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A co receives a perpetuity of $20,000 p.a. in arrears and pays 30% corp tax 12 months after the end of the year to which the cash flows relate. At a cost of capital of 10%, what is the after tax present value?
The answer is :
PV of perpetuity = 20,000 x 1/0.1 = 200,000
less} PV of tax (20,000 x 30%) x (AF 2)
where AF2= (1/0.1)- DF1 =10 – 0.909=9.091
PV of tax = 20,000 x 30% x 9.091=(54,546)
answer = 200,000- 54,546 = 145,545I understand a perpetuity is equal amounts and i understand the 1/0.1. but…..
1-shouldnt the 20,000x 30% be multiplied by 1/0.1?
OR, if it has to be multiplied by the AF, then…2- shouldn’t the present value of the 20,000 x 30% be multiplied by the annuity factor for 2 years @ a discount rate of 10% which from the tables is 1.736?
I dont understand why its done that way. Please explain & thanks in advance. I am looking at the exercises/examples in the notes but they seem a lot simpler.
The flows before tax are 20,000 a year from 1 to infinity.
You are happy multiplying this by 1/0.1 – this is the discount factory for a perpetuity that goes from time 1 to infinity.The tax flow is 20,000 x 30% = 6,000 a year. However, because this is one year later, it is from time 2 to infinity (so the discount factor is no longer simply 1/r).
1/r will give the total discount factor from 1 to infinity.
So if we subtract the discount factor for 1 year, we will be left with the total discount factor for 2 to infinity.There is an alternative way of getting it (which is what you are trying to do).
The alternative is to say that if it was 1 to infinity, then we multiply by 1/r. However, since it starts 1 year later, then to get back to the present value, we multiply the ordinary discount factor for 1 year.Both approaches give the same answer (there will be a slight difference because of rounding – the tables only go to 3 decimal places – but that is irrelevant in the exam).
I do assume that you are watching the lectures with the notes – the notes on their own are not enough. It is in the lectures that I make points such as this one.
Also, if you are still having problems then you might find the relevant F2 lectures helpful because the discounting part of it is revision of F2. In Paper F9, the discounting itself is never worth many marks – the real problem is F9 is arriving at the cash flows, and that is where most of the marks are.
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