Major Points



DIVIDENDS TO COMMON STOCKHOLDERS: PROBLEMS & DETAILED SOLUTIONS (copyright © 2016 Joseph W. Trefzger)

Basic Definitional

1. The total number of shares of common stock that have been issued by Amazon Acrylic, Inc. (and are currently “outstanding” in the hands of investors) is 5,100,000. How many shares will exist if Amazon’s board of directors declares a 5-for-3 stock split? A 1-for-2 reverse stock split? A 5% stock dividend? If the stock currently sells in the market for $19.95 per share, what would we expect the value per share to be if each of these possible changes were to be undertaken?

Type: Basic definitions. A stock split or stock dividend (as opposed to a cash dividend) is simply the creation of new “pieces of paper” (once-popular paper stock certificates actually have been largely replaced with electronic entries in the modern era) that should not, by itself, be expected to change the common stockholders’ total claim against the company’s future cash flows. (The only exception might be if the change in the number of shares coincided with a change that had real economic significance, for example if the firm created a greater number of shares without reducing the quarterly per-share cash dividend from its recent level. Typically, a company that creates new shares through a stock split or dividend reduces its per-share cash dividend proportionally, so the common stockholders, individually and as a group, receive no additional cash each quarter.)

Indeed, the accounting treatment of a stock split (including the reverse variety) is merely to change the stated number of shares and stated par value per share; all dollar figures in the stockholders’ equity section of the balance sheet remain the same. (For a stock dividend, accountants reallocate book value from retained earnings to the common stock accounts, but total stockholders’ equity

is unchanged.) Arguments that a stock split or dividend can move a common stock’s value into its “optimal trading range” are unconvincing in an era when so many individual investors own common stock through mutual funds (whose buying would not be stifled by a high cost for the traditional 100-share “round lot” trading unit).

A 5-for-3 split replaces every 3 “old” shares of common stock with 5 “new” shares. So after such

a split there would be 5/3 x 5,100,000 = 8,500,000 total shares. With 5/3 times as many shares outstanding, each should be worth 3/5 times the pre-split value, or 3/5 x $19.95 = $11.97. That way, someone who had held 300 shares worth a total of 300 x $19.95 = $5,985 before the split would have 500 shares worth a total of 500 x $11.97 = $5,985 after the split, as well.

A 1-for-2 reverse split replaces every 2 “old” common shares with 1 “new” share. So after such

a reverse split there would be 1/2 x 5,100,000 = 2,550,000 total shares. With 1/2 times as many shares outstanding, each should be worth 2/1 times the pre-split value, or 2 x $19.95 = $39.90. That way, someone who had held 200 shares worth a total of 200 x $19.95 = $3,990 before the reverse split would have 100 shares worth a total of 100 x $39.90 = $3,990 afterwards, as well.

Finally, a 5% stock dividend supplements every 100 existing shares of common stock with 5 “new” shares. So after such a stock dividend there would be 1.05 x 5,100,000 = 5,355,000 total shares. With 1.05 times as many shares outstanding, each should be worth 1/1.05 = .952381 times the pre-stock dividend value, or .952381 x $19.95 = $19. That way, someone who had held 100 shares of Amazon common stock worth a total of 100 x $19.95 = $1,995 before the stock dividend would have 105 shares worth a total of 105 x $19 = $1,995 after the stock dividend, as well.

2. The most recent year’s net income for Danube Diesel Works was $78,000,000. If the company’s owners jointly held 19,500,000 shares of common stock (i.e., if there were 19.5 million shares of common stock outstanding), what was earnings per share (EPS) for the year? If Danube paid out 55% of its net income as cash dividends to common stockholders, for a 55% “payout ratio,” what was the “retention ratio?” What was the dividends per share (DPS) figure? Would we typically expect a company to pay a constant percentage, such as 55%, of its net income as cash dividends to the common stockholders?

Type: Basic definitions. Earnings per share is simply total net income, or earnings, divided by the number of outstanding shares of common stock, computed here as $78,000,000 ( 19,500,000 = $4.00. If 55% of EPS is paid out as dividends, then DPS is .55 x $4.00 = $2.20. If management

can either use net income to pay cash dividends to the owners, or else retain some or all of it to increase the size of the company the owners own, then if 55% was paid out as cash dividends the other 45% constitutes the “retention ratio” portion that was retained.

