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CHAPTER 6 B - 1
23. The dividend yield is the dividend divided by the stock price, so:
Dividend yield = Dividend/Stock price
.027 = Dividend/$34.18
Dividend = $.92
The “Net Chg” of the stock shows the stock increased by $.19 on this day, so the closing stock price
yesterday was:
24. To find the number of shares owned, we can divide the amount invested by the stock price. The share
price of any financial asset is the present value of the cash flows, so, to find the price of the stock we
need to find the cash flows. The cash flows are the two dividend payments plus the sale price. We also
need to find the aftertax dividends since the assumption is all dividends are taxed at the same rate for
all investors. The aftertax dividends are the dividends times one minus the tax rate, so:
Year 1 aftertax dividend = $2.65(1 – .20)
We can now discount all cash flows from the stock at the required return. Doing so, we find the price
of the stock is:
CHAPTER 6 B - 2
25. Here we have a stock paying a constant dividend for a fixed period, and an increasing dividend
thereafter. We need to find the present value of the two different cash flows using the appropriate
quarterly interest rate. The constant dividend is an annuity, so the present value of these dividends is:
Now we can find the present value of the dividends beyond the constant dividend phase. Using the
present value of a growing annuity equation, we find:
P12 = $41.88
This is the price of the stock immediately after it has paid the last constant dividend. So, the present
value of the future price is:
The price today is the sum of the present value of the two cash flows, so:
26. Here we need to find the dividend next year for a stock with nonconstant growth. We know the stock
price, the dividend growth rates, and the required return, but not the dividend. First, we need to realize
that the dividend in Year 3 is the constant dividend times the FVIF. The dividend in Year 3 will be:
D3 = D(1.04)
The equation for the stock price will be the present value of the constant dividends, plus the present
value of the future stock price, or:
P0 = D/1.098 + D/1.0982 + D(1.04)/(.098 – .04)]/1.0982
We can factor out D in the equation. Doing so, we get:
Reducing the equation even further by solving all of the terms in the braces, we get:
D = $3.67
CHAPTER 6 B - 3
27. The required return of a stock consists of two components, the capital gains yield and the dividend
yield. In the constant dividend growth model (growing perpetuity equation), the capital gains yield is
the same as the dividend growth rate, or algebraically:
R = D1/P0 + g
We can find the dividend growth rate by the sustainable growth rate equation, or:
28. First, we need to find the annual dividend growth rate over the past four years. To do this, we can use
the future value of a lump sum equation, and solve for the interest rate. Doing so, we find the dividend
growth rate over the past four years was:
FV = PV(1 + R)t
$2.36 = $1.73(1 + R)4
29. a. We can find the price of all the outstanding company stock by using the dividends the same way
we would value an individual share. Since earnings are equal to dividends, and there is no growth,
the value of the company’s stock today is the present value of a perpetuity, so:
CHAPTER 6 B - 4
The price-earnings ratio is the stock price divided by the current earnings, so the price-earnings
ratio of each company with no growth is:
PE = 8.33 times
b. Since the earnings have increased, the price of the stock will increase. The new price of all the
outstanding company stock is:
P = D/R
c. Since the earnings have increased, the price of the stock will increase. The new price of the all
the outstanding company stock is:
P = D/R
PE = 11.67 times
30. a. Using the equation to calculate the price of a share of stock with the PE ratio:
P = Benchmark PE ratio × EPS
So, with a PE ratio of 19, we find:
P = $72.77
b. First, we need to find the earnings per share next year, which will be:
EPS1 = $4.08
CHAPTER 6 B - 5
Using the equation to calculate the price of a share of stock with the PE ratio:
P1 = $77.50
c. To find the implied return over the next year, we calculate the return as:
R = .065, or 6.5%
Notice that the return is the same as the growth rate in earnings. Assuming a stock pays no
dividends and the PE ratio is constant, this will always be true when using price ratios to evaluate
the price of a share of stock.
31. We need to find the enterprise value of the company. We can calculate EBITDA as sales minus costs,
so:
EBITDA = Sales – Costs
EBITDA = $31,500,000 – 17,300,000
EBITDA = $14,200,000
Solving the EV/EBITDA multiple for enterprise value, we find:
Stock price = $70.26
32. a. To value the stock today, we first need to calculate the cash flows for the next 6 years. The sales,
costs, and net investment all grow by same rate, namely 14 percent, 12 percent, 10 percent, 8
percent, respectively, for the following 4 years, then 6 percent indefinitely. So, the cash flows for
each year will be:
CHAPTER 6 B - 6
Net income
$42,600,000
$48,564,000
$54,391,680
$59,830,848
$64,617,316
$68,494,355
Investment
15,000,000
17,100,000
19,152,000
21,067,200
22,752,576
24,117,731
Cash flow
$27,600,000
$31,464,000
$35,239,680
$38,763,648
$41,864,740
$44,376,624
To find the terminal value of the company in Year 6, we can discount the Year 7 cash flows as a
growing perpetuity, which will be:
b. In this case, we are going to use the PE multiple to find the terminal value. All of the cash flows
from part a will remain the same. So, the terminal value in Year 6 is:
Challenge
33. We are asked to find the dividend yield and capital gains yield for each of the stocks. All of the stocks
have a 17 percent required return, which is the sum of the dividend yield and the capital gains yield.
To find the components of the total return, we need to find the stock price for each stock. Using this
CHAPTER 6 B - 7
Capital gains yield = .17 – .07 = .10, or 10%
X: P0 = D0(1 + g)/(R – g) = $3.65/(.17 – 0) = $21.47
Dividend yield = D1/P0 = $3.65/$21.47 = .17, or 17%
In all cases, the required return is 17 percent, but the return is distributed differently between current
income and capital gains. High-growth stocks have an appreciable capital gains component but a
34. a. Using the constant growth model, the price of the stock paying annual dividends will be:
b. If the company pays quarterly dividends instead of annual dividends, the quarterly dividend will
be one-fourth of the annual dividend, or:
Quarterly dividend = $2.96(1.04)/4
Quarterly dividend = $.77
To find the equivalent annual dividend, we must assume that the quarterly dividends are
CHAPTER 6 B - 8
The effective annual dividend will be the FVA of the quarterly dividend payments at the effective
quarterly required return. In this case, the effective annual dividend will be:
35. Here we have a stock with nonconstant growth, but the dividend growth changes every year for the
first four years. We can find the price of the stock in Year 3 since the dividend growth rate is constant
P3 = $75.21
The price of the stock today will be the PV of the first three dividends, plus the PV of the stock price
in Year 3, so:
36. Here we want to find the required return that makes the PV of the dividends equal to the current stock
price. The equation for the stock price is:
We need to find the roots of this equation. Using spreadsheet, trial and error, or a calculator with a
root solving function, we find that:
