I do not quite understand Q4 – could you please explain why the statement ‘There is only ever one IRR’ is not correct?
And also the statement about a graph with NPV on “Y” and interest rate on “X” – wouldn’t it have a negative slope?

For a conventional set of cash flows (i.e. an outflow followed by a series of inflows) then there will be only one IRR and there will be a negative slope.
However, if there is more than one change of sign (e.g. outflow followed by inflows followed by outflow) then there can be more than one IRR and the graph will be a curve with an upward and a downward slope.
This is one of the standard possible problems with using IRR and I do explain it in the free lecture.

The NPV at 20% is -0.266. I haven’t converted anything.

(It is actually of course -266,000, and the NPV at 15% is actually +343,000, but using those figures will obviously give exactly the same answer with more messaging around)

Have you watched my free lectures on this? (Because there is no point in attempting the tests if you have not watched the lectures!)

If you have watched the lectures then you will know that the 10 year annuity factor is the total of the discount factors for years 1 to 10.

If we subtract the 2 year annuity factor (which is the total of the discount factors for years 1 to 2), the we are left with the total of the factors for years 3 to 10, which is what we want 🙂 )

The discount factor for a perpetuity is 1/r (which in this case is 1/0.11).
However this gives the present value when the first receipt is in 1 years time – so 1 to infinity.

In this question the first receipt is immediate – time 0 – and then we get receipts for 1 to infinity.
The PV of a receipt at time 0 is the amount of the receipt, and so to get the total PV we need to add this on.

Question 3
IRR 20%
I calculated (2400*0.833) + (3100*0.694) + (2100*0.579) + (1800*0.482) = 6234
Less 6500 = 266
Please let me know where I went wrong.

For question 3, i keep getting 0.343 for the 15% discount factor?
Also why is 0.307 and 0.2659 added together to get the IRR, isn’t 0.2659 a minus number?

Because discounting the perpetuity gives the PV when the first flow is in one years time.
In this question the first flow is immediate, and the PV of 12,000 receivable immediately is 12,000.

For Q5, currently to work out the DF for a 9 year annuity i am using the tables and adding each year e.g. for 10% 0.909 + 0.826 + 0.751 + …+ 0.424 = 5.758. However I’m finding this quite time consuming and there is the chance to enter a number incorrectly.

I was just wondering is there a formula that you can you to quickly work out the DF?

Why don’t you just use the annuity tables that are provided in the exam? Those tables do it for you!!

I do suggest that you watch our free lectures on this (and the relevant F2 lectures as well if needed, because the discounting itself is all revision of Paper F2).

In Question 5 Why is it that the cash inflow period is 3-9 years and not 3-10 years? Is it not the first receivable in 3 years and then add 7 years you get 10.
I have the same doubt in the lecture as well

There are 7 years of flows in total and the first is in 3 years time. So the second is in 4 years time, the third is in 5 years time, and so on. If you carry on counting then you will find that the last of the 7 years of flows is in 9 years time 🙂

If there are any where you do not understand the answer then do ask in the Ask the Tutor Forum 🙂
(and I do assume you are watching our free lectures – they are a complete course for Paper F9)

Justyna says

Dear John,

I do not quite understand Q4 – could you please explain why the statement ‘There is only ever one IRR’ is not correct?

And also the statement about a graph with NPV on “Y” and interest rate on “X” – wouldn’t it have a negative slope?

Thank you!

John Moffat says

For a conventional set of cash flows (i.e. an outflow followed by a series of inflows) then there will be only one IRR and there will be a negative slope.

However, if there is more than one change of sign (e.g. outflow followed by inflows followed by outflow) then there can be more than one IRR and the graph will be a curve with an upward and a downward slope.

This is one of the standard possible problems with using IRR and I do explain it in the free lecture.

Justyna says

Thank you! Now I get it 🙂

John Moffat says

That’s good 🙂

karan says

sir,

in question 3 how do you converted 266 in 0.266?

John Moffat says

I don’t know what you mean.

The NPV at 20% is -0.266. I haven’t converted anything.

