Equity valuation:
concepts and basic tools (Reading
52)
|
Exercise
Problems:
|
1. An investor gathered the
following data in order to estimate the value of the company's preferred
stock:
Par value
of preferred
stock offered at a 6% dividend rate
|
$100
|
Company's
sustainable growth rate
|
5%
|
Yield on
comparable preferred stock issues
|
11.5%
|
Investor's
marginal tax rate
|
30%
|
The value of the company’s preferred
stock is closest to:
A. $52.17
B. $74.53
C. $96.92
|
|
Ans: A;
The
formula to calculate the intrinsic value of a non-callable, non-convertible
preferred stock is:
Intrinsic
Value= Dp/ kp
where Dp refers to the fixed dividend and kp refers to the required rate of return.
Therefore,
intrinsic value = $100×0.060/0.115 = $52.17
|
2. A
company’s $100 par perpetual preferred stock has
a dividend rate of 7 percent and a required rate of return of 11 percent.
The company’s earnings are expected to grow at a constant rate of
3 percent per year. If the market price per share for the preferred
stock is $75, the preferred stock is most appropriately described
as being:
A. overvalued by
$11.36.
B. undervalued by
$15.13.
C. undervalued by
$36.36.
|
|
Ans: A;
Intrinsic
Value of perpetual preferred stock
= Dp/ kp
=
$7/0.11
=
$63.64
Therefore,
the stock is overvalued by $75.00-64.64 = $11.36
|
3. A
company’s series B, 8% preferred stock with a par value of $ 50 pays
quarterly dividends. Its current market value is $35. The shares are
retractable (at par) with the retraction date set for three years
from today. Similarly rated preferred issues have an estimated nominal
required rate of return of 12%. Analysts expect a sustainable growth
rate of 4% for the company’s earnings. The intrinsic value estimate
of a share of this preferred issue is closest to:
A. $33.33
B. $52.00
C. $45.02
|
|
Ans: C;
Quarterly
dividend = ($50) (0.08) / 4 = $1 a share;
Quarterly
required return = 12% / 4 = 3%;
V0 = $1/1.03 +1/1.032 +1 / 1.033 + …+1/1.0312 + 50/1.03 12
=$ 45.02
Using
a financial calculator:
PMT
= $1;
N=12;
FV
= 50$;
I
= 3%;
Compute
PV = $ 45.02.
|
4. An
investor evaluating a company's common stock for investment has gathered
the following data:
Earnings
per share (2012)
|
$2.50
|
Dividend
payout ratio (2012)
|
60%
|
Dividend
growth rate expected during Years 2013 and 2014
|
25%
|
Dividend
growth rate expected after Year 2014
|
5%
|
Investors'
required rate of return
|
12%
|
Using the two-stage
dividend discount model, the value per share of this common stock
in 2012 is closest to:
A. $28.57
B. $31.57
C. $38.70
|
|
Ans: B ;
Dividend
per share (2012) = $2.50 (0.6) = $1.50.
V2012
=1.50(1.25)/1.12+1.50(1.25)2/1.122+1.50(1.25)2 (1.05)/(0.12??0.05)×1/1.122
=
$1.67 + $1.87 + $28.03
=
$31.57.
|
5. A company
earned $3 a share last year and just paid a dividend of $2 a share.
The company’s dividends are expected to grow by 8 percent annually
for the next two years. An investor with an 11 percent required rate
of return expects to sell the stock at $75 two years from now. The
maximum amount the investor should be willing to pay for this company’s
stock (in $) today is
closest to:
A. 58.68.
B. 64.71.
C. 66.63.
|
|
Ans: B;
The
value of the stock
=
D1/
(1 + k) + D2/
(1 + k) 2 +
SP2 / (1 + k) 2
=
2×1.08/1.11+2×1.08 2 /1.11 2 +75/1.11 2
=
$64.71
|
6. An
analyst gathers the following information about a company:
Current
year’s dividend per share:
|
??2.00
|
Growth
rate in dividend during the next three years:
|
30%
in each of the years 1 and 2;
20%
in year 3
|
Growth rate
in dividend for year 4 and beyond:
|
8%
|
Weighted
average cost of capital:
|
12%
|
Cost of
equity capital:
|
15%
|
Risk-free
return
|
5.0%
|
The best estimate
of the company’s value per share is closest to:
