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Dear John, here’s a question that I don’t understand…
Question – BPP Revision Kit 111
A company receives a perpetuity of $20,000 per year 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?It says the perpetuity is received ‘per year in arrears’, so I calculate the perpetuity from the second year using 20,000*(1/0.1-DF1), believing that ‘in arrears’ means the perpetuity will be delayed to the next year. However, the answer calculates the perpetuity from the first year, using 20,000*1/0.1. I don’t understand why. Could you please explain this? Thank you!
For discounting, cash flows occur at points in time that are one year apart.
Time 0 (“now”) is the start of the first year.
Time 1 is 1 year from ‘now’ and is the end of the first year / beginning of the second year.
Time 2 is 2 years from’ now’ and is the end of the second year / beginning of the third year
and so on,
Here, the $20,000 is received in arrears, i.e. at the end of each year. So the first receipt is in 1 years time.
(Had the $20,000 been receive in advance i.e. at the start of each year, then the first receipt would be at time 0 )Make sure you are clear about the way the timing works, because getting the timings correct in the exam is where the problem often lies – the discounting itself is easy 🙂
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