinitely divisible, when explaining that the remaining $100 can be given back to the shareholders as dividends, why specifically as dividends and not simply give it back?

Is there a reason for this?

Aren’t dividends paid from distributable profits?

Thank you,

Great lecture as always!

John Moffat says

You can’t simply give money back to shareholders! The only way you give them money is by paying them a dividend.

Legally, you can only pay dividends out of profits that have been realised, but you need to have cash to pay it. The reason most companies do not pay out all their profits as dividends is because they retain and use the cash to expand the company. If they are not able to invest it profitably then they should pay more dividends.

Uber says

Thank you very much John!

Much appreciated! 🙂

John Moffat says

You are welcome 🙂

Shimon says

Hi,

I think your lectures are very clear and helpful. Thank you.

On the point regarding returning the $100 to the investors. If the money has not been borrowed to invest but is sitting in your bank, are you not still earning the cost of capital on that money? I understood that the cost of capital was either the cost of having that money you invested because you had to borrow it, or it was the money you could have made from it if it had just sat in the bank. In which case it would still be making some money?

John Moffat says

The cost of capital is always the cost of raising money, and money is either raised from the shareholders (and we have the cost of equity) or borrowed from long-term bonds etc. (and we have the cost of debt) or both (and we have the WACC).

sruthi says

Hello john grt lecture, as usual.

However in part a when we had divisible projects the order of choosing them was D, C , A. This was before considering the divisibility.

So, the same can be considered as a rule for non divisibility projects as well right? Why do we consider total npv instead? And how does this make a difference?

Thank u sir.

John Moffat says

No – the same rule cannot be used for non-divisible projects (and this is in fact explained in the lecture).

When they are divisible we are able to invest all of the capital available. However, when they are indivisible it is likely to not be possible to invest all of the capital and we have no choice but to simply look at the various combinations of projects available.

Our object always is to get the maximum NPV.

sruthi says

Ohh ok thnk u John 🙂

John Moffat says

You are welcome 🙂

rmnihad says

How i can download this video?

John Moffat says

Lectures can only be watched online – it is the only way that we can keep this website free of charge.

Kamal says

Hi John, just wanna say thank u for the lecture notes and the videos that go with them, I found them to be very useful. I feel more confident now approaching the F9 Dec 2015 exam.

John Moffat says

Thank you 🙂

Anzor says

Dear John,

Regarding your example on part c (non-infinitely divisible) if we calculate NPV per invested $:

ABC NPV – 143 Total cost – 1400 NPV per $ – 0.102

ABD NPV – 157 Total cost – 1500 NPV per $ – 0.10466

ACD NPV – 143 Total cost – 1200 NPV per $ – 0.119

BCD NPV – 136 Total cost – 1300 NPV per $ – 0.10461

We should chose fraction ACD with highest NPV per $ at the same time we save (no borrow thereby less cost of capital) $400

My question is can I get on exam the same marks for this type of answer or is it better your answer ABD higher NPV?

Thank you!

Anzor

John Moffat says

No – your answer would not get the marks.

We always want the highest total NPV, and the only correct answer is ABD.

Remember that the NPV is the surplus after repaying the borrowing (together with interest).

To explain, here is a very very basic illustration.

Suppose you could borrow $10 and get back $20 – a surplus of $10 ignoring interest.

Alternatively, you could borrow $100 and get back $120 – a surplus of $20 ignoring interest.

Which would you prefer? The first one gives surplus of $1 per $1 (10/10) and the second one only gives a surplus of $0.20 per $. (20/100).

However, surely you would prefer the second and end up with a surplus (cash profit) of $20 after repaying the borrowing as opposed to a surplus of only $10.

The only problem (and this is only relevant for a written part of a question) is that we are assuming that the returns are certain. If there is uncertainty then by choosing the second one we are taking more risk. However for the numbers part of questions we would always assume certainty.

Anzor says

Thank you John!

That is clear.

Best regards,

Anzor

arad says

Now that the F9 exam has a multiple choice component, will it now be necessary to read the text book from cover to cover.

John Moffat says

If you watch all our lectures (together with the lecture notes) then you will have enough to pass the exam well.

What is essential is that you have a current edition of Revision Kit and that you practice all of the questions.

seanduffy47 says

Hi Mr Moffat

Thanks to yourself and Open Tuition for the lectures.

A question regarding the answer to example 1(c) if I may (this question was asked by louise06111 back in Feb-12 but, and no disrespect to tameablebunchy, I’m not convinced by the answer given at that time, but I may be missing something).

The answer given to 1(c) in the lecture, is to choose the projects giving the greatest NPV, being A, B and D. However, A, C and D give the highest return per $ invested ($0.113 per $ invested compared to £0.105 per $ invested, if my maths are correct).

Using the same sort of logic, take this example (a spurious one but it’s simply to make the point):

A – cost $10000, NPV $1000

B – cost $2000, NPV $999

Assuming a capital restriction of $11000, and the projects are not infinitely divisible, A has the greater NPV, but B has much better return on investment. Surely B would be the better choice?

