Chapter 1
Time Value of Money
•
•
•
•
Future value
Present value
Rates of return
Amortization
CHY
1
Time lines show timing of cash flows.
0
1
2
3
CF1
CF2
CF3
i%
CF0
Tick marks at ends of periods, so Time 0
is today; Time 1 is the end of Period 1;
or the beginning of Period 2.
CHY
2
Time line for a $100 lump sum
due at the end of Year 2.
0
i%
1
2 Year
100
CHY
3
Time line for an ordinary
annuity of $100 for 3 years.
0
1
2
3
100
100
100
i%
CHY
4
Time line for uneven CFs: -$50
at t = 0 and $100, $75, and
$50 at the end of Years 1
through 3.
0
1
2
3
100
75
50
i%
-50
CHY
5
What’s the FV of an initial
$100 after 3 years if i = 10%?
0
1
2
3
10%
100
FV = ?
Finding FVs (moving to the right
on a time line) is called compounding.
CHY
6
After 1 year:
FV1 = PV + INT1 = PV + PV (i)
= PV(1 + i)
= $100(1.10)
= $110.00.
After 2 years:
FV2 = FV1(1+i) = PV(1 + i)(1+i)
= PV(1+i)2
= $100(1.10)2
= $121.00.
CHY
7
After 3 years:
FV3 = FV2(1+i)=PV(1 + i)2(1+i)
= PV(1+i)3
= $100(1.10)3
= $133.10.
In general,
FVn = PV(1 + i)n.
CHY
8
Three Ways to Find FVs
• Solve the equation with a regular
calculator.
• Use a financial calculator.
• Use a spreadsheet.
CHY
9
Financial calculator: HP17BII
• Adjust display contrast: hold down CLR
and push + or -.
• Choose algebra mode: Hold down
orange key (i.e., the shift key), hit
MODES (the shifted DSP key), and
select ALG.
• Set number of decimal places to display:
Hit DSP key, select FIX, then input
desired decimal places (e.g., 3).
CHY
10
HP17BII (Continued)
• Set decimal mode: Hit DSP key, select
the “.” instead of the “,”. Note: many
non-US countries reverse the US use of
decimals and commas when writing a
number.
CHY
11
HP17BII: Set Time Value Parameters
• Hit EXIT until you get the menu starting
with FIN. Select FIN.
• Select TVM.
• Select OTHER.
• Select P/YR. Input 1 (for 1 payment per
year).
• Select END (for cash flows occuring at
the end of the year.)
CHY
12
Financial Calculator Solution
Financial calculators solve this
equation:
n
FVn PV 1i 0










.
There are 4 variables. If 3 are
known, the calculator will solve
for the 4th.
CHY
13
Here’s the setup to find FV:
INPUTS
3
N
10
-100
I/YR PV
0
PMT
OUTPUT
FV
133.10
Clearing automatically sets everything
to 0, but for safety enter PMT = 0.
Set: P/YR = 1, END.
CHY
14
Spreadsheet Solution
• Use the FV function: see spreadsheet in
Ch 02 Mini Case.xls.
– = FV(Rate, Nper, Pmt, PV)
– = FV(0.10, 3, 0, -100) = 133.10
CHY
15
What’s the PV of $100 due in
3 years if i = 10%?
Finding PVs is discounting, and it’s
the reverse of compounding.
0
1
2
3
10%
100
PV = ?
CHY
16
Solve FVn = PV(1 + i )n for PV:
PV =
FVn
1 


n = FVn 
 1+ i
1+ i
n
3
1 


PV = $100
 1.10 
= $100 0.7513  = $75.13.
CHY
17
Financial Calculator Solution
INPUTS
OUTPUT
3
N
10
I/YR
PV
-75.13
0
PMT
100
FV
Either PV or FV must be negative. Here
PV = -75.13. Put in $75.13 today, take
out $100 after 3 years.
CHY
18
Spreadsheet Solution
• Use the PV function: see spreadsheet.
– = PV(Rate, Nper, Pmt, FV)
– = PV(0.10, 3, 0, 100) = -75.13
CHY
19
Finding the Time to Double
0
1
2
?
20%
2
-1
FV = PV(1 + i)n
$2 = $1(1 + 0.20)n
(1.2)n = $2/$1 = 2
nLN(1.2) = LN(2)
n = LN(2)/LN(1.2)
n = 0.693/0.182 = 3.8.
CHY
20
Financial Calculator
INPUTS
N
OUTPUT 3.8
20
I/YR
-1
PV
CHY
0
PMT
2
FV
21
Spreadsheet Solution
• Use the NPER function: see
spreadsheet.
– = NPER(Rate, Pmt, PV, FV)
– = NPER(0.10, 0, -1, 2) = 3.8
CHY
22
Finding the Interest Rate
0
1
2
3
?%
2
-1
FV = PV(1 + i)n
$2 = $1(1 + i)3
(2)(1/3) = (1 + i)
1.2599 = (1 + i)
i = 0.2599 = 25.99%.
CHY
23
Financial Calculator
INPUTS
OUTPUT
3
N
I/YR
25.99
-1
PV
CHY
0
PMT
2
FV
24
Spreadsheet Solution
• Use the RATE function:
– = RATE(Nper, Pmt, PV, FV)
– = RATE(3, 0, -1, 2) = 0.2599
CHY
25
What’s the difference between an
ordinary annuity and an annuity due?
Ordinary Annuity
0
i%
1
2
3
PMT
PMT
PMT
1
2
3
PMT
PMT
Annuity Due
0
i%
PMT
PV
CHY
FV
26
What’s the FV of a 3-year
ordinary annuity of $100 at
10%?
0
1
2
100
100
3
10%
CHY
100
110
121
FV = 331
27
FV Annuity Formula
• The future value of an annuity with n
periods and an interest rate of i can be
found with the following formula:
(1  i)  1
 PMT
i
n
(1  0.10)  1
100
 331.
0.10
3
CHY
28
Financial Calculator Formula
for Annuities
Financial calculators solve this
equation:
n 1
(1

i)
FVn PV 1i PMT
 0.
i





n





There are 5 variables. If 4 are
known, the calculator will solve
for the 5th.
CHY
29
Financial Calculator Solution
INPUTS
3
10
0
-100
N
I/YR
PV
PMT
FV
331.00
OUTPUT
Have payments but no lump sum PV,
so enter 0 for present value.
CHY
30
Spreadsheet Solution
• Use the FV function: see spreadsheet.
– = FV(Rate, Nper, Pmt, Pv)
– = FV(0.10, 3, -100, 0) = 331.00
CHY
31
What’s the PV of this ordinary
annuity?
0
1
2
3
100
100
100
10%
90.91
82.64
75.13
248.69 = PV
CHY
32
PV Annuity Formula
• The present value of an annuity with n
periods and an interest rate of i can be
found with the following formula:
1
1n
(1  i)
 PMT
i
1
13
(1  0.10)
100
 248.69
0.10CHY
33
Financial Calculator Solution
INPUTS
OUTPUT
3
10
N
I/YR
PV
100
0
PMT
FV
-248.69
Have payments but no lump sum FV,
so enter 0 for future value.
CHY
34
Spreadsheet Solution
• Use the PV function: see spreadsheet.
– = PV(Rate, Nper, Pmt, Fv)
– = PV(0.10, 3, 100, 0) = -248.69
CHY
35
Find the FV and PV if the
annuity were an annuity due.
0
1
2
100
100
3
10%
100
CHY
36
PV and FV of Annuity Due
vs. Ordinary Annuity
• PV of annuity due:
– = (PV of ordinary annuity) (1+i)
– = (248.69) (1+ 0.10) = 273.56
• FV of annuity due:
– = (FV of ordinary annuity) (1+i)
– = (331.00) (1+ 0.10) = 364.1
CHY
37
Switch from “End” to “Begin”.
Then enter variables to find PVA3 =
$273.55.
INPUTS
OUTPUT
3
10
N
I/YR
PV
100
0
PMT
FV
-273.55
Then enter PV = 0 and press FV to find
FV = $364.10.
CHY
38
Excel Function for Annuities
Due
Change the formula to:
=PV(10%,3,-100,0,1)
The fourth term, 0, tells the function
there are no other cash flows. The
fifth term tells the function that it is an
annuity due. A similar function gives
the future value of an annuity due:
=FV(10%,3,-100,0,1)
CHY
39
What is the PV of this uneven
cash
flow stream?
0
1
2
3
4
100
300
300
-50
10%
90.91
247.93
225.39
-34.15
530.08 = PV
CHY
40
• Input in “CFLO” register:
CF0
CF1
CF2
CF3
CF4
= 0
= 100
= 300
= 300
= -50
• Enter I = 10%, then press NPV button to
get NPV = 530.09. (Here NPV = PV.)
CHY
41
Spreadsheet Solution
1
A
B
C
D
E
0
1
2
3
4
100
300
300
-50
2
3
530.09
Excel Formula in cell A3:
=NPV(10%,B2:E2)
CHY
42
Nominal rate (iNom)
• Stated in contracts, and quoted by banks and
brokers.
• Not used in calculations or shown on time
lines
• Periods per year (m) must be given.
• Examples:
– 8%; Quarterly
– 8%, Daily interest (365 days)
CHY
43
Periodic rate (iPer )
• iPer = iNom/m, where m is number of
compounding periods per year. m = 4 for
quarterly, 12 for monthly, and 360 or 365 for
daily compounding.
• Used in calculations, shown on time lines.
• Examples:
– 8% quarterly: iPer = 8%/4 = 2%.
– 8% daily (365): iPer = 8%/365 = 0.021918%.
CHY
44
Will the FV of a lump sum be
larger or smaller if we
compound more often, holding
the stated I% constant? Why?
LARGER! If compounding is more
frequent than once a year--for
example, semiannually, quarterly,
or daily--interest is earned on interest
more often.
CHY
45
FV Formula with Different
Compounding Periods (e.g., $100
at a 12% nominal rate with
semiannual compounding for 5
mn
years)
iNom