Because common stockholders are believed to prefer receiving cash dividends that are steady or rising in amount from quarter to quarter (to provide a predictable stream of cash inflows), we would not expect a company to pay an unchanging proportion of net income as cash dividends from quarter to quarter unless net income (and perhaps more importantly, the cash flows remaining after all non-owner parties have been given fair financial returns) were very stable over time.

3. Niagara Nickel Corporation’s net income in the most recent year was $27,000,000. If the company’s board of directors decided to retain $12,000,000 for internal use, what might they have done with the remaining $15,000,000?

Type: Dividends vs. retained earnings vs. repurchase. Recall that net income belongs to, and should be used for the benefit of, a company’s owners. If the company is a corporation, those owners are called common stockholders. Corporate decisions on what to do with the common stockholders’ net income are made by “management,” meaning the board of directors. (We should actually think in terms of cash flows remaining for a firm’s common stockholders rather than accrual-based net income, but in this discussion we treat net income as a reasonable approximation of those cash flows.) In our early coverage of accounting issues, we stated that the directors can choose to do either of two things with net income:

• Retain it for use within the company, for example to purchase additional productive assets.

If the new assets are needed and are wisely chosen, then each common stockholder benefits because his or her proportional ownership claim now applies, for future years, to the cash flows of a bigger, stronger company. This retention of earnings constitutes an added investment

made by the common stockholders, on which they rightly expect to earn a fair rate of return

on equity in subsequent years. The investment is somewhat involuntary, in that the directors typically do not consult directly with the common stockholders before deciding how much of

a given year’s net income to retain. However, there is a voluntary element as well, in that the common stockholders elect the directors, and can replace the current directors with new ones when the next vote is held (typically at the next annual meeting) if they feel that the directors’ decisions have not been in the common stockholders’ best long-term interests.

• Pay it out to the common stockholders as cash dividends, which provide a benefit in the form of money that the common stockholders can spend any way they wish. (One choice would be to buy some additional shares of the company’s common stock from willing sellers in the open market.)

Or, of course, some portion can be retained and the remainder paid as cash dividends, as we see in the current case. Here we would tend to assume that the $15,000,000 not retained was paid in cash to the common stockholders as dividends. A couple of points to note:

• A third possibility would be for Niagara to use the non-retained $15,000,000 to repurchase some shares from existing common stockholders who want to sell. This action would have the potential to benefit the remaining common stockholders by reducing the number of fellow claimants with whom cash flows available to the owners would have to be shared in subsequent years (making the “back of the line” smaller).

• The amount of earnings retained in a specific year ($12,000,000 for the most recent year, in this example) is shown on the company’s statement of retained earnings. But it also becomes an addition to the accumulated total of retained earnings shown on the lower right-hand side of the balance sheet.

For example, let’s say that Niagara has been in business for three years, and that every year

the directors have opted to retain $12,000,000 of net income to buy additional assets. At the end of the first year of operations, the statement of retained earnings showed $12,000,000 retained for the year, and the balance sheet showed $12,000,000 of earnings retained (and used to pay for assets) in total over the company’s one-year life. At the end of the second year, the statement of retained earnings showed $12,000,000 retained for the year, and the balance sheet showed $24,000,000 retained in total over the company’s two-year life. And at the end of the third (most recent) year, the statement of retained earnings showed $12,000,000 retained for the year, and the balance sheet showed $36,000,000 retained in total over the company’s three-year life.

Work These for Sure

4. Nile Numismatic Industries is owned by individuals and institutions (banks, pension funds, mutual funds) that jointly hold 10,000,000 shares of common stock. The firm’s net income last year was $57,000,000. Total cash dividends paid to the common stockholders was $25,650,000. Compute the year’s earnings per share (EPS), dividends per share (DPS), and dividend payout ratio. What would these figures have been if Nile’s board of directors had decided, at some point during the year, to declare a 4-for-1 stock split? What if the board had instead decided, at some point during the year, to declare a 1-for-5 reverse stock split?

