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Examiner ‘s report F9 March 2016 has the following question:
Cant Co has a cost of equity of 10% and has forecast its future dividends as follows:Current year: No dividend
Year 1: No dividend
Year 2 :$0.25 per share
Year 3: $0.5 per share and increasing by 3% per year in subsequent years
What is the current share price of Cant Co using the dividend valuation model?
A. $7.35
B. $5.57
C. $6.11
D. $6.28
The answer give the share price = (0.826*0.5)/(0.1-0.03)+0.826*0.25=$6.11 per share, which is C.I think, this question is quite frustrated, as the price should be evaluated using both DGM (dividend growth model) and DVM (dividend valuation model), and the share price should be =(0.751*0.5*(1+0.03))/(0.1-0.03) + 0.25*0.826= 5.73$ as the dividend is growing at the rate 3% per year since year 3 so first the annuity should be discounted to year 3 before discounted to the current year. So the correct answer should be $5.73. No answer is correct!
Please help me verify the answer!
Thank you!The dividend growth model and the dividend valuation model are actually the same thing – the formula is simply calculating the PV of a growing dividend 🙂
However, the problem is the 0.50 per share growing at 3% per year.
If it had been the case that the current dividend was 0.50 growing at 3%, then it would mean that the first dividend would be at time 1 and would be (0.50 x 1.03) and the formula would give the PV at time 0. (The Do (1+g) in the formula is the dividend in 1 years time)Here, the first dividend is 0.50 and is in 3 years time, which is 2 years later than in 1 years time.
Therefore using the formula means using 0.50 instead of Do(1+g), and the result from the formula will be PV two years later as well – i.e. at time 2 instead of at time 0.
We therefore need to take the result from the formula (0.50 / (0.1 – 0.03) and discount it for 2 years to get a PV now, by multiplying by the 2 year discount factor which is 0.826.I understand the idea in the question, but to be accurate, the share price should be =(0.751*0.5*(1+0.03))/(0.1-0.03) + 0.25*0.826= 5.73$. The share price in the answer = (0.826*0.5)/(0.1-0.03)+0.826*0.25=$6.11 should only be roughly approximate and to be the best answer in 4 options. If this is not a multiple choice question, the answer should be $5.73
No – the answer is perfectly correct and is not a rough approximation.
In the formula, the Do(1+g) is the next dividend which is the dividend in 1 years time. and the formula gives the PV at time 0.
In this question we know the dividend in 3 years time, and it is 0.50 – not 0.50(1.03) and so using 0.50 as the numerator in the formula gives a PV in 2 years time. This then needs discounting for 2 years to get the PV now.
(If you find it easier to understand, then you can do it another way and get the same answer. If I told you that we had just paid a dividend of 0.50, then you would get the PV now by 0.50(1.03)/(0.10-0.03) = 7.357 this would be the PV of dividends from time 1 onwards.
Now jump forward 3 years, and suppose again we have just paid a dividend of 0.50. If we then use the formula we would still get 7.357 as the PV in 3 years time, and this would be the PV for dividends from time 4 onwards.
So now you have a dividend of 0.25 in 2 years time, a dividend of 0.50 in 3 years time, and a PV of the dividends from 4 years onwards as 7.357 in 3 years time.
The PV of these is (0.25 x 0.826) + (0.50 x 0.751) + (7.357 x 0.751) = $6.11)
Obviously do it whichever way you find the easiest to follow, but make sure you do get it sorted because in recent years the examiner has asked this sort of question many times.
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