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Dear Sir:
Last December exam, Q4(a) asked for calculating the NPV of PDur05.
The suggested answer is:
When calculating the PV of “the operating cash inflows commencing at END of year FOUR and last for 15 years”. The suggested answer is: $970,000 x 7.191 x 1.11^(–3),
BUT I think it should be: $970,000 x 7.191 x 1.11^(–4), because the cash flow starts at the END of year 4, not START of year 4.
Furthermore, if my opinion is correct (I do think so!), then the total NPV should be negative which will be -$122,000, not the suggested $383,000.
Could you please have a quick review on this question?
Thanks a lot for your time!
His answer is correct.
The reason is this…….
If the first flow had been at the end of the first year (i.e. time 1) then you would simply have used the annuity factor (7.191) and it would have given the present value (i.e. the amount now).
However, instead of starting at time 1, the annuity starts at time 4 – i.e. three years later. This would mean that multiplying by the annuity factor would give the present value three years later i.e. at time 3.
So we need to discount an extra 3 years as he has done.
Thank you very much sir for your reply! But my point was not at the annuity factor (7.191, and I understand that thoroughly).
My arguement is the Present Value factor he used on calculating “the operating cash inflows commencing at END of year FOUR and last for 15 years”. I think, the PV factor should be 1.11^(-4), not 1.11^(-3) he used. The reason is the cash flow starts at END OF YEAR 4, not BEGINNING of YEAR 4!!
THERE SHOULD BE ANOTHER ONE YEAR From beginning of year4 till end of year4!
Thats my point. Please give a consideration and thank you for your time!!
Plus:
Simply saying, the annuity should be discounted an extra FOUR years not 3 years as he has done, coz the cash flow starts at END of year 4, not beginning of year 4!
Cheers again.
I do realise what you were asking, and my answer (and the examiners answer) is correct.
‘Now’ (time 0) is the beginning of the first year. The end of the first year is 1 year from now (time 1).
If the annuity started in 1 years time (the end of the first year) then simply multiplying by the annuity factor would give the present value – the amount now at time 0.The annuity actually starts at the end of the 4th year – i.e. 4 years from now – time 4.
This is three years later than a ‘simple’ annuity (it starts at the end of the 4th year (time 4) instead of a the end of the 1st year (time 1).
Therefore we need to discount for an extra 3 years to get the present value.
There should NOT be another year!
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