FVn = PV 1 +

FV5S

m
.
0.12

= $100 1 +


2 
= $100(1.06)10
CHY
2x5
= $179.08.
46
FV of $100 at a 12% nominal
rate for 5 years with different
compounding
FV(Annual)= $100(1.12)5 = $176.23.
FV(Semiannual)= $100(1.06)10=$179.08.
FV(Quarterly)= $100(1.03)20 = $180.61.
FV(Monthly)= $100(1.01)60 = $181.67.
FV(Daily) = $100(1+(0.12/365))(5x365)
= $182.19.
CHY
47
Effective Annual Rate (EAR =
EFF%)
• The EAR is the annual rate which causes PV to
grow to the same FV as under multi-period
compounding Example: Invest $1 for one year at
12%, semiannual:
FV = PV(1 + iNom/m)m
FV = $1 (1.06)2 = 1.1236.
 EFF% = 12.36%, because $1 invested for one
year at 12% semiannual compounding would
grow to the same value as $1 invested for one
year at 12.36% annual compounding.
CHY
48
• An investment with monthly
payments is different from one with
quarterly payments. Must put on
EFF% basis to compare rates of
return. Use EFF% only for
comparisons.
• Banks say “interest paid daily.”
Same as compounded daily.
CHY
49
How do we find EFF% for a nominal
rate of 12%, compounded
semiannually?
iNom m
EFF% = 1 +
-1
m
(
)
= (1 + 0.12) - 1.0
2
2
= (1.06)2 - 1.0
= 0.1236 = 12.36%.
CHY
50
Finding EFF with HP17BII
•
•
•
•
•
Go to menu starting TVM.
Select ICNV (for int.rate conversion).
Select PER (for periodic compounding).
Enter nominal rate and select NOM%.
Enter number of periods per year and
select P.
• Select EFF%, which returns effective rate.
CHY
51
EAR (or EFF%) for a Nominal
Rate of of 12%
EARAnnual
= 12%.
EARQ
= (1 + 0.12/4)4 - 1
= 12.55%.
EARM
= (1 + 0.12/12)12 - 1
= 12.68%.
EARD(365) = (1 + 0.12/365)365 - 1 = 12.75%.
CHY
52
Can the effective rate ever be
equal to the nominal rate?
• Yes, but only if annual compounding is
used, i.e., if m = 1.
• If m > 1, EFF% will always be greater
than the nominal rate.
CHY
53
When is each rate used?
iNom: Written into contracts, quoted
by banks and brokers. Not
used in calculations or shown
on time lines.
CHY
54
iPer: Used in calculations, shown on
time lines.
If iNom has annual compounding,
then iPer = iNom/1 = iNom.
CHY
55
EAR = EFF%: Used to compare
returns on investments
with different payments
per year.
(Used for calculations if and only if
dealing with annuities where
payments don’t match interest
compounding periods.)
CHY
56
Amortization
Construct an amortization schedule
for a $1,000, 10% annual rate loan
with 3 equal payments.
CHY
57
Step 1: Find the required
payments.
0
1
2
3
PMT
PMT
PMT
10%
-1,000
INPUTS
3
10
-1000
N
I/YR
PV
OUTPUT
0
PMT
FV
402.11
CHY
58
Step 2: Find interest charge
for Year 1.
INTt = Beg balt (i)
INT1 = $1,000(0.10) = $100.
Step 3: Find repayment of principal in
Year 1.
Repmt = PMT - INT
= $402.11 - $100
= $302.11.
CHY
59
Step 4: Find ending balance
after
Year 1.
End bal = Beg bal - Repmt
= $1,000 - $302.11 = $697.89.
Repeat these steps for Years 2 and 3
to complete the amortization table.
CHY
60
YR
BEG
BAL
1 $1,000
2
698
3
366
TOT
PMT
INT
$402
$100
402
70
402
37
1,206.34 206.34
PRIN
PMT
END
BAL
$302 $698
332
366
366
0
1,000
Interest declines. Tax implications.
CHY
61
$
402.11
Interest
302.11
Principal Payments
0
1
2
3
Level payments. Interest declines because
outstanding balance declines. Lender earns
10% on loan outstanding, which is falling.
CHY
62
• Amortization tables are widely used-for home mortgages, auto loans,
business loans, retirement plans,
and so on. They are very important!
• Financial calculators (and
spreadsheets) are great for setting
up amortization tables.
CHY
63
On January 1 you deposit $100 in an
account that pays a nominal interest
rate of 11.33463%, with daily
compounding (365 days).
How much will you have on October
1, or after 9 months (273 days)?
(Days given.)
CHY
iPer = 11.33463%/365
= 0.031054% per day.
0
1
2
273
0.031054%
FV=?
-100
FV273 = $1001.00031054 
= $1001.08846 = $108.85.
273
Note: % in calculator, decimal in equation.
CHY
iPer = iNom/m
= 11.33463/365
= 0.031054% per day.
INPUTS
273
N
-100
I/YR
PV
0
FV
PMT
108.85
OUTPUT
Enter i in one step.
Leave data in calculator.
CHY
What’s the value at the end of
Year 3 of the following CF
stream if the quoted interest
rate is 10%, compounded
semiannually?
0
1
2
4
3
5%
100
100
CHY
5
6
6-mos.
periods
100
67
• Payments occur annually, but
compounding occurs each 6 months.
• So we can’t use normal annuity
valuation techniques.
CHY
68
1st Method: Compound Each
CF
0
5%
1
2
3
4
100
100
5
6
100.00
110.25
121.55
331.80
FVA3 = $100(1.05)4 + $100(1.05)2 + $100
= $331.80.
CHY
69
2nd Method: Treat as an Annuity
Could you find the FV with a
financial calculator?
Yes, by following these steps:
a. Find the EAR for the quoted rate:
EAR =
(
0.10
1+ 2
2
) - 1 = 10.25%.
CHY
70
b. Use EAR = 10.25% as the annual rate
in your calculator:
INPUTS
3
10.25
0
-100
N
I/YR
PV
PMT
OUTPUT
FV
331.80
CHY
71
What’s the PV of this stream?
0
1
2
3
100
100
100
5%
90.70
82.27
74.62
247.59
CHY
72
You are offered a note which pays
$1,000 in 15 months (or 456 days)
for $850. You have $850 in a bank
which pays a 6.76649% nominal rate,
with 365 daily compounding, which
is a daily rate of 0.018538% and an
EAR of 7.0%. You plan to leave the
money in the bank if you don’t buy
the note. The note is riskless.
Should you buy it?
CHY
iPer =0.018538% per day.
0
365
-850
456 days
1,000
3 Ways to Solve:
1. Greatest future wealth: FV
2. Greatest wealth today: PV
3. Highest rate of return: Highest EFF%
CHY
1. Greatest Future Wealth
Find FV of $850 left in bank for
15 months and compare with
note’s FV = $1,000.
FVBank = $850(1.00018538)456
= $924.97 in bank.
Buy the note: $1,000 > $924.97.
CHY
Calculator Solution to FV:
iPer = iNom/m
= 6.76649%/365
= 0.018538% per day.
INPUTS
456
N
-850
0
PV
PMT
I/YR
FV
924.97
OUTPUT
Enter iPer in one step.
CHY
2. Greatest Present Wealth
Find PV of note, and compare
with its $850 cost:
PV = $1,000/(1.00018538)456
= $918.95.
CHY
INPUTS
6.76649/365 =
456 .018538
N
OUTPUT
I/YR
PV
0
1000
PMT
FV
-918.95
PV of note is greater than its $850
cost, so buy the note. Raises your
wealth.
CHY
3. Rate of Return
Find the EFF% on note and
compare with 7.0% bank pays,
which is your opportunity cost of
capital:
FVn = PV(1 + i)n
$1,000 = $850(1 + i)456
Now we must solve for i.
CHY
INPUTS
456
N
OUTPUT
-850
I/YR
PV
0.035646%
per day
0
1000
PMT
FV
Convert % to decimal:
Decimal = 0.035646/100 = 0.00035646.
EAR = EFF% = (1.00035646)365 - 1
= 13.89%.
CHY
Using interest conversion:
P/YR = 365
NOM% = 0.035646(365) = 13.01
EFF% = 13.89
Since 13.89% > 7.0% opportunity cost,
buy the note.
CHY
OVERVIEW AND
THE COST OF
CAPITAL
[公司理財與資金成本
]
CHY
82
I. OVERVIEW OF FINANCIAL
MANAGEMENT
The value of any investment
= present value of the future cash
flows that it is expected to generate
for the investor.
( 投資價值
= 投資人預計未來現金流入的現值 )
CHY
83
經理人應該 . . .
1. Use the existing firm assets in ways that
will maximize the cash flows that can be
generated from them, and which are free
to be paid to the investors 〔尋求自由現
金流量最大〕.
2. Accelerate these free cash flows into
nearby time periods [如果能夠早日回收, 現
值會更高] to the extent it is feasible to do
so, because it is the present value of the
free cash flows that determine
shareholder value.
CHY
84
經理人應該 . . .
3. Balance the cash flow generation potential
of the firm against the risks that must be
taken to achieve it. Investors know that
some risk has to be taken to operate a
business. However, they do not like
management to take unwarranted risks. 〔
避免承擔無謂的風險〕
4. Make capital budgeting decisions that will
enhance the economic value of the firm and
its equity shares. [適當的資本預算決策,選擇有
利的投資方案]
CHY
85
5. Minimize the firm’s cost of capital by designing
an optimum capital structure. [適當的資本結構
決策, 尋求低資金成本〕
6. Choose an optimal dividend policy [適當的股
利政策] that will properly balance the following
objectives:
– Fund all worthwhile investment
opportunities. [不要為發放股利犧牲好方案]
– Maintain the optimum capital structure. [盡量
維持最適資本結構]
– Satisfy shareholder preferences for
dividends versus capital gains 〔資本利得
〕.
CHY
86
B. AGENCY ISSUES〔代理人問題
〕
•
~ 【利益衝突】但是經理人未必以上
述當作之事為首要目標，而或有自利
心
~ 今天大家談公司治理, 實為解決代理
問題
CHY
87
B. AGENCY ISSUES〔代理人問題〕
– Managers may opt to increase their salaries and
perquisites [經理人在意薪資津貼, 勝過如何為股東
賺取股利], rather than increase shareholder
dividends.
– Managers may engage in “ empire building” by
using corporate cash flow to make acquisitions
that increase the size of the enterprise in order to
enhance their own prestige without
commensurately enhancing earnings. 〔利用企
業資源, 建立自己的王國〕
CHY
Page 13 88
– Managers might use corporate funds to
contribute to their favorite charities or political
parties to enhance their own reputations at the
expense of maximizing shareholder wealth. 〔
利用企業資金, 參與社會, 政治活動〕
– Managers might employ various measures to
insulate themselves from investors who are
dissatisfied with their performance by
recommending persons that are friendly to them
for positions on the board of directors, enacting
“golden parachutes,” and so forth 〔防範股東
牽絆, 找友好者擔任董事; 制定”金降落傘”
協議(如果企業被併購,
將鉅額酬庸經理人)〕
CHY
89
C. MANAGEMENT MOTIVATION
•
•
•
•
Management Compensation 〔隨績效變動
經理人薪酬; 高階員工認股權Executive
Stock Options〕
Intervention 〔強有力的機構投資人
Institutional Investors 干預經理人不當決策
〕
Replacement [汰換不適任者]
Takeover Threats 〔如果內部制衡機制不
彰, 併購與解聘威脅可以讓經理人不至於
濫用企業資源或鬆懈〕
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90
AGENCY ISSUES〔代理人問題〕
其實又有兩類
• 經理人 (Managers) 與 股東
(Shareholders)間 有 代理人問題
• 債權人 (Banks, Bondholders)與 股
東 (Shareholders)間 也有 代理人問
題
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91
II.
THE COST OF CAPITAL
〔資金成本]
A. THE COST OF A FIRM’S CAPITAL
COMPONENTS
– Debt
〔負債〕
– Preferred equity [特別股]
– Retained earnings 〔保留盈餘〕
– Newly issued common stock[新的普通股
有發行成本flotation costs]
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92
A. THE COST OF A FIRM’S
CAPITAL COMPONENTS
•
The Cost of Debt 〔負債〕 Capital
rafter-tax = (1-t)rD
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Example:
A firm’s bonds are rated Baa.
Currently, new Baa bonds are being issued
with a coupon of 7%.
Assuming a corporate income tax rate of
35%, what is the after-tax cost of debt capital
for the firm?
Answer:
rafter-tax = (1-t)rD =(1-0.35)(7%) =4.55%
[如果同時看到coupon 與Yield to Maturity, 請用
CHY
94
YTM]
A. THE COST OF A FIRM’S
CAPITAL COMPONENTS
2. The Cost of Preferred Stock [特別股]
Capital
rp 
DIV p
PPS
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95
Example:
What is the cost of the preferred capital
of a firm whose currently outstanding
preferred shares pay a dividend of $4.50 per
share and the preferred shares are trading
at $60 per share?
Answer:
rp = DIVp = $4.50 = 7.5%
PPS
$60
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A. THE COST OF A FIRM’S
CAPITAL COMPONENTS
3. The Cost of Retained Earnings 〔保留
盈餘〕(Common equity)
a. The Capital Asset Pricing Model (CAPM)
Approach [資本資產定價模型]:
rCE = rF + βCS(rM – rF)
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97
Example:
The Acme Corporation’s common shares
have a beta of 1.2. The stock market has a
long-run expected return of 10% per year. If
the risk-free rate is 4%, estimate Acme’s
cost of retained earnings.
Answer:
rCE = rF + βCS(rM – rF)
= 4% + 1.2(10% -4%)
= 11.2%
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98
A. THE COST OF A FIRM’S
CAPITAL COMPONENTS
3. The
Cost of Retained Earnings 〔保留盈餘〕
(Common equity)
b. The Dividend-Yield-Plus-GrowthRate ( or Implied Return) Approach:
rCE
DIV1

