Chapter 17 ◼ Dividends, Dividend Policy, and Stock Splits 577
20. DRIPs. Western Railroad has a dividend reinvestment program for shareholders. From 2013
to 2017, the company had the following share prices and dividends.
Year
Share Price After Dividend
Dividend per Share
2013
$28.00
$2.50
2014
$30.75
$2.75
2015
$35.15
$3.00
2016
$40.50
$3.50
2017
$41.25
$4.00
If you started with 100 shares of stock at $20 per share and participated fully in the DRIP, how
many shares of stock would you have at the end of 2017? What would be the total value of your
shares?
ANSWER
Start: 100 Shares
Yr #shares Dividend Purchased shares
$299.55
$450.79
$559.72
$250.00
578 Brooks ◼ Financial Management: Core Concepts, 4e
Solutions to Advanced Problems for Spreadsheet Application
1. Dividend irrelevancy problem (no taxes).
Dividend Policy Stock Price Before 28.00$ Stock Price After 26.50$
No cash dividend Shareholder No. 1 Shareholder No. 2 Shareholder No. 3 Shareholder No. 4 Shareholder No. 5
Shares Before 5,000 25,000 5,000 25,000 90,000
Wealth Before (Shares times Price) 140,000.00$ 700,000.00$ 140,000.00$ 700,000.00$ 2,520,000.00$
Desired Cash Dividend 8,000.00$ 45,000.00$ –$ –$ 100,000.00$
Shares Needed to Sell 285.7143 1,607.1429 – – 3,571.4286
Shares After Homemade Dividend 4,714.29 23,392.86 5,000.00 25,000.00 86,428.57
Homemade Cash Dividend 8,000.00$ 45,000.00$ –$ –$ 100,000.00$
Paper Wealth (Value of Remaining Shares) 132,000.00$ 655,000.00$ 140,000.00$ 700,000.00$ 2,420,000.00$
Cash Plus Paper Wealth After 140,000.00$ 700,000.00$ 140,000.00$ 700,000.00$ 2,520,000.00$
CHANGE IN OVERALL WEALTH –$ –$ –$ –$ –$
Cash Dividend of $1.50 per Share
Shares Before 5,000.00 25,000.00 5,000.00 25,000.00 90,000.00
Wealth Before (Shares times Price) 140,000.00$ 700,000.00$ 140,000.00$ 700,000.00$ 2,520,000.00$
Cash Dividend of $1.50 per Share 7,500.00$ 37,500.00$ 7,500.00$ 37,500.00$ 135,000.00$
Desired Cash Dividend 8,000.00$ 45,000.00$ –$ –$ 100,000.00$
Over (Under) Cash Desired Dividend 500.00$ 7,500.00$ (7,500.00)$ (37,500.00)$ (35,000.00)$
Need to Sell Shares YES YES NO NO NO
Need to Buy Shares NO NO YES YES YES
Number of Shares to Sell at $26.50 18.87 283.02 0.00 0.00 0.00
Number of Shares to Buy at $26.50 0.00 0.00 283.02 1415.09 1320.75
Cash From Sale of Shares/Purchase 500.00$ 7,500.00$ (7,500.00)$ (37,500.00)$ (35,000.00)$
Shares After Homemade Dividend 4,981.13 24,716.98 5,283.02 26,415.09 91,320.75
Total Homemade Cash Dividend 8,000.00$ 45,000.00$ –$ –$ 100,000.00$
Paper Wealth (Value of Remaining Shares) 132,000.00$ 655,000.00$ 140,000.00$ 700,000.00$ 2,420,000.00$
Cash Plus Paper Wealth After 140,000.00$ 700,000.00$ 140,000.00$ 700,000.00$ 2,520,000.00$
CHANGE IN OVERALL WEALTH –$ –$ –$ –$ –$
Difference Between Two Policies
Difference in Homemade Cash Dividend –$ –$ –$ –$ –$
Difference in Paper Wealth –$ –$ –$ –$ –$
580 Brooks ◼ Financial Management: Core Concepts, 4e
Part 2:
Dividend Policy Stock Price Before 28.00$ Stock Price After 26.875$
No cash dividend Shareholder No. 1 Shareholder No. 2 Shareholder No. 3 Shareholder No. 4 Shareholder No. 5
Shares Before 5,000 25,000 5,000 25,000 90,000
Wealth Before (Shares times Price) 140,000.00$ 700,000.00$ 140,000.00$ 700,000.00$ 2,520,000.00$
Desired Cash Dividend 8,000.00$ 45,000.00$ –$ –$ 100,000.00$
Shares Needed to Sell 307.1017 1,727.4472 – – 3,838.7716
Shares After Homemade Dividend 4,692.90 23,272.55 5,000.00 25,000.00 86,161.23
Homemade Cash Dividend 8,000.00$ 45,000.00$ –$ –$ 100,000.00$
Paper Wealth (Value of Remaining Shares) 131,401.15$ 651,631.48$ 140,000.00$ 700,000.00$ 2,412,514.40$