A. ??48.68.
B. ??50.68
C. ??85.93
|
|
Ans: A
Time
period
|
Dividend
|
PVIF
@15%
|
Present
Value
|
1
|
2×1.30=2.60
|
0.8696
|
??2.26
|
2
|
2×1.302=3.38
|
0.7561
|
??2.56
|
3
|
2×1.302×1.20=4.06
|
0.6575
|
??2.67
|
4
and Beyond
|
V3=(.06×1.08)
/(15-0.08) =62.64
|
0.6575
|
??41.19
|
Value
per share
|
|
|
??48.68
|
|
7. An
investor uses the data below and Gordon’s constant growth dividend
discount model to evaluate a company’s common stock. To estimate growth,
she uses the average value of the:
1) compounded
annual growth rate over the period 2006–2011
2) sustainable
growth rate for the year 2011.
Year
|
EPS
|
DPS
|
ROE
|
2011
|
$3.20
|
$1.92
|
12%
|
2010
|
$3.60
|
$1.85
|
17%
|
2009
|
$2.44
|
$1.74
|
13%
|
2008
|
$2.08
|
$1.62
|
15%
|
2007
|
$2.76
|
$1.35
|
11%
|
2006
|
$2.25
|
$1.25
|
9%
|
If her
required return is 15%, the stock’s intrinsic
value
is closest to:
A. $23.71.
B. $25.31.
C. $30.14.
|
|
Ans: B ;
V0
= D1/(k – g)
To
estimate growth, which is the average value of 1) and 2):
1)
Dividend growth rate over the period 2006–2011
=
1.25(1 + g) 5 =
1.92;
Compounded
annual growth rate g = 8.96% ≈ 9%.
2)
sustainable growth rate for the year 2011 g
=
b × ROE
=Earnings
retention ratio ×
ROE
=
(1- Dividend payout ratio) × ROE
=(1-1.92/3.20)
× 12%
=4.8%
Therefore
the average of the two approaches = (9+4.8)/2 = 6.9%
V0
= D1/(k – g)
= 1.92 ×1.069/(0.15 ??0.069)
= 2.05/0.081
= $25.31.
|
8. The
Gordon growth model is most appropriate for valuing the common stock
of a dividend-paying company that is:
A. young and just entering the growth phase.
B. experiencing a higher than the sustainable growth rate.
C. mature and relatively insensitive to the economic fluctuations.
|
|
Ans: C ;
The
Gordon growth model is most appropriate for valuing common stock of
a dividend-paying company that is mature and relatively insensitive
to the business cycle or economic fluctuations.
|
9. An
analyst gathered the following data about a company in order to estimate
its P/E ratio.
Expected
dividend payout ratio
|
40%
|
Return on
equity
|
15%
|
Required
rate of return
|
12%
|
Stock’s
current market price
|
$75
|
The P/E ratio is closest to:
A. 6.7x
B. 13.3x
C. 20.0x
|
|
Ans: B
Growth
rate = g = Retention ratio × ROE =(1-0.40) × 15 = 9%
P/E
= D1/E1 /(k - g) = 0.40 /(0.12 - 0.09) = 13.33
|
10. Ming
Xi, an analyst, collects the following data for two companies, Walnert
and Almand. Using a required return of 12.4% for both companies, she
computes the justified forward P/E ratios, which are also given below.
Company
|
ROE (%)
|
Payout Ratio
(%)
|
Justified forward
P/E
|
Walnert
|
12.0
|
30
|
7.5
|
Almand
|
14.0
|
40
|
10.0
|
If
Company M increases its dividend payout ratio to 40% and Company N
decreases its dividend payout ratio to 30%, which of the following
will most likely occur? The justified P/E ratio of:
A. both companies would increase.
B. both companies would decrease.
C. Walnert would increase but Almand would decrease
|
|
Ans: A;
Dividend
growth rate = (1 – Payout ratio) × ROE;
Justified
forward P/E: P0/E1 = p/(k – g).
Using
the new payout ratios, the justified forward P/Es, calculated below,
of both firms would increase.
