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CHAPTER 16 B - 1
12. If you only want $200 in Year 1, you will buy:
Shares to buy at Year 1 = ($1,950 – 200)/$56.52
Shares to buy at Year 1 = 30.96 shares
at Year 1. Your dividend payment in Year 2 will be:
13. a. If the company makes a dividend payment, we can calculate the wealth of a shareholder as:
Dividend per share = $10,988/4,100 shares
Dividend per share = $2.68
The stock price after the dividend payment will be:
b. If the company pays dividends, the current EPS is $4.50, and the PE ratio is:
PE = $81.32/$4.50
PE = 18.07
If the company repurchases stock, the number of shares will decrease. The total net income is the
EPS times the current number of shares outstanding. Dividing net income by the new number of
shares outstanding, we find the EPS under the repurchase is:
CHAPTER 16 B - 2
14. a. Since the firm has a 100 percent payout policy, the entire net income, $115,000 will be paid as a
dividend. The current value of the firm is the discounted value one year from now, plus the
current income, which is:
b. The current stock price is the value of the firm, divided by the shares outstanding, which is:
Stock price = $1,601,486.49/30,000
Stock price = $53.38
Since the company has a 100 percent payout policy, the current dividend per share will be the
company’s net income, divided by the shares outstanding, or:
c. i. According to MM, it cannot be true that the low dividend is depressing the price. Since
dividend policy is irrelevant, the level of the dividend should not matter. Any funds not
distributed as dividends add to the value of the firm, hence the stock price. These directors
merely want to change the timing of the dividends (more now, less in the future). As the
calculations below indicate, the value of the firm is unchanged by their proposal. Therefore,
share price will be unchanged.
To show this, consider what would happen if the dividend was increased to $5.25. Since
only the existing shareholders will get the dividend, the required dollar amount to pay the
dividends is:
CHAPTER 16 B - 3
This money can only be raised with the sale of new equity to maintain the all-equity
financing. Since those new shareholders must also earn 11 percent, their share of the firm
one year from now is:
ii. The new shareholders are not entitled to receive the current dividend. They will receive only
the value of the equity one year hence. The present value of those flows is:
Present value = $1,602,825.00/1.11
Present value = $1,443,986.49
And the current share price will be:
15. a. The current price is the current cash flow of the company plus the present value of the expected
cash flows, divided by the number of shares outstanding. So, the current stock price is:
b. To achieve a zero dividend payout policy, he can invest the dividends back into the company’s
stock. The dividends per share will be:
Dividends per share = [($1,600,000)(.50)]/345,000
Dividends per share = $2.32
And the stockholder in question will receive:
CHAPTER 16 B - 4
Number of shares to buy = 41.88
16. a. Using the formula from the text proposed by Lintner:
Div1 = Div0 + s(t EPS1 – Div0)
Div1 = $2.61
b. Now we use an adjustment rate of .60, so the dividend next year will be:
Div1 = Div0 + s(t EPS1 – Div0)
c. The lower adjustment factor in part a is more conservative. The lower adjustment factor will
Challenge
17. Assuming no capital gains tax, the aftertax return for the Gordon Company is the capital gains growth
rate, plus the dividend yield times one minus the tax rate. Using the constant growth dividend model,
we get:
Aftertax return = g + D(1 – t) = .12
Solving for g, we get:
18. Using the equation for the decline in the stock price ex dividend for each of the tax rate policies, we
get:
CHAPTER 16 B - 5
a. P0 – PX = D(1 – 0)/(1 – 0)
P0 – PX = D
b. P0 – PX = D(1 – .15)/(1 – 0)
c. P0 – PX = D(1 – .15)/(1 – .20)
d. With this tax policy, we need to multiply the personal tax rate times one minus the dividend
P0 – PX = 1.3769D
e. Since different investors have widely varying tax rates on ordinary income and capital gains,
19. Since the $2,300,000 cash is after corporate tax, the full amount will be invested. So, the value of each
alternative is:
Alternative 1:
The firm invests in T-bills or in preferred stock, and then pays out as a special dividend in 3 years.
If the firm invests in T-Bills:
If the firm invests in T-bills, the aftertax yield of the T-bills will be:
Since the future value will be paid to shareholders as a dividend, the aftertax cash flow will be:
If the firm invests in preferred stock:
If the firm invests in preferred stock, the assumption would be that the dividends received will be
reinvested in the same preferred stock. The preferred stock will pay a dividend of:
Since 70 percent of the dividends are excluded from tax:
And the taxes the company must pay on the preferred dividends will be:
Taxes on preferred dividends = $10,384.50
So, the aftertax dividend for the corporation will be:
This means the aftertax corporate dividend yield is:
Aftertax corporate dividend yield = .0385, or 3.85%
The future value of the company’s investment in preferred stock will be:
Alternative 2:
The firm pays out a dividend now, and individuals invest on their own. The aftertax cash received by
shareholders now will be:
The individuals invest in Treasury bills:
If the shareholders invest the current aftertax dividends in Treasury bills, the aftertax individual yield
will be:
CHAPTER 16 B - 7
FV of investment in T-bills = $2,020,467.07
The individuals invest in preferred stock:
If the individual invests in preferred stock, the assumption would be that the dividends received will
be reinvested in the same preferred stock. The preferred stock will pay a dividend of:
20. a. Let x be the ordinary income tax rate. The individual receives an after-tax dividend of:
Aftertax dividend = $1,000(1 – x)
which she invests in Treasury bonds. The Treasury bond will generate aftertax cash flows to the
investor of:
Aftertax cash flow from Treasury bonds = $1,000(1 – x)[1 + .035(1 – x)]
If the firm invests the money, its proceeds are:
CHAPTER 16 B - 8
dividend or receives the proceeds from the firm’s investment and pays taxes on that amount. To
find the rate at which the investor would be indifferent, we can set the two equations equal, and
solve for x. Doing so, we find:
Note that this argument does not depend upon the length of time the investment is held.
b. Yes, this is a reasonable answer. She is only indifferent if the after-tax proceeds from the $1,000
c. Since both investors will receive the same pre-tax return, you would expect the same answer as
in part a. Yet, because Carlson enjoys a tax benefit from investing in stock (70 percent of income
x = .1050, or 10.50%
d. It is a compelling argument, but there are legal constraints, which deter firms from investing large
