<p>The textbook probably means growth rate and not absolute growth. Given your assumptions
$$
\frac{\frac{d}{dt}Div_t}{Div_t}=
\frac{\frac{d}{dt}\text{Earnings}_t}{\text{Earnings}_t}
$$
does hold.</p>

CC BY-SA 4.0
2018-05-24T16:16:26.263Z
2018-05-24T16:16:26.263Z
Giskard
<p>Let $Div_t$ be the dividend per share at date $t$.</p>

<p>$\displaystyle Div_t=\frac{\text{Earnings}_t}{\text{Shares Outstanding}_t}\times\text{Dividend Payout Rate}_t$ ------------------- (1)</p>

<p>My textbook says that if $\text{Shares Outstanding}_t$ is constant and $\text{Dividend Payout Rate}_t$ is constant, growth in dividends will equal growth of earnings.</p>

<p>However, differentiating (1), we get</p>

<p>$\displaystyle\frac{d}{dt}Div_t=\frac{\text{Dividend Payout Rate}_t}{\text{Shares Outstanding}_t}\frac{d}{dt}\text{Earnings}_t$</p>

<p>Clearly, $\displaystyle\frac{d}{dt}Div_t\ne\frac{d}{dt}\text{Earnings}_t$</p>

<p>Where have I gone wrong?</p>

<stock-market><financial-economics>
Growth in dividends will equal growth of earnings
Siddhartha
# Growth in dividends will equal growth of earnings

(Asked by: username_0 on 2018-05-24)

Let $Div\_t$ be the dividend per share at date $t$.

$\displaystyle Div\_t=\frac{\text{Earnings}\_t}{\text{Shares Outstanding}\_t}\times\text{Dividend Payout Rate}\_t$ ------------------- (1)

My textbook says that if $\text{Shares Outstanding}\_t$ is constant and $\text{Dividend Payout Rate}\_t$ is constant, growth in dividends will equal growth of earnings.

However, differentiating (1), we get

$\displaystyle\frac{d}{dt}Div\_t=\frac{\text{Dividend Payout Rate}\_t}{\text{Shares Outstanding}\_t}\frac{d}{dt}\text{Earnings}\_t$

Clearly, $\displaystyle\frac{d}{dt}Div\_t\ne\frac{d}{dt}\text{Earnings}\_t$

Where have I gone wrong?

**Tags:** stock-market, financial-economics

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## 1 answers

### Answer by username_1 on 2018-05-24. Score: 4 | Accepted answer

The textbook probably means growth rate and not absolute growth. Given your assumptions
$$
\frac{\frac{d}{dt}Div\_t}{Div\_t}=
\frac{\frac{d}{dt}\text{Earnings}\_t}{\text{Earnings}\_t}
$$
does hold.


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