Company
Walnert:
New
dividend growth rate = (1 – 0.4) x 12% = 7.2%;
New
Justified forward P/E = 0.4/(0.124 – 0.072) = 7.7x.
Company
Almand:
New
dividend growth rate = (1 – 0.3) x 14% = 9.8%;
New
Justified forward P/E = 0.3/(0.124 – 0.098) = 11.5x.
|
11. An
investor gathers the following data of a stock:
Year
|
EPS ($)
|
DPS ($)
|
ROE
|
2011
|
3.20
|
1.92
|
12%
|
2010
|
3.60
|
1.80
|
17%
|
2009
|
2.44
|
1.71
|
13%
|
2008
|
2.50
|
1.60
|
15%
|
To estimate the
stock's justified forward P/E, the investor prefers to use the compounded
annual earnings growth and the average of the payout ratios over the
relevant period (2008–2011). If the investor uses 11.5% as her required
rate of return, the stock's justified forward P/E ratio is closest
to:
A. 10
B. 12
C. 21
|
|
Ans: C ;
Justified
forward P/E
= ===
Dividend
Payout Ratio (ex 2011)=1.92/3.20=0.60
Average
Payout Ratio=(0.60+0.50+0.70+0.64)/4=0.61
Earning
growth rate (g) over the period of 2008 to 2011 :
2.50 (1+g) 3 =3.20; g=8.6%
Required
rate of return = 11.5% , which is given.
Therefore, justified forward P/E =0.61/(0.115-0.086)=21.0
|
12. A
stock selling at $50 has a P/E multiple of 20 on the basis of the
current year’s earnings. An analyst estimates that next’s earnings
per share will be 10% higher and that the stock should be valued on
a forward looking basis at the industry average P/E of 18. Based on
the analyst’s assessment, it is most likely that the stock
is currently:
A. undervalued.
B. fairly valued.
C. overvalued.
|
|
Ans: C ;
If
company P/E > industry P/E, overvalued;
If
company P/E = industry P/E, fairly valued;
If
company P/E < industry P/E, undervalued;
Next
year’s EPS = ($50 / 20) × 1.10 = $2.75;
?? Company
forward P/E = $50/2.75 = 18.18
Since company forward P/E (18.18) is greater than the industry
forward P/E (18), the stock is overvalued.
|
13. An
analyst has gathered the following data for a company whose common
stock is currently priced at $40 per share:
Current
annual earnings per share E0
|
$6.00
|
Current
annual dividend per share D0
|
$2.40
|
Required
return on common stock
|
15.0%
|
Expected
constant growth rate in E and D
|
8.0%
|
If markets are in equilibrium, which of the following statements best
describes the company’s price-to-earnings (P/E) ratio? The company’s
P/E ratio based on the infinite period dividend discount model ( DDM)
is :
A. greater than the company’s trailing P/E ratio
B. the same as the company’s trailing P/E ratio
C. less than the company’s trailing P/E ratio
|
|
Ans: C;
Trailing
P/E ratio
=Current
stock price / Current or Trailing 12-month EPS
DDM
P/E ratio
=Current
stock price / Expected 12-month EPS
For
trailing P/E, since markets are in equilibrium, current stock price
(P) reflects the value determined by the constant growth dividend,
which equals to ($2.40) (1+8%) / (15.0%-8%) = $37.03. Therefore, The
trailing P/E = $37.03 / $6 = 6.17
For
DDM P/E, since expected 12-month earnings = ($6.00) (1+8%) = $6.48,
the DDM P/E = $37.03 / $6.48 = 5.71
6.17
> 5.71
DDM
P/E is less than trailing P/E.
|
14. An
analyst gathers the following information about a company:
Net profit
margin
|
8.0%
|
Return on
assets
|
10.0%
|
Financial
leverage: total assets/equity
|
2.5
|
Beta for
the company’s stock
|
1.5
|
Expected
return on the market index
|
10.0%
|
Risk-free
return
|
5.0%
|
The analyst
expects the information above to accurately reflect the future. If
the company wants to achieve a growth rate of 15% without changing
its capital structure or issuing new equity, the company’s maximum
dividend payout ratio ( in %) is closest to:
A. 25.
B. 40.
C. 60.
|
|
Ans: B;
ROE
= ROA × Financial Leverage
= (10.0%) (2.5)
= 25%;
Retention
ratio = growth rate / ROE
= 0.15/0.25
= 0.60;
Payout
ratio = 1 – Retention ratio
=
1 – 0.60
=40%
|
15. A
analyst gathers the following data on two companies:
|
Company
X
|
Company
Y
|
Return
on assets
|
10.9%
|
9.0%
|
Return
on equity
|
15.4%
|
14.3%
|
Div.
