# Investment Appraisal Discounted Cash Flow – Annuities and Perpetuities

1. Dear John Sir,

In this Annuity Lecture , why you have removed the 1-3 years although we know that the first Receivable would be in Year 4 and last would be in Year 13 so I am little confused that why the 1-3 years are removed .

• says

The 13 year annuity factor is the total of the discount factor from years 1 to 13 inclusive.

We want the total factor for years 4 to 13, so we need to remove the total for years 1 to 3, i.e. the 3 year annuity factor.

• says

The lecture is working fine. Have you checked the technical support page? The link to it is above.

• says

Hi Hailu, the video works for me. The problem could be the internet browser you are using. You may consider a different internet browser (firefox, google chrome, operamini, etc)

Thanks.

2. says

Dear Opentuition team,
the video is not being seen in my computer.

Regards
Henok Hailu
ACCA Student

3. says

Dear John,
You really make the problems look easy. All credit to you. Your explanations are very concise and to the point. Thank you so much.

• says

Yes – I make this clear in the very first lecture for F9!!!!

You get given the present value tables, the annuity tables, and a formula sheet

4. says

Thank you so much Mr Moffat. YOu are an amazing teacher . Everything makes so much sense now and in fact I have gone from hating this paper to loving it. Open tuition thank you.

5. says

Just a doubt… Are we marked per step for our answers when it comes to sums ??

6. says

I think the interpretion on Qn 5 pg 40 is wrong:Look at how i think it should be counted and end of the tenth year would year 14 and not 13
Receivable in 4 years time:
year 1 2 3 4 5 6 7 8 9 10 11 12 13 14
There after for total 10 years 1 2 3 4 5 6 7 8 9 10
Am i correct to think this way????
Thanks
Ac

• says

Question says the “first recieable in 4 years”.ie it assumes the first reciept is by the end of fourth year,and follows until 10th year completes.

• says

I know that the wording may confuse, but it is likely wording in the exam.

The first receipt is in 4 years time – time 4 – and there are 10 receipts in total (not 10 receipts in addition).

So for 10 receipts in total, the receipts are at times 4 5 6 7 8 9 10 11 12 and 13.

7. says

hi, john. trying to calculate the answer to Q7 on page 41 by using the other method, and the answer was different. the way i’ve done it was: if there will be receiveables from year 5 to infinity, then on year 5 the discount factor will be:
1/0.05 x 0.784= 15.68 . i agree the way that have been shown in the vid is less confusing and if i was right then the figures should be the same. can you help, please? thank you!

• says

The formula 1/r is the discount factor for perpetuities.
So if you assume receivables happen from time=0 to time=infinity, the discount factor for this example is 20, and the present value of 18,000 annually in perpetuity is 18,000×20 = 360,000. (This means if you put 360,000 in the bank now you will get 18,000 every year)

The only thing you are left with now, is to remove years 1-4.
You can do this by removing each year individually (by multiplying 18,000 by the 1,2,3 and 4 year discount rate in the present value table) or by removing years 1-4 in one lump sum by multiplying 18,000 by the discount rate in the annuity table for year 4.

The Annuity table is simply the present value table, summed to include all preceding years.

In this example…
Year 1 discount factor = 0.952
Year 2 = 0.907
Year 3 = 0.864
Year 4 = 0.823

Because net cash flow is the same each year (18,000), instead of multiplying 18,000×0.952, and 18,000×0.907, and 18,000×0.864 and 18,000×0.823, we can instead say that it is the same as 18,000x(0.952+0.907+0.864+0.823) = 18,000 x 3.546.

So the answer would be (18,000 x 1/0.05) – (18,000 x 3.546).

• says

y10829

I may be mistaken, but lukedavidizard seems to be just repeating what is in the video lecture!

The approach that you are trying to take is fine, but you have made one error.

The discount factor for a perpetuity is certainly 1/r, and if the perpetuity started in 1 years time then this would give the present value (the amount now).
However, the perpetuity starts in 5 years time, which is 4 years later. So multiplying by 1/r would give a value 4 years later – i.e. at time 4. To get back to the present value you would then need to multiply by the ordinary discount factor for 4 years (not 5 years as you have written).

If you do this then you will get the same answer. (In fact it will probably be a little different, but this will be simply due to rounding and does not matter).

• says

thank you, john. i understand now!

8. says

Hi please tell me how to get the percentage figure 0.870, 0.756…., cos my calculator give me the different figure. Please help! Thank you.

• says

hasanali95 is correct – since you are given tables you do not need to calculate.
However, I would try and sort out your calculator – you will need to do other things with it even though you will not need to calculate the discount factors (which are not percentages by the way!)