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Learning outcomes.

After watching this video you will be able to relate earnings growth

rate to dividend growth rate.

Determine when increasing the retention rate will increase stock price and

when it will decrease stock price.

The growth rate of dividends.

Last time, we saw that one realistic way to calculate today's stock

price was to treat the dividend stream as a growing perpetually and

then use the garden growth model to calculate today's price.

But how do we go about determining what the growth rate of dividends will be?

Let's define the dividend payout rate as the fraction

of a company's earnings paid out as dividends each year.

The dividend per share for the company will be the company's earnings, or

net income, for

the year divided by the shares outstanding times the dividend payout rate.

A company can potentially increase it's dividends per share by

increasing earnings, increasing the dividend payout rate,

or decreasing it's shares outstanding.

Let's keep the shares outstanding fixed and

look at only the trade-off between earnings and the dividend payout rate.

A company can do two things with its earnings.

Pay them out as dividends or retain them and reinvest them in the company.

Let's also assume that the company does not grow if there is no investment.

Any change in earnings may be attributed to the amount of the new

investment made and the return that it earns.

This can be returned as change in earning equals new investments

made by the company times the return on the new investment.

New investments made by the company is, itself,

equal to its earnings times the retention rate,

where the retention rate is 1 minus the dividend payout rate.

Substituting new investments in the equation for

change in earnings, gives us change in earnings,

equals earnings times retention rate, times return on new investment.

Dividing through by earnings gives us the change in earnings over earnings.

Which is the Earnings Growth Rate = Retention Rate x Return on new investment.

If the company chooses to keep its dividend payout rate a constant it

can easily be shown that the earnings growth rate is the same as

the dividend growth rate.

Now we have the dividend growth rate (g) equals retention rate

times return on new investment.

A firm can increase its dividend growth rate by returning more of its earnings,

but this means it will be able to pay out less as dividends.

If a company wants to increase its stock price, should it increase its

retention rate and invest more or reduce retention and increase dividend.

The answer depends on the profitability of the firm's investment.

Let's look at an example to better understand this tradeoff.

A firm is expected to have an earnings of $5 next year.

Without any growth expectations, it decides to payout of its earnings as

dividends and its current stock price is $50.

This means that the firm's expected return rE,

is the dividend of 50 over its current price,

50 plus the growth of dividend 0, which gives us 10%.

Say the company now decides to increase its retention rate to 25% and invest

the retained earnings in investments that give a return on investment of 12%.

Will this change the company's stock price?

If so, in which direction.

Growth rate g is now the retention rate of 25% times

the return on new investment, 12%, which gives us 3%.

The stock price today, P sub 0,

would be the reduced dividend of 5 times 1- 0.25

/ (0.10-0.03), which comes to $53.57.

Clearly having a return on new investment of 12% increases the stock's

price if the company decides to increase its retention rate.

What would happen to the stock if the return on new investment were only 8%?

The growth rate g would be 25% times the return on investment,

8% which gives us 2%.

The stock price today P sub 0 would be

the reduced dividend of 5(1+0.25) /

(0.10-0.02) which comes to 46.875.

What if the return on new investment were 10%?

You can verify that this would not change the stock price.

What does this tells us when increasing retention rates will increase

stock prices and when it will lead to a decrease in stock prices.

If the return on new investments is greater than the discount rate or

the expected return on the stock,

Increasing retention rate will increase stock prices.

On the other hand when the return on new investments is less than the discount

rate, increasing retention rate will decrease stock prices.

Next time we will look at another way of valuing stocks,

namely valuation based on compatible forms.