„ Solutions to Problems

P7-1. LG 2: Authorized and available shares

Basic
a. Maximum shares available for sale
Authorized shares 2,000,000
Less: Shares outstanding 1,400,000
Available shares 600,000
$48,000,000
b. Total shares needed = = 800,000 shares
$60
The firm requires an additional 200,000 authorized shares to raise the necessary funds at
$60 per share.
c. Aspin must amend its corporate charter to authorize the issuance of additional shares.

P7-2. LG 2: Preferred dividends

Intermediate
a. $8.80 per year or $2.20 per quarter
b. $2.20 For a noncumulative preferred only the latest dividend has to be paid before dividends
can be paid on common stock.
c. $8.80 For cumulative preferred all dividends in arrears must be paid before dividends can be
paid on common stock. In this case the board must pay the three dividends missed plus the
current dividend.

P7-3. LG 2: Preferred dividends

Intermediate
A $15.000 quarters in arrears plus the latest quarter
B $ 8.80 only the latest quarter
C $ 11.00 only the latest quarter
D $25.500 quarters in arrears plus the latest quarter
E $ 8.10 only the latest quarter

P7-4. LG 2: Convertible preferred stock

Challenge
a. Conversion value = conversion ratio × stock price = 5 × $20 = $100
b. Based on comparison of the preferred stock price versus the conversion value the investor
should convert. If converted, the investor has $100 of value versus only $96 if she keeps
ownership of the preferred stock.
c. If the investor converts to common stock she will begin receiving $1.00 per share per year
of dividends. Conversion will generate $5.00 per year of total dividends. If the investor keeps
the preferred they will receive $10.00 per year of dividends. This additional $5.00 per year in
dividends may cause the investor to keep the preferred until forced to convert through use of
the call feature. Furthermore, while common stock dividends may be cut or eliminated all
together with no protection, preferred dividends are typically fixed and cumulative provision.
 Chapter 7 Stock Valuation 135

P7-5. LG 2: Personal finance: Stock quotation

Basic
a. Wednesday, December 13
b. $81.75
c. $81.75
d. The price increased by $1.63. This increase tells us that the previous close was $80.12.

P7-6. LG 4: Common stock valuation–zero growth: P0 = D1 ÷ rs

Basic
a. P0 = $2.40 ÷ 0.12 = $20
b. P0 = $2.40 ÷ 0.20 = $12
c. As perceived risk increases, the required rate of return also increases, causing the stock price
to fall.

P7-7. LG 4: Personal finance: common stock valuation–zero growth

Intermediate
$5.00
Value of stock when purchased = = $31.25
0.16
$5.00
Value of stock when sold = = $41.67
0.12
Sally’s capital gain is $10.42 ($41.67 − $31.25) per share.
Sally’s total capital gain is 100 × $1042.00

P7-8. LG 4: Preferred stock valuation: PS0 = Dp ÷ rp

Intermediate
a. PS0 = $6.40 ÷ 0.093
PS0 = $68.82
b. PS0 = $6.40 ÷ 0.105
PS0 = $60.95
The investor would lose $7.87 per share ($68.82 − $60.95) because, as the required rate of return
on preferred stock issues increases above the 9.3% return she receives, the value of her stock
declines.

P7-9. LG 4: Common stock value–constant growth: P0 = D1 ÷ (rs − g)

Basic

Firm P0 = D1 ÷ (rs − g) Share Price

A P0 = $1.20 ÷ (0.13 − 0.08) = $ 24.00
B P0 = $4.00 ÷ (0.15 − 0.05) = $ 40.00
C P0 = $0.65 ÷ (0.14 − 0.10) = $ 16.25
D P0 = $6.00 ÷ (0.09 − 0.08) = $600.00
E P0 = $2.25 ÷ (0.20 − 0.08) = $ 18.75
136 Gitman • Principles of Managerial Finance, Brief Fifth Edition

P7-10. LG 4: Common stock value–constant growth

Intermediate
D1
a. rs = +g
P0
$1.20 × (1.05)
rs = + 0.05
$28
$1.26
rs = + 0.05 = 0.045 + 0.05 = 0.095 = 9.5%
$28
$1.20 × (1.10)
b. rs = + 0.10
$28
$1.32
rs = + 0.10 = 0.047 + 0.10 = 0.147 = 14.7%
$28

