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Kindly help with this question John. I will ask some questions afterwards because the answer seems confusing.
Target paid a dividend of $250,000 this year. The current shareholders of companies in the same industry at target is 12%, although it is expected that an additional risk premium of 2% will be applicable to target, being a smaller and unquoted company. Compute the expected valuation of target, if the dividend is expected to grow at a 3% rate for 3 years and 2% afterwards.
You discount the future dividend stream at 14%.
The future dividend stream is:
1 250,000 x 1.03
2 250,000 x 1.03^2
3 250,000 x 1.03^3
and thereafter 250,000 x 1.03^3 growing at 2% per annum.
The first three flows you discount in the normal way using the discount tables.For the flow from 4 to infinity you use the dividend valuation formula and then discount the answer for 3 years – I explain exactly how to deal with this in my free lectures on the valuation os securities.
The lectures are a complete free course for Paper FM and cover everything needed to be able to pass the exam well.
Thank you for your answer John. The way you explained it is different from what I am seeing in the text. In the text, they multiplied the dividend at period 4 (279k) by an “annuity to infinity”. This annuity to infinity formula was = 1÷(ke-g) = 1÷ 0.12 = 8.333.
279k × 8.333 = $2,325k, which was then discounted at 14%. Year 3 was used to discount the PV from year 4 onwards.
Then it became 2325k × 0.675 = 1569
226+205+185+ 1569 = $2,185k. (Expected valuation)Now my questions are:
Where did they get the annuity to infinity formula? Why not just do it like this:
250,000 (1.02) ÷ 0.14-0.02. This is the real dividend valuation formula you used in the OT video.Secondly, in discounting the PV, why did they use discount factor for period 3 (0.675) instead of period 4 (0.592). Since the dividend is supposed to grow after year 3?
But the answer you give from your book is exactly the same as what I wrote in my previous reply, and is the way I do it in the lecture!!!!
There is no ‘annuity to infinity formula’ – it is the dividend valuation formula that is given on the formula sheet.
The dividend in 3 years time is 250,000 x 1.03^3 = 273,182.
From time 4 onwards this is inflating at 2% per annum.So putting it in the formula gives a PV = (273,182 x 1.02) / (0.14 – 0.02) = 279K / (0.14 – 0.02).
The dividend valuation formula gives the PV now (time 0) when the first dividend is in 1 years time. Here, the first dividend is in 4 years time, which is 3 years later, and so the PV resulting is also 3 years later (i.e. at time 3 instead of time 0) and therefore needs discounting for 3 years to get the PV now.
Again, I explain this in my free lectures.
Thank you for your time and explanation. I alternatively got 279k by multiplying 273k by 1.02. I hope that this is valid.
Thank you again.
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