Type: Basic Definitions. Earnings per share for Nile’s common stock was simply the $57 million

in earnings divided by the 10 million outstanding shares, or $57,000,000 ÷ 10,000,000 = $5.70. Dividends per share was simply the $25,650,000 in cash dividends divided by the 10,000,000 shares, or $25,650,000 ÷ 10,000,000 = $2.565. And the payout ratio was just the proportion of net income that was paid to the common stockholders as cash dividends (rather than retained for the company’s internal use), so with $25,650,000 of the $57,000,000 net income paid in cash as dividends the payout ratio was $25,650,000 ÷ $57,000,000 = .45, or 45%. (The proportion of earnings retained, or “retention ratio,” was therefore 55%.)

If the directors had declared a 4-for-1 stock split, then each common stockholder would be deemed to have 4 “new” shares to replace every 1 “old” share previously held. So instead of 10 million total shares there would be 4 x 10 million = 40 million total shares after such a split (someone who had held 100 pre-split shares would have 400 post-split shares). Nothing of economic substance would have changed; we would simply think of the total ownership claim in Nile as being broken into 40 million smaller post-split pieces instead of 10 million bigger pre-split pieces. (If we merely replaced a $20 bill with four $5 bills, the recipient would have four times as many pieces of paper but no change in her claim on economic values.) So EPS would instead have been $57,000,000 ÷ 40,000,000 = $1.425 and DPS would have been $25,650,000 ÷ 40,000,000 = $.64125. (So an owner receiving $2.565 DPS x 100 shares = $256.50 in total cash dividends without the split would receive $.64125 DPS x 400 shares = the same $256.50 in total cash dividends if the split occurred.) With economically meaningful values like net income (and, more importantly, the related cash flows for the owners) and total cash dividends unchanged, the payout ratio would still have been $25,650,000 ÷ $57,000,000 = 45%. Recall that stock splits and reverse splits are said, by proponents, to help move share prices to a more desirable level (lower with a split if “too high,” higher with a reverse split if “too low”), but this logic of an “optimal trading range” can be hard to follow in the modern era of mutual funds and more efficient information/transactions management.

If the directors had instead declared a 1-for-5 reverse stock split, then each common stockholder would be deemed to have 1 “new” share to replace every 5 “old” shares previously held. So instead of 10 million total shares there would have been 10 million ÷ 5 = 2 million total shares after the reverse split (someone who had held 100 pre-reverse split shares would have 20 post-reverse split shares). Nothing of economic substance would have changed; we would simply think of the total ownership claim in Nile as being broken into 2 million bigger post-reverse split pieces instead of 10 million smaller pre-reverse split pieces. (It’s as though I replaced your five $10 bills with a $50 bill.) So EPS would instead have been $57,000,000 ÷ 2,000,000 = $28.50 and DPS would instead have been $25,650,000 ÷ 2,000,000 = $12.825 (an owner receiving $2.565 DPS x 100 shares = $256.50 in total cash dividends without the reverse split would get $12.825 DPS x 20 shares =

the same $256.50 in total cash dividends if the reverse split occurred). But, again, economically meaningful values like net income, cash flows, and total dividends are not changed by creating more/fewer “pieces of paper” to represent total ownership, so the payout ratio would still have been $25,650,000 ÷ $57,000,000 = 45%.

5. The net income earned by Rhine Refrigeration Company during the past year (which just ended today) was $125,000,000. The company expects to earn approximately this same annual net income level in each of the next several years. The board of directors has retained $50,000,000 of the past year’s $125,000,000 net income to buy new production equipment. But instead of paying cash dividends with the remaining $75,000,000, as it might in a typical year, the board has decided to repurchase 600,000 of the 15,000,000 outstanding shares of the company’s common stock, which currently sells in the market for $125 per share. If this repurchase were not expected to have any impact on subsequent years’ net income (or cash flows available to the common stockholders) or the relationship between a year’s net income and the stock’s market value, how would this action be expected to benefit the remaining common stockholders?