Cash Plus Paper Wealth After 139,401.15$ 696,631.48$ 140,000.00$ 700,000.00$ 2,512,514.40$
CHANGE IN OVERALL WEALTH 598.85$ 3,368.52$ –$ –$ 7,485.60$
Cash Dividend of $1.50 per Share
Shares Before 5,000 25,000 5,000 25,000 90,000
Wealth Before (Shares times Price) 140,000.00$ 700,000.00$ 140,000.00$ 700,000.00$ 2,520,000.00$
Cash Dividend of $1.50 per Share 7,500.00$ 37,500.00$ 7,500.00$ 37,500.00$ 135,000.00$
Tax on Dividend 1,875.00$ 9,375.00$ 1,875.00$ 9,375.00$ 33,750.00$
Net Cash Dividend 5,625.00$ 28,125.00$ 5,625.00$ 28,125.00$ 101,250.00$
Desired Cash Dividend 8,000.00$ 45,000.00$ –$ –$ 100,000.00$
Over (Under) Cash Desired Dividend (2,375.00)$ (16,875.00)$ 5,625.00$ 28,125.00$ 1,250.00$
Need to Sell Shares YES YES NO NO NO
Need to Buy Shares NO NO YES YES YES
Number of Shares to Sell at $26.875 94.65 672.48 0.00 0.00 0.00
Number of Shares to Buy at $26.875 0.00 0.00 209.30 1046.51 46.51
Cash From Sale of Shares/Purchase 2,375.00$ 16,875.00$ (5,625.00)$ (28,125.00)$ (1,250.00)$
Shares After Homemade Dividend 4,905.35 24,327.52 5,209.30 26,046.51 90,046.51
Total Homemade Cash Dividend 8,000.00$ 45,000.00$ –$ –$ 100,000.00$
Paper Wealth (Value of Remaining Shares) 131,831.41$ 653,802.15$ 140,000.00$ 700,000.00$ 2,420,000.00$
Cash Plus Paper Wealth After 139,831.41$ 698,802.15$ 140,000.00$ 700,000.00$ 2,520,000.00$
CHANGE IN OVERALL WEALTH 168.59$ 1,197.85$ –$ –$ –$
Difference Between Two Policies
Difference in Homemade Cash Dividend –$ –$ –$ –$ –$
Difference in Paper Wealth (430.26)$ (2,170.67)$ –$ –$ (7,485.60)$
Chapter 17 ◼ Dividends, Dividend Policy, and Stock Splits 581
Solutions to Mini-Case
East Coast Warehouse Club
1. The following is a partial list of comments made by staffers at the meeting. To help Frank
make a decision, identify the dividend policy or theory they reflect and comment on the
usefulness of each.
a. “What difference does it make if we pay dividends or not? Shareholders can always
sell a few shares and make their own dividends?” Response: “That works for the big
shareholders, but what about the little guys?”
b. “From a tax perspective, our shareholders would be better off paying the capital gains
tax than paying the tax on dividends.”
A revised version of the dividend irrelevance theory states that investors would be
better off not receiving dividends if dividends are taxed at a higher rate than capital
gains, which was the case for long periods of time. The best answer to this question is
c. “Stock prices go up and down due to market factors we can’t control. A dividend is
something you can count on.”
This theory is sometimes known as the “bird–in–hand” theory. Future capital gains are
582 Brooks ◼ Financial Management: Core Concepts, 4e
d. “The fact is some of our shareholders want dividends. You heard that at the
shareholders’ meeting.” Response: “That’s right, but of course maybe some of them
don’t. They might prefer that we try to grow the business faster.”
This comment reflects most clearly the clientele theory of dividends. Unfortunately, it is
e. “Our business has been doing well, but we’re in tough times. A lot of retailers are
hurting, and the market is down. By paying a dividend, we send a message to our
shareholders that we expect to stay strong for the foreseeable future.”
f. “Before we think of paying dividends, we should be sure that we have enough cash to
cover our operating expenses and capital budget.” Response: “That’s right, and once
we start paying dividends, we will never be able to cut them.”
