Comparing Two Ways to Distribute Cash
A company with cash available for distribution can pay a cash dividend or use cash to repurchase its own shares. To compare these choices precisely, track four quantities: the company’s cash outlay, the cash a particular shareholder receives, the shares that shareholder retains, and the company’s cash and total shares after the transaction.
The comparison in this tutorial is a mechanical one. Assume a single class of common shares, a cash payout funded from the company’s existing cash, and no taxes, transaction fees, financing changes, or other cash flows. For a repurchase, take the execution price as given and assume the company buys the stated number of shares at that price. These assumptions isolate the payout arithmetic; they do not establish that one method is preferable in every setting.
The equal-cash comparison requires the same company outlay \(C\) under both alternatives. It does not require every shareholder to receive the same cash under both. A dividend is distributed according to shares owned: each share receives the same amount. A repurchase pays only shareholders who sell shares, and each seller receives the execution price for each share sold.
The Core Calculations
For a cash dividend, the dividend per share is the total payout divided by the shares entitled to it. A holder of \(h\) shares receives the per-share amount multiplied by \(h\), and keeps the same number of shares. For a repurchase at price \(P\), the company’s total shares repurchased are the cash budget divided by the price per share. A shareholder selling \(q\) shares receives \(qP\) and retains \(h-q\) shares.
Provided the company has enough cash, the cash remaining after either payout is \(B-C\). Under a repurchase, total shares outstanding after completion are \(N-C/P\), assuming the company retires the shares it buys. Under a dividend, the share count remains \(N\). These company-level calculations are separate from the individual shareholder’s decision to tender shares.
Why Pro-Rata Participation Matches Dividend Cash
A useful comparison arises when every shareholder sells the same proportion of their holdings into the repurchase. The company then buys a fraction \(C/(NP)\) of all shares outstanding, because its budget \(C\) buys \(C/P\) shares out of the original \(N\). A holder with \(h\) shares sells that same fraction of their position.
The final expression is exactly the dividend cash that the holder would have received. This is a result of the stated pro-rata assumption and the arithmetic of an equal company outlay; it does not mean the shareholder retains the same number of shares. After the repurchase, the holder keeps \(h-q\), while a dividend leaves the holder with all \(h\) shares.
The comparison also depends on participation. A holder who sells no shares into a repurchase receives no repurchase cash, while a dividend pays that holder according to their shares. A holder who sells more than the pro-rata fraction can receive more cash than under the dividend, but retains fewer shares. The number of shares sold cannot exceed the holder’s holding, and the total shares bought cannot exceed the company’s cash budget divided by the execution price.
Use the same \(C\) for the dividend and repurchase alternatives; check that the company has at least \(C\) in available cash.
Find \(C/N\), multiply by the shareholder’s \(h\) shares, and leave both the holder’s and company’s share counts unchanged.
Find \(C/P\) shares bought. Use the shareholder’s stated tender quantity \(q\), not an assumed pro-rata quantity, to calculate cash \(qP\) and retained shares \(h-q\).
For either alternative, subtract \(C\) from company cash. For the repurchase only, subtract \(C/P\) from total shares outstanding.
Worked Comparisons
Worked Example: Equal Cash Under Pro-Rata Participation
A company has 120,000 shares outstanding and $900,000 in cash. It will distribute $240,000 either as a cash dividend or through a repurchase at $30 per share. An investor owns 750 shares. Under the repurchase, assume every shareholder sells the same proportion of their holdings. Calculate the investor’s cash and shares under each choice, and the company’s remaining cash and shares.
Method. Calculate the dividend per share first, then find the repurchase fraction and apply it to the investor’s holdings.
Dividend. The dividend per share is $240,000 ÷ 120,000 = $2.00. The investor receives 750 × $2.00 = $1,500.00 and retains 750 shares. Company cash becomes $900,000 − $240,000 = $660,000; shares outstanding remain 120,000.
