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I’ve watched your lecture on Chapter 15 (example 7) of the notes. I have two questions related to this chapter. Please correct me if I am wrong anywhere!
[Question 1]
Omega plc has just paid a dividend of 20c per share. It is intended that the dividend will remain at 20c for each of the next 2 years and thereafter will grow at 4% per year. The shareholders required rate of return is 15% p.a.Calculate the market value per share.
[Answer 1]
Since the dividend growth model applies from Time 3 because it is the time when we have growing dividend.Dividend Growth Model:
Po = 20 (1.04) / (0.15 – 0.04)
Po = $1.89Since we have growing dividend from Time 3 onwards then the Share Price would be $1.89 in Time 2 as u said in the lecture (I have no problem until here!)
The logic behind $1.89 being MV of Share Price in Time 2 is that DVM (formula) shows Market Value of Share Price NOW by taking the future dividend which is 20 (1.04) = 20.8c
Lastly we are going to calculate MV by taking out the PV of future dividend:
PV (Time 1) = 20 x 0.870 = 17.4
PV (Time 2) = 20 x 0.756 = 15.12
PV (Time 2) = 1.89 x 0.756 = 142.88Total MV of Share Price (Time 0) = 175.4c ($1.754 ex-div)
[Question 2]
ABC has just paid a dividend of 20c per share. It is intended that the dividend will remain at 20c for each of the next 2 years and will grow at 4% per year for each of the next 2 years thereafter. The shareholders required rate of return is 15% p.a.Calculate the market value per share.
[Answer 2]
Since the dividend growth model applies from Time 3 because it is the time when we have growing dividend onwards.Dividend Growth Model:
P2 = 20 (1.04) / (0.15 – 0.04)
P2 = $1.89P3 = 20 (1.04)^2 / (0.15 – 0.04)
P3 = $1.96Lastly we are going to calculate MV by taking out the PV of future dividend:
PV (Time 1) = 20 x 0.870 = 17.4
PV (Time 2) = 20 x 0.756 = 15.12
PV (Time 2) = 189 x 0.756 = 142.88
PV (Time 3) = 196 x 0.657 = 128.78Total MV of Share Price (Time 0) = 304.18c ($3.0418 ex-div)
Thanks in advance for your time 🙂
Your answer to the first example is correct.
However you are wrong in the second example.
The dividend growth formula only applies to a dividend growing in perpetuity.
As you have typed the question, there are only dividends for 4 years (which is not logical because the company is going to have to pay a dividend at some stage).
If it were the case that there were only dividends for 4 years (but it will not be the case in the exam) then you would simply discount each of the 4 dividends at 15%.So we will only be asked in exam to calculate the MV of Share Price [at Time 0] when the dividend growth remain constant in perpetuity otherwise DVM simply will not work!
I was not able to understand what u said here “there are only dividends for 4 years (which is not logical because the company is going to have to pay a dividend at some stage)” – Can you please clear this line to me?
According to your very last line where you said that “you would simply discount each of the four dividends at 15%” then the answer would be like this:
PV (Time 1) = 20 x 0.870 = 17.40
PV (Time 2) = 20 x 0.756 = 15.12
PV (Time 3) = 20.8 x 0.657 = 13.66
PV (Time 4) = 21.632 x 0.572 = 12.37Total MV of Share Price (Time 0) = 58.55 ($0.5855 ex-div)
[We have to calculate dividend at Time 3 & Time 4 with the respective growth rate OR We don’t have to apply dividend growth here because we are not using DVM formula – which one is correct?]
In short, if we are not given dividend growth for perpetuity then we simply discount all the yearly dividends at shareholder’s require rate of return.
Please correct me If I am wrong anywhere!
The dividend growth formula is only valid when there is a contact rate of growth in perpetuity.
Your second question only has dividends for 4 years and if that were the same then your answer in your latest post is correct.
It is however not a practical question because a company will never simply stop paying dividends completely after 4 years – shareholders will be expecting there to be a dividend at some time in the future (unless they were expecting the company to close down after 4 years in which case they would be expecting some payment from the assets in the company).
Thank you! I still have a little query to ask you before I am completely sure. I hope you don’t mind asking me this long query neatly!
[Question – non-constant dividend]
If the company has dividend growth of 3% for two years & then the growth for a further two years would be 4% thereafter. The shareholders required rate of return is 15% p.a.[Answer]
Since there is a non-constant dividend then the MV of Share Price will be calculated by simply discount each of the yearly dividends at 15% at shareholders rate of return. (as you said – it is correct)
______________________________________PV (Time 1) = 20 x 0.870 = 17.40
PV (Time 2) = 20 x 0.756 = 15.12
PV (Time 3) = 20.8 x 0.657 = 13.66
PV (Time 4) = 21.632 x 0.572 = 12.37Total MV of Share Price (Time 0) = 58.55c ($0.5855 ex-div)
______________________________________BUT if there is a constant dividend growth then the MV of Share Price will be calculated using DVM formula at the time when the dividend growth remains constant in perpetuity such as:
[Question – constant dividend]
If the company has paid a dividend of 30c per share. It is intended that the dividend will remain at 30c for the next 3 years but it will grow at 4% per year thereafter. The shareholders required rate of return is 15% p.a.[Answer]
Dividend Growth Model:
P3 = 30 (1.04) / (0.15 – 0.04)
P3 = $2.83
___________________________PV (Time 1) = 30 x 0.870 = 26.10
PV (Time 2) = 30 x 0.756 = 22.68
PV (Time 3) = 30 x 0.657 = 19.71
PV (Time 3) = 283 x 0.657 = 185.931Total MV of Share Price (Time 0) = 254.421c ($2.54421 ex-div)
___________________________Now, my question is that why the Market Value of Share Price using DVM is quite higher when there is constant dividend growth in perpetuity as compared to the MV of Share Price in non-constant dividend growth which is quite smaller!
Difference would be : 254.421c – 58.55c = 195.871
Is this true that in non-constant dividend growth, there is only 4 yearly dividends therefore the MV of Share Price is quite smaller.
BUT in constant dividend growth in perpetuity, there are many years dividends therefore the MV of Share Price eventually quite higher.
Thanks for your patience 🙂
The share price is the PV of future expected dividends, and therefore if they are expected dividends to continue in perpetuity then the share price will be higher than if they were only expecting dividends for 4 years.
However, I repeat, the first example in your latest post is not practical and could not happen in the exam. Shareholders are never going to expect that there will be dividends for only 4 years and that they will then stop completely. It just cannot happen.
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