# A company earns $5 per share; it is capitalized at a rate of 10% and has a rate of return on investments of 16%. According to Walter’s model what should be the price per share at 50% dividend pay...

A company earns $5 per share; it is capitalized at a rate of 10% and has a rate of return on investments of 16%. According to Walter’s model what should be the price per share at 50% dividend pay out ratio?

Is this the optimum pay out ratio according to Walter?

(Moved to math to enable the equation editor)

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### 1 Answer

Let E = earnings per share = $5.00

Let `k_e` = rate of capitalization = 10% = 0.10

Let r = rate of return = 16% = 0.16

Let DP = pay out ratio = 50% = 0.50

Let D = dividend per share

According to Walter's model:

`D = E*DP` and `P=(D+(r/k_e)(E-D))/k_e`

Substituting in what we know:

`D = (5)(0.5)=2.50`

`P=(2.50+(0.16/0.10)(5-2.50))/0.10=65`

Therefore, according to Walter's model, the price per share should be $65.

Also, according to Walter, when `rgtk_e` the optimum payout ratio is 0. Therefore, $65 is higher than the optimum price per share of $0. Essentially, this means that if the company keeps all of its earnings (no dividend), the shares will be worth the maximum market value.

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