P7-13. Personal finance: Common stock value—variable growth
LG 4; Challenge
P0 
0 1
1
(1 )
(1 )
N t
t
ts
D g
r
=
´ +
+
å
1
2
1
(1 ) ( )
N
N
s s
D
r r g
+
´
+ –
P0 PV of dividends during initial growth period PV of price of stock at end of growth period.
Steps 1 and 2: Value of cash dividends and PV of annual dividends
D1 $3.40 (1.00) $3.40
t Dt1/(1.14)t
PV
of Dividends
1 $3.40 0.8772 $ 2.98
Step 3: PV of price of stock at end of initial growth period
P4 [D5 (rs g)]
Step 4: Sum of PV of dividends during initial growth period and PV price of stock at end of growth
period
P7-14. Common stock value—variable growth
LG 4; Challenge
a.
t D01.08tDt1/(1.11)t
PV
of Dividends
$5.11
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Chapter 7 Stock Valuation    128
PV of stock at end of year 3
b. The PV of the first 3 year’s dividends is the same as in part a.
c. The PV of the first 3 year’s dividends is the same as in part a.
D4 D3(1.10) 2.50
P7-15. Personal finance: Common stock value—all growth models
LG 4; Challenge
a. P0 (CF0 r)
c. Steps 1 and 2: Value of cash dividends and PV of annual dividends
t D01.12tDt1/(1.18)t
PV
of Dividends
$78,626.83
Step 3: PV of price of stock at end of initial growth period
D2 1 $53,312 (1 0.07)
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Chapter 7 Stock Valuation    129
Step 4: Sum of PV of dividends during initial growth period and PV price of stock at end of growth
period
P7-16. Free cash flow (FCF) valuation
LG 5; Challenge
a. The value of the total firm is accomplished in three steps.
(1) Calculate the PV of FCF from 2021 to infinity.
(2) Add the PV of the cash flow obtained in (1) to the cash flow for 2020.
(3) Find the PV of the cash flows for 2016 through 2020.
Year FCF 1/(1.11)tPV
2016 $200,000 0.9009 $ 180,180
b. Calculate the value of the common stock.
c. Value per share $2,151,874 200,000 shares $10.76
P7-17. Personal finance: Using the free cash flow valuation model to price an IPO
LG 5; Challenge
a. The value of the firm’s common stock is accomplished in four steps.
(1) Calculate the PV of FCF from 2020 to infinity.
Year FCF 1/(1.08)tPV
2016 $700,000 0.9259 $ 648,130
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Chapter 7 Stock Valuation    130
(4) Calculate the value of the common stock using Equation 7.8.
b. Based on this analysis, the IPO price of the stock is over valued by $0.74 ($12.50 $11.76), and you
should not buy the stock.
c. The revised value of the firm’s common stock is calculated in four steps.
(1) Calculate the PV of FCF from 2020 to infinity.
(2) Add the PV of the cash flow obtained in (1) to the cash flow for 2019.
(3) Find the PV of the cash flows for 2016 through 2019.
Year FCF 1/(1.08)tPV
2016 $700,000 0.9259 $ 648,130
(4) Calculate the value of the common stock using Equation 7.8.
VS VC VD VP
P7-18. Book and liquidation value
LG 5; Intermediate
a. Book value per share:
Book value of assets (liabilities + preferred stock at book value)
number of shares outstanding
–
$780,000 $420,000
Book value per share $36 per share
10,000
–
= =
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Chapter 7 Stock Valuation    131
b. Liquidation value:
Cash $40,000 Liquidation Value of Assets 722,000
Marketable
Liquidation value of assets
Liquidation value per share Number of shares outstanding
=
$302,000
Liquidation value per share $30.20 per share
10,000
= =
c. Liquidation value is below book value per share and represents the minimum value for the firm. It is
P7-19. Valuation with price/earnings multiples
LG 5; Basic
Firm EPS P/EStock Price
A 3.0 (6.2) $18.60
P7-20. Management action and stock value
LG 6; Intermediate
a. P0 $3.15 (0.15 0.05) $31.50
P7-21. Integrative—risk and valuation and CAPM formulas
LG 4, 6; Intermediate
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Chapter 7 Stock Valuation    132
P7-22. Integrative—risk and valuation
LG 4, 6; Challenge
a. 14.8% 10% 4%
b. N 6, PV $1.73, FV $2.45
c. A decrease in the risk premium would decrease the required rate of return, which in turn would
increase the price of the stock.
P7-23. Integrative—risk and valuation
LG 4, 6; Challenge
a. Estimate growth rate:
b. (1) rs 0.14
(2) rs 
P7-24. Ethics problem
LG 4; Intermediate
a. This is a zero-growth dividend valuation problem, so
b. Using the new discount rate of 12% (11% 1% credibility risk premium), we have
The value decline is the difference between parts a and b:
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Chapter 7 Stock Valuation    133
Case 
Case studies are available on www.myfinancelab.com.
Assessing the Impact of Suarez Manufacturing’s Proposed Risky Investment on Its
Stock Value
a. Current per-share value of common stock growth rate of dividends:
Chapter 7 Stock Valuation    134
Spreadsheet Exercise 
The answer to Chapter 7’s Azure Corporation spreadsheet problem is located on the Instructor’s Resource Center
at www.pearsonhighered.com/irc under the Instructor’s Manual.
Group Exercise 
Group exercises are available on www.myfinancelab.com.
This chapter’s exercise takes the groups back to the future. The semester began with the fictitious firms having
Integrative Case 3: Encore International 
This case focuses on the valuation of a firm. The student explores various methods of valuation, including the
a.
b.
$40
/ ratio 6.4
$6.25
P E = =
c. (1) rs RF risk premiumEncore
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Chapter 7 Stock Valuation    135
As risk premiums rise, required return also rises.
d. Zero growth:
1
0
s
D
Pr
=
0
$4.00 $25
0.16
P= =
e. (1) Constant growth:
1
0
( )
s
D
Pr g
=–
0
($4.00 1.06) $4.24 $42.40
(0.16 0.06) 0.10
P´
= = =
–
(2) Variable growth model: PV of dividends
1
0 1
0
12
(1 ) 1
(1 ) (1 ) ( )
nN
N
ts s s
D g t D
Pr t r r g
+
=
æ ö é ù
´ +
= + ´
ç ÷ ê ú
+ + –
è ø ë û
å
Steps 1 and 2: Value of cash dividends and PV of annual dividends
Year t D01.08tDt1/1.16t
PV
of Dividends
2016 1 $4.00 1.080 $4.32 0.8621 $3.72
Step 3: PV of price of stock at end of initial growth period
D2018 $4.67 (1 .06) $4.95
Step 4: Sum of PV of dividends during initial growth period and PV price of stock at end of
growth period
f.
Valuation Method Per Share
Market value $40.00
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Chapter 7 Stock Valuation    136
Variable growth 43.98
© 2015 Pearson Education, Inc.