## Sunday, 30 April 2017

### Dividend Discount Model

Dividend Discount Model

Where:
V = the value
D1 = the dividend next period
r = the required rate of return

1.  One year holding period

If our holding period is just one year, the value that we will place on the stock today is the present value of the dividends that we will receive over the year plus the present value of the price that we expect to sell the stock for at the end of the holding period.

Present Value of the dividends that we will receive over one year

Present value of the price we expect to sell the stock for at the end of the holding period
= Year-end price / (1+k)^1

Value
= PV of dividends receive over 1 year + PV of price we expect to sell at end of 1 year
= [Dividend to be received/(1+k)^1]  +  [Year-end price /(1+k)^1]

k = cost of equity or required rate of return

2.  Multiple-Year Holding Period DDM

We apply the same discounting principles for valuing common stock over multiple holding periods.

In order to estimate the intrinsic value of the stock, we first estimate the dividends that will be received every year that the stock is held and the price that the stock will sell for at the end of the holding period.

Then we simply discount these expected cash flows at the cost of equity (required return).

PV of Dividends received in Year 1 = D1/(1+k)^1
PV of Dividends received in Year 2 = D2/(1+k)^2
PV of Dividends received in Year .. =
PV of Dividends received in Year n= Dn/(1+k)^n
Price of stock sold at end of holding period n = Pn / (1+k)^n

Value
= PV of D1 + PV of D2 + PV of D3 +.................. PV of Dn + PV of Holding-Period Price
= [D1/(1+k)^1]  + [D2/(1+k)^2]  + .[D3/(1+k)^3]..........[.Dn/(1+k)^n]  + [Pn / (1+k)^n]

3.  Infinite Period DDM (Gordon Growth Model)

Assumptions of the Infinite Period DDM (Gordon Growth Model):

• The infinite period dividend discount model assumes that a company will continue to pay dividends for an infinite number of periods.
• It also assumes that the dividend stream will grow at a constant rate (g) over the infinite period.

In this case, the intrinsic value of the stock is calculated as:

Value = PV of D1 + PV of D2 + PV of D3 + ...........PV of Dn....... + PV of Dinfinity

PV of Dividends received in Year 1 = D1/(1+k)^1 = D0(1+g)^1/(1+k)^1
PV of Dividends received in Year 2 = D2/(1+k)^2 = D0(1+g)^2/(1+k)^2
PV of Dividends received in Year .. =
PV of Dividends received in Year n= Dn/(1+k)^n = DO(1+g)^infinity / (1+k)^infinity

D0 = Dividends received at year 0

This equation simplifies to:

PV at year 0
= D0(1+g)^1/(k-g)^1
= D1/(k-g)

The critical relationship between k and g in the infinite-period DDM (Gordon Growth Model)

The relation between k and g is critical:

• As (k-g) increases, the intrinsic value of the stock falls.
• As (k-g) narrows, the intrinsic value of the stock rises.
• Small changes in either k or g, can cause large changes in the value of the stock.

For the infinite-period DDM model to work, the following assumptions must hold:

• Dividend grows at a rate, g, which is not expected to change (constant growth).
• k must be greater than g; otherwise the model breaks down because of the denominator being negative.
(k-g) = difference between k and g or difference between cost of equity or required rate of return and growth rate.

Return on investment = Dividend Yield + Growth over Time:

Rearranging the DDM formula:

PV = D1 / (k-g)

= (D1/PV) + g
= Dividend yield + growth over time.

This expression for the cost of equity (required rate of return) tells us that the return on an equity investment has two components:

• The dividend yield (D1/PV at year 0)
• Growth over time (g)