P7-11. LG 4: Personal finance: Common stock value–constant growth: P0 = D1 ÷ (rs − g)

Intermediate
Computation of growth rate:
FV = PV × (1 + r)n
$2.87 = $2.25 × (1 + r)5
$2.87 ÷ $2.25 = FVIFr %,5
1.276 = FVIFk%,5
g = r at 5%
a. Value at 13% required rate of return:
$3.02
P0 = = $37.75
0.13 − 0.05
b. Value at 10% required rate of return:
$3.02
P0 = = $60.40
0.10 − 0.05
c. As risk increases, the required rate of return increases, causing the share price to fall.

P7-12. LG 4: Personal finance: Common stock value–all growth models

Challenge
a. P0 = (CF0 ÷ r)
P0 = $42,500 ÷ 0.18
P0 = $236,111
b. P0 = (CF1 ÷ (r − g))
P0 = ($45,475* ÷ (0.18 − 0.07)
P0 = $413,409.10
Calculator solution: $413,409.09
*
CF1 = $42,500(1.07) = $45,475
 Chapter 7 Stock Valuation 137

P7-13. LG 5: Free cash flow (FCF) valuation

Challenge
a. The value of the total firm is accomplished in three steps.
1. Calculate the PV of FCF from 2015 to infinity.
$390,000(1.03) $401,700
FCF2115→∞ = = = $5,021,250
0.11 − 0.03 0.08
2. Add the PV of the cash flow obtained in (1) to the cash flow for 2014.
FCF2014 = $5,021,250 + 390,000 = $5,411,250
3. Find the PV of the cash flows for 2010 through 2014.

Year FCF PVIF11%, n PV

2010 $200,000 0.901 $ 180,200
2011 250,000 0.812 203,000
2012 310,000 0.731 226,610
2013 350,000 0.659 230,650
2014 5,411,250 0.593 3,208,871
Value of entire company, Vc = $ 4,049,331
Calculator solution: $ 4,051,624

b. Calculate the value of the common stock.

VS = VC − VD − VP
VS = $4,049,331 − $1,500,000 − $400,000 = $2,149,331
$2,149,331
c. Value per share = = $10.75 Calculator solution: $10.76
200,000

P7-14. LG 5: Personal finance: Using the free cash flow valuation model to price an IPO
Challenge
a. The value of the firm’s common stock is accomplished in four steps.
1. Calculate the PV of FCF from 2011 to infinity.
$1,100,000(1.02) $1,122,000
FCF2014→∞ = = = $18,700,000
0.08 − 0.02 0.06
2. Add the PV of the cash flow obtained in (1) to the cash flow for 2013.
FCF2013 = $18,700,000 + 1,100,000 = $19,800,000
3. Find the PV of the cash flows for 2010 through 2013.

Year FCF PVIF8%, n PV

2010 $700,000 0.926 $ 648,200
2011 800,000 0.857 685,600
2012 950,000 0.794 754,300
2013 19,800,000 0.735 14,533,000
Value of entire company, Vc = $16,621,100
138 Gitman • Principles of Managerial Finance, Brief Fifth Edition

4. Calculate the value of the common stock using Equation 7.8.

VS = VC − VD − VP
VS = $16,621,100 − $2,700,000 − $1,000,000 = $12,921,100
$12,921,100
Value per share = = $11.75
1,100,000
Calculator solution: $10.77
b. Based on this analysis the IPO price of the stock is over valued by $0.75 ($12.50 − $11.75)
and you should not buy the stock.
c. The value of the firm’s common stock is accomplished in four steps.
1. Calculate the PV of FCF from 2014 to infinity.
$1,100,000(1.03) $1,133,000
FCF2014→∞ = = = $22,660,000
0.08 − 0.03 0.05
2. Add the PV of the cash flow obtained in (1) to the cash flow for 2013.
FCF2013 = $22,660,000 + 1,100,000 = $23,760,000
3. Find the PV of the cash flows for 2010 through 2013.

