If we instead kept $80,000 in the bank then we would have earned interest of $8,000, $8800, $9680, $10,648 respectively in each of the 4 years. this is our loss as we will not get this interest because of this investment. So to get the amount we will actually earn in these four years, why don’t we subtract each of the amounts I mentioned above from $20,000, $30,000, $40,000, $20000 respectively?

Assuming we were not given the NPV at 15%, and we are to derive the IRR using only the NPV at 10% with the Knowledge that NPV at 0% will be $30,000. I.e., $110,000 – $80,000.
The IRR would be 12.85% which is less than your value at 13.77%

That would be fine. As I explain in the lecture an IRR calculated using 2 ‘guesses’ is only ever an approximation, and the further apart the two rate are then the worse will be the approximation.

$6,660 is not the profit. It is the cash surplus expressed in present value terms (the are getting back the 80,000 and making a surplus of 6,660). If they can find something else to do with their $80,000 then they will do that instead. If there is nothing else to do with their $80,000 then they would be silly just to leave it sitting there!

We are ‘removing’ interest on the receipts in order to find out how much ‘now’ is equivalent to the receipts. If it is more than the original investment then it is worth investing. If it is less, then it isn’t worth investing.

As I explain in the lectures, we could calculate the terminal value instead and would arrive at the same decision. However we always look at the present value instead because it makes it easier to (for example) compare investments which last for different periods.

Dear sir, I was trying to the do NPV using (FV x 1.r^-n ) formula [I find this way quite quick to compute compared to FV x 1/(1.r^-n) ] and I see the answer using the formulas could differ upto more than 10-15 digits, per calculation, from the Present value tables at times. Could this not pose as a problem during the exam, if the answer is a fill in the blank type answer instead of mcq ?

Sir,
For the above question in the comment, do we take the additional revenue as the cash flows per year minus the extra cost?? because we are not provided with any other cash flows, and we do this using annuity table right??

Hi Sir,
I know how to calculate NPV and IRR % but I got some tricky question in the exam.
I would like to ask about my previous some exam question which I was failed.
(Not exactly but some I still remember)
Given net cash flow $9500 for 5 years ,cost of capital 12%
Q1@ ask me to find investment if NPV $20000 (this amount not sure may be $2000 )
Q2@ ask me to find investment amount if IRR 18%…
Can you help me how to calculate?

In future, please ask this kind of question in the Ask the Tutor Forum, and not as a comment on a lecture.

For the first question, you first discount the 9,500 cash flows by multiplying by the 5 year annuity discount factor at 12%.
You then subtract 20,000 and this tells you what the initial investment will be.

For the second question, the IRR is the interest rate at which the NPV equals zero. So discount the 9,500 cash flows by multiplying by the 5 year annuity factor at 18%. The initial investment must equal the present value of the cash flows that you have just calculated.

Great lecture! But I am a bit confused.. For the NPV, why are we applying the discount factor to the cash generated amount and not to the 80,000? For example, if we had borrowed 80,000 for the project at 10% rate, at the end of the 4 years period we would have paid in total (including interest) 117,128 and earned 110,000 (cash generated + scrap value of project), which would let us with a 7,128 cash deficit. I don’t understand that approach :/, is there any tip to help me to see what I am missing? Thanks a mil!!

It would. seem that you have not watched the previous lectures on interest and on discounting, because I do explain in these lectures what is happening with discounting and why.

(The reason you would not end up with your cash deficit is because when you receive the money each year you will be using to pay back some of the borrowing and so the interest will be a lot lower.)

Still trying to get my head around this, having watched all the previous lectures and still not getting it, I think I am having the same misunderstanding as Elaine above.

What I don’t understand is that, if we assume the interest would be received on cash (rather than payable on borrowing), it amounts to higher than the 110,000 on the project. Other than using the DF, I can’t see how this positive NPV is logically earning more than if we simply earned interest on the cash, instead of the project, which would be £117,128.