 g DIV
PCS
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99
Example:
The Ajax Company currently （小
心 這是關鍵字）pays a dividend of $2.00 per
share on its common shares. The long-term
dividend growth rate is expected to be 5% per
year. If Ajax common shares are currently selling
at $25 per share, estimate Ajax’s cost of
retained earnings capital.
Answer:
rCE
DIV0 (1  g DIV )

 g DIV
PCS
$2(1.05)

 5%  13.4%
$25
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A. THE COST OF A FIRM’S
CAPITAL COMPONENTS
3. The Cost of Retained Earnings 〔保留盈
餘〕(Common equity)
c. The Bond-Yield-Plus-Risk-Premium
Approach
rCE  rD  rERP
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Example:
The XYZ Corporation’s common
shares should sell at a premium of 4%
over its long-term debt yield to compensate
for their risk. If XYZ’s long-term debt is
selling to yield 6.3%, estimate XYZ’s cost
of internal equity.
Answer:
rCE  rD  rERP  6.3%  4%  10.3%
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A. THE COST OF A FIRM’S
CAPITAL COMPONENTS
4. Cost of Newly Issued Common Stock
[新的普通股 有發行成本flotation costs]
(Also Called the Cost of External Equity)
rnewCE
DIV1

 g DIV
PCS (1  f )
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103
Example:
The XYZ Corporation’s common
shares are trading at $40. The Company currently
is paying a dividend of $2.50 per share on its
common stock.
If it were to sell additional common shares, its
flotation cost 〔發行成本〕 would be 15%. If the
Company has a 4% long-term growth rate in
dividends per share, calculate its cost of newly
issued common stock (external equity).
Answer:
rnewCE
DIV0 1  g DIV 
$2.50(1.04)

 g DIV 
 .04  11.65%
PCS (1  f )
$40(1  .15)
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104
B. DETERMINING A FIRM’S
OPTIMUM CAPITAL STRUCTURE
•
•
•
The optimal capital structure (最適資本結構
) of a firm is defined as that mix of capital
sources that will maximize the value of a
firm taken as a whole.
One of the important issues in finance is
how a management should determine what
its optimal capital structure should be.
Once determined, this is target capital
structure that the firm should seek to
maintain.
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C. THE WEIGHTED-AVERAGE COST
OF CAPITAL 〔加權平均資金成本〕
• The firm’s weighed-average cost of capital
(WACC) can be found using the target
capital structure [要用目標的資本結構] and
the component capital costs.
• A firm’s cost of funds is called its weightedaverage cost of capital
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106
WACC
 VD 
 VP 
 VCE
rw  (1  t )rD    rP    rCE 
 VA 
 VA 
 VA
•