Year FCF PVIF8%, n PV

2010 $ 700,000 0.926 $ 648,200
2011 800,000 0.857 685,600
2012 950,000 0.794 754,300
2013 23,760,000 0.735 17,463,000
Value of entire company, VC = $19,551,700

4. Calculate the value of the common stock using Equation 7.8.

VS = VC − VD − VP
VS = $19,551,700 − $2,700,000 − $1,000,000 = $15,851,700
$15,851,700
Value per share = = $14.41
1,100,000
If the growth rate is changed to 3% the IPO price of the stock is under valued by $1.91
($14.41 − $12.50) and you should buy the stock.

P7-15. LG 5: Book and liquidation value

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
 Chapter 7 Stock Valuation 139

b. Liquidation value:

Cash $40,000 Liquidation value of assets 722,000

Marketable
Securities 60,000 Less: Current Liabilities (160,000)
Accounts Rec. Long-term debt (180,000)
(0.90 × $120,000) 108,000 Preferred Stock (80,000)
Inventory Available for CS $302,000
(0.90 × $160,000) 144,000
Land and Buildings
(1.30 × $150,000) 195,000
Machinery & Equip.
(0.70 × $250,000) 175,000
Liq. Value of Assets $722,000

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 possible for liquidation value to be greater than book value if assets are
undervalued. Generally, they are overvalued on a book value basis, as is the case here.

P7-16. LG 5: Valuation with price/earnings multiples

Basic
Firm EPS × P/E = Stock Price
A 3.0 × (6.2) = $18.60
B 4.5 × (10.0) = $45.00
C 1.8 × (12.6) = $22.68
D 2.4 × (8.9) = $21.36
E 5.1 × (15.0) = $76.50

P7-17. LG 6: Management action and stock value: P0 = D1 ÷ (rs − g)

Intermediate
a. P0 = $3.15 ÷ (0.15 − 0.05) = $31.50
b. P0 = $3.18 ÷ (0.14 − 0.06) = $39.75
c. P0 = $3.21 ÷ (0.17 − 0.07) = $32.10
d. P0 = $3.12 ÷ (0.16 − 0.04) = $26.00
e. P0 = $3.24 ÷ (0.17 − 0.08) = $36.00
The best alternative in terms of maximizing share price is (b).
140 Gitman • Principles of Managerial Finance, Brief Fifth Edition

P7-18. LG 4, 6: Integrative–valuation and CAPM formulas

Intermediate
P0 = D1 ÷ (rs − g) rs = RF + [b × (rm − RF)]
$50 = $3.00 ÷ (rs − 0.09) 0.15 = 0.07 + [b × (0.10 − 0.07)]
rs = 0.15 b = 2.67

P7-19. LG 4: 6: Integrative–risk and valuation

Challenge
a. rs = RF + [b × (rm – RF)]
rs = 0.10 + [1.20 × (0.14 – 0.10)]
rs = 0.148
b. g: FV = PV × (1 + r)n
$2.45 = $1.73 × (1 + r)6
$2.45
= FVIFk%,6
$1.73
1.416 = FVIF6%,6
g = approximately 6%
P0 = D1 ÷ (rs − g)
P0 = $2.60 ÷ (0.148 − 0.06)
P0 = $29.55
Calculator solution: $29.45
c. A decrease in beta would decrease the required rate of return, which in turn would increase
the price of the stock.

P7-20 LG 4, 6: Integrative–valuation and CAPM

Challenge
a. g: FV = PV × (1 + r)n
$3.44 = $2.45 × (1 + r)5
$3.44 = $2.45 × (1 + r)5
$3.44 ÷ $2.45 = FVIFk%,5
1.404 = FVIF7%,5
r = approximately 7%
rs = 0.09 + [1.25 × (0.13 − 0.10)]
rs = 0.14
D1 = ($3.44 × 1.07) = $3.68
P0 = $3.68 ÷ (0.14 − 0.07)
P0 = $52.57 per share Calculator solution: $52.77
b. 1. rs = 0.09 + [1.25 × (0.13 −0.09)]
D1 = $3.61($3.44 × 1.05)
P0 = $3.61 ÷ (0.14 − 0.05)
P0 = $40.11 per share Calculator solution: $40.25
 Chapter 7 Stock Valuation 141