Type: Stock repurchase. An alternative to paying cash dividends to a company’s common stockholders is for management to buy shares of the common stock from willing sellers and then take those shares

out of circulation, thereby leaving fewer claims at the “back of the line” in subsequent operating periods. If the income (or, more importantly, cash flow) remaining after all operating costs, taxes to the government, and interest payments to lenders have been met is split fewer ways, then each remaining owner has a greater proportional remaining claim. For example, here the holder of one share would be at least a little better off sharing future back-of-the-line claims with 14,400,000 other shares than with 15,000,000.

In terms of specific dollar values, earnings per share (EPS) without the repurchase would be $125,000,000 net income ÷ 15,000,000 shares = $8.333. With 600,000 shares repurchased the EPS would be $125,000,000 net income ÷ 14,400,000 shares = $8.681. So the total claim on the company’s net income for the holder of 100 shares of Rhine common stock would rise from about $833 to $868 per year because of the repurchase. If some portion of that net income were, in at least some years, paid to the common stockholders as cash dividends, each remaining stockholder would expect to receive higher dividends per share (DPS) and total dividends after the repurchase.

Another way to analyze the situation is through the relationship known as the price-to-earnings,

or P/E, ratio. This relationship measures the current price per share of a company’s common stock relative to the most recent year’s actual (or the coming year’s expected) EPS. Here the P/E ratio

is $125/$8.333 = 15. If this relationship stays relatively stable as earnings per share rise or fall

(a possibility that is at least somewhat plausible, in at least some cases, since the value of being

a common stockholder is the claim on the owners’ cash flows, which we think of as relating to measured earnings), then as the repurchase causes EPS to rise from $8.333 to $8.681, the indicated value of each remaining share should rise from 15 x $8.333 = $125 to 15 x $8.681 = $130.22. So a repurchase of shares from willing sellers among existing common stockholders might be expected to benefit the remaining common stockholders both by increasing the value of their shares immediately and by increasing their expected future EPS and DPS claims.

Two final points: first, proponents of share repurchases see buying back shares as preferable

to paying dividends because repurchases provide common stockholders with more choices. For example, if dividends are paid then all tax-paying common stockholders must pay income taxes on them for the year when received (charitable organizations and other non-taxed holders of the stock do not), even if they had no desire to receive any cash. But a repurchase allows choice: those who want some cash can be share sellers (and pay whatever taxes such transactions might bring about), while those with no need for cash can just sit tight and watch their investment values rise, without engaging in the kinds of transactions that trigger income/capital gain taxes. Second, we have assumed here that the 600,000 shares were all to be repurchased at one time. If shares were instead repurchased in small amounts over a longer period, we might assume the price would rise from the initial $125 to the post-repurchase $130.22 in tiny increments, rather than all at once.

6. The chief financial officer of St. Lawrence Sandblasting expects the company’s net income in the coming year to be $29,000,000. A recently approved plan calls for capital spending over the coming year to be $36,000,000. The optimal capital structure for St. Lawrence is believed to be 38% debt/62% equity. If the company follows a residual dividend policy, how much in cash dividends should its managers plan to pay to the common stockholders in the coming year? What if net income were instead expected to be $40,000,000, $25,000,000, or $22,320,000?

Would this type of dividend payment plan lead to a constant dividend payout ratio?

Type: Residual dividend policy. If a company adheres to a residual dividend policy, then it does not initially make direct plans regarding the payment of dividends. Rather, it plans for its need to retain some portion of the expected net income, and then treats the remainder – the residual – as the amount that can be paid out in cash as dividends. In other words: don’t plan dividends, don’t think dividends; think about the need to retain earnings, and then whatever amount remains from net income after the needed retention (if we can think of net income as a good approximation of cash flow remaining for the common stockholders) can be paid out as cash dividends.

Here we have a company that expects to spend $36,000,000 on new long-lived equipment. If 38% of that amount (.38 x $36,000,000 = $13,680,000) is borrowed (this amount could include some preferred stock, which is essentially a type of debt), then the remaining 62% (.62 x $36,000,000 = $22,320,000) must come from the owners (common stockholders). The most cost-effective way

for a company’s managers to obtain money from the owners is to retain earnings that belong to the owners while those earnings are already under management’s control. So here, the plan should be to retain $22,320,000 of the $29,000,000 in expected net income. Then the remaining, or residual, $29,000,000 – $22,320,000 = $6,680,000 should be paid to the common stockholders as dividends.

