Dividend discount model (DDM)

Preferred stock valuation
Dividend is fixed and the income stream continues forever.

Preferred stock value = Dividend / Required rate of return = D/k

Common Stock Value

One-year holding period
P0 = (D1+P1)/(1+k)

Two-year holding period
P0 = D1/(1+k) + (P1+ D2) / (1 + k)²

n-year holding period
P0 = D1/(1+k) + D2/(1+k)² + .....+ Dn/(1+k)ⁿ

Infinite period model (a.k.a constant growth model)
P0= D1 / (k - g) = [D0 x (1+g)] / (k - g)
Where:
the growth rate (g) is lower than the cost of capital (k) and stays constant forever.

Note:
· From the constant growth model, increase in k and decrease in g will lead to decline in stock value. However, just increase in D cannot conclude to increase stock value as it also lead to decrease in growth, under the assumption that ROE is fixed.

DDM with supernormal growth
Assume the company dividends will grow at a high rate for a period of time before declining into a constant growth rate.

P0 = D1 / (1 + k) + D2 / (1 + k)² + … + Dn / (1 +k)ⁿ + Pn/ (1 +k)ⁿ
Where:
Pn = Dn+1 / (k - g_c) and g_c is the constant growth rate

Estimated inputs to be used in DDM
· Dividend
· Future price
· Required rate of return
· Expected growth rate

Required Rate of Return (K)
k = (R_series = R_f + ß_series(R_market - R_f)

Expected Growth Rate (g)
g= (retention rate)(ROE)

Dividend
Last year’s earnings x payout ratio x (1+g)

Future Price
The future price for the company can be derived with next year’s dividend divided by the difference in the company’s required rate of return and its growth rate.

Implied Dividend Growth Rate
A company’s dividend growth rate can be derived from a company’s ROE and its retention rate.

Growth rate = (retention rate)(ROE)

The retention rate of a company is the amount of earnings a company retains for its internal growth. A company’s ROE is the return on the funds invested back into the company.