2. rs = 0.09 + [1.00 × (0.13 − 0.09)]

rs = 0.13
D1 = $3.68
P0 = $3.68 ÷ (0.13 − 0.07)
P0 = $61.33 per share Calculator solution: $61.60
The CAPM supplies an estimate of the required rate of return for common stock. The resulting
price per share is a result of the interaction of the risk-free rate, the risk level of the security, and
the required rate of return on the market. For Craft, the lowering of the dividend growth rate
reduced future cash flows resulting in a reduction in share price. The decrease in the beta reflected
a reduction in risk leading to an increase in share price.

P7-21. Ethics problem

Intermediate
a. This is a zero-growth dividend valuation problem, so:
P0 = D/r = $5/0.11 = $45.45
b. Using the new discount rate of 12% (11% + 1% credibility risk premium), we have:
P0 = D/r = $5/0.12 = $41.67
The value decline is the difference between Problems a and b:
Value decline = $41.67 − $45.45
= −$3.78
The stock sells for almost $4 less because of company’s financial reports cannot be fully trusted.
Lack of integrity is seen to hurt stock prices because of the credibility premium.

„ Case
Assessing the Impact of Suarez Manufacturing’s Proposed Risky Investment
on Its Stock Values
This case demonstrates how a risky investment can affect a firm’s value. First, students must calculate the
current value of Suarez’s stock, rework the calculations assuming that the firm makes the risky investment,
and then draw some conclusions about the value of the firm in this situation. In addition to gaining
experience in valuation of stock, students will see the relationship between risk and valuation.
1. Current per share value of common stock growth rate of dividends:
g can be solved for by using the geometric growth equation as shown below in (a) or by finding the
PVIF for the growth as shown in (b).

1.90
a. g= 4 = (1.46154)1/ 4 − 1 = 1.0995 − 1 = 0.0995 = 10.0%
1.30
1.30
b. g= = 0.6842
1.90
PV factor for 4 years closest to 0.6842 is 10% (0.683).
Use the constant growth rate model to calculate the value of the firm’s common stock.
D1 $1.90(1.10) $2.09
P0 = = = = $52.25
rs − g 0.14 − 0.10 0.04
142 Gitman • Principles of Managerial Finance, Brief Fifth Edition

2. Value of common stock if risky investment is made:

D1 $1.90(1.13) $2.15
P0 = = = = $71.67
rs − g 0.16 − 0.13 0.03

The higher growth rate associated with undertaking the investment increases the market value of
the stock.

3. The firm should undertake the proposed project. The price per share increases by $19.42 (from
$52.25 to $71.67). Although risk increased and increased the required return, the higher dividend
growth offsets this higher risk resulting in a net increase in value.

4. D2010 = 2.15(stated in case)

D2011 = 2.15(1 + 0.13) = 2.43
D2012 = 2.43(1 + 0.13) = 2.75
D2013 = 2.75(1 + 0.10) = 3.02
D2013 $3.02 $3.02
P2012 = = = = $50.33
rs − g 0.16 − 0.10 0.06

Year Cash Flow PVIF16%, n PV

2010 2.15 0.862 $ 1.85
2011 2.43 0.743 1.81
2012 2.75 + 50.33 0.641 34.02
P0 = $37.67

Now the firm should not undertake the proposed project. The price per share decreases by $14.58
(from $52.25 to $37.67). Now the increase in risk and increased the required return is not offset by
the increase in cash flows. The longer term of the growth is an important factor in this decision.

„ Spreadsheet Exercise
The answer to Chapter 7’s Azure Corporation spreadsheet problem is located in the Instructor’s Resource
Center at www.prenhall.com/irc.

„ A Note on Web Exercises

A series of chapter-relevant assignments requiring Internet access can be found at the book’s Companion
Website at http://www.prenhall.com/gitman. In the course of completing the assignments students access
information about a firm, its industry, and the macro economy, and conduct analyses consistent with those
found in each respective chapter.