payout ratio
|
0.35
|
14.3%
|
Required
return on equity
|
13.0%
|
12.4%
|
WACC
|
11.8%
|
11.7%
|
Based on the information provided, the most accurate
conclusion is that Company X’s stock is more attractive relative to
that of Company Y’s because of its:
A. greater financial leverage
B. smaller P/E ratio
C. higher dividend growth rate
|
|
Ans: B ;
|
Company
X
|
Company
Y
|
Financial
Leverage =ROE/ROA
|
15.4
/ 10.9 = 1.4x
|
14.3
/ 9.0 = 1.6x
|
P/E
=Payout ratio/(k-g)
|
0.35
/ (0.13-0.10) = 11.7x
|
0.30
/ (0.124-0.10) = 12.5x
|
Div.
growth rate = Retention ratio×ROE
|
15.4
(1-0.35) = 10.0%
|
14.3
(1-0.30) = 10.0%
|
From
the above table, we could conclude that
1).
Company X has a lower financial leverage,;
2).
Company X has a smaller P/E ratio;
3).
Company X and Y share the same dividend growth.
Therefore,
Company X’s stock is more attractive because of its smaller P/E ratio.
|
16. Most
of the differences
among companies with respect to quality of earnings are addressed
when companies are compared using:
A. price to earnings ratio.
B. price to cash flow ratio.
C. both price to earnings ratio
and price to cash flow ratios
|
|
Ans: B ;
The
price to cash flow ratio is less subject to manipulation by management
than earnings, generally more stable than earnings, and it addresses
the issue of differences in accounting conservatism between companies.
|
17. The
issue of differences in accounting conservatism between companies
is best addressed when companies are compared using which of
the following ratios?
A. Price-to-earnings
B. Price-to-cash
flow
C. Price-to-book value
|
|
Ans: B;
Using
price-to-cash flow rather than price-to-earnings addresses the issue
of differences in accounting conservatism between companies (differences
in quality of earnings).
|
18. Among a
company’s price to earnings (P/E), price to sales (P/S), and price
to cash flow (P/CF) ratios, it is most accurate to state that
P/E ratios are generally more stable period to period than:
A. P/S
ratios but not P/CF ratios.
B. P/CF
ratios but not P/S ratios.
C. neither P/S ratios nor P/CF ratios.
|
|
Ans: C;
Both
sales and cash flow tend to be more stable than earnings, making the
multiples based on sales and cash flow more stable than those based
on EPS.
|
19. Which of the following
is the least accurate rationale to justify the use of price-to-book
value (P/B) ratio as a measure of relative valuation of companies?
A. P/B
is a useful measure of value for firms that are not expected to continue
as a going concern.
B. Compared
to P/E, the P/B ratio is not influenced by such accounting effects
as expensing a capital investment as opposed to capitalizing it.
C. P/B is particularly appropriate to value
companies primarily composed of liquid assets, for example, those
in the financial services industry.
|
|
Ans: B;
Choice
B is a drawback rather than a rationale for using P/B as a measure
of relative valuation. P/B does not correctly reflect a company’s
value due to the historical cost basis of assets in P/B ratio.
Choice
A and C are both rationale for using P/B ratio as a measure of relative
valuation.
|
20. In
calculating free cash flow to equity, adjustment is needed for payments
made to which of the following capital providers?
|
Debt holders
|
Preferred
Stockholders
|
A.
|
Yes
|
No
|
B.
|
Yes
|
Yes
|
C.
|
No
|
Yes
|
|
|
Ans: B;
Free
cash flow to equity is after subtracting payments to both debt holders
and preferred stockholders.
|
21. Which
of the following is the most appropriate reason for using a free-cash-flow-to-equity
(FCFE) model to value equity of a company?
A. FCFE models provide more accurate valuations than the dividend
discount models.
