Investment Analysis (FIN 670)
Fall 2009
Homework 8
Instructions: please read carefully
•
•
You should show your work how to get the answer for each calculation question to get full
credit
The due date is Tue Dec 15, 2009. Late homework will not be graded.
Name(s):
Student ID
1. A constant-growing stock just paid $2 dividend and has a current market price of $30. Determine the
stock's required rate of return if the company's constant growth rate is 5%.
a. 5%
b. 7%
c. 12%
d. 14%
1. c
R = D1/Po + g = 2(1+0.05)/30 + 0.05 = 0.12
2. Stock analysts just predicted that Hybrid Engine Company's earnings and dividends will grow at 20%
each year for the next two years due to its new invention. After that, its growth rate will stabilize at
5% per year indefinitely. Assume that the rate of return on the stock is 14% and its last dividend was
$1 per share. Determine the current price of the company's stock.
a. $16.8
b. $15.1
c. $16.1
d. $13.8
2. b
Step 1: compute D1, D2
D1 = D0(1+g*) = 1(1+.2)= 1.2
D2 = D1(1+g*) = 1.2(1+1.2) = 1.44
Step 2: compute P2 = D3/(k-g)
D3 = D2(1+g) = 1.44(1+0.05)= 1.512
P2 = 1.512/(0.14-0.05) = 16.8
Step 3: Compute P0 by discounting D1, D2, and P2 to present
P0 =
1.2
1.44
16.8
+
+
= 15.1
1
2
(1 + 0.14)
(1 + 0.14)
(1 + 0.14) 2
3. Southwest Technology's common stock is selling at $30 per share today. Southwest just paid a $2
dividend. Its dividend is expected to grow by 5% in the coming year. The required rate of return on
Southwest is 15%. Determine the common stock's dividend yield and capital gain yield for the first
year.
a. 10%; 5%
b. 7%; 8%
c. 5%; 10%
d. 6.7%; 8.3%
3. b
dividend yield = D1/P0
D1 = D0(1+g) = 2(1+0.05) = 2.1
So dividend yield = 2.1/30 = 0.07
We have total return = dividend yield + capital gain yield
15% = 7% + capital gain yield
So capital gain yield = 15% - 7% = 8%
4. Heavenly Hotels, Inc. will not pay any dividends for the next three years. Heavenly will pay its first
dividend of $2.00 per share at the end of year four and its dividends will stay the same forever. The
required rate of return on the company's common stock is 10%. What price should the stock be
selling now?
a. $20
b. $16
c. $12
d. $15
Step 1: Compute D1, D2, D3, D4
D1 = D2 = D3 = 0
D4 = 2
Step 2: compute P4 = D5/(k-g)
P4 = 2/(0.1-0) = 20
Step 3: Find P0 by discounting D1, D2, D3, D4 to present. In this case, D1 = D2= D3 = 0, so we only
need to discount D4 and P4
P0 =
2.0
20
+
= 15
4
(1 + 0.1)
(1 + 0.1) 4
5. If two firms have the same current dividend and the same expected growth rate, their stocks must sell
at the same current price or else the market will not be in equilibrium.
a. True.
b. False.
5.b
P0 = D1/(k-g), so the current stock price not only depends on dividend, growth rate, but also on required
return k
6. According to the dividend discount model, the current stock price of a company is ______________.
a. the sum of all future dividends
b. the sum of the present values of all future dividends
c. zero if the company does not pay dividends
d. All of the above are correct.
6.b
7. If two firms have the same current P/E ratio and the same EPS, their stocks must sell at the same
current price or else the market will not be in equilibrium.
a. True.
b. False.
7. a
8. A company's stock price will rise with an increase of its plowback ratio if ______________.
a. the company's ROE = its required rate of return
b. the company's ROE < its required rate of return
c. the company's ROE = its growth rate
d. the company's ROE > its required rate of return
8. d
9. Which of the following statements is most correct for a zero growth stock?
a. The stock's price one year from now should be the same as its current price.
b. The stock's dividend yield is larger than the stock's required rate of return.
c. The stock pays zero dividends.
d. None of the above is correct.
