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Question related to delayed perpetuity.
A perpetuity of $2000 starting in 6 year’s time, growing at 3% per annum. Interest rates are 10%
1- ? Growing Perpetuity factor @10% = 14.286 i.e.[1/(0.1-0.03)]
Less: 1-5 annuity factor @10% = 3.791So,14.286 – 3.791=10.495
$2,000×10.495= $20,990The answer in the book is $17,741.
Could you please tell me where am I wrong.
I’m also confused with delayed Perpetuity which grows at specific rate of interest per annum.What you have done would effectively be assuming that it was $2,000 at current prices and so would be 2,000 x 1.03^6 by the time of the first flow. This is not the case because the first flow is an actual $2,000.
Using the perpetuity factor of 14.286 gives a PV of 28,572.
However this would be the PV now if the first flow was in 1 years time.Since the first flow is in 6 years time (i.e. 5 years later than in 1 years time), the 28,572 is the PV in 5 years time.
To get the PV now, we therefore need to discount for 5 years at 10% p.a., which then gives a PV of $17,741.
The most likely place for this to be relevant in the exam is the valuation os shares from the future dividends, and I do work through several examples like this in my free lectures.
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