Question

Assess the three different models used to value stocks based on different dividend patterns. List the different models and provide an example of each.

Answer 1

Answer-

The Different models to based on different dividend patterns are

1) Gordon constant growth model
2) Two-stage growth model
3) H-model and
4) Three-stage growth model.

The first three models with examples and solutions to make the concepts clear are given below:-

1)

Gordon constant growth model - This model assumes that the dividends grow at a constant rate.

V0 = D0 x (1+g) / (1+r) + D0 x (1+g)2 / (1+r)2 + D0 x (1+g)3 / (1+r)3 + --- + D0 x (1+g)n / (1+r)n

V0 = D0 x ( 1+g) / (r -g) = D1 / (r-g)

V0 = fundamental value of stock
D0 = dividend just paid
D1 = Dividend expected after 1 year
r = requiered return on equity or cost of equity
g = dividend growth rate

Example

If the current price and most recent dividend for a company are $ 25 and $ 1.5 If the required return on the company is 7.5% what is the implied growth rate?

V0 = D0 x ( 1+g) / (r-g) = $ 1.5 x ( 1+g) / ( 7.5 % - g)

$ 25 =  $ 1.5 x ( 1+g) / ( 7.5 % - g)

$ 25 = $1.5 x ( 1+g) / (0.075 -g)

$ 25 x (0.075 -g) = $ 1.5 + 1,.5 g
$ 1.875 - $ 25 g = $ 1.5 + 1.5 g
26.5 g = 0.375
g = 0.375 / 26.5
g = 0.01415
g = 1.415 %

2)

Two stage growth model - This model assumes that te company grows at a high rate for a short period of time which is the gfirst stage and then reverts to long run growth rate in perpetuity.

Example

A company pays a dividend of $ 2. The estimated growth of 10 % for the next two years followed by a 3 % growth in perpetuity. The required return is 14 %. Calculate the curent stock price?

V0 =  D0 x (1+g) / (1+r) + D0 x (1+g)2 / (1+r)2 + D0 x (1+g)2 x ( 1 +gs)  / (1+r)2 x ( r-g)

Note - [ D0 = $ 2, g = 10 %., gs = 3 %, r = 14 % ]

V0 = $ 2 x ( 1.1) / 1.14 + $ 2 x ( 1.1)2 / (1.14)2  + $ 2 x (1.1)2 x ( 1.03) / 1.142 x ( 0.14 - 0.03)

V0 = $ 2.2 / 1.14 + $ 2.42 / 1.2996 + $ 2.493 / 0.1429

V0 = 1.928 + $ 1.862 + $ 17.446

V0 = $ 21.236

3)

H-model - The model solves the unrealistic assumption that the stock will experience high growth for a period and will fall immediately to long run perpetuity growth level. In H-model the growth rate starts at a high level and declines linearly over the high growth stage and reaches the long run gowth of perpetuity.

V0 = D0 x ( 1 + gL ) / (r - gL) + D0 x H x (gs - gL) / (r - gL)

H = t/2 = half life of high growth period in years
gs = short term growth rate
gL = long term growth rate
t = length of high growth period

Example

Suppose a company pays a dividend of $ 2 . The growth rate currently is 25 % and is expected to decline linearly over the next 8 years to a stable rate of 5 % thereafter. The required return is 10 %. Calculate the current stock price?

V0 = D0 x ( 1 + gL ) / (r - gL) + D0 x H x (gs - gL) / (r - gL)

[ D0 = $ 2, gL = 5 %, gs = 25 %, r = 10 %]

V0 = $ 2 x 1.05 / ( 0.10 - 0.05 ) + $ 2 x (8/2) x ( 0.25 - 0.05) / ( 0.10 - 0.05)

V0 = $ 2.1 / 0.05 + $ 1.6 / 0.05

V0 = $ 42 + $ 32
V0 = $ 74