The value of the company is the sum of the
market values 【盡量用市值而非帳面值】of
each component, while the value of the stock
is the market value of the firm’s outstanding
common stock.
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Example:
Consider a company with the following capital
structure:
Capital Structure
Book Value 帳面值 Market Value市值
Debt
$100 million
$106 million
Preferred Stock 50
52
Common Equity 350
842
Total Invested
Capital
$500 million
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$1,000 million
108
Example continued…
Some other characteristics of the company are:
•
•
•
•
•
•
Beta of the common stock………….1.07x
Expected secular growth rate ………6.0%
Quality of debt ……..…………………..Aa
Quality of preferred shares…..……….A
Expected Dividend yield on common
stock…….3.7%
Marginal income tax rate…………..35.0%
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109
Example continued…
The prevailing financial market conditions are as
follows:
Quality
Aaa
Aa
A
Baa
Quality
A
B
C
Yields on Newly Issued Bonds by Qlty
6.9%
7.0
7.2
7.5
Yields on Newly Issued Preferred
Stocks by Quality
7.5%
8.0
8.9
Risk-free rate………………………………
Equity risk premium over bonds ………….
Expected return on stockCHYmarket index……
6.5%
2.7
9.5110
Example continued…
What is the company’s weighted-average cost of
capital 〔加權平均資金成本〕?
Answer:
From these data we can find each of the
component costs and, subsequently, the
weighted-average cost of capital.
The cost of debt is 7.0% on a pretax basis, as this
is the cost of newly issued bonds of equal quality
(Aa rating).
The cost of preferred stock is 7.5%, which is
equal to the cost of newly issued preferred stocks
of similar quality.
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Continue on next page111
The cost of common equity capital, which is the
cost of retained earnings, (rCE) can be calculated in
one of three ways:
•
rCE=rD+rERP=7.0% + 2.7%=9.7%*
•
rCE
DIV1

 g DIV  E ( Div .Yield )  g DIV
PCS
 3.7%  6.0%  9.7% *
•
rCE=rF+bCS(rm-rF)
= 6.5% +1.07(9.5-6.5)
=9.7%*
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112
Therefore, the weighted-average cost of capital
〔加權平均資金成本〕 of the firm under these
conditions is:
 VD 
 VP 
 VCE 

rw  (1  t )rD    rP    rCE 
 VA 
 VA 
 VA 
 106m 
 52m 
 842m 
 (1  .35)(. 07)
  0.75
  0.97