(It is actually of course -266,000, and the NPV at 15% is actually +343,000, but using those figures will obviously give exactly the same answer with more messaging around)

Helen says

Please sir, can you explain question 5

John Moffat says

Have you watched my free lectures on this? (Because there is no point in attempting the tests if you have not watched the lectures!)

If you have watched the lectures then you will know that the 10 year annuity factor is the total of the discount factors for years 1 to 10.

If we subtract the 2 year annuity factor (which is the total of the discount factors for years 1 to 2), the we are left with the total of the factors for years 3 to 10, which is what we want 🙂 )

Cynthia says

i still don’t get question 1.

could you please explain it again?

John Moffat says

The discount factor for a perpetuity is 1/r (which in this case is 1/0.11).

However this gives the present value when the first receipt is in 1 years time – so 1 to infinity.

In this question the first receipt is immediate – time 0 – and then we get receipts for 1 to infinity.

The PV of a receipt at time 0 is the amount of the receipt, and so to get the total PV we need to add this on.

jacinta says

Thank you so much.

Deborah says

Question 3

IRR 20%

I calculated (2400*0.833) + (3100*0.694) + (2100*0.579) + (1800*0.482) = 6234

Less 6500 = 266

Please let me know where I went wrong.

John Moffat says

6234 – 6500 = (266), which is the same as in the ‘pop-up’ answer.

Deborah says

Thank you for all youtr help John

John Moffat says

You are welcome 🙂

hlipschutz says

For question 3, i keep getting 0.343 for the 15% discount factor?

Also why is 0.307 and 0.2659 added together to get the IRR, isn’t 0.2659 a minus number?

John Moffat says

The NPV is 0.343. It is an error and I will have it corrected.

As far as adding the two NPV’s together, the difference between + .307 and – .2659 is the two added together.

The correct answer is IRR = 15% + (0.343 / (0.343 + 0.2659) x 5% = 17.8%

hlipschutz says

Thank you so much!

John Moffat says

Thank you for spotting the error 🙂

Achilleas says

Q1: Can you please explain why you add 12,000 to 109,100 (1/0.11*12,000)? Thanks

John Moffat says

Because discounting the perpetuity gives the PV when the first flow is in one years time.

In this question the first flow is immediate, and the PV of 12,000 receivable immediately is 12,000.

Achilleas says

Thanks a lot John

John Moffat says

You are welcome 🙂

stan15 says

Q2: I got $109,100.

Why should we add the $ 12,000 to the $ 109,100. Please help.

Q3: How do you get +0.307 for NPV 15%? I got +0.343 {(-6.5) +2.088+2.3436+1.3818+1.0296}

John says

For Q5, currently to work out the DF for a 9 year annuity i am using the tables and adding each year e.g. for 10% 0.909 + 0.826 + 0.751 + …+ 0.424 = 5.758. However I’m finding this quite time consuming and there is the chance to enter a number incorrectly.

I was just wondering is there a formula that you can you to quickly work out the DF?

John Moffat says

Why don’t you just use the annuity tables that are provided in the exam? Those tables do it for you!!

I do suggest that you watch our free lectures on this (and the relevant F2 lectures as well if needed, because the discounting itself is all revision of Paper F2).

John says

Thanks, its all come back now

John Moffat says

You are welcome 🙂

Cherry says

For the third question, how is the npv at 15% and 20% calculated? I’m just not coming up with the answers.

Vineeth says

In Question 5 Why is it that the cash inflow period is 3-9 years and not 3-10 years? Is it not the first receivable in 3 years and then add 7 years you get 10.

I have the same doubt in the lecture as well

John Moffat says

There are 7 years of flows in total and the first is in 3 years time. So the second is in 4 years time, the third is in 5 years time, and so on. If you carry on counting then you will find that the last of the 7 years of flows is in 9 years time 🙂

Vineeth says

Oh alright. Thank you 🙂

John Moffat says

You are welcome 🙂

Sayem says

Wow, its a great practice for me but I always stuck on Theory based mcq’s Sir Moffat.

John Moffat says

If there are any where you do not understand the answer then do ask in the Ask the Tutor Forum 🙂

(and I do assume you are watching our free lectures – they are a complete course for Paper F9)