This comment expresses the residual dividend policy. Under such a policy, the firm pays
dividends only if it has excess cash flows. The response expresses the idea that
2. When Frank thought he had gathered enough ideas about dividend theory and policy, he
asked the following question: “Let’s say we decide that our shareholders want some kind
of distribution. What’s the best way to do it?” Evaluate the merits of the following
suggestions.
a. “How about a 20% or 30% stock dividend? They will feel like they’re getting
something, and it won’t use any cash.”
A stock dividend really conveys nothing of value to the shareholders. Small shareholders
b. “Our stock has been trading between $65 and $80 for the last year. How about a 2-for-
1 or 3-for-1 stock split.”
Chapter 17 ◼ Dividends, Dividend Policy, and Stock Splits 583
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would not be expected to significantly change the value of the company or shareholder
wealth. The disgruntled shareholders seem to want cash.
c. “What about a stock repurchase plan?”
d. Frank: “Nice thoughts, but the institutional investors seem to be the ones asking for
dividends. They won’t be easily fooled. Let’s focus on cash dividends for now.”
3. Assume an investor holds 1,000 shares of East Coast stock which is trading at $72 per
share immediately before the following actions. Calculate the probable value of the stock,
the amount of cash received, and total investor wealth immediately after the following
actions. Consider each action independently.
a. East Coast pays a 20% stock dividend.
b. East Coast splits its stock 3-for-1.
c. East Coast pays a $2.00 per share cash dividend. The tax rate on dividends is 15%.
d. East Coast pays a $2.00 per share cash dividend. The investor holds her shares in a tax–
sheltered retirement account.
e. The investor sells 100 shares, which were purchased for $52 per share. The tax rate on
capital gains is 15%
Chapter 17 ◼ Dividends, Dividend Policy, and Stock Splits 585
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Operations
$157,500
$166,950
$176,967
$187,585
Maintenance
$32,400
$34,344
$36,405
$38,589
Investing
$39,600
$41,976
$44,495
$47,164
Expected Excess
$85,500
$90,630
$96,068
$101,832
The year 1 dividend would be $95,000/42,500 = $2.235. The year 2 dividend would be
$90,630/42,500 = $2.13. One thing about dividends that is known with some certainty is that
investors do not like dividend cuts and interpret them as a signal that the company is
experiencing cash flow problems, so a strict residual policy would be very confusing to investors
and probably not a good idea.
Additional Problems with Solutions
1. Stock price around dividend. On April 4, Forex Corporation announced that it would pay a
dividend of $0.75 per share to all shareholders that were on record as of April 11, with
checks being mailed on April 21. Determine what the stock price of Forex Corporation will
be after the cash dividend announcement in a world of no taxes. Assume that the current
price is $37.50 per share and that the price does not change between April 4 and April 21.
On what day does the price change? What is the cost to a buyer after the announcement?
What is the sales revenue to a seller after the announcement? Assume that stock
settlements take two days.
ANSWER (Slides 17-46 to 17-47)
Ex-dividend date = April 9
2. Change to low-dividend-payout policy (no taxes). Joan currently owns 800 shares of RST,
Inc. The company has a high-dividend-payout policy, and this year will pay $3.00 cash
dividend on its shares selling currently at $30.00 per share. Joan wants a low-dividend–
Before Ex-Date
After Ex-Date
Dividend
Dividend
New Owner
+$0.75
Old Owner
$37.50
$37.50
36.750
+$0.75
$37.50
586 Brooks ◼ Financial Management: Core Concepts, 4e
payout policy of 5% of the stock price. What will Joan need to do to convert this high-
dividend-payout policy to a low dividend-payout policy for her?
ANSWER (Slides 17-48 to 17-49)
3. Change to high dividend policy. Pearl currently owns 600 shares of Ajax, Inc. Ajax has a low-
payout-dividend policy, and this year will pay 4% cash dividend on its shares selling currently
at $40. Pearl wants a high-payout-dividend policy of 9% of the stock price. What will Pearl
need to do to convert this low-payout-dividend policy to a high-payout-dividend policy for
herself? Assume a world of no taxes
ANSWER (Slides 17-50 to 17-51)
588 Brooks ◼ Financial Management: Core Concepts, 4e
$962.09
$815.93