9. a
The following information is for question 10-12
Even Better Products has come out with a new and improved product. As a result, the firm projects an
ROE of 20%, and it will maintain a plowback ratio of 0.30. Its earning this year will be $2 per share
(E1=2). Investor expect 12% rate of return on the stock
10. At what price and P/E ratio would you expect the firm to sell
e. $23.33 and 11.67
f. $20.00 and 11.50
g. $24. 33 and 12.67
h. $22.23 and 13.47
i. $23.33 and 12.67
a.
g = ROE × b = 0.20 × 0.30 = 0.06 = 6.0%
D1 = $2(1 – b) = $2(1 – 0.30) = $1.40
P0 =
D1
$1.40
=
= $23.33
k − g 0.12 − 0.06
P/E = $23.33/$2 = 11.67
11. What is the present value of growth opportunity
a. 6.66
b. 7.66
c. 8.66
d. 5.66
11.a
PVGO = P0 –
E0
$2.00
= $23.33 –
= $6.66
k
0.12
12. Calculate the P/E ratio and the present value of growth opportunities if the firm planned to reinvest
only 20% of its earning.
g = ROE × b = 0.20 × 0.20 = = 0.04 = 4.0%
D1 = $2(1 – b) = $2(1 – 0.20) = $1.60
P0 =
D1
$1.60
=
= $20.00
k − g 0.12 − 0.04
P/E = $20/$2 = 10.0
PVGO = P0 –
E0
$2.00
= $3.33
= $20.00 –
k
0.12
13. MF Corp. has an ROE of 16% and a plowback ratio of 50%. If the coming year earning are expected
to be $2 per share (E1=2), required return is 12%. What price will the stock sell today?
a.
b.
c.
d.
e.
a.
25
26
27
28
29
g = ROE × b = 0.16 × 0.5 = 0.08 = 8.0%
D1 = $2(1 – b) = $2(1 – 0.50) = $1.00
P0 =
D1
$1.00
=
= $25.00
k − g 0.12 − 0.08
Your preliminary analysis of two stocks has yielded the information set forth below. The required return
for both stock A and B is 10% per year
Expected return on equity, ROE
Estimated earnings per share E1
Estimated dividends per share, D1
Current market price per share, P0
Stock A
14%
$2.00
1.00
27
Stock B
12%
$1.65
1.00
25
14. What are the expected dividend payout ratios for the 2 stocks
Dividend payout ratio = 1 – b
Stock A
$1/$2 = 0.50
Stock B
$1/$1.65 = 0.606
15. What are the expected dividend growth rates of each?
Growth rate = g = ROE × b
0.14 × 0.5 = 7.0%
0.12 × 0.394 = 4.728%
16. What is the intrinsic value of each stock (assume constant growth dividend model)
c.
Intrinsic value = V0
$1/(0.10 – 0.07)
= $33.33
$1/(0.10 – 0.04728)
= $18.97
17. Which stock would you choose to buy? Which stock would you choose to sell/short sell
You would choose to invest in Stock A since its intrinsic value exceeds its price. You
might choose to sell short stock B since its intrinsic value is lower than market price
18. Rio National Corp. is a U.S.-based company and the largest competitor in its industry. Exhibits
18A–18C present financial statements. Exhibit 18D presents relevant industry and market data.
a. The portfolio manager of a large mutual fund comments to one of the fund’s analysts, Katrina
Shaar: “We have been considering the purchase of Rio National Corp. equity shares, so I would like
you to analyze the value of the company. To begin, based on Rio National’s past performance, you
can assume that the company will grow at the same rate as the industry. Assume this rate is constant
over time, calculate the value of a share of Rio National equity on December 31, 2002, using the
constant growth model and the capital asset pricing model.
a. The value of a share of Rio National equity using the Gordon growth model
and the capital asset pricing model is $22.40, as shown below.
Calculate the required rate of return using the capital asset pricing model:
k = rf + β (kM – rf) = 4% + 1.8(9% – 4%) = 13%
Calculate the share value using the Gordon growth model:
P0 =
D o × (1 + g) $0.20 × (1 + 0.12)
=
= $22.40
k−g
0.13 − 0.12
b. Now if Katrina Shaar decides not to use the growth rate of the industry to be the growth rate of
Rio National. She decides to calculate the growth rate of the company itself. Calculate the
sustainable growth rate of Rio National on December 31, 2002. Use 2002 beginning-of-year
balance sheet values. Assumes this growth rate is constant over time, what should be the intrinsic
value of the stock on December 31, 2002?
