Discounting, Annuities, Perpetuities – ACCA Management Accounting (MA)
Reader Interactions
Comments
Leave a Reply
You must be logged in to post a comment.
Free ACCA & CIMA online courses from OpenTuition
Free Notes, Lectures, Tests and Forums for ACCA and CIMA exams
20% off ACCA & CIMA Books
OpenTuition recommends the new interactive BPP books for September 2025 exams.
Get your discount code >>
Hi John.
For example six I used the formula 1200/(1.13^12) and I ended up with 276.8 as opposed to the answer when using the table of 277.2.
I understand that if working to the nearest dollar that this would not make a difference – but is this coincidence? Should I always opt to use the table despite working faster with the calculator just to be safe?
Hi sir, so the answer of Example 8 would be 1000*4.959 = $4959?
Sorry it’s discussed in the lecture, no need for a reply. Thanks!
Sir , First we calculate perpetuity and then the 5000 added to 41667 is this right ?
It is if the first receipt is immediate. This is because the perpetuity discount factor discounts flows starting in 1 years time.
Example 6
I’m confused, we had to calculate the present value of $2500 after 12 years at a rate of 13%. And in accordance to what I have been learning the formula is as thus; PV=FV/(1+r)n
Therefore the workings would be as follows: PV=2500/(1+0.13)12 =2500/(1.13)12
which would be equals to $576.76 but you, sir used 1200 which would be 276.85 present value.
How did we arrive at $1200 but yet the example stated a $2500 figure? Is that I was not paying attention or a mistake at your end, sir?
The example in the notes asks for the PV of 1200 a year – I don’t know where you got 2500 from 🙂
Think in the video lecture, the lecturer says 2500 – but means to quote the example from the notes which is 1200 🙂
Excellent lectures in general though!!
Hi John,
In the receivables example, I got 276.85 calculating it manually (not using the table) – it reconciles back better than your answer.
You got your discount rate from the table. Why is it slightly different? My manual discount rate was 0.230
If both answers aren’t the same – which one should I use in the exam? Thank you
As I do explain in the lectures, the tables are rounded to three decimal places which can often make a small difference. In the exam this is not a problem because questions ask for answers to (for example) the nearest thousand in which case the rounding is not relevant.
Sir, Is 500 a cash inflow or outflow that you have done in the annuity question? Are we investing 500 p.a or receiving it p.a.
Hi John! Could you please explain why is putting $2484 in the bank now better than receiving $500 each year for 8 years?
It isn’t better. It is the same because with interest at 12% we could put $2,484 in the bank now and be able to take out $500 per year for 8 years.
Hello Sir, This is probably a silly question but in the workings for annuities example 8 where do you get the 12. (4-12). I don’t get it.
Thank you!
The first receipt is at time 4. If you count for a total of 9 receipts (including that at time 4) then you find that the last receipt is at time 12.
Right. Got it now. Thank you, very much.
You are welcome 🙂
From practice question: What is the present value of $6,000 per annum first receivable immediately, and thereafter in perpetuity with an interest rate of 9.5% per annum? Can you explain too me why did we add the $6,000 to the total of $63,158 which gives us a grand total of $69,158 and we did not add the $5,000 in example 9?
Using annuity factors is for equal annual flows that start in 1 years time.
If there is $6,000 receivable immediately, then this is not dealt with by the annuity factor, and so it needs adding on (and obviously the PV of 6,000 is 60,000 🙂 )
Thank you!
Hi,
With example 7, why would you not just do 500/1.12= ÂŁ446.42 (8 times)?
If its 8 separate ÂŁ500’s each year with 12% interest each time, why isnt the total PV not 446.42*8= ÂŁ3571?
Is the interest or 500 changing each year? or are they 8 * 500 separate payments each year?
They are 8 separate payments. The receipt in 1 year is discounted to remove 1 years interest. The receipt in 2 years is discounted to remove 2 years interest, and so on.
Lovely lecture and explanation.
Sir, in the formula for Perpetuity, what does “A” stand for (A/r).
Secondly, I would like to thank you for the logics behind every formula.
Lastly I would like to thankyou for the easy annuity formula you provided (when the receipt starts from between the years), and it’s easy logic. Because the formula provided in my institute book is more complicated.
Your class is like our Emergency S.O.S class lol.
If it wasn’t for my discovery of you and the Kaplan Text books, that I came across by God’s grace, I dread to imagine the quality of progress today.
A is the equal annual amount.
Apart from perpetuities it is not so common to need the other formulas – for most question it is more sensible to use the tables provided.
How is equal annual amount = 1 ?
I was referring to the formula where we minus the annuity factor of the last year with the annuity factor of the year we wish to remove from the calculation, and then multiply this balance of this difference with the FV, to obtain the PV.
ie the simple formula you used in the video using the Annuity tables.
Dear Sir,
Q1) when calculating annuity in Ex.7 of $500 every year. If in 2nd yr $500 additional is added, why should we not total the first year $500 and this second year $500, and then calcluate present value of this total ? {in regards to when you were using the Pv table and not Annuity table).
Q2) The PV answer that you got $2484 for Ex.7, is it possible to reverse calculate and show the working how it gets broken into FV $500 per year for 8 yrs @12% interest p.a ?
hi John, I now know the answer no need to reply, if the perpetuity is paid immediately then we add the initial payment but if it is paid in 1 year’s time then we dont add it on. Thank you
Correct 🙂
hi John, on the perpetuity question in the mock exam, $41667 do you add the 5000 on top or just $41667 is the correct answer. I have seen the mock question which appears to add the investment amount.
In the mock question the money is receivable immediately whereas in the lecture question the money is receivable after the first year
That is correct 🙂
Sir, I wonder if you deposit $41667 in ex-wife’s account so as to fulfill the condition of $5000 a year, then she will receive both principal $41667 and interests $5000. Why don’t u keep it in your account and just give interests to her each year despite you don’t want to make contact.
I mean using above method, she will be received beyond the condition, which is just $5000 a year.
I did not say that I would put the money in her account. I would put it in a separate account which would generate the interest for ever.
Hello John thank you for the lecture, have you ignored the Advanced annuities and perpetuities (Some regular cash flows may start now (at T0) rather than in one years’ time (T1). and Annuities/Perpetuities in arrears (Some regular cash flows may start later than T1). or they are out of exam syllabus? Please kindly clarify!
Can someone send me the table for discounted factor ?
The tables are printed in our free lecture notes (you can download the notes free of charge).
Hi John, I wanted to know if we can find example no 8 through the formula for present value or can we only solve this example using the present value annuity table.
You can do it either way, but it is obviously quicker to use the annuity tables when it is an equal cash flow each year.
In the formula,what value will we take for number of years.Will it be 9 or 12?
Because I don’t seem to be the getting the answer using either of it as number of years in the given formula.
You use the annuity factor for 12 years less the annuity factor for 3 years – just as I explain in the lecture.
Whether you get the factors from the tables or you calculate them yourself using the formula doesn’t matter, but it is ridiculous to use the formula when you are given the annuity table in the exam.
I have no idea how to write 800 X 1/(1.1)to the power of 4 in a calculator. What am I missing?
It depends on what calculator you have. It will explain in the manual (and if you have lost the manual then you can find it by typing the model number into Google).
However, for 4 years at 10% it makes more sense to use the tables provided in the exam anyway (and I explain how to use the tables in the lectures).
use ^ as a power of any number.
Hope you did.