What about the other net income levels shown? Because it has a need to retain $22,320,000, the amount of dividends St. Lawrence would expect to pay would be

$40,000,000 – $22,320,000 = $17,680,000 if net income were expected to be $40,000,000

$25,000,000 – $22,320,000 = $ 2,680,000 if net income were expected to be $25,000,000

$22,320,000 – $22,320,000 = $ 0 if net income were expected to be $22,320,000

If net income (actually the cash flow to owners, which we estimate with the more readily available net income figure) were expected to be anything less than the $22,320,000 St. Lawrence wants to retain for capital spending purposes, then the company would have to make a difficult decision. One possible choice would be to scale back capital spending plans; another would be to obtain additional owners’ money by going through the expensive process of paying an investment banking firm to locate new owners; and a third would be to borrow more than $13,680,000, thereby moving away from the 38%/62% debt/equity split that has been identified as optimal.

The residual dividend idea can be contrasted to the idea of planning for dividend payments (either through a planned payout ratio or, perhaps more commonly, a planned total dollar level of dividends). Indeed, a residual dividend policy would result in a constant proportion of income paid as dividends only if the dollar levels of both net income and capital spending were fairly steady from quarter to quarter/year to year.

Strong economic arguments can be made in favor of following a residual dividend policy: if a company has identified an optimal capital structure, then it should obtain further money for capital spending in keeping with that structure (in this example, 38% from lenders and 62% from owners), and

the most cost-effective way to get money from owners is to retain earnings while they are under management’s control, rather than paying investment bankers to locate new ownership money.

However, in practice we do not see much evidence that companies pay cash dividends to common stockholders based on a residual dividend model (though some observers feel that firms may meet the spirit of the residual dividend idea over a period of several years). The reasons are not known with certainty (we call the entire dividend payment question the “dividend puzzle”), but could relate to two issues often discussed in connection with dividend policy: the clientele effect (stockholders used to getting steady dividends can be harmed if more is retained in a given year when capital spending needs are higher) and/or information content (cutting dividends from earlier-year levels, even to pay for needed equipment, could be interpreted by some as a signal of financial problems).

7. The directors of Volga Vineyards believe in paying cash dividends to their common stockholders in accordance with the residual dividend theory. The company has a plan to spend $945,000 on new wine pressing and bottling equipment over the coming year. If the year’s net income is expected to be $730,000 and the company’s optimal capital structure is believed to be 60% debt/40% equity, what is the total amount of cash dividends that Volga should plan to pay? What if the planned level of capital spending were instead $0? What if it were $1,350,000? At what level of capital spending would following a residual dividend policy no longer be a workable possibility?

Type: Residual dividend policy. This firm expects to spend $945,000 on new capital equipment. If 60% of that amount (.60 x $945,000 = $567,000) is borrowed, then the other 40% (.40 x $945,000 = $378,000) must come from the owners (common stockholders). The most cost-effective way for managers to get money from common stockholders is to retain earnings that belong to the common stockholders while that money is under management’s control. So here, the plan should be to retain $378,000 of the $730,000 in expected net income. Then the remaining $730,000 – $378,000 = $352,000 is the expected “residual” that Volga should plan to pay to the common stockholders as cash dividends.

If there were no planned capital spending, then there would be no need to retain any of the net income, and Volga’s board of directors would expect to pay the entire $730,000 in net income as cash dividends to Volga’s common stockholders. (With nothing to be purchased, there would also be no need to borrow any additional funds.)

If it instead expected to spend $1,350,000 on new capital equipment, Volga would expect to borrow 60% of that amount (.60 x $1,350,000 = $810,000) and get the remaining 40% (.40 x $1,350,000 = $540,000) by retaining from the owners’ net income. In this case, the planned cash dividend level would be only the remaining, or residual, $730,000 – $540,000 = $190,000.