My only guess is that this is due to the fact that the return amount say for year 1 is £20,000 which is then effectively freed up capital with further interest earning potential? So the overall benefit of the project would essentially be the £110,000, plus the potential interest earned on the receipts generated each year?

Are we therefore using the DF to determine how much is needed to invest today, to receive the £20,000 after 1 year? Surely the real opportunity cost is the actual interest on the £80k which amounts to more than the £110k? Unless the £20,000 after 1 year is then available for further interest?

To understand, I just need to clarify if we are assuming that the £20k earned after 1 year, and subsequent years earnings has future earning potential in addition to the £80K invested? So its a matter of receiving higher return on capital sooner (with additional earnings potential), than overall amount generated by project vs interest on the £80k?

Thanks so much, I find your videos really helpful!

Can you please explain how you got the discount factors, i have looked up the previous lectures and still can’t relate how you got 0.909 as a discount factor for 20000.. Please help!

i got lost getting to the IRR=13.78,from the lecture,it says IRR = 10% + (6660/8820 X 5%)
= 10% + 3.78% ??????
I get totally different answers…..off the grid,please help!!

Able ltd is considering a new project for which the following information is available:

Initial cost – $300,000
Expected life – 5 years
Estimated scrap value – $20,000
Additional revenue from the project – $120,000 per year
Incremental cost of the project – $30,000 per year
Cost of capital – 10%
A) calculate the Net present Value of the project (to the nearest $)

Please answer this for me as i am bit confused about how to deal with incremental costs.

You must ask this kind of question in the Ask the Tutor Forum and not as a comment on a lecture.
The word incremental means extra – so incremental costs are extra costs.

Sir,
For the above question in the comment, do we take the additional revenue as the cash flows per year minus the extra cost?? because we are not provided with any other cash flows, and we do this using annuity table right??

hi sir, how solve this question?
Using an interest rate of 10% per year the net present value (NPV) of a project has been correctly calculated as $50. If the interest rate is increased by 1% the NPV of the project falls by $20.

What is the internal rate of return of the project?

mannannagpal says

How is it okay to accept the project even if the surplus comes out to be only +1?

John Moffat says

Because they would be better off – even if it is just $1 !!

In practice we might not prepared to take the risk when the benefit is only $1, but discussion of this is not relevant until Paper FM).

mannannagpal says

If we instead kept $80,000 in the bank then we would have earned interest of $8,000, $8800, $9680, $10,648 respectively in each of the 4 years. this is our loss as we will not get this interest because of this investment. So to get the amount we will actually earn in these four years, why don’t we subtract each of the amounts I mentioned above from $20,000, $30,000, $40,000, $20000 respectively?

John Moffat says

Discounting is taking account of that.

ficasej says

Assuming we were not given the NPV at 15%, and we are to derive the IRR using only the NPV at 10% with the Knowledge that NPV at 0% will be $30,000. I.e., $110,000 – $80,000.

The IRR would be 12.85% which is less than your value at 13.77%

John Moffat says

That would be fine. As I explain in the lecture an IRR calculated using 2 ‘guesses’ is only ever an approximation, and the further apart the two rate are then the worse will be the approximation.

hermela says

Sir it is a nice lecture but I don’t get the concept … If one factory invest on 80000 machine it is worthy the get only 6660 profit after 6 years?

John Moffat says

$6,660 is not the profit. It is the cash surplus expressed in present value terms (the are getting back the 80,000 and making a surplus of 6,660). If they can find something else to do with their $80,000 then they will do that instead. If there is nothing else to do with their $80,000 then they would be silly just to leave it sitting there!

sabya2k says

Sir, I tried doing this IRR sum with 20% instead of 15% and the answer was 14.07%

Is this variance normal or should the answer have been 13.78% ?

John Moffat says

Yes, it is no problem. The answer is always approximate because the relationship is not linear.