 1000m 
 1,000m 
 1,000m 
 9.0%
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113
D. THE MARGINAL COST OF
CAPITAL 〔加權平均資金成本〕
Example: A company’s capital structure is as
follows:
Source Capital Structure Weight Component Cost
Debt
$400 million
50%
6%
Equity
400 million
50%
12%
WACCexisting = 9%
The firm must raise $100 m in new capital and
plans to maintain its current capital structure.
Assume that retained earnings are exhausted
as a source of new capital.
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114
＝＞Thus, new debt in the amount of $50 m
will be issued at an after-tax cost of 6%
and the other $50 m will come from newly
issued common equity.
Because of floatation costs, new common
shares have a cost of 14% instead of the
12% cost of retained earnings. Under
these conditions,
• what will be the firm’s marginal
cost of this $100 million unit of
capital? 〔新籌措$100Mil 資金的邊
際成本〕
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115
Answer:
The firm’s marginal cost of this last $100 million unit
of capital is 10%, which is calculated as follows:
Source
Capital Struc.
Debt $50 million
Equity 50 million
Weight
50%
50%
CHY
Component
W.
Cost
Cost
6% 0.5(6%) =3%
14% 0.5(14%) = 7%
=10%
116
E. FACTORS AFFECTING THE
COST OF CAPITAL
•
Factors That the Firm Can Control
– Capital Structure 〔資本結構影響加權平均
資金成本〕
– Dividend Policy 〔多付股利會增加負債比率,
影響資金成本〕
– Investment Policy [投資於高風險方案者資金成
本高]
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THE BASICS OF CAPITAL
BUDGETING
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118
I. INTRODUCTION
Capital budgeting is the process of
analyzing projects in order to decide which
ones should be undertaken.
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119
II. RANKING CAPITAL PROJECTS
A. FOUR METHODS AND THEIR
CALCULATION
1.Payback Period
2.Discounted Payback Period
3.Net Present Value (NPV)
4.Internal Rate of Return (IRR)
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120
3. Net Present Value (NPV)
Example:
Calculate the net present value of the above
project whose cost of capital is 10%.
Answer:
Year
0
1
2
3
4
5
Cash Flow
$(100,000)
20,000
40,000
60,000
30,000
10,000
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P.V. of Cash Flow
$(100,000)
18,182
33,058
45,079
20,490
6,209
$ 23,018
121
3. Net Present Value (NPV)
•
A project whose net present value is equal to
or greater than zero is one that is expected to
produce a rate of return that is equal to or
greater than the cost of capital required to
justify it. Such a project should be undertaken.
A project with a negative net present value is
one that is expected to produce a rate of return
less than the cost of capital required to justify
it. Such a project should be rejected.
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122
4. Internal Rate of Return (IRR)
Example:
What is the internal rate of return for the
project in the previous problem?
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123
4. Internal Rate of Return (IRR)
Answer:
An internal rate of return requires a trial and error
solution. However, using the cash flow functions of a
financial calculator, the internal rate of return can be
quickly determined. This is shown using the following
cash flows:
Year
Cash Flow
0
$(100,000)
1
20,000
2
40,000
3
60,000
4
30,000
5
10,000
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124
4. Internal Rate of Return (IRR)
Answer continued:
HP12C
TIBA2+
1000【CHS】【g】【CF0】
【CF】1000 【+/-】【ENTER】【↓】
200
【g】【CFj】
200 【ENTER】【↓】
400
【g】【CFj】
400 【ENTER】【↓】
600
【g】【CFj】
600 【ENTER】【↓】
300
【g】【CFj】
300 【ENTER】【↓】
100
【g】【CFj】【f】【IRR】
100 【ENTER】【IRR】【CPT】
The answer is: 18.91%
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125
a. Modified Internal Rate of Return
(MIRR)
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126
B.
INTERPRETING THE VARIOUS
METHODS OF RANKING PROJECT
RETURNS
• Payback Period
• Discounted Payback Period
• Net Present Value (NPV)
– The net present value method is generally
regarded as the best method for ranking
investment projects
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127
3. Net Present Value (NPV)
Example:
Three projects, each with a cost of 15%, have the
following free cash flows:
Year
Project A Project B Project C
0
$(50,000)
$(120,000) $(20,000)
1
40,000
(50,000) 2,000
2
20,000
150,000 15,000
• 10,000
75,000
15,000
• If the projects are independent, which one(s)
should be undertaken?
• If the projects are mutually exclusive, which
one should be undertaken?
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128
Answer:
1. The NPVS of the projects are:
Yr
NPV of Proj A
NPV of Proj B
@15%
@15%
0
$(50,000)
$(120,000)
1
34,783
(43,478)
2
15,123
113,422
3
6,575
49,314
$ 6,481
$ (742)
NPV of Proj C
@15%
$(20,000)
1,739
11,342
9,863
$2,944
If the projects are independent, undertake Project A and C
because both have positive NPVS.
2. If the projects are mutually exclusive, undertake Project A
because it has the highest NPV.
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129
4. Internal Rate of Return (IRR)
•
•
If two projects are independent of each other, then
the internal rate of return methodology will
produce the same decision with regard to
undertaking projects as the net present value
method
if projects are mutually exclusive, the internal rate
of return may produce a different ranking than the
net present value method; when both the internal
rate of return and the net present value methods
produce “accept” decisions, the order of the
rankings among alternative projects produced by
the two methods can differ.
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130
•
•
When one project is more expensive
than another (the sizes of the two
investments differ).
When the timing of the cash flows differ
such that most of the cash flows come in
the early years for one project, while
most of the cash flows come in the later
years for the other project.
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131
a. Modified Internal Rate of
Return (MIRR)
• The MIRR method is better than the IRR
method, but still inferior to the NPV
method, for ranking capital projects.
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132
III. POST-AUDIT AND CAPITAL
RATIONING
A. THE POST-AUDIT PROCESS
• Improve forecasts through employees
learning why their original forecasts were
missed and the employees knowing that their
actions are being monitored.
• Improve operations through the desire of
employees to meet their forecasts. The
employee(s) will work harder to make sure
operations are improving so that forecasts will
be met.
B. CAPITAL RATIONING
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133
CASH FLOW ESTIMATION AND
OTHER CAPITAL BUDGETING
TOPICS
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134
I.
INTRODUCTION
A. CASH FLOW VS. ACCOUNTING PROFIT
B. DEFINITIONS
a. The incremental free cash flow of a project should be calculated
before financing costs, because the method of financing an asset’s
purchase has no bearing on the value of the asset.
b. The cost of capital used as the discount rate in determining the
present value of the net free cash flows is an after-tax cost (as it is in
the conventional WACC formulation).
. Sunk costs are costs that would be incurred regardless of whether or
not an investment is made in the asset or project being evaluated.
d. Opportunity costs are cash flows that could be generated from
assets already owned by a firm if they were not used for the target
project.
e. Externalities are the positive or negative changes in the cash flows
of projects (other than the target project) that are attributable to the
target project.
f. Shipping and installation costs associated with a target project
should be included as part of its incremental net free cash flows to be
CHY
135
analyzed.
•
•
Therefore, the weighted-average cost of
capital of a firm is the proper discount rate
at which to discount the future projected
net free cash flows it is expected to
generate. This implicitly assumes that the
target project’s risk is about the same as
the average risk inherent in a firm’s normal
business activities.
Since the weighted-average cost of capital
is used as the discount rate, the
incremental unleveraged free cash flow of
the project should be the variable that is
discounted in calculating its net present
value (NPV).
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136
II. PROJECT ANALYSIS
A. ANALYSIS OF AN EXPANSION
PROJECT
Example:
A company is attempting to decide whether or not to enter the widget
business over the next 5 year. It estimates that it could generate widget
sales of $600,000 and earn a net income of $88,980 per year over a 5year period beginning next year.
However, to enter the widget business, an initial investment outlay of
$512,000 will be required, of which $510,000 is for a widget-making
machine and $2,000 is for working capital . The widget-making
machine has a useful life of 5 years and a salvage value of $10,000.
Management intends to depreciate it over its useful life using the
straight-line method for both book and tax purposes. The purchase of
the machine will be financed entirely with 7% debt.
Management uses the accrual method of accounting for both book and
tax purposes. The following pro forma data depicts management’s
estimates of the annual incremental revenues, expenses, and working
capital outlays associated with the widget business in each of the next
5 years of operation:
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137
Example continued:
Incremental Annual Effects of the Widget Project
Sales
$ 600,000
Direct Expenses
300,000
Depreciation
100,000
Selling Expenses and Externalities
16,000
Administrative Expenses
0 (1)
EBIT
$ 184,000
Interest Expense
35,700
Pretax Income
$ 148,300
Income Tax Expense @40%
59,320
Net Income
$ 88,980
Required Additional
Working Capital Outlay
$ 40,000 (2)
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138
Example continued:
(1) Administrative expenses are sunk costs
because they would be incurred whether or not
the widget project is undertaken. Thus they
add no incremental cost to the widget project.
(2) The additional working capital requirements of
the widget project must be included in the
analysis because capital budgeting decisions
are based on an incremental cash flow
analysis, and not a net income analysis. The
net increase in working capital required by the
widget project is necessary because it will be
used as a negative adjustment to pro forma
net income to bring it down to cash flow.
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139
Example continued:
• In addition, it is assumed that a terminalyear cash flow will be produced in the sixth
year consisting of $10,000 for selling the
widget-making machine for its salvage
value, $2,000 of closing expenses, and the
collection of $40,000 from outstanding
receivables and the sale of unsold
inventory at cost.
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140
Example continued:
The capital structure of the Company is as
follows:
Capital Structure
Book Value Market Value
Negotiated Debt
$10,000,000 $11,000,000
Preferred Stock
5,000,000
6,000,000
Common Equity
70,000,000
83,000,000
Total Invested Capital $85,000,000 $100,000,000
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141
Example continued:
• Current conditions in the financial markets
suggest that yields on newly issued bonds and
preferred stocks whose risks and other
characteristics are the same as those of the
Company are as follows:
Bond Yields………………………..7.0%
Preferred Stock Yields…………….6.0
• The Company’s common shares are currently
paying a $3.00 dividend per share and are
trading on the stock exchange at $30 per
share. The Company is mature, with an
expected long-term dividend growth rate of 6%
per year.
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142
Example continued:
Given this inform and assuming the widget business
is similar in terms of risk to the Company’s other
product lines, answer the following questions:
•
•
•
•
•
Calculating the initial investment outlay for the
widget project.
Calculate the incremental cash flows of the
project for the operating years (Years 1-5).
Calculate the terminal-year cash flow (Year 6).
Calculate the weighted average cost of capital
of the firm.
Determine whether or not the widget project
should be undertaken.
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143
Answer:
1. Calculating the initial investment outlay (Year 0)
Cost of the Widget-making Machine
$510,000
Additional Working Capital
2,000
Initial Investment Outlay
$512,000
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144
2. Calculating the incremental cash flows
during the operating years (Years 1-5):
The table below shows how the pro forma income and additional working capital information is used to
determine the incremental cash flows during the operating years:
Projected
Projected
Pro Forma
(Free) Cash
Income
Flows
Sales
$600,000
$600,000
Direct Expenses
300,000
300,000
Depreciation
100,000
100,000
Selling Expenses and Externalities
16,000
16,000
EBIT
$184,000
$184,000
Interest Expense
35,700
Pretax Income
$148,300
Income Tax Expense @40%
59,320
73,600(40% of
EBIT)
Net Income
$ 88,980
EBIT(1-t)
