Question

What two conditions must be met to go from Formula 10-7 to Formula 10-8 in using the dividend valuation model?

${\mathbf{P}}_{\mathbf{0}}\mathbf{=}\frac{{\mathbf{D}}_{\mathbf{1}}}{{\mathbf{K}}_{\mathbf{e}}\mathbf{-}\mathbf{g}}\mathbf{.}\mathbf{...................}\mathbf{(}\mathbf{10}\mathbf{-}\mathbf{8}\mathbf{)}$

Short answer

The formula would change having met two conditions –

a)The firm must have a constant dividend growth rate (g).

b) The discount rate (Ke) must be higher than the growth rate (g).

Step-by-step solution

Dividend valuation model in case of constant growth dividend

In the case of a constant growth dividend, each year’s dividend is valued against the constant growth rate and time period from the investment date.

the general formula for this would be –

${\mathrm{P}}_0=\frac{{\mathrm{D}}_0{(1+\mathrm{g})}^1}{{(1+{\mathrm{k}}_{\mathrm{e}})}^1}+\frac{{\mathrm{D}}_0{(1+\mathrm{g})}^2}{{(1+{\mathrm{k}}_{\mathrm{e}})}^2}+\frac{{\mathrm{D}}_0{(1+\mathrm{g})}^3}{{(1+{\mathrm{k}}_{\mathrm{e}})}^3}+...+\frac{{\mathrm{D}}_0{(1+\mathrm{g})}^{\mathrm{\infty }}}{{(1+{\mathrm{k}}_{\mathrm{e}})}^{\mathrm{\infty }}}$

Change in the general formula

The general formula can be changed to a simplified formula if two conditions are satisfied –

1. The firm must have a constant dividend growth rate (g).

2. The discount rate (Ke) must be higher than the growth rate (g).

Then the general formula would be compressed in to the following from –

${\mathrm{P}}_0=\frac{{\mathrm{D}}_1}{({\mathrm{k}}_{\mathrm{e}}-\mathrm{g})}$