MLAZIMILANO says

Splendid job, Sir Moffat!! Exceptionally done as usual 😀

John Moffat says

Thank you for your comment 🙂

alxstellini says

Hi sir,

I cannot understand why we remove the interest for the full $110,000 in the first example. If we are paying $80,000 aren’t we paying interest on that?

Thank you, your lectures are great 🙂

John Moffat says

We are ‘removing’ interest on the receipts in order to find out how much ‘now’ is equivalent to the receipts. If it is more than the original investment then it is worth investing. If it is less, then it isn’t worth investing.

alxstellini says

But are we not over compensating for the interest? Shouldnt the interest be on what we pay not earn?

John Moffat says

Not at all.

As I explain in the lectures, we could calculate the terminal value instead and would arrive at the same decision. However we always look at the present value instead because it makes it easier to (for example) compare investments which last for different periods.

Asif110 says

Dear sir, I was trying to the do NPV using (FV x 1.r^-n ) formula [I find this way quite quick to compute compared to FV x 1/(1.r^-n) ] and I see the answer using the formulas could differ upto more than 10-15 digits, per calculation, from the Present value tables at times. Could this not pose as a problem during the exam, if the answer is a fill in the blank type answer instead of mcq ?

Asif110 says

Correction : compared to FV x 1/(1.r^+n)

John Moffat says

No it won’t be a problem in the exam. Questions will ask for the answer to be (for example) to the nearest thousand.

Nobody worried about a few thousand in real life, and nor is it a problem in the exam 🙂

Asif110 says

Thanks ?

Asif110 says

It was a smiley, but the website converted it to a Question mark. Haha

Sir, what about IRR, same rounding to nearest figure in exam ?

John Moffat says

Yes 🙂

sruthiann says

Sir,

For the above question in the comment, do we take the additional revenue as the cash flows per year minus the extra cost?? because we are not provided with any other cash flows, and we do this using annuity table right??

cynthiamyint says

Hi Sir,

I know how to calculate NPV and IRR % but I got some tricky question in the exam.

I would like to ask about my previous some exam question which I was failed.

(Not exactly but some I still remember)

Given net cash flow $9500 for 5 years ,cost of capital 12%

Q1@ ask me to find investment if NPV $20000 (this amount not sure may be $2000 )

Q2@ ask me to find investment amount if IRR 18%…

Can you help me how to calculate?

Thanks,

Cynthia

John Moffat says

In future, please ask this kind of question in the Ask the Tutor Forum, and not as a comment on a lecture.

For the first question, you first discount the 9,500 cash flows by multiplying by the 5 year annuity discount factor at 12%.

You then subtract 20,000 and this tells you what the initial investment will be.

For the second question, the IRR is the interest rate at which the NPV equals zero. So discount the 9,500 cash flows by multiplying by the 5 year annuity factor at 18%. The initial investment must equal the present value of the cash flows that you have just calculated.

elainew says

Great lecture! But I am a bit confused.. For the NPV, why are we applying the discount factor to the cash generated amount and not to the 80,000? For example, if we had borrowed 80,000 for the project at 10% rate, at the end of the 4 years period we would have paid in total (including interest) 117,128 and earned 110,000 (cash generated + scrap value of project), which would let us with a 7,128 cash deficit. I don’t understand that approach :/, is there any tip to help me to see what I am missing? Thanks a mil!!

John Moffat says

It would. seem that you have not watched the previous lectures on interest and on discounting, because I do explain in these lectures what is happening with discounting and why.

(The reason you would not end up with your cash deficit is because when you receive the money each year you will be using to pay back some of the borrowing and so the interest will be a lot lower.)

hamza591 says

classic! way better than my actual teacher.

https://anlac-symphony.com/biet-thu-lien-ke-shophouse-an-lac-green-symphony/

Assesina89 says

Hi John,

Still trying to get my head around this, having watched all the previous lectures and still not getting it, I think I am having the same misunderstanding as Elaine above.