The highest level of expected spending that would allow Volga to follow a residual dividend policy would be the expected net income (again, we think of net income as a good proxy for the cash flow that would remain for the common stockholders after all other parties had received their financial returns) divided by the equity proportion of the capital structure, in this case $730,000 ( .40 = $1,825,000. (Think of it this way: there is some level of expected spending S such that .40 x S = $730,000, at which point the company runs out of retainable net income as the source of additional money from the owners. To solve for this S, we simply divide the $730,000 expected net income by the .40 equity proportion in the capital structure.) Beyond that level of spending, Volga’s managers would have to either locate additional owners’ money with the help of an investment banker, or else borrow more than $1,825,000 – $730,000 = $1,095,000, thereby moving away from the 60%/40% debt/equity split that is believed to be optimal.

Work These for Extra Practice

8. Cash dividends are paid to the common stockholders of Yangtze Enterprises based on the residual dividend theory. Net income is expected to be $61,000,000 in the coming year, and planned capital expenditures for the

year are $82,000,000. If the optimal capital structure is thought to be 46% debt/54% equity, what total amount of cash dividends should Yangtze plan to pay its common stockholders in the coming year? What if planned capital spending were instead $10,000,000, or $110,000,000? How large an amount could capital spending be before the residual dividend approach would no longer lead to a viable outcome?

Type: Residual dividend policy. Yangtze expects to spend $82,000,000 on new capital equipment.

If 46% of that amount (.46 x $82,000,000 = $37,720,000) comes from borrowers (including, perhaps, preferred stockholders), then the remaining 54% (.54 x $82,000,000 = $44,280,000) must come from the common stockholders. The most cost-effective way for management to

get money from the company’s true owners is to retain earnings. So here, the plan should be to retain $44,280,000 of the $61,000,000 in expected net income. Then the remaining (residual) $61,000,000 – $44,280,000 = $16,720,000 should be paid to the common stockholders as dividends.

If there were only $10,000,000 in planned capital spending, then the plan would be for 54% of that amount ($5,400,000) to be retained from net income and the remaining $61,000,000 – $5,400,000 = $55,600,000 to be paid by Yangtze’s directors as cash dividends to the company’s common stockholders. (It should be easy to see that $4,600,000 would be borrowed.)

If it instead expected to spend $110,000,000 on new capital equipment, Yangtze would expect

to borrow 46% of that amount (.46 x $110,000,000 = $50,600,000) and get the remaining 54%

(.54 x $110,000,000 = $59,400,000) by retaining from the owners’ net income. In this case, the planned cash dividend level would be only the remaining $61,000,000 – $59,400,000 = $1,600,000. It should be evident that the company could not expect to spend too much more than $110 million without running out of earnings to retain.

The highest level of expected spending that would allow Yangtze to follow a residual dividend policy would be the expected net income (once again, a convenient approximation for cash flow available

to the owners) divided by the equity proportion of the capital structure, here $61,000,000 ( .54 = $112,962,963. (Think of it this way: there is some level of expected spending S such that .54 x S = $61,000,000, at which point the firm runs out of retainable net income as the source of additional money from the owners. To solve for S, we simply divide the $61,000,000 expected net income

by the .54 equity proportion in the capital structure.) Beyond that level of spending, Yangtze’s managers would have to either locate additional owners’ money with the help of an investment banker, or else borrow more than $112,962,963 – $61,000,000 = $51,962,963, thereby moving away from the 46%/54% debt/equity split that has been identified as optimal.

9. The managers of Zambezi Industries believe that the company’s optimal debt/equity ratio is 76%. Net income

(which we treat as a reasonable approximation for the cash flow available to the company’s common stockholders)

is expected to be $6,950,000 in the coming year and $5,650,000 in the following year. Spending on new capital equipment is expected to be $11,000,000 in the coming year and $12,000,000 the following year. How much money should Zambezi expect to pay in total dividends each year, and how much should it plan to borrow each year, if:

1. it always pays 40% of net income as cash dividends to the common stockholders?

2. it pays $5,650,000 in total cash dividends to the common stockholders each year?

3. it strictly adheres to a residual dividend policy?

Would the company’s common stockholders be likely to have a preference for one of these three plans?

Type: Dividend policy. If Zambezi follows a 40% constant percentage payout ratio, then its focus is

on the cash dividends it pays, rather than on retaining earnings and staying with an optimal capital structure. Under this constant payout ratio, we would see the following dividend and debt results.

