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Dear tutor,
I want to ask you about this question which interpret the way to calculate annuity factor when cashflow in perpetuity. It confuses me
” A co. Receives a perpetuity of $20,000 pa in arrears, and pay 30% corporation tax 12 months after the end of the yr to which the cash flows relate. A c.o.c of 10%. What is the after tax pv of the perpetuity?”
And its answer:
Pv of perpetuity :
20,000/0.1 = 200,000Pv of tax:
20,000×30%x AF (yr2-indefinite)AF (yr2-indefinite) = 1/0.1- DF yr 1
= 10- 0.909 = 9.091( can you explain for me this formula, im not quite clearly understand about this)
Other than that it’s ok
Have you watched my free lectures (and if necessary the F2 lectures on this, because this bit is revision of F2).
The thing is that 1/r gives the present value of a perpetuity starting in 1 years time.
Here, the tax starts in 2 years time (which is 1 year later than in 1 years time), so using the 1/r gives a present value 1 year later as well, so it needs to be discounting by 1 more year in order too get a present value now. (and the factor for discount for 1 more year at 10% is 0.909).
You can either discount by 1/r and then discount by one more year (as explained above).Alternatively, you can get the discount factor for 1 to infinity (1/r) and then subtract the discount factor for 1 year (0.909) to end up with the factor for 2 to infinity.
Both ways will give the same answer – maybe a little difference because the tables are rounded to 3 decimal places, but that is not relevant for the exam and would not lose any marks.
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