Plus: Depreciation
Less: Capital Expenditures
Less: Required Additional
Working Capital Outlay
Incremental Cash Flow in the
Operating Years
$110,400
100,000
0
40,000
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$170,400
145
Notice that the calculation of the incremental
cash flow accruing to the firm from the
normal operation of the widget project is
really the (unrevealed) free cash flow to the
firm, defined as:
FCFF = EBIT(1-t) + DEPR –CAPX –ΔWC
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146
In performing this calculation, remember:
1. Interest expense is not counted as a cost in
calculating this free cash flow to the firm from the
operation of the widget business, even though it
is counted as a cost in calculating the project’s
net income. This is because the cost of debt
capital is included in the firm’s weighted average
cost of capital that will be used to discount these
cash flows to their present value. To include the
effects of leverage in both the cash flow
calculation and the discount rate used to reduce it
to NPV would count the effect of leverage twice.
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147
In performing this calculation, remember:
•
The income tax “expense” is not the same when
calculating the free cash flow to the firm as the actual
income tax expense used to calculate net income. In
the free cash flow to the firm calculation, the income
tax “expense” is computed by multiplying the income
tax rate by EBIT, whereas the actual income tax
expense used to determine net income is computed by
multiplying the income tax rate by pretax income. The
difference in the two calculations is the interest tax
shield that is produced by financial leverage:
•
Difference in Income Tax Calculation
= $73,600 – 59,320 = $14,280
•
Interest Tax Shield
= t(INT) =0.40($35,700) = $14,280
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148
In effect, the free cash flow to the firm calculation
excludes the impact of the interest tax shield on a
firm’s cash flow. This is appropriated because all of the
effects of financial leverage are taken into account
when the firm’s weighted average cost of capital is
used to discount these projected cash flows to their
present value. To include the interest tax shield effects
of financial leverage in both the cash flow calculation
and the discount rate used to reduce it to present
value would count the effect of leverage twice.
•
The required additional working capital is
counted as a cash outflow when computing
the free cash flow to the firm, while it is not
counted as an expense in computing net
income.
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149
3. Calculating the terminal-year cash
flow (Year 6):
•
The cash flow accruing to the firm in the terminal year is
as follows:
Cash Flow
Pretax
After-Tax
Cash from Sale of Machine
$10,000
$10,000--(1)
Plus: Cash from Collection of
Receivables and sale of
unsold inventory
40,000
40,000—(2)
Less: Closing expenses, net
of taxes
2,000
1,200—(3)
Terminal-year cash flow
48,000
48,000
CHY
150
(1) The machine is sold for its book value. Therefore, no
tax is owed or saved on the transaction.
(2) The Company uses accrual accounting for book and
tax purposes. Therefore, no tax is due when
receivables are collected, because it was paid in prior
years when the income on sales were reported
Inventories were sold at cost, so no taxes are owed or
saved at this time.
(3) Closing expense are tax deductible. Therefore, there is
a tax savings of $800 that (presumably) can be used to
reduce the Company’s over all tax burden for the year.
Thus, the net closing expenses after this tax saving is:
Net Closing Expense = $2,000(1-0.4) = $1,200
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151
4. Calculating the firm’s weighted
average cost of capital:
•
To calculate the firm’s weighted average cost
of capital, first compute the firm’s cost of
common equity:
rCE =DIV1/PCS + gDIV
=$3(1.06)/30 + 0.06 = 16.6%
•
The weighted-average cost of capital of the
firm is, therefore:
rw = (1-t)rD (VD/ VA) + rP (VP/ VA) + rCE (VCE/ VA)
rW = (1-0.4)(0.07)(11,000,000/100,000,000)
+0.06(6,000,000/100,000,000)
+0.166(83,000,000/100,000,000) = 14.6%
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152
5. Making the capital budgeting
decision:
The best way to make the capital budgeting
decision is to compute the net present value
(NPV) of all of the cash flows to the firm (the
initial cash outlay, the cash generated from the
project over its operating years, and the
terminal-year cash flow), using the firm’s
weighted average cost of capital as the
discount rate. If the NPV is positive, the project
should be undertaken; if it is negative, it should
not be undertaken.
CHY
153
Note:
•
The cost of capital for the project is the
weighted average cost of capital of the firm
because this project has approximately the
same risk that is inherent in the firm’s overall
business. While the widget machine was
financed entirely with 7% debt capital, this is
not the cost of capital for the project because,
ultimately, the firm’s capital structure must be
rebalanced back to its target proportions of
debt, preferred stock, and common equity.
CHY
154
The table below depicts the projected cash flows over the
life of the widget project and the NPV of the project when
these cash flows are discounted to their present value
using the firm’s WACC:
Year
0
1
2
3
4
5
6
Cash Flow
$(512,000)
170,400
170,400
170,400
170,400
170,400
48,800
PV of Cash Flow @14.6%
$(512,000)
148,691
129,748
113,218
98,794
86,208
21,543
$ 86,202
Since the NPV of the free cash flows to the firm
generated by the project is positive, the expected return
on the project is greater than the firm’s cost of capital.
Therefore, the widget project
should be undertaken. 155
CHY
B. ANALYZING A
REPLACEMENT PROJECT
Example:
A company is thinking of replacing a machine and buying
a new one.
•
•
•
•
The annual cash operating expenses associated with the current
machine are $100,000.
the machine is being depreciated by $10,000 per year (straight
line). It has a useful life of five additional years and, if sold today, it
could fetch $5,000 in the used machine market, which is $2,000
below its book value.
The new machine would probably be used for 5 years, at which
time it would be fully depreciated. However, it could be sold for
$7,000 at the end of Year 5(which is an estimate and not a
“salvage value” for purposes of computing depreciation from a tax
perspective).
The cash operating expenses required to operate the new
machine are only $60,000 per year, but it would also require an
additional working capital each year of $3,000. The price of the
new machine is $90,000. CHY
The firm’s cost of capital is 15% and
156its
marginal income tax rate is 40%.
Example continued:
•
Calculate the initial investment outlay for the analysis:
The initial investment outlay in Year 0 is the cost of the
new machine, less the cash received from selling the old
machine and the tax savings that accrues to the benefit of
the Company because it sells the old machine at a loss:
Cash Outlay
Cost of New Machine
$90,000
Less: Sale of Old Machine
5,000
Less: Tax Savings on Sale of Old
Machine
800【0.40×$2,000
loss】
Initial Investment Outlay
$84,200
CHY
157
Example continued:
•
Calculate the operating cash flows for the
“normal” years(1-4):
The table below summarizes the calculation of the regular operating cash
flows from this replacement project:
After-tax reduction in cash operating costs
Depreciation on new machine
Depreciation on old machine
Increase in depreciation
Tax savings on increase in depreciation
Less: Increase in required working capital
Operating cash flow
Cash Flow
$24,000 (1)
$18,000
10,000
$ 8,000
3,200 (2)
3,000
$24,200
(1) (1-t)(100,000 –60,000) = (0.60)(40,000) = $24,000
(2) Tax Savings = t (Increase in depreciation) = 0.40($8,000) = $3,200
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158
Example continued:
3. Calculate the terminal-year cash flow (Year 5):
The cash flows in the terminal year are the regular
operating cash flow of $24,200 associated with the
project and the special cash flows that occur in Year 5
as summarized in the table below:
Cash Flow
Regular operating cash flow
$24,200
Proceeds from sale of machine
7,000
Less: Tax on gain from sale of machine
2,800 (3)
Terminal-year cash flow
$28,400
(3) Tax on gain from sale = t (Gain on sale) = 0.40($7,000) =$2,800
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Example continued:
4. Construct a cash flow table for the life of the new machine.
This table should depict the cash flows resulting from the
replacement project from Year 0 through Year 5, and calculate the
net present value (NPV) of those cash flows.
The cash flow for this replacement project and the NPV calculation is
contained in the following table:
Year
0
1
2
3
4
5
Cash Flow
$(84,200)
24,200
24,200
24,200
24,200
24,200
PV of Cash Flow @15%
$(84,200)
21,299
18,299
15,912
13,836
14,020
NPV $(1,090)
Answer:
The old machine should not be replaced because the NPV of the
project is negative.
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III. OTHER CAPITAL BUDGETING
TOPICS
A. MAKING DECISIONS REGARDING
PROJECTS WITH DIFFERENT USEFUL
LIVES
• The methods described previously for
ranking projects are applicable only if the
projects all have the same time horizon.
CHY
161
Example:
•
The management of the Gadget Manufacturing Company must
decide which of two machines to buy in order to make one of the
components of the gadget that they manufacture more cheaply.
•
Machine A costs $600,000 to buy and would save the
Company $300,000 of operating costs per year. Its
useful life is three years.
Machine B costs $700,000 to buy and would save the
company $200,000 per year to operate and has a
useful life of six years.
Both machines can produce the same output and
make the same contribution to revenues every year.
One or the other machine will be bought; it is only a
matter of which is the cheapest to operate, all factors
considered.
The company has a weighted average cost of capital of
14%. Both machines have zero salvage value.
162
Which machine shouldCHY
purchased?
•
•
•
•
answer:
1. The Equivalent Annuity (EAA) Approach
• The equivalent annual annuity is defined
as the size of the annuity payment
required each year of an asset’s life to
make the present value of the operating
cash flows equal the NPV of the asset,
using the cost of capital for the asset as
the discount rate. The asset with the
algebraically highest EAA is considered to
be the best investment.
CHY
163
answer:
1. The Equivalent Annuity (EAA) Approach
•
Applied to this problem, the EAAs for the two machines are calculated as follows, using a financial calculator. The
annual operating cash flows generated by Machine A and Machine B and their respective present values are:
Year
0
1
2
3
4
5
6
Machine A
Operating
Cash Flows
P.V. of A
Operating
CF @14%
$(600,000)
300,000
300,000
300,000
$(600,000)
263,158
230,840
202,491
$ 96,489
CHY
Machine B
Operating
CF
$ (700,000)
200,000
200,000
200,000
200,000
200,000
200,000
P.V of B
Operating
CF @14%
$(700,000)
175,439
153,894
134,994
118,416
103,874
91,117
$ 77,734
164
Machine A
Machine B
PV = 96,489
n=3
i = 14
FV = 0
EAA = PMT = $41,561
PV =77,734
n=6
i = 14
FV = 0
EAA = PMT = $19,990
The decision is to buy Machine A because it
has the algebraically higher equivalent annual
annuity per year.
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公司財務研討 I
In Class Question
P57
CHY
166
Other Capital Budgeting Topics
MAKING DECISIONS REGARDING
PROJECTS WITH DIFFERENT USEFUL
LIVES
• For the projects with different time horizon
• (A方案NPV 較負, 但是該機器可以用10年;
• B方案NPV 沒有那麼負, 但是只能用5年; ) . . .
CHY
167
釋例:
•
The management of the Gadget Manufacturing
Company must decide which of two machines
to buy in order to make one of the components
of the gadget that they manufacture more
cheaply.
•
Machine A costs $600,000 to buy & would
save the Company $300,000 of operating
costs per year. Its useful life is three years.
•
Machine B costs $700,000 to buy & would
save the company $200,000 per year to
operate & has a useful
CHY life of six years.
168
釋例:
•
The management of the Gadget Manufacturing
Company must decide which of two machines
to buy in order to make one of the components
of the gadget that they manufacture more
cheaply.
•
Machine A costs $600,000 to buy & would
save the Company $300,000 of operating
costs per year. Its useful life is three years.
•
Machine B costs $700,000 to buy & would
save the company $200,000 per year to
operate & has a useful
CHY life of six years.
169
釋例: [續]
• Both machines can produce the same output &
make the same contribution to revenues every
year. One or the other machine will be bought; it
is only a matter of which is the cheapest to
operate, all factors considered.
• The company has a weighted average cost of
capital of 14%. Both machines have zero salvage
value.
• Which machine should purchased?
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170
2. The Replacement Chain
(Common Life) Approach
•
The replacement chain (Common Life) method
solves the problem by equalizing the lives of the
two machines.
•
This is done by extending the life of Machine A
