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Hello John,
ACCA Questions: https://www.accaglobal.co.uk/content/dam/acca/global/PDF-students/acca/p4/exampapers/P4_2012_dec_q.pdf
ACCA Answers: https://www.accaglobal.co.uk/content/dam/acca/global/PDF-students/acca/p4/exampapers/P4_2012_dec_a.pdfI’m looking at line 5 of the ACCA’s answer to Q4)a). They’ve got:
($2,500,000)+($1,200,000 x 1.11^-1) + ($1,400,000 x 1.11^-2) + $970,000 x 7.191 x 1.11^-3
and I’ve got (the last number is different):
($2,500,000)+($1,200,000 x 1.11^-1) + ($1,400,000 x 1.11^-2) + $970,000 x 7.191 x 1.11^-2As annuity payments start in year 1 (not year 0) isn’t 1 year’s discount already built into the annuity, therefore shouldn’t the discount for the starting date be reduced by 1 year (i.e. be “2” instead of “3” above)?
Thanks,
DD
If the annuity started at time 1, then using the annuity factor would give a present value at time 0.
However the annuity starts at time 4 (three years later) and so using the annuity factor gives a present value at time 3 (three years later) and so we need to discount for another three years.Hi John,
Sorry I’m confused, why are both time 4 and time 3, three years later?
DD
Read my post carefully 🙂
Time 4 is three years later than time 1 – the annuity factor on its own applies to an annuity starting at time 1.
Time 3 is three years later than time 0.
Using the annuity factor on an annuity starting at time 1 gives a value at time 0, so using the factor on an annuity starting at time 4 gives a value at time 3 (which then needs discounting for three more years to get time time 0)Hi John,
I’ve just re-read this line in the question:
“PDur05 project’s annual operating cash flows commence at the end of year four and last for a period of 15 years”Does this mean there are no cash flows in year four? And first cash flow is in year 5?
Therefore the annuity factor discounts to year 4, then a further 3 year discount takes us back to year 1 (now)
Does this sound right?
Thanks,
DesperateDan
The first year starts now (time 0) and ends in one years time (time 1). Time 0 is not a year – it is one point in time.
(So if, for example, we buy a machine on the first day of a year then that flow occurs at time 0. The revenue for the first year is always assumed to occur at the end of the year, and so that is at time 1 – it is 12 months away and therefore needs to be discounted for a year.)If the first cash flow occurs at the end of the fourth year, then it is at time 4 (4 years from now) and therefore using the annuity factor discounts it to time 3 which then needs three years more discounting to get back to a present value now.
Hi John,
Sorry I’m still confused because I think the years are offset in the quesiton (i.e. Year 1 = time 0, Year 2 = time 1 etc):
Year 1 (time 0)
Year 2 (time 1)
Year 3 (time 2)
Year 4 (time 3) Operating cashflow commences and last for 15 yearsIf the cashflows start in Year 4 (time 3) then doesn’t the annuity calculation takes us back to Year 3 (time 2), and then 2 (as opposed ot 3) more years of discounting takes us back to Year 1 (time 0)?
Thanks ,
DesperateDan
Time 0, time 1 etc are points in time – they are not whole years.
So the first year starts now (time 0) and it finishes in one years time (time 1).
The second year starts in 1 years time (time 1) and finishes in 2 years time.
and so on.Hi John,
Thank you very much for your patience! 🙂 Yes I got confused because investments are at the start of years and the positive cash flows occur at the end of years. I think the below breakdown is now correct, thank you!
Stu
start of Year 1 (time 0) – Year 1 investment
start of Year 2 (time 1) – Year 2 investment
start of Year 3 (time 2) – Year 3 investment
start of Year 4 (time 3)
end of Year 4 (time 4) – Operating cashflow commences and last for 15 years
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Hi,
It’s terrible I don’t know how to calculate annuity at 25%.
Answer is given and I still can’t figure out how it’s done, any help is greatly appreciated.
R – 25%
N- 4 yearsAnswer given – 2.362
Formula: 1-(1.25)4/.25
Please tell me the order of the buttons I need to press on my calculator.
I am sorry, I cannot help because it all depends on what calculator that you have. Many calculators use reverse Polish logic which I always find confusing 🙂
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Thank you for your reply John,
Can you please check my answer below and let me know if I have missed something,
I’ve tried 1-(1.25 * 1.25*1.25*1.25)/.25, which gives me 1-2.44/.25= 5.765.
Thank you!
Your answer is wrong.
The (1+r) on the top of the equation is not to the power n, but to the power -n (which is the same as 1/(1+r)^n
So it should be (1 – (1/1.25)^3)/0.25
This gives 1.952
(You could get the same answer by calculating the ordinary discount factors for 1 year, 2 year and 3 year and adding them up.)
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Thank you so much John!
I got the answer I was looking for
1- (1/1.25* 1/1.25* 1/1.25*1/1.25)/.25 = 2.3616
Sorry – I was doing it for 3 years.
For 4 years, your answer is now correct.
Same Question,
1) We’ve to find the AF for 4th year onwards to 15th year.
My way of doing is AF(year 1 to year 15) MINUS AF(yeat 1 to year 3), leaving us with the annuity factor of year 4 to 15. Can we use this?2) Why isnt $.97m multiplies with 12, for 12 years that the cash flows in for?
1. No – you have misread the question. It says that the flows commence at time 4 and last for 15 years. So the final flow is at time 18.
What you can do is take the annuity factor for 18 years and subtract the annuity factor for 3 years. (The answer would be slightly different but only due to rounding which does not matter for the exam.)
However, because the tables only go up to 15 years, you would have to calculate the 18 year annuity factor yourself on the calculator.2. I can’t understand why you want to multiply by 12 (or even by 15 since you misread the question). That would give the PV if there was no interest. Multiplying by the annuity factor is giving the total after accounting for interest.
Sir, could please explain me the sensitivity analysis calculation? I am
Just not able to follow itThe answer has done it in a strange way and made it over-complicated 🙂
You should be happy from paper F9 that the sensitivity is the NPV as a % of the present value of the flows that change (which in this case are the sales revenue flows).
(If you have forgotten this then watch the free Paper F9 lectures on investment appraisal under uncertainty).I assume you are happy with the calculation of the NPV of $0.381M.
The revenue flows are $4.2M a year for 15 years starting in 4 years time.
So the present value is 4.2M x 7.191 (the 15 year annuity factor) x 0.731 (the 3 year present value factor because the annuity starts 3 years late – at time 4 instead of time 1).
This equals 22.078MTherefore the sensitivity = 0.381/22.078 = 1.73%
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