The sustainable growth rate of Rio National is 9.97%, calculated as follows:
g = b × ROE = Earnings Retention Rate × ROE = (1 – Payout Ratio) × ROE =
Net Income
$30.16
⎛ DPS ⎞
⎛ $0.20 ⎞
= ⎜1 −
= 0.0934 = 9.34%
⎜1 −
⎟×
⎟×
EPS ⎠ Average Equity ⎝ $1.89 ⎠ 0.5 × (307.31 + 270.35)
⎝
P0 =
D o × (1 + g) $0.20 × (1 + 0.0934)
=
= $6.07
k−g
0.13 − 0.0934
EXHIBIT
18A
Rio National Corp. Summary year-endbalance sheets (U.S. $ millions)
EXHIBIT
18B
Rio National Corp. Summary income statement for the year ended December
31, 2002 (U.S. $ millions)
EXHIBIT
18C
Rio National Corp. Common equity data for 2002
EXHIBIT
18D
Industry and market data December 31, 2002
19.
Shaar (from the previous problem) has revised slightly her estimated earnings growth rate for Rio
National and, using normalized (underlying trend) EPS, which is adjusted for temporary impacts on
earnings, now wants to compare the current value of Rio National’s equity to that of the industry,
on a growth-adjusted basis. Selected information about Rio National and the industry is given in
Exhibit 19A.
EXHIBIT
19A
Rio National Corp. vs. industry
Compared to the industry, is Rio National’s equity overvalued or undervalued on a P/E-to-growth
(PEG) basis, using normalized (underlying) earnings per share. Assume that the risk of Rio
National is similar to the risk of the industry.
Rio National’s equity is relatively undervalued compared to the industry on a P/E-togrowth (PEG) basis. Rio National’s PEG ratio of 1.33 is below the industry PEG ratio of
1.66. The lower PEG ratio is attractive because it implies that the growth rate at Rio
National is available at a relatively lower price than is the case for the industry. The PEG
ratios for Rio National and the industry are calculated below:
Rio National
Current Price = $25.00
Normalized Earnings per Share = $1.71
Price-to-Earnings Ratio = $25/$1.71 = 14.62
Growth Rate (as a percentage) = 11
PEG Ratio = 14.62/11 = 1.33
Industry
Price-to-Earnings Ratio = 19.90
Growth Rate (as a percentage) = 12
PEG Ratio = 19.90/12 = 1.66
20. Helen Morgan, CFA, has been asked to use the DDM to determine the value of Sundanci, Inc.
Morgan anticipates that Sundanci’s earnings and dividends will grow at 32% for two years and
13% thereafter.
Assume the current year is the year 2000 (year 0). Use the data in year 2000 as the data in year 0.
Calculate the current value of a share of Sundanci stock by using a two-stage dividend discount
model and the data from Tables 20A and 20B.
TABLE
20A
Sundanci actual 1999 and 2000 financial statements for fiscal years
ending May 31 ($ million, except pershare data)
TABLE
20B
Selected financial information
Using a two-stage dividend discount model, the current value of a share of Sundanci is
calculated as follows:
D3
D1
D2
(k − g)
V0 =
+
+
1
2
(1 + k )
(1 + k )
(1 + k ) 2
$0.5623
$0.3770 $0.4976 (0.14 − 0.13)
=
+
+
= $43.98
1.14 2
1.141
1.14 2
where:
E0 = $0.952
D0 = $0.286
E1 = E0 (1.32)1 = $0.952 × 1.32 = $1.2566
D1 = E1 × 0.30 = $1.2566 × 0.30 = $0.3770
E2 = E0 (1.32)2 = $0.952 × (1.32)2 = $1.6588
D2 = E2 × 0.30 = $1.6588 × 0.30 = $0.4976
E3 = E0 × (1.32)2 × 1.13 = $0.952 × (1.32)3 × 1.13 = $1.8744
D3 = E3 × 0.30 = $1.8744 × 0.30 = $0.5623
21. Peninsular Research is initiating coverage of a mature manufacturing industry. John Jones, CFA, head
of the research department, gathered the following fundamental industry and market data to help in his
analysis:
a. Compute the price-to-earnings (P0/E1) ratio for the industry based on this fundamental data. Use
government bond yield to proxy for risk-free rate.