until it equals that of Machine B by treating the
problem as if Machine A 陸續接力 【 at the end of
Year 3, 續用 Machine A . . . 】
•
In that case, the operating cash flows of the two
machines & their associated present values would
CHY
171
appear as follows:
2. The Replacement Chain
(Common Life) Approach @ 14%
continued…
Year
Machine A
P.V. of
Machine B
Operating
Machine A Operating
Cash Flows Operating
Cash Flows
P.V of
Machine B
Cash Flows
0
1
2
3
4
5
6
$(600,000)
300,000
300,000
(300,000)(*)
300,000
300,000
300,000
$(700,000)
175,439
153,894
134,994
118,416
103,874
91,117
$ 77,734
$(600,000)
263,158
230,840
(202,491)
177,624
155,811
136,767
$ 161,618
CHY
$ (700,000)
200,000
200,000
200,000
200,000
200,000
200,000
172
(*) 接力點 If a new Machine A is
purchased at the end of the third
year, the cash flows in that year
will be:
$300,000-600,000 = $ (300,000)
This approach leads to the decision to
buy Machine A, because it has the
higher net present value of its cash
flows.
CHY
173
Other Capital Budgeting
Topics
THE EFFECT OF INFLATION ON
NPV ANALYSIS
• Cost of Capital r 已經含有 EXPECTED
INFLATION, 所以 Incremental Cash Flow
也要考慮到未來物價上漲趨勢
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174
CAPITAL BUDGETING RISK
ANALYSIS
I. TYPES OF RISK
• Stand-alone Risk
• Corporate (Within-firm) Risk
• Market Risk (Beta)
CHY
175
釋例 Which of the following statements
is true?
(A)Stand-alone risk is the best way for a conglomerate
to analyze the risk associated with a potential new
acquisition.
(B)Corporate risk measures do not take into account the
principle that diversification reduces risk.
(C)Market risk affects the impact that a potential new
project can have on the price of the stock of the firm
that is contemplating to undertake the project.
(D) Fully diversified stockholders in a firm are more
concerned with the corporate risk of a project that a
company whose stock they own is undertaking than
CHY
176
they are about its market
risk.
解析:
C
A is false because corporate or market risk
should be the way for a conglomerate to
analyze a new acquisition since diversification
may reduce overall risk relative to the
acquisition’s stand-alone risk.
B is false because corporate risk does take into
account the principle that diversification
reduces risk.
D is false because diversified investors are
more concerned with market risk than with
corporate risk.
CHY
177
Measuring Stand-alone Risk
Scenario Analysis
• The probabilities assigned to each scenario are
subjective.
• “Outlier” scenarios (war, famine, & pestilence),
which represent the largest risks to the viability of
a project, do occur from time to time.
• Yet, such scenarios are not often included in the
analysis because they are very unlikely.
• The tendency to ignore highly improbable, yet
very costly, scenarios results in an
underestimation of project risk.
CHY
178
Sensitivity Analysis
NPV 結果對那個變數最敏感?
Monte Carlo Simulation
Simulating probable events & generate
estimated returns & risk indexes
考慮到特殊事件 (Outliers)
但是: 變數的分配要主觀認定, 且操作複
雜
CHY
179
Measuring Market risk
THE SECURITY MARKET LINE
r = rF +β（rM-rF）
• USING A MARKET (SYSTEMATIC;
BETA) RISK MEASURE TO
DETERMINE THE REQUIRED
RETURN ON A CAPITAL PROJECT
FINANCED WITH EQUITY CAPITAL
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180
IRR
Project
Using the SML to Estimate the
Risk-Adjusted Cost of Equity
Capital
SML
Good
A
projects
30%
B
5%
C
Bad projects
Firm’s risk (beta)
2.5
An all-equity firm should accept a project whose IRR
exceeds the cost of equity capital & reject projects
whose IRRs fall short of the cost of capital.
CHY
181
釋例 Which of the following is
NOT an appropriate way of
measuring stand-alone risk?
A. Sensitivity analysis. B. Scenario
analysis.
C. Monte Carlo simulation.
D. Security market line analysis.
解析:
D
The SML approach is used to
measure market risk.
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182
釋例
The Greenhouse Grocery
Corporation, a large grocery store retailer, is
thinking about acquiring the Fly-by-Nite Airline
Company.
Based on the information given below, what is the
most appropriate discount rate that should be
applied to the incremental free cash flows to
equity expected to be generated by this
acquisition in order to decide whether or not this
acquisition is worthwhile?
CHY
183
• Risk-free rate
5.00%
• Expected stock market return
10.00%
• Grocery industry market beta
0.85
• Airline industry market beta
1.50
• Greenhouse grocery’s WACC
8.00%
• Market return on unleveraged investments
9.00%
a.8.00%
b. 9.00%
c.9.25%
d. 12.50%
CHY
184
解析:
D
Given the choices, the
best one would be the return calculated
from the security market line using the
CAPM approach & an airline industry
beta. Greenhouse’s WACC is
inappropriate because an airline is an
entirely different business from the one
Greenhouse is in; hence the risks are
different.
r = rF +βairlines（rM-rF）
CHY
= 5%+1.5(10-5)=12.5%
185
MEASURING THE BETA OF A
PROJECT
• The Pure Play Method ~ 找Single
Product Company (Pure Player) 看她的
Beta
CHY
186
INCLUDING A RISK
ADJUSTMENT
• Certainty Equivalent Approach ~ All cash
flows not known with certainty are scaled
down. (e.g., 都乘以0.8, 然後以rF 折現)
• Risk-Adjusted Discount Rate ~ cash flows
not scaled down, 但是以Risk-Adjusted
Cost of Equity Capital 折現
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187
CAPITAL
STRUCTURE &
LEVERAGE
Page 83
CHY
188
THE TARGET CAPITAL STRUCTURE
～ 以下變數Trade-off 的結果
• Business Risk (純資產的產銷風險)
• Tax Position (Tax Shield 稅盾)
• Financial Flexibility (如果有Future
Capital Needs, Balance Sheet 必須好
看)
• Managerial Conservatism (經理人風
險偏好)
CHY
189
2-1 ANALYZING BUSINESS RISK
【營業風險】
• Volatility of Sales 【營業收入波動性】
• Volatility of Resource Costs 【投入要素成本波
動性】
• Operating Leverage 【營業槓桿】 of the
Business (固定成本多者Degree of Operating
Leverage 高)
Degree of Operating Leverage 【營業槓桿】
(DOL) ~ 當Sales變動1% , EBIT變動的百分比
= %∆EBIT = 1+
CF固定成本
CHY
190
%∆Sales
EBIT 息前稅前盈餘
2-2 ANALYZING FINANCIAL RISK
【財務風險】
• Financial leverage refers to using fixed-cost
sources of investment capital, such as debt, to
finance a firm.
• Financial risk is the extra risk to shareholders
that results from using financial leverage. [買
聯電股票的風險 >買聯電晶圓廠的風險 ]
• Financial risk can be measured by standard
measures of financial leverage, such as the
Debt/Total Capital or Debt/Equity ratios.
CHY
191
• However, a more useful measure of financial
leverage is the degree of financial leverage 【財
務槓桿】( DFL),
• defined as the percent change in pretax income
that occurs every time there is a one-percent
change in EBIT. (DFL) can be calculated in a
number of ways that are mathematically
equivalent.
~ 當EBIT變動1% , 稅前淨利變動的百分比
CHY
192
• DFL =
%ΔPretax Income
%ΔEBIT
= EBIT / Pretax Income
= EBIT / (EBIT-INTEREST)
CHY
193
Degree of Total Leverage
【總槓桿】
• DTL 【總槓桿】
= DOL【營業槓桿】 × DFL【財務槓桿】
• %ΔPretax Income =
ΔPretax Income
Pretax Income
= DOL × DFL x % ΔSales
CHY
194
• %ΔEPS
= DOL × DFL x %ΔSales
• EPS2006
= EPS2005 (1 + DOL × DFL x %ΔSales)
• DOL & DFL 像是擴大器
CHY
195
The Effect of Financial Leverage
on Earnings per Share
• [如果企業希望EPS增長] If a company expects
its EBIT> breakeven EBIT, debt should be
employed in its capital structure because the
financial leverage will enhance its EPS;
• [如果企業希望EPS增長] if it expects its EBIT <
breakeven EBIT, it should have lower debt in its
capital structure because the financial leverage
will result in per-share earnings being less than
they would be if financial leverage were not
CHY
196
employed.
Financial Leverage財務槓桿, EPS
每股盈餘& EBIT息前稅前盈餘
EPS ($)
D/E = 1
Levered
Firm
3
2.5
2
1.5
1
D/E = 0 Unleveraged
Firm
0.5
0
– 0.5
–1
0
0.2
0.4
0.6
0.8
CHY
1
EBIT ($ millions,
no taxes)
197
• Leveraged firms 【使用負債挹注資金的
企業】
• Unleveraged firms 【未使用負債挹注資金
的企業】
CHY
198
【釋例 ～ 如果旨在增加 EPS】
As a general rule:
A. Firms that expect to have low earnings before
interest & taxes should use financial leverage in
order to enhance their earnings per share.
B. Firms that expect to have high earnings before
interest & taxes should use financial leverage in
order to ↑ their EPS.
C. Leveraged firms will generate the same
earnings per share for a given level of earnings
before interest & taxes as unleveraged firms.
D. Unleveraged firms always
generate a lower199
CHY
earnings per share than leveraged
• 解析: B
Leveraged firms produce
higher EPS if their EBIT is above their
financing breakeven point & lower EPS
if their EBIT is below their breakeven
point.
• => A, & C, are incorrect. (D) X because
leverage can have a positive or negative
influence on earnings per share.
CHY
200
Real World Complications
• Cost of Debt 隨D/E 上升
• Cost of Equity 隨D/E上升
• 所以固然expects its EBIT to be greater than
its breakeven EBIT 時, 如果增加D/E => EPS
上升, 但是WACC 也會增加
• Common shareholder wealth is Not
(necessarily) maximized by maximizing
earnings or dividends per share. [畢竟企業
目的不在極大化其EPS]
• 應該是 Maximize present value of the
CHY
future cash flows
201
CAPITAL STRUCTURE THEORIES
A.
MODIGLIANI & MILLER’S CAPITAL
STRUCTURE IRRELEVANCE PROPOSITION
[MM 資本結構無關企業價值理論]
Assumptions
• There are no brokerage costs.
• There are no taxes.
• There are no bankruptcy costs.
• Investors & corporation can borrow at the same rate.
• All investors have the same information about the
firm’s future investment opportunities as the firm’s
management. 〔企業不需要用高負債來顯示其看好未
來獲利〕
CHY
202
• EBIT is not affected by the
use of debt.
MM with Taxes
1. The Effect of Taxes [ 實務上因
為負債有Tax Shield 效果, 增加借
貸可以省資金成本]
2. The Effect of Bankruptcy Costs [
實務上破產成本驚人, 故企業不敢
借太兇]
CHY
203
B. THE TRADE-OFF THEORY
• The optimal capital structure for a firm is one
that will maximize the value of its assets (or
minimize its weighted average cost of capital 〔最
低之加權平均資金成本〕)
• debt is beneficial to a firm, but only up to a point.
• In contrast to the Modigliani-Miller irrelevance
proposition, an optimal capital structure does exist
[存在最適資本結構]. It is that mix of debt,
preferred stock, & common equity that minimizes
CHY
204
the firm’s weighted average
cost of capital.
CHY
205
CHY
206
【釋例】 The value of a firm is
enhanced when:
A. The cost of equity capital equals a firm’s
weighted average cost of capital.
B. The firm’s weighted average cost of
capital is minimized.
C. The cost of a firm’s equity capital is
minimized.
D. The cost of avoiding financial distress is
minimized.
CHY
207
CHY
208
解析: (B) The value of a firm is the present
value of its (unleveraged) free cash flows
discounted by the firm’s WACC. This value
is maximized when WACC is minimized.
• (C) X because the cost of equity relates to
the value of the firm’s equity capital only &
not the firm as a whole.
• (D) X because the cost of avoiding financial
distress is minimized by having no debt,
which is usually not an optimal capital
structure
CHY
209
C. SIGNALING THEORY
[訊號理論]
• 〔發行新股籌資顯示企業認為股價高於真實價
值〕Management would want to raise capital
by selling common equity if it believed that the
firm’s common equity was significantly
overvalued.
• The announcement of a stock offering is
generally taken by the market to be a signal
that management believes that its firm’s stock
is overpriced relative to the firm’s future
prospects.
CHY
210
【融資順位理論】Pecking
Order Theory
• 有好消息的企業 ：先以自有資金融資 => 短期
債融資 =>長期債融資 =>可轉債融資 => 股票
融資
• 有壞消息的企業 ：最後才是自有資金融資 =>
短期債融資 =>長期債融資 =>可轉債融資 =>
股票融資
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211
SIGNALING THEORY
～ 發行股票有缺點
• It raises a firm’s marginal cost of capital, thereby
making some projects uneconomical that would have
been worthwhile if they could have been financed with
less expensive debt capital. [權益資金成本比負債資金
成本貴]
• It tends to reduce the value of the firm as investors
downgrade their outlook for the growth rate of the
company to correspond with what they interpret as a
signal from management that the prospects for the
company are really less than the market had been
presuming. 〔發行新股籌資顯示企業認為股價高於
真實價值〕
CHY
212
【釋例】 The static trade-off theory
differs from the Modigliani-Miller Theorem
in that:
A. The static trade-off theory suggests that
financial leverage cannot enhance the value of
a firm because of the cost associated with
financial distress, while Modigliani-Miller
suggests that the use of debt can enhance a
firm’s value.
B. The static trade-off theory introduces the effect
of the cost of avoiding financial distress〔當負
債比率增加, 負債資金成本也上升〕, while
Modigliani-Miller assumes that the cost of debt
& equity capital remain unchanged even at very
CHY
213
high debt-to-equity ratios.
C. The static trade-off theory can determine
an optimal debt-to-equity ratio that fits the
unique circumstances of a firm, while
Modigliani-Miller cannot define any
uniquely optimal debt-to-equity ratio that
fits the facts & circumstances that relate to
a particular firm.
D. MM Theorem is more realistic than the
static trade-off theory.
CHY
214
解析:
C
• (A) X because both theories claim that firm
value can be enhanced by using debt
(leverage).
• (B) X because MM does not assume that
the cost of equity capital remains
unchanged as the debt-to-equity ratio↑.
• D is clearly incorrect.
CHY
215
Corporate Finance
Important Equations
The Cost of Debt Capital
rafter-tax = (1-t)rD
The Cost of Preferred Stock Capital
DIV P
rP 
PPS
CHY
216
The Capital Asset Pricing Model (CAPM)
Approach:
rCE = rF + βCS(rM – rF)
The Dividend-Yield-Plus-Growth-Rate ( or
Implied Return) Approach
rCE
DIV1

