Share valuation using the Discounted Dividend / Gordon Growth model
Posted: September 23rd, 2018, 10:01 am
One of the share valuation models that I've recently looked at is called the Discounted Dividend Model, which may well also be known as Gordon's Growth Model. It works by assuming that a share's current worth is that of the sum of all of the discounted dividends received in perpetuity.
I did spend some time subsequently looking the derivation and also at a worked example using Marshalls Plc (MSLH).
That aside, it strikes me as an odd valuation model since it is obviously useless for stocks which don't pay dividends, and at first glance seems odd to suggest the behaviour of the stock is to be modelled forever, i.e. in perpetuity.
The Gordon model, briefly is as follows:
where Dn is the present value of the dividend received n years after the share's purchase.
The PV of Dn, is best approached by looking at the dividend which will be received after the first year. To establish this figure the model assumes a growth rate to the dividend payouts (this is where I start to struggle with the model, because I can't conceive a company which sustainably pays divs which grow faster than inflation, it seems more realistic to have a model that can end the projection at a point where estimation reliability falls, but I'm content to park those thoughts presently).
So if the last year's div was D0 then the future value of the next year's div (D1) will be:
hence the model has us assume a rate, 'g' at which the dividends are imagined to grow each year.
However, to make the value of future dividends seem consistent with the current day, they need to be discounted, using a discount rate r.
So the first year's dividend payout is assumed to have a present worth of:
If the calculation for the above first year's div is repeated in perpetuity, which is what the wiki derivation does, then we arrive at the formula for the share's estimated value:
I'm planning on looking at an example of this model later on using Marshalls as an example. But for now I'm finishing this post with another link, which describes how to assign possible values to discount rate mentioned above.
M&M
I did spend some time subsequently looking the derivation and also at a worked example using Marshalls Plc (MSLH).
That aside, it strikes me as an odd valuation model since it is obviously useless for stocks which don't pay dividends, and at first glance seems odd to suggest the behaviour of the stock is to be modelled forever, i.e. in perpetuity.
The Gordon model, briefly is as follows:
Share price today P = D1 + D2 + ...... + Dn + ....
where Dn is the present value of the dividend received n years after the share's purchase.
The PV of Dn, is best approached by looking at the dividend which will be received after the first year. To establish this figure the model assumes a growth rate to the dividend payouts (this is where I start to struggle with the model, because I can't conceive a company which sustainably pays divs which grow faster than inflation, it seems more realistic to have a model that can end the projection at a point where estimation reliability falls, but I'm content to park those thoughts presently).
So if the last year's div was D0 then the future value of the next year's div (D1) will be:
D1 = D0(1 + g)
hence the model has us assume a rate, 'g' at which the dividends are imagined to grow each year.
However, to make the value of future dividends seem consistent with the current day, they need to be discounted, using a discount rate r.
So the first year's dividend payout is assumed to have a present worth of:
D1 = D0(1 + g)/(1 + r)
If the calculation for the above first year's div is repeated in perpetuity, which is what the wiki derivation does, then we arrive at the formula for the share's estimated value:
P = D0(1 + g)/(r - g)
I'm planning on looking at an example of this model later on using Marshalls as an example. But for now I'm finishing this post with another link, which describes how to assign possible values to discount rate mentioned above.
M&M