What am I missing?

Thanks again for the assistance you provide.

John Moffat says

The NPV is the cash surplus we end up with (after accounting for interest).

To take your examples, if you invest in project A then you end up with a cash surplus of $1000 (the amount not invested earns nothing.

If you take project B, then you end up with a cash surplus of $999 (the remaining $9,000 of the cash available earns nothing).

I would prefer to end up with a surplus of $1000 than a surplus of $999 🙂

(If we could invest all our money in B (i.e. 9.5 B’s) then certainly B would be better – we would end up with a much bigger cash surplus. However, that is not the case – we either invest in just one A or just one B)

seanduffy47 says

Mr Moffat, thanks for replying.

Of course, the interest on the source of the capital in the first place (cost of capital) is already being accounted for in coming to the NPV, so choosing to ‘borrow’ the additional capital in the first place is the better option as it gives a greater NPV.

Knew I was missing something.

Thanks again.

Regards

sandra1964 says

What happens when the projects are mutually exclusive/ inclusive

John Moffat says

If the projects were all mutually exclusive, it would mean that you could only do one of them – then you would simply select the project with the higher NPV.

If just 2 of them were mutually exclusive then you need to do the exercise twice. (If, for example, A and B were mutually exclusive, then you would do as normal first as though only A, C and D were available, and then as though only B, C and D were available. Whichever of the two solutions gave the higher NPV would be the best.

There is no such term as mutually inclusive. If they are all available, then it is the normal solution. I suppose what you could have (although extremely unlikely indeed for the exam) was that if, for example, we were to do A then we would be forced to do B. If that did happen, then you would treat A and B as being one project (simply adding them together) and then continue as normal. However, I do not think there is any chance at all of that being relevant for the exam.

sandra1964 says

Thanks John you are a star.

Nelson says

Thank you for the lecture, it is really helpful.

John Moffat says

You are welcome 🙂

Ahmed says

Could we in the exam say that the amount of 100$ leftover can be used as working capital in the projects so as to avoid the trap of fast expansion and working capital cash management?

Wadah says

Hey all.

I have a question regarding investment appraisal,

When do I add Working Capital Recovery in DCF?.

I have noticed that some times it is added and sometimes it is just ignored.?

hamzaharoon says

Thank You So much Sir, An Excellent Lecture It Refreshed My memories Learning Limiting Factor Analysis and Throughput Accounting 🙂

cecel says

Hi John,

After listening to this lecture I finally fully understand capital rationing! Thank you for simplifying for me!!

sdmaalex says

Thanks alot! The lectures are simple and easy to understand 🙂

mahoysam says

I feel am studying F5! It reminded me of key factor analysis and throughput accounting! Feels good that I still remember the stuff after the exam lol!

Tyler says

I’m studying F5 as well, so I’m finding F5+F9 an amazing combination 😀

prudence7 says

Please assist.. Dec 2009…Q 3. I wanna calculate part a TERP not the way it has been calculated in the answer somebody let me know the other optional method we have..

Vipin says

it is really helpful, good points , good tutor

Miss A.. says

thnx a lot OT for making acca’s students life easier…

henrytenywa says

thanks f9 has been eased for me instead of calming things i real understand the concept open tuition is far better than these colleges were we pay heavily and get sub standard lectures with out you i don’t know how i would have made it thankes

mahoysam says

Completely agree!!!! I have got no problem with paying money, in fact my study is half funded by my company, yet am so not gonna pay to have less quality lectures, that would be stupid! I can understand paying for a higher quality, but less quality! O.o! Opentuition is far better than the institute I was going to, it feels bad to be paying and then come to a free resource to understand everything you did not understand in the classes you have been paying for!!

louis06111 says

Dear tutor,

Regarding part(c) of Eg1, I am confused.

We choose ABD combination which gives the highest total NPV, but why don’t we analyse the efficiency as we do in part(b)?

ABC: 1400 input, we get 143 output, the efficiency is 10.21%;

ABD: 1500 input, 157 output, 10.46%;

ACD: 1200 input, 136 output, 11.33%;

BCD: 1300 input, 143 output, 11.00%.

(OMG, I hope I’ve made it clear~)

From my view I may think ACD is the most efficient investment combinations and I am wondering whether I got something wrong. Can you please help check my thought? Thx a lot.

tameablebunchy says

@louis06111,

part B is infinitely divisible, this means you can do a fraction of a project, therefore you start with the highest NPV first and so forth what capital is left is invested into a fraction of the project B which 66.6666%.

With part C, capital is restricted to 1600 so you choose the best option that will return highest NPV per project because these projects are non infinitely divisible you have to choose the best option so you only have to borrow or use the amount of cash that is needed.

The key is to find the highest return/NPV for investment

louis06111 says

@tameablebunchy,

Thanks a lot for your time and effort,

It does help!

donhitler says

video lecture notes helpful but sometimes difficult to view.