Repurchase. At $30 per share, the company buys $240,000 ÷ $30 = 8,000 shares. This is 8,000 ÷ 120,000 = 1/15 of the outstanding shares. Under pro-rata participation, the investor sells 750 × 1/15 = 50 shares and receives 50 × $30 = $1,500.00. The investor retains 750 − 50 = 700 shares. The company has $660,000 in cash and 120,000 − 8,000 = 112,000 shares outstanding.
Check. The repurchase cash paid is 8,000 × $30 = $240,000, matching the dividend outlay. The investor’s pro-rata repurchase cash, $1,500.00, matches the dividend, while the investor’s share count differs.
Common mistake avoided: treating a matching cash payment as if it also left the shareholder’s share count unchanged. The investor sells 50 shares in the repurchase but sells none under the dividend.
Worked Example: A Holder Chooses How Many Shares to Tender
A company has 50,000 shares outstanding and $1,200,000 in cash. It will pay out $300,000 either as a dividend or through a repurchase at $24 per share. An investor owns 600 shares and chooses to tender 200. Calculate the investor’s cash and remaining shares under each alternative, as well as the company’s remaining cash and shares after the repurchase.
Method. The dividend is allocated across all shares. For the repurchase, use the investor’s actual tender of 200 shares; do not assume the investor participates pro rata.
Dividend. The dividend per share is $300,000 ÷ 50,000 = $6.00. The investor receives 600 × $6.00 = $3,600.00 and retains 600 shares. Company cash becomes $1,200,000 − $300,000 = $900,000, and shares outstanding remain 50,000.
Repurchase. The company buys $300,000 ÷ $24 = 12,500 shares in total. The investor tenders 200 and receives 200 × $24 = $4,800.00, retaining 600 − 200 = 400 shares. The other shareholders must tender 12,500 − 200 = 12,300 shares for the full budget to be spent. After completion, company cash is $1,200,000 − $300,000 = $900,000, and shares outstanding are 50,000 − 12,500 = 37,500.
Check. The investor’s repurchase proceeds are $1,200 greater than the dividend because this investor sells 200 shares rather than the 150 shares that would represent the pro-rata fraction: 12,500 ÷ 50,000 = 25%, and 25% × 600 = 150.
Common mistake avoided: applying the company’s repurchase percentage to this investor after the problem specifies a different tender quantity. The actual tender controls the individual’s proceeds and retained shares.
Worked Example: Repurchase at a Stated Premium
A company has 60,000 shares outstanding and $500,000 in cash. It will distribute $198,000 either as a dividend or by repurchasing shares at an execution price of $33. An investor owns 2,000 shares. First calculate the investor’s outcome if they participate pro rata; then calculate it if they tender only 100 shares. Find the company’s remaining cash and share count.
Method. Use the stated $33 execution price to calculate the repurchase quantity. The price is not needed to calculate the dividend per share.
Dividend. The dividend per share is $198,000 ÷ 60,000 = $3.30. The investor receives 2,000 × $3.30 = $6,600.00 and retains 2,000 shares.
Pro-rata repurchase. The company buys $198,000 ÷ $33 = 6,000 shares, which is 6,000 ÷ 60,000 = 10% of the outstanding shares. The investor sells 2,000 × 10% = 200 shares and receives 200 × $33 = $6,600.00, retaining 2,000 − 200 = 1,800 shares.
Repurchase when the investor tenders 100 shares. The investor receives 100 × $33 = $3,300.00 and retains 2,000 − 100 = 1,900 shares. The company’s total purchase is still 6,000 shares, so other shareholders tender 5,900 shares to complete it.
Company check. Under either payout, cash becomes $500,000 − $198,000 = $302,000. After the repurchase, shares outstanding become 60,000 − 6,000 = 54,000; after the dividend, they remain 60,000. The repurchase cash paid is 6,000 × $33 = $198,000.
