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A company receives a perpetuity of $20000 per annum in arrears, and pays 30% corporation 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 of the perpetuity?
Please do not simply set test questions and expect me to provide an answer. You must have an answer in the same book in which you found the question, so in future ask about whatever it is in the answer that you are not clear about and then I will explain.
The cash flows are:
1 to infinity 20,000
2 to infinity. (6,000) (30% x 20,000)There are several ways of arriving at the same answer.
The most efficient way is to say that the PV of the 20,000 is 20,000 x 1/0.1 = 200,000.
The tax flows are 30% of the inflows, but all 1 year later. So the PV of the tax flows will be 30% of the PV of the inflows, discounted for 1 year.
So the PV of the tax flows is 30% x 200,000 x 1/1.1 = 54,545Therefore the PV of all the flows is 200,000 – 54,545 = 145,455.
If you are unsure about the discounting then do watch my free Paper FM lectures – they are a complete free course for Paper FM and cover everything needed to be able to pass the exam well. If needed, also watch the free Paper MA lectures on discounting, because this is revision from Paper MA.
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