B. A firm’s borrowing activities could influence dividend decisions
but they would not impact FCFE.
C. FCFE is a measure of the firm’s
dividend-paying capacity.
|
|
Ans: C ;
FCFE
is a measure of the firm’s dividend paying capacity.
|
22. The measures
of free cash flow and discount rate to use when estimating the total
value of a firm, respectively, are:
A. Operating
cash flow before interest payments on debt; cost of equity
B. Operating
cash flow before interest payments on debt but after deducting base
capital expenditures; cost of equity
C. Operating cash flow before interest payments
on debt but after deducting base capital expenditures; cost of equity;
weighted average cost of capital.
|
|
Ans: C;
In
estimating the value of total firm, we should use the free cash flow
available to both stockholders and bondholders. Therefore, operating
cash flow before debt related costs and after subtracting the required
capital expenditure is the appropriate measure of free cash flow.
As
the value of the total firm includes the value of equity and the value
of debt, the weighted average cost of capital is the relevant discount
rate.
|
23. Which
of the following multiples is most helpful when comparing with significant
differences in capital structure?
A. EV/EBITDA.
B. Price-to-book ratio.
C. Price-to cash flow ratio
|
|
Ans: A ;
EBITDA
is computed prior to payment to any of the company’s financial stakeholders
and is not impacted by the amount of debt leverage and therefore most
useful when comparing companies with significant differences in capital
structure.
|
24. An
analyst using the enterprise value approach to valuation gathers the
following data:
EBITDA
|
$65.8m
|
Value of
debt
|
$90.0m
|
Value of
preferred stock
|
$25.4m
|
Cash &
marketable securities
|
$6.9m
|
No. of common
shares outstanding
|
$12.5m
|
Firm’s tax
rate
|
30%
|
Appropriate
EV/EBITDA multiple
|
6x
|
The value
per share of the company’s stock is closest to:
A. $13.43
B. $22.35
C. $22.90
|
|
Ans: C;
Step
1: compute the enterprise value (EV) from EBITDA × EV/EBITDA multiple;
Step
2: determine market capitalization (value of equity) using EV
=
Market capitalization + MV of preferred stock + MV of debt –Cash and
investments
Step3:
compute the value per share
=Market
capitalization/No. of common stock outstanding
Enterprise value
|
6×65.8=394.8
|
-MV
of debt
|
-90
|
-MV
of preferred stock
|
-25.4
|
+cash
& marketable sec.
|
+6.9
|
=Market
Capitalization
|
=286.3
|
/No.
of shares outstanding
|
/12.5
|
Value
per share
|
$22.90
|
|
25. Rebecca
Lee, CFA, gathers the following information about a company.
Balance
Sheet:
Assets
|
Liabilities
and Shareholders’ Equity
|
Cash
|
$
5,000
|
Accounts
payable
|
$
10,000
|
Accounts
receivable
|
15,000
|
Notes
payable
|
15,000
|
Inventory
|
25,000
|
Long-term
debt
|
40,000
|
Net
fixed assets
|
80,000
|
Common
shareholders’ equity
|
60,000
|
Total
Assets
|
$125,000
|
Total
liabilities and equity
|
$125,000
|
Additional
Information:
|
Number
of outstanding shares
|
7,000
|
Market
value of long-term debt
|
$45,000
|
Market
value of accounts receivable and inventory
|
90%
of reported values
|
Net
fixed assets
|
120%
of reported values
|
Accounts
payable and notes payable
|
Same
as the reported values
|
|
|
|
|
|
Using asset-based valuation approach, the estimated
value per share is closest to:
A. $ 9.57.
B. $10.29.
C. $11.00.
|
|
Ans: A;
Asset-based
Model: Equity value is the market value of assets minus the market
value of liabilities.
MV
of Assets
|
$5,000
+ $40,000(0.90) + $80,000(1.20)
|
$137,000
|
MV
of Liab.
|
10,000
+ $15,000 + $45,000
|
$70,000
|
Est.
value per share
|
($137,000
- $70,000) / 7,000 shares
|
$9.57/share
|
|
26. An
investor wants to determine the intrinsic value of the common stock
for a company with the following characteristics:
??
The firm maintains a constant dividend payout ratio
??
Goodwill and patents account for 40% of the firm’s assets
??