Common mistake avoided: calculating the dividend using the repurchase price. The dividend is $3.30 per share because it is $198,000 divided by 60,000 shares; $33 is the price paid for shares tendered into the repurchase.
Reading the Comparison Correctly
Equal company cash outlays answer a company-level question: how much cash leaves the company under each alternative? They do not by themselves answer how much cash an individual receives. That shareholder-level result requires the shareholder’s ownership and, for a repurchase, the number of shares sold.
A compact comparison is useful when the problem provides a single shareholder’s tender decision:
| Quantity | Cash dividend | Share repurchase |
|---|---|---|
| Company cash paid | \(C\) | \(C\) |
| Cash received by holder | \(hC/N\) | \(qP\) |
| Holder’s shares afterward | \(h\) | \(h-q\) |
| Company cash afterward | \(B-C\) | \(B-C\) |
| Company shares afterward | \(N\) | \(N-C/P\) |
The table assumes the entire repurchase budget is spent at the stated price. In a real transaction, execution constraints or an undersubscribed offer can prevent that assumption from holding. If a problem states that only \(R\) shares are actually bought, use the actual outlay \(RP\), not the budget \(C\), to find company cash remaining.
Common Errors and a Practical Check
- Using the wrong denominator for a dividend. Divide the total dividend by shares entitled to receive it, then multiply by the holder’s shares. Do not divide by the company’s cash balance or by the repurchase price.
- Confusing shares bought with shares sold by one holder. \(C/P\) is the company’s total repurchase quantity. The shareholder’s proceeds use their own \(q\), unless the problem explicitly specifies pro-rata participation.
- Subtracting the dividend payout from the share count. A cash dividend reduces company cash, not the number of shares owned or outstanding in this calculation.
- Forgetting the cash reconciliation. If the full equal outlay is paid, both methods leave \(B-C\) in company cash. The method changes the share count only in the repurchase calculation.
- Assuming pro-rata participation without being told. It is a useful comparison case, not a default description of every tender decision. Check the problem’s wording before assigning \(q\).
Check Your Understanding
For each problem, track the shareholder’s cash and shares as well as the company’s remaining cash or share count where requested.
- A company has 40,000 shares and $500,000 in cash. It pays out $80,000 as a dividend. An investor owns 900 shares. Find the dividend per share, the investor’s cash and remaining shares, and company cash afterward. (Answer: $2.00 per share; $1,800.00 received; 900 shares retained; $420,000 company cash.)
- A company with 25,000 shares and $700,000 in cash repurchases $150,000 of shares at $30 each. An investor owns 400 shares and tenders 80. Find the investor’s proceeds and remaining shares, the total shares bought, and company cash afterward. (Answer: $2,400.00 proceeds; 320 shares retained; 5,000 shares bought; $550,000 company cash.)
- A company has 100,000 shares and $2,000,000 in cash. It distributes $250,000, either as a dividend or by repurchasing at $25 per share. A 1,500-share investor participates pro rata in the repurchase. Compare the investor’s cash and shares under each method, and find the company’s post-payout cash. (Answer: dividend $3,750.00 and 1,500 shares retained; repurchase $3,750.00 and 1,350 shares retained; $1,750,000 company cash.)
- A company with 32,000 shares and $400,000 in cash pays out $96,000. Compare a dividend with a repurchase at $24 per share for an investor owning 250 shares who tenders 75 shares. Find the investor’s cash under each alternative, the repurchase share count, and company cash afterward. (Answer: dividend $750.00; repurchase $1,800.00; 4,000 shares bought; $304,000 company cash.)
- A company has 90,000 shares and $1,100,000 in cash. It spends $360,000 repurchasing shares at $40 each. An investor owns 1,000 shares and tenders 150. Compare the investor’s repurchase proceeds and retained shares with the dividend alternative using the same $360,000 outlay. (Answer: repurchase $6,000.00 and 850 shares retained; dividend $4.00 per share, $4,000.00 received, and 1,000 shares retained.)