• Coming year: Pay 40% of net income, or .40 x $6,950,000 = $2,780,000 as dividends. The other $6,950,000 – $2,780,000 = $4,170,000 would be retained to help pay for the $11 million in new equipment. Thus the remaining $11,000,000 – $4,170,000 = $6,830,000 would be borrowed.

• Following year: Pay 40% of net income, or .40 x $5,650,000 = $2,260,000 as dividends. The other $5,650,000 – $2,260,000 = $3,390,000 would be retained to help pay for the $12 million in new equipment. Thus the remaining $12,000,000 – $3,390,000 = $8,610,000 would be borrowed.

It should be clear that a constant dividend payout ratio could cause a company’s cash dividends to differ from year to year, and cause capital structure to change somewhat from year to year (and change considerably over time if net income and capital spending were to differ considerably from year to year, as in this problem). If Zambezi instead paid out an unchanging dollar total as dividends each year, we would see the following results.

• Coming year: Pay $5,650,000 as dividends. The other $6,950,000 – $5,650,000 = $1,300,000 would be retained help pay for the $11 million in new equipment. Thus the remaining $11,000,000 – $1,300,000 = $9,700,000 would have to be borrowed.

• Following year: Pay $5,650,000 as dividends, leaving nothing to retain toward paying for the $12 million in new equipment. Thus the entire $12,000,000 would have to be borrowed. If net income were to be less than $5,650,000, then Zambezi’s managers might actually consider borrowing additional money so they could continue paying the expected $5,650,000 in annual cash dividends.

It should be clear that while a constant dollar payout would keep a company’s dividends stable from year to year, it would cause capital structure to change even more than in the constant percentage payout case if net income (actually, cash flow remaining for the owners) and capital spending were to differ considerably from year to year.

Finally, if Zambezi instead were to strictly follow a residual dividend policy, we would have to first compute the debt and equity proportions in the optimal capital structure. Here we are given an optimal debt/equity ratio, which we must convert to a debt/assets ratio. Debt/equity of 76% indicates that 76¢ should be invested by lenders (which could include some preferred stock) for every $1.00 put up by owners. So we can think of $1.76 in assets, paid for $.76/$1.76 = 43% by lenders and $1.00/$1.76 = 57% by owners. To keep these proportions intact, we would expect lenders to pay for 43% of the coming year’s $11,000,000 planned capital spending ($4,730,000) and the owners to pay for the remaining 57% ($6,270,000). And we would expect lenders to pay for 43% of the following year’s $12,000,000 planned capital spending ($5,160,000) and the owners to pay for the remaining 57% ($6,840,000). So we would expect debt and dividend results as follows.

• Coming year: Borrow 43% of the $11,000,000 to be spent = $4,730,000. Pay for the remaining $11,000,000 – $4,730,000 = $6,270,000 by retaining from the $6,950,000 expected net income. The residual of $6,950,000 – 6,270,000 = $680,000 would be paid as cash dividends to the common stockholders.

• Following year: Borrow 43% of the $12,000,000 to be spent = $5,160,000. Pay for the remaining $12,000,000 – $5,160,000 = $6,840,000 by retaining from the $5,650,000 in expected net income. Then the residual of $5,650,000 – $6,840,000 = -$1,190,000 would be “paid out” as cash dividends. In other words, no dividends would be paid, and the company would have to pay an investment banking firm to help it locate $1,190,000 in new equity money to maintain the 43%/57% capital structure intact.

Textbook examples often allude to payout ratios that remain constant over time, but unless the company’s net income/cash flow to owners were fairly steady over time the result would be cash dividends (which some stockholders, like retirees, might rely on to help meet their living expenses) that could differ considerably from year to year. Real-world observations suggest that common stockholders prefer steady dividend payments, even though an accompanying result is to make it difficult to keep the capital structure at its targeted level. The residual dividend idea is supported by economic logic (keeping an optimal capital structure intact and obtaining equity money cheaply, by retaining earnings rather than paying investment bankers to locate new owners). But this approach would definitely create an erratic quarter-to-quarter (and thus year-to-year) cash dividend stream for the company’s common stockholders.

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