The firm’s revenues and earnings are highly correlated with the business
cycle
??
Further, the investor focuses on the firm’s capacity to pay dividends
rather than expected dividends.
Considering
the above, the investor will most likely use which of the following
valuation models?
A. Asset-based valuation model.
B. Free-cash-flow-to-equity model.
C. Gordon dividend growth model.
|
|
Ans: B ;
Choice
B is correct. Free-cash-flow-to-equity (FCFE) is a measure of the
firm’s dividend-paying capacity which should be reflected in the cash
flow estimates rather than expected dividends.
Choice
C is not correct. Analysts must make projections of financials to
forecast future FCFE and thus the constant growth assumption as in
the Gordon growth model is not an issue.
Choice
A is not correct. An asset-based valuation model is not appropriate
considering the high proportion of intangibles (goodwill and patents)
in the firm’s assets.
|
27. The
latest annual report of Giolias, Inc. presents the following data:
Common stock
$0.50 par value- Issued ( 2,000,000 shares)
|
$1,000,000
|
Additional
paid-in-capital:
|
$10,000,000
|
Retained
earnings:
|
$4,000,000
|
Treasury
stock (500,000 shares):
|
$5,000,000
|
Current
price per share:
|
$15
|
The company’s ending inventories based on
LIFO are valued at $5,000,000 and a footnote to financial statements
reports inventories valued using FIFO basis would be $ 6,000,000.
The company’s tax rate is 30%. The un-adjusted and adjusted price-to-book
values of Giolias, respectively, are closest to:
|
Unadjusted
P/BV
|
Adjusted
P/BV
|
A.
|
1.88
|
1.94
|
B.
|
2.25
|
2.10
|
C.
|
2.25
|
2.42
|
|
|
Ans: B;
Unadjusted
P/BV
|
Adjusted
P/BV
|
BV
per share = $ (1m+10m+4m-5m)/15 sh. = $6.67
|
Inventory
adj. = (6m – 5m) ×0.7= $0.7 m
Adj.
BV per share = $ (1m+10m+4m-5m+0.7m)/15 sh. = $7.13
|
P/BV
= $15 / $6.67 = 2.25
|
Adj. P/BV
= $15 / $7.13= 2.10
|
|
28. An
analyst gathers the following information about a company:
|
2004
|
2011
|
Sales
|
$128.4
million
|
$220.0
million
|
ROE
|
10
percent
|
10
percent
|
Net
Profit Margin
|
6
percent
|
7
percent
|
Number
of shares outstanding
|
5
million
|
6
million
|
The analyst expects
sales in 2012 to grow at the historical compound annual growth rate
from the year 2004 to 2011. For the year 2012, the net profit margin
and the number of shares outstanding are expected to remain unchanged
from the year 2011. The company's earnings per share (EPS) for the
year 2012 is closest to:
A. $2.77.
B. $2.83.
C. $3.96.
|
|
Ans: A;
To
compute the compounded Annual Sales Growth g:
128.4
× (1+g) 7=220.0
g=8%
EPS
2009
=
Sales 2008× (1+g) × NPM / # of shares
=
220 (1.08) (0.07) / 6
=$2.77
|
29. An
analyst gathers the following information about a company:
Return on
equity
|
20%
|
Earnings
retention rate
|
50%
|
Current
DPS paid on common stock
|
??2.00
|
Required
rate of return on common stock
|
15%
|
Current
stock price
|
??50
|
Company’s
P/E ratio
|
30x
|
Industry
average P/E ratio
|
20x
|
Stock’s
beta
|
0.7
|
Using the dividend
discount model and the other data given, the company’s stock is best described as a:
A. speculative stock.
B. cyclical stock.
C. growth stock.
|
|
Ans: B;
A
speculative stock is
1) Substantially
overvalued.
2) Its
P/E is much higher than the industry average P/E.
Intrinsic
value of the stock = ??2.00 / (15%-10%) = ??44.00
where
the implied dividend growth rate
=
ROE × Retention Rate
=
20%×0.5
=10%.
1) current
stock price (50) > intrinsic value (44) : substantially overvalued;
2) Company
P/E (30x) > Industry average P/E (20x)
?? The company’s stock
is best described as a speculative stock.
|