Q4 Dec 2012: Arbore Co

You are wrong I am afraid. If there is an annuity starting from time 1, then the annuity factor gives a present value at time 0. Here, the annuity starts at time 4 (3 years later than time 1) and so it gives a value at time 3 (3 years later than time 0). So we need to discount by another 3 years to get back to time 0.

just make it a clear of "end of year four" and "at year four" By the table provided by them, from year one to year three are all "at the start" of each individual year. If they say, operation cash flow come from year four, we could assume "at the start" of year four as consistence. If it was "at the start" of year four, which is same as "at the end" of year three and discount rate of 1/1.1^3 is correct. However, it is "end of year four", not "start of year four".

No - we assume that operating flows (sales revenue; expenses etc) occur at the ends of years unless we are told differently. So for example sales revenue for the second year occurs at the end of the second year - i.e. in 2 years time. Time 2. I think you are confused about what I wrote in my previous reply. If there are flows occurring from T1 to T5 (for example) then to get the present value you multiply by the 5 year annuity factor - that gives you the present value, i.e. the equivalent amount now (time 0). However, if the flows are from T4 to T8 (so still 5 years of flows, but everything is 3 years later (T4 is three years later than T1; T8 is three years later than T5), then multiplying by the 5 year annuity factor will give you an equivalent amount 3 years later than before (so an equivalent amount at T3 instead of T0). So....to get back to a present value now we need to discount by 3 more years. (I hope that now makes sense, but if not then the free lectures on discounting for F2 and F9 will help you more.)

I understand the rule but just have one point we should focus. " at the end of year four" is entirely different to "at the start of year four" which are used by the answer. The Answer and your explanation are all concerned as "at the start of year four"? But the question quoted that is "at the end of year four" "At the end of year four": discounted at 1/1.1^4 WHILE "at the beginning of year four": discounted at 1/1.1^3 (as chose by you and examiner) This is only one i confused.

You have not read my previous reply properly. Using the annuity factor will discount flows starting from time 1 to time 0. Using the same annuity factor will therefore discount flows starting at time 4to time 3. So we then need to discount by another 3 years to get back to time 0. (Again, if you are still unsure then you do need to watch the Paper F2 lectures on discounting)

I am sure that both you and the answer make a link from "start of time 1" -> time 0 to "start of time 4" -> time 3 discounting. That true in principle. But in this case, that is not "start of time 4", it is "at the end of time 4". Any way, this is the only case i did not agree about discounting factor from both paper F5, F9 or P4. And it is likely that i can not make a change here. So, we should stop. For all of your supports, many thanks Mr. John :)

You are still misreading what I have written. There is no such thing as "start of time 1". Time 1 is one year from now - it does not have a start or an end. The first year starts at time 0 and finishes at time 1. We assume flows occur at the ends of years, and so the first years flows occur at time 1. When we discount flows starting at time 1 using the annuity factor it gives us a present value at time 0. So if the flows start 3 years later (and three years later than time 1 is time 4 - the end of the 4th year), then using the annuity factor gives us a present value 3 years later as well i.e. at time 3 instead of time 0. Therefore we need an extra 3 years discounting.

Mr. John: "You are still misreading what I have written. There is no such thing as “start of time 1?. Time 1 is one year from now – it does not have a start or an end." the different here :). The question clearly stated " at the start of year 1" (as your Time 1), and "at the end of year four" (as your time 4) :D. Anyway, i do not wish waste your time any more, Mr. John :D. Many thanks for your so enthusiasm and supports so far :)

The first year starts now (time 0) The fourth year ends in 4 years time (time 4) Anyway, I will leave it at that, and you are welcome :-)