The industry’s estimated P/E can be computed using the following model:
P0/E1 = payout ratio/(r − g)
However, since r and g are not explicitly given, they must be computed using the
following formulas:
gind = ROE × retention rate = 0.25 × 0.40 = 0.10
rind = government bond yield + ( industry beta × equity risk premium)
= 0.06 + (1.2 × 0.05) = 0.12
Therefore:
P0/E1 = 0.60/(0.12 − 0.10) = 30.0
b. Jones wants to analyze how fundamental P/E ratios might differ among countries. He gathered
the following economic and market data:
Determine whether each of these fundamental factors would cause P/E ratios to be generally
higher for Country A or higher for Country B.
(i)
Forecast growth in real GDP would cause P/E ratios to be generally
higher for Country A. Higher expected growth in GDP implies
higher earnings growth and a higher P/E.
(ii)
ii. Government bond yield would cause P/E ratios to be generally
higher for Country B. A lower government bond yield implies a
lower risk-free rate and therefore a higher P/E.
(iii)
iii. Equity risk premium would cause P/E ratios to be generally
higher for Country B. A lower equity risk premium implies a
lower required return and a higher P/E.
22. The Stambaugh Corporation currently has earnings per share of $8.25. The company has no growth
and pays out all earnings as dividends. It has a new project which will require an investment of $1.60 per
share in one year. The project is only a two-year project, and it will increase earnings in the two years
following investment by $2.10 and $2.45 per share, respectively. Investors require a 12% return on
Stambaugh stock.
a. What is the value per share of the company's stock assuming the firm does not undertake the
investment opportunity?
If the company does not make any new investments, the stock price will be the present value of
the constant perpetual dividends. In this case, all earnings are paid dividends, so,
applying the perpetuity equation, we get:
P = Dividend / R
P = $8.25 / .12
P = $68.75
b. If the company does undertake the investment, what is the value per share of the stock now?
The investment is a one-time investment that creates an increase in EPS for two years. To
calculate the new stock price, we need the no growth price plus the PVGO. In this case,
the PVGO is simply the present value of the investment plus the present value of the
increases in EPS. So, the PVGO will be:
PVGO = C1 / (1 + R) + C2 / (1 + R)2 + C3 / (1 + R)3
PVGO = –$1.60 / 1.12 + $2.10 / 1.122 + $2.45 / 1.123
PVGO = $1.99
So, the price of the stock if the company undertakes the investment opportunity will be:
P = $68.75 + 1.99
P = $70.74
c. Again, assume the company undertakes the investment, what will be the price per share 4 years from
now?
After the project is over, and the earnings increase no longer exists, the price of the stock will
revert back to $68.75, the value of the company as a cash cow.
23. The stock of Nogro Corporation is currently selling for $10 per share. Earnings per share in the
coming year are expected to be $2. The company has a policy of paying out 50% of its earnings each year
in dividends. The rest is retained and invested in projects that earn a 20% rate of return per year. This
situation is expected to continue indefinitely.
a. Assuming the current market price of the stock reflects its intrinsic value as computed using the
constant growth rate DDM, what rate of return do Nogro’s investors require?
a. D1 = 0.5 × $2 = $1
g = b × ROE = 0.5 × 0.20 = 0.10
Therefore:
k=
D1
$1
+g =
+ 0.10 = 0.20 = 20.0%
$10
P0
b. By how much does its value exceed what it would be if all earnings were paid as dividends and
nothing were reinvested?
Since k = ROE, the NPV of future investment opportunities is zero:
PVGO = P0 −
E0
= $10 − $10 = $0
k
c. If Nogro were to cut its dividend payout ratio to 25%, what would happen to its stock price?
What if Nogro eliminated the dividend?
Since k = ROE, the stock price would be unaffected if Nogro were to cut its
dividend payout ratio to 25%. The additional earnings that would be reinvested
would earn the ROE (20%).
Again, if Nogro eliminated the dividend, this would have no impact on Nogro’s
stock price since the NPV of the additional investments would be zero.