I don’t understand why the first formula is <=14000 since any capital not invested in time zero may be put into a deposit. In real life, we will definitely put it into a deposit to earn the 7% interest even though it is less than the cost of capital of 10% so the formula should always be =14000. Theoretically, though, it is possible to not put the unused capital into a deposit and it could be <=14000. Is this where you are coming from?

Why on earth would you definitely put money on deposit when it is being borrowed at 10% and depositing it only earns 7%? !! It would be better simply not to borrow it (unless being able to use the money a year later could end up giving a higher return than the amount being lost in the first year).

sir so if we use NPV per $ invested we realise that A and B are better options compared to C. But we can remain invested in 1/6th of project C (infinitely divisible) at T0. And at T1 1/6th of C would need $1000 of investment and A would $4000 of investment, which will be fully covered by $5000 of cash surplus at T1.

The point where am i trying to get to is that, when deciding between Project C and depositing at 7%(both of which are feasible but mutually-exclusive) at T0, do we compare C’s overall IRR with deposit rate or look at the fact that in 1year’s time C reaps no return whereas depositing the money at least lands 7%? As in on what basis do we decide the fate of remaining $14000-$5000-$8000=$1000??

I know in the exam we may never have to recommend, but just out of curiosity i was wanting to know this. Would be glad if you could shed some light on this sir!

Sir i am confused because in answer of this example provided in notes
the equation is written as Maximise NPV= 976a+2529b+862c+(1.07/1.1 x-x)
there is no -0.027

Thank you, sir, for your lecture. It is well explained.

I do have a little question regarding the deposit.

If I get it right, you mentioned in the lecture the reason we do not need to put a deposit in year 1 is that there no limitation on time 2, so we don’t need to borrow.

Why no need to borrow leads to no deposit. Can’t I put a deposit just because I have more available money or I want to lower the risk?

They are certainly entitled to put money on deposit if they want to, but there would be no point given that the interest they would earn is less than the cost of borrowing.

Dear Sir
Thanks for the explanation. I’m getting it Right till 0.973 but I’ve heard you say in the lecture 🙁 the npv is 0.1 – 0.973) .
So maybe I can’t really catch that can you please tell how 0.1 is really the investment of po ??

Thanks for the reply. But why have you shown the inflow of 1.07 in brackets meaning negative. The inflow should be positive right? And then divided by 1.1- ??

I have simply used brackets to show I am multiplying, not because it is negative!!!

Dividing by 1.1 is the same as multiplying by 0.909 (that is how discount factors are calculated, as you should remember from Papers MA (was F2) and FM (was F9) !!!)

What I wrote before is perfectly correct!
Po x 1.07 / 1.1 = 0.973 Po
Subtract the investment of Po and the NPV is – 0.027Po

I don’t really understand the objective of your working on Year 0 and 1.

I suppose Year 0 there is only $14,000 available cash flow. To invest I would choose Project B (8,000) and A (5,000) because of the NPV ranking, this will left me $1000 (14k – 8k – 5k) to be brought forward to Year 1 with another cash available of $5,000, which is $6000 (5k + 1k) in total, then I will be able to go for Project C. Am i missing something? Thanks

Firstly, you say B is better than A because of the NPV ranking. B is better but I assume you mean because of the NPV per $ invested ranking (as per single period capital rationing from Paper FM (was F9).

Secondly, you say that you then have 6,000 available to invest in C at time 1. But C needs an investment of 6,000 at time 0 – nothing in the question says that C can be delayed.

Thirdly, even if C could be delayed, what about the fact that A gives a higher NPV per $ than A. Why do you prefer to invest in C rather than in A?

There is no requirement to invest all 14,000 – the money is being borrowed and there is only any point in investing it if the return covers the cost of borrowing.

julianleong says

Hi Mr. Moffat,

I don’t understand why the first formula is <=14000 since any capital not invested in time zero may be put into a deposit. In real life, we will definitely put it into a deposit to earn the 7% interest even though it is less than the cost of capital of 10% so the formula should always be =14000. Theoretically, though, it is possible to not put the unused capital into a deposit and it could be <=14000. Is this where you are coming from?

John Moffat says

Why on earth would you definitely put money on deposit when it is being borrowed at 10% and depositing it only earns 7%? !! It would be better simply not to borrow it (unless being able to use the money a year later could end up giving a higher return than the amount being lost in the first year).

naveez says

Sir,

is it right if I formulate the constraint for Y this way:

4000a + 6000c ? 5000 + 1.07x +2000b

Pls Advise!

naveez says

^^

Year 1

4000a + 6000c <(less than or equal) 5000 + 1.07x +2000b

karang says

Hi John

Do we take interest on debt while calculating the NPV of a project in project appraisal in our cash flows as we will having a cash outflow??

So if we are not considering than it will PBIT to which we will deduct tax and add back dep right??

bolajiekundayo says

Hello sir

Can you please explain how did you get the npv of po (0.027) ?? does it mean the pv of Po is 0.946

if the NPV = 0.973Po – Po = – 0.027Po

Thanks

Bola

John Moffat says

0.973xPo – 1xPo = Po (0.973 – 1) = Po x 0.027

Noah098 says

sir so if we use NPV per $ invested we realise that A and B are better options compared to C. But we can remain invested in 1/6th of project C (infinitely divisible) at T0. And at T1 1/6th of C would need $1000 of investment and A would $4000 of investment, which will be fully covered by $5000 of cash surplus at T1.

