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Hi John,
I have a question to the following BPP question:
Masco Co is expected to pay a dividend of $0.60 for the next three years after which it is
expected that the dividend will grow by 4% per year. Musco Co’s cost of equity is 10%.
What is the dividend valuation of Masco Co’s shares?
The correct answer is: $9.30.
Present value of dividends from time 1-3 = $0.60 x 2.487 = $1.49
Present value of dividend from time 4 onwards = $0.60 x 1.04/(0.10 – 0.04) x 0.751 = $7.81 – Total = $1.49 + $7.81 = $9.30.Why do I have to use PV DF10% for Y3 and not Y4 (0.683)?
Many thanks in advance!
JennyThe dividend valuation formula gives the market value ‘now’ (time 0) when the first dividend is in 1 years time.
If the first dividend is in 4 years time, then it is 3 years later than in 1 years time, therefore it gives a MV three years later – time 3 instead of time 0. So we need to discount for 3 years to get the value now.
Sorry to be a pain, John – the timings really confuse me 🙁
So, basically the question is “what is the mv of all expected dividends for the next 4 years?” / “how much are theses future dividends worth ‘now’ “? Correct?
First dividend will be in Y1 = 0.6×1/1.10 = 0.55
Second in Y2: 0.60 x 1/1.10^2 = 0.50
Third in Y3: 0.60 x 1/1.10^3 = 0.45
And then the forth incl. growth of 4% = 0.60 x 1/1.10^4 = 0.41 x 1.04 / (0.10 – 0.04) = 7.10That’s how I understand it. or alternatively:
First dividend will be paid in Y0 = 0.60
Second in Y2: 0.6×1/1.10 = 0.55
Third in Y3: 0.60 x 1/1.10^2 = 0.50
And then the forth incl. growth of 4% = 0.60 x 1/10^3 = 0.45 x 1.04 / (0.10 – 0.04) = 7.80But neither is correct. I’m sorry to bother you with something that is probably so simple, but I just don’t get it ?
The question is asking for the MV of the expected dividends for ever – not just the next 4 years.
First dividend will be at time 1 = 0.6×1/1.10 = 0.55
Second at time 2: 0.60 x 1/1.10^2 = 0.50
Third at time 3: 0.60 x 1/1.10^3 = 0.45What you have done there is correct (although it would have been quicker to use the 3 year annuity discount factor at 10% !!!
For the dividends from time 4 onwards, we use the dividend valuation formula:
0.60 x 1.04 / (0.10 – 0.04) = 10.4
However, the dividend valuation formula gives the present value of the dividends when the first dividend is in 1 years time. Here, the first dividend is in 4 years time, which is 3 years later. So the answer of 10.4 is the PV in 3 years time. Therefore we need to discount the 10.4 for 3 years at 10%, which is 10.4 x 1/1.1^3 (although again it would be more sensible to use the tables provided!!!) = 7.80
Therefore the total MV = 0.55 + 0.50 + 0.45 + 7.80 = $9.30
I do suggest that you watch my free lectures on the valuation of securities, because I do go through a similar example and explain.
(The lectures are a complete free course for Paper F9 and cover everything needed to be able to pass the exam well.)Ah, thank you so much!!! Really appreciate your quick reply!
I have watched all your lectures already, but will re-watch this one.
Thanks for all your help 🙂NOT SURE WHERE YOU GET 9.30 , It could well be right , but see below – this is how i would calculate and i get 8.81 – Any one able to comment
CF DF at 10% NPV
Y1 0.6 0.090 0.0540
Y2 0.6 0.826 0.4956
Y3 0.6 0.751 0.4506
Y3 (End) 10.4 7.8104
8.8106For 4 years onward, we are calculating at the end of Y3
60(1.04) 62.4 1040 Cents or 10.40
0.1-0.04 0.1-.04Corrected Y1 DF
CF DF at 10% NPV
Y1 0.6 0.909 0.5454
Y2 0.6 0.826 0.4956
Y3 0.6 0.751 0.4506
Y3 (End) 10.4 7.8104
9.3020For 4 years onward, we are calculating at the end of Y3
60(1.04) 62.4 1040 Cents or 10.40
0.1-0.04 0.1-.049.3 is correct, you need to discount Y4 10.4 0.751 7.8
see John’s answer:
“The dividend valuation formula gives the present value of the dividends when the first dividend is in 1 years time. Here, the first dividend is in 4 years time, which is 3 years later. So the answer of 10.4 is the PV in 3 years time. Therefore we need to discount the 10.4 for 3 years at 10%, which is 10.4 x 1/1.1^3 (although again it would be more sensible to use the tables provided!!!) = 7.80”Therefore the total MV = 0.55 + 0.50 + 0.45 + 7.80 = $9.30
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