What I don’t understand is that, if we assume the interest would be received on cash (rather than payable on borrowing), it amounts to higher than the 110,000 on the project. Other than using the DF, I can’t see how this positive NPV is logically earning more than if we simply earned interest on the cash, instead of the project, which would be £117,128.

My only guess is that this is due to the fact that the return amount say for year 1 is £20,000 which is then effectively freed up capital with further interest earning potential? So the overall benefit of the project would essentially be the £110,000, plus the potential interest earned on the receipts generated each year?

Are we therefore using the DF to determine how much is needed to invest today, to receive the £20,000 after 1 year? Surely the real opportunity cost is the actual interest on the £80k which amounts to more than the £110k? Unless the £20,000 after 1 year is then available for further interest?

To understand, I just need to clarify if we are assuming that the £20k earned after 1 year, and subsequent years earnings has future earning potential in addition to the £80K invested? So its a matter of receiving higher return on capital sooner (with additional earnings potential), than overall amount generated by project vs interest on the £80k?

Thanks so much, I find your videos really helpful!

Lou

jwang8 says

classic! way better than my actual teacher.

John Moffat says

Thank you for your comment 🙂

muddyzaahid says

Good day,

Can you please explain how you got the discount factors, i have looked up the previous lectures and still can’t relate how you got 0.909 as a discount factor for 20000.. Please help!

John Moffat says

You take the present value tables, and look at the column headed up 10% and the row for 1 period.

muddyzaahid says

Thank you for the response.. Didn’t expect it to be this quick, have a great day ahead ?

sadafwaheed1 says

There is a formula also discount factor = 1/(1+r)^n

Where r is the interest 10%= 0.1

And N is the period

syedsami says

can u say how do we get the discount factor?

John Moffat says

I explain how to get the discount factors in the lectures covering the previous chapter of our notes!!!

littlegirl18 says

i got lost getting to the IRR=13.78,from the lecture,it says IRR = 10% + (6660/8820 X 5%)

= 10% + 3.78% ??????

I get totally different answers…..off the grid,please help!!

samirh says

I am having the same issue, did you figure it out?

John Moffat says

Divide 6660 by 8820, multiply the answer by 5 and you get 3.78.

Add 3.78 to 10 and you get 13.78.

Gabriel says

i got a little lost, +6660 and -2160 is 8820? or in this step we just ignore the mathematical signs and just do regular addition?

John Moffat says

The difference between +6,660 and zero is 6,660

The difference between + 6,660 and – 2,160 is bigger and is 8,820.

This is standard arithmetic 🙂

saroj says

Able ltd is considering a new project for which the following information is available:

Initial cost – $300,000

Expected life – 5 years

Estimated scrap value – $20,000

Additional revenue from the project – $120,000 per year

Incremental cost of the project – $30,000 per year

Cost of capital – 10%

A) calculate the Net present Value of the project (to the nearest $)

Please answer this for me as i am bit confused about how to deal with incremental costs.

John Moffat says

You must ask this kind of question in the Ask the Tutor Forum and not as a comment on a lecture.

The word incremental means extra – so incremental costs are extra costs.

sruthiann says

Sir,

For the above question in the comment, do we take the additional revenue as the cash flows per year minus the extra cost?? because we are not provided with any other cash flows, and we do this using annuity table right??

davthev says

hi sir, how solve this question?

Using an interest rate of 10% per year the net present value (NPV) of a project has been correctly calculated as $50. If the interest rate is increased by 1% the NPV of the project falls by $20.

What is the internal rate of return of the project?

11.7%

20.0%

7.5%

12.5%

John Moffat says

You know that the NPV at 10% is $50.

You know that the NPV at 11% (10 + 1) is $30 (50 – 20).

Now you have two ‘guesses’ and you continue as I do in the example in my free lectures.

davthev says

tqvm sir for yr quick response. May God continue to bless u

John Moffat says

You are welcome 🙂

TANYASHARMA29 says

can someone show me by solving this here ?

Thank you so much