The point where am i trying to get to is that, when deciding between Project C and depositing at 7%(both of which are feasible but mutually-exclusive) at T0, do we compare C’s overall IRR with deposit rate or look at the fact that in 1year’s time C reaps no return whereas depositing the money at least lands 7%? As in on what basis do we decide the fate of remaining $14000-$5000-$8000=$1000??

I know in the exam we may never have to recommend, but just out of curiosity i was wanting to know this. Would be glad if you could shed some light on this sir!

naini008 says

hello john

when we divide 1.07 by 1.10 it does not equal to -0.027

Please can u ellaborate how you calculated -0.027

John Moffat says

Nowhere do I say it is equal to -0.027. It is equal to 0.973 exactly as I wrote.

Therefore the NPV = 0973Po – Po = – 0.027Po

naini008 says

Sir i am confused because in answer of this example provided in notes

the equation is written as Maximise NPV= 976a+2529b+862c+(1.07/1.1 x-x)

there is no -0.027

John Moffat says

(1.07/1.1)X – X = – 0.027X

There is absolutely no point at all in using the notes without watching the lectures – they are only lecture notes to be used with the lectures.

confideans says

could you please elaborate on the meaning of ” infinitely divisible”? Thank you.

confideans says

and plus is it ok with 0<=P(0)<=14000 for precision?

John Moffat says

For the first, it means you can do any fraction of a project.

For the second, it is OK.

megan95 says

Thank you, sir, for your lecture. It is well explained.

I do have a little question regarding the deposit.

If I get it right, you mentioned in the lecture the reason we do not need to put a deposit in year 1 is that there no limitation on time 2, so we don’t need to borrow.

Why no need to borrow leads to no deposit. Can’t I put a deposit just because I have more available money or I want to lower the risk?

opentuition_team says

They are certainly entitled to put money on deposit if they want to, but there would be no point given that the interest they would earn is less than the cost of borrowing.

chimmm says

Dear Sir

Thanks for the explanation. I’m getting it Right till 0.973 but I’ve heard you say in the lecture 🙁 the npv is 0.1 – 0.973) .

So maybe I can’t really catch that can you please tell how 0.1 is really the investment of po ??

John Moffat says

I did not say that in the lecture.

The PV of the inflow is 0.973Po

The time 0 outlay is Po

Therefore the NPV = 0.973Po – Po = – 0.027Po

chimmm says

Sir ,

Can you please explain how did you get the npv of po (0.027) ??

chimmm says

In the multi period capital rationing .

John Moffat says

But I actually show the workings for this in the lecture!!!!

There is an outflow of Po at time 0, and an inflow of Po(1.07) in 1 years time.

So the NPV is Po(1.07)/1.1 – Po = – 0.027

chimmm says

Thanks for the reply. But why have you shown the inflow of 1.07 in brackets meaning negative. The inflow should be positive right? And then divided by 1.1- ??

chimmm says

Isn’t it should be like this :

Inflow of 1.07 × 0.909 (10% disc factor) and the ans will be 0.973.

John Moffat says

I have simply used brackets to show I am multiplying, not because it is negative!!!

Dividing by 1.1 is the same as multiplying by 0.909 (that is how discount factors are calculated, as you should remember from Papers MA (was F2) and FM (was F9) !!!)

What I wrote before is perfectly correct!

Po x 1.07 / 1.1 = 0.973 Po

Subtract the investment of Po and the NPV is – 0.027Po

zhixiang85 says

Hi John,

I don’t really understand the objective of your working on Year 0 and 1.

I suppose Year 0 there is only $14,000 available cash flow. To invest I would choose Project B (8,000) and A (5,000) because of the NPV ranking, this will left me $1000 (14k – 8k – 5k) to be brought forward to Year 1 with another cash available of $5,000, which is $6000 (5k + 1k) in total, then I will be able to go for Project C. Am i missing something? Thanks

John Moffat says

You are missing a few things.

Firstly, you say B is better than A because of the NPV ranking. B is better but I assume you mean because of the NPV per $ invested ranking (as per single period capital rationing from Paper FM (was F9).

Secondly, you say that you then have 6,000 available to invest in C at time 1. But C needs an investment of 6,000 at time 0 – nothing in the question says that C can be delayed.

Thirdly, even if C could be delayed, what about the fact that A gives a higher NPV per $ than A. Why do you prefer to invest in C rather than in A?

sid84 says

here the 1st equation <=14000 ..where we have 14000 to invest

John Moffat says

Are you asking a question?

sid84 says

yes … all three projects are giving positive npv but here the 1st equation <=14000 ..where we have $14000 to invest ?? why <= 14000 ?

John Moffat says

There is no requirement to invest all 14,000 – the money is being borrowed and there is only any point in investing it if the return covers the cost of borrowing.