Investing / income

Dividend reinvestment

Reinvesting a dividend buys shares, and those shares pay the next dividend. The arithmetic is a share count rather than a balance, which is why the effect is so much larger than the yield suggests. This models both paths — reinvested and taken as cash — side by side.

Starting shares294.1Final shares465.8Current yield2.82%

Value with reinvestment

$71,302

$465.78 shares at $153.08

Dividends received

$20,988

1.58× the starting share count

Yield on cost

9.76%

on the $25,000 originally invested

Reinvestment advantage

$12,313

against taking the same dividends as cash

Reinvestment schedule

Dividends buy shares at the price on the payment date, so every later dividend is paid on a larger count.

15 years

Reinvestment schedule
Year	Share price	Dividend/share	Shares	Income	Value
1	$88.40	$2.40	302.1	$705.88	$26,706
2	$91.94	$2.54	310.5	$768.55	$28,543
3	$95.61	$2.70	319.2	$837.21	$30,522
4	$99.44	$2.86	328.4	$912.47	$32,655
5	$103.42	$3.03	338.0	$995.02	$34,956
6	$107.55	$3.21	348.1	$1,086	$37,440
7	$111.85	$3.40	358.7	$1,185	$40,123
8	$116.33	$3.61	369.8	$1,294	$43,022
9	$120.98	$3.83	381.5	$1,415	$46,158
10	$125.82	$4.05	393.8	$1,547	$49,551
11	$130.85	$4.30	406.8	$1,693	$53,226
12	$136.09	$4.56	420.4	$1,853	$57,208
13	$141.53	$4.83	434.7	$2,030	$61,526
14	$147.19	$5.12	449.8	$2,225	$66,213
15	$153.08	$5.43	465.8	$2,441	$71,302

The share price grows independently of the dividend. A company that raises its dividend faster than its price grows shows a rising yield on cost, which is the number long-term holders actually watch.

Reinvested against cash

The gap is the shares the cash dividends would have bought and the dividends those shares would have paid.

Where the final value comes from

Original capital, price appreciation and the shares the dividends bought.

Canonical equations

The exact relationships implemented by this engine.

Δn = D / P · D is the cash dividend, P the price on the payment date.

D_t = n_t · d₀(1 + g)^t · Paid on the shares held at the start of the year.

D_t / cost · Rises even when the current yield does not.

cash += D(1 − t) · Dividends are taxed when received outside a sheltered account.

Show model notation and computationOpen the symbolic form, the variable definitions, and the step-by-step derivation when you need the detail.

A clear path from inputs to results.

Reinvesting a dividend buys shares, and those shares pay the next dividend. The arithmetic is a share count rather than a balance, which is why the effect is larger than the yield suggests. This models both paths — reinvested and taken as cash — side by side, so the difference is visible rather than asserted.

Step-by-step methodWorked exampleAssumptions explained

How to use

Enter the amount invested, the share price and the current dividend per share.

Set the dividend growth rate and the separate share-price growth rate.

Choose whether dividends are reinvested or taken as cash.

Add the tax rate that applies to dividends received.

Read the final share count, the income and the value of each path.

The formula

n_{t+1} = n_t\left(1 + \frac{d_0(1+g)^t}{P_t}\right) \;;\; \mathrm{yield\ on\ cost} = \frac{D_t}{\mathrm{cost}}

Reference: Standard dividend-reinvestment arithmetic; the yield-on-cost convention follows the CFA Institute's equity income treatment.

Worked example

$25,000 at $85 with a $2.40 dividend

Inputs

$25,000 invested at $85 a share.
Dividend $2.40, growing 6% a year.
Share price growing 4% a year, 15 years.
Dividends reinvested; 15% tax on cash dividends for the comparison.

Calculation path

1
The initial purchase is 294.12 shares.
2
Year one pays 294.12 × $2.40 = $706, which buys 7.6 more shares at the $88.40 price.
3
Each year the dividend rises 6% and is spread over a larger share count, so the income compounds twice over.
4
After fifteen years the holding is 465.8 shares — 58% more than the starting count.
5
At $153 a share that is $71,302, of which $20,988 came from dividends along the way.
6
Taking the same dividends as cash, after 15% tax, leaves $58,989 — $12,313 less.

Result

294.12 → 465.8 shares · $71,302 · $12,313 ahead of taking the cash.

Interpreting the result

The share count is the thing to watch. A 2.8% yield looks like a rounding error against a 4% price gain, but over fifteen years it adds more than half again to the number of shares, and those shares participate in every subsequent price move and dividend. The yield on cost rises to 9.76% — which is what long-term holders actually mean when they say the income has grown.

Assumptions & limitations

Dividends are paid annually on the shares held at the start of the year.

Reinvestment happens at the price on the payment date, with no commission or spread.

The dividend and the share price grow at constant, independent rates.

Cash dividends are taxed at the stated rate in the year received; reinvested dividends are not taxed in this model.

The share price falls by roughly the dividend on the ex-date in reality; this model treats price growth and dividend separately.

Frequently asked questions

Is a dividend free money?

No. On the ex-dividend date the share price falls by approximately the dividend, so the payment moves value from the share price into cash. What changes with reinvestment is how many shares you hold afterwards, not whether you got richer that day.

Are reinvested dividends taxed?

In a taxable account, yes — in the year they are paid, even though you never see the cash. The cost basis of the new shares is the reinvested amount, so you are not taxed twice, but you do need to track the lots.

Does reinvestment beat taking the cash and reinvesting yourself?

Only if it avoids commissions and timing decisions. Mechanically the two are identical; the behavioural advantage of automatic reinvestment is that it removes the decision, which is where most of the difference actually comes from.

Why does the yield on cost keep rising?

Because it divides today's dividend by the original cost. If the dividend grows 6% a year and you have held for fifteen years, the payout has more than doubled against a fixed denominator — even though the current yield, measured against today's price, may be unchanged.

Is a high yield always better?

No. A yield is high either because the dividend is generous or because the price has fallen. The second case is common and usually signals a cut. The sensitivity chart shows what a higher starting yield does mechanically, not what it implies about the business.