 g DIV
PCS
CHY
217
The Bond-Yield-Plus-Risk-Premium
Approach
rCE = rD+ rERP
Cost of Newly Issued Common Stock
(Also Called the Cost of External
Equity)
rnewCE
DIV1

 g DIV
PCS (1  f )
CHY
218
The weighted-average cost of capital
rw = (1-t)rD (VD/ VA) + rP (VP/ VA) + rCE
(VCE/ VA)
Free Cash Flow from an Expansion
Project
FCFF = EBIT(1-t) + DEPR –CAPX –
ΔWC
CHY
219
Degree of Operating Leverage
DFL = %ΔEBIT = 1+CF
%Δsales EBIT
Degree of Financial Leverage
% Pr etaxIncome
EBIT
EBIT
DFL 


%EBIT
Pr etaxIncome EBIT  INT
CHY
220
Quantifying Total Company Risk
DTL  DOL  DFL
 Pr etaxIncome
% Pr etax _ Income 
 DOL  DFL  %Sales
Pr etax _ Income
%EPS  DOL  DFL  %Sales
EPS1  EPS0 (1  DOL  DFL  %Sales )
CHY
221
DIVIDEND POLICY 【股利政策】
• I. Dividend 【股利】 & Cash
Buyout [庫藏股買回]
• II. DETERMINING A FIRM’S
OPTIMUM DIVIDEND
POLICY 【股利政策】
Page 101
CHY
222
Procedure for Cash Dividend
Payment
25 Oct.
1 Nov.
2 Nov.
6 Nov.
7 Dec.
…
Declaration
Date
ExCumdividend dividend
Date
Date
Record
Date
Payment
Date
Declaration Date[ 宣佈日]: The Board of Directors declares a
payment of dividends.
Cum-Dividend Date〔含息基準日〕: The last day that the
buyer of a stock is entitled to the dividend.
Ex-Dividend Date 〔除息日〕: The first day that the seller
of a stock is entitled to the dividend.
Record Date 〔記錄日〕: The corporation prepares a list of
all individuals believed toCHY
be stockholders as of 6 November.
223
Price Behavior around the ExDividend Date
• In a perfect world, the stock price will fall by the
amount of the dividend on the ex-dividend date.
-t
…
-2
-1
0
+1
+2
…
$P
$P - div
The price drops by the
Examount of the cash
dividend
Date
dividend
Taxes complicate things a bit. Empirically, the
price drop is less than the dividend and occurs
within the first
CHYfew minutes of the ex-date.
224
A. THREE THEORIES ON
DIVIDEND POLICY
1. MM: Dividend Irrelevance Theory
(MM股利無關企業價值論)
This dividend irrelevance theory suggests that
the dividend payout ratio & dividend policy
is irrelevant on determining the value of
firms.
CHY
225
The Miller-Modigliani Hypothesis: Dividends
do not affect value (MM股利無關企業價值論)
If a firm's investment policy (and hence cash flows) don't
change, the value of the firm cannot change with
dividend policy. Investors have to be indifferent to
receiving either dividends or capital gains.
- Underlying Assumptions:
A. No tax differences between dividends & capital gains.
B. If companies pay too much in cash, they can issue new
stock, with no flotation costs (發行成本) to replace this
cash.
C. If companies pay too little in dividends, they do not use
the excess cash for bad projects or acquisitions 〔無
CHY
226
代理人問題〕.
MM:
d. NO Signaling Effect (沒有訊號效果)
• Many companies pay a regular cash
dividend.
• Corporations “Smooth” Dividends.
• Dividends Provide Information to the Market
(Signaling long-run dividend policy; 實業界
默契： 企業不輕易變動股利, 投資人見股
利減少即大賣)
e. Investors Can Create Homemade
CHY
227
Dividends(自己發自己現金股利)
Homemade Dividends
(自己發自己現金股利)
• Bianchi Inc. stock Price=$42 about to pay a $2 cash
dividend. [當然配息以後股價理論上會跌$2]
• Bob Investor owns 80 shares and prefers $3 cash
dividend.
• Bob’s homemade dividend strategy:
– Sell 2 shares ex-dividend
homemade dividends
Cash from dividend ($D x 80) $160
Cash from selling stock
$80
Total Cash
$240
Value of Stock Holdings $40 × 78 股
CHY
＝$3,120
$3 Dividend
$240
$0
$240
$39 × 80 股
228
＝ $3,120
f. 高Dividend Payout %者Internal
Growth Rate 低 [今天多拿到$
=> 未來少拿到$ ]
Internal Growth Rate (g)
= ROE (1-k)
Where: ROE is the return on equity
（淨值報酬率）.
K is the payout ratio （股利
支付率）.
CHY
229
【釋例】 An investor in a stock can
create a “homemade” dividend by:
A. Selling off a portion of the shares owned.
B. Buying the stock on margin.
C. Buying futures contracts on the shares.
D. All of the above techniques will create
“homemade” dividends.
(A) V 賣出部份持股
CHY
230
2. The Bird-in-the –Hand [
一鳥在手] Theory
Higher Div Payout => Better
DIV1
KE1
PCS 

rCE  g DIV rCE  g E
CHY
231
PRICE cs
= DIV1 / (r – g)
= Div Payout Ratio
x Expected EPS at period 1
÷ (r – g)
CHY
232
3. The Tax Preference Theory
The tax preference theory suggests that
high dividend payout policies reduce the
value of common shares and, hence,
the value of the firm.
CHY
233
• In the presence of personal taxes:
1. A firm should not issue stock to pay a
dividend.
2. Managers have an incentive to seek
alternative uses for funds to reduce
dividends.
3. Personal taxes mitigate against the payment
of dividends
CHY
234
4. A Summary of the Three
Theories
• The bird-in-the-hand theory [一鳥在手]
suggests that the higher the payout ratio,
the higher will be the value of the firm &
its common stock.
• The tax preference theory states that the
higher the payout ratio, the lower will be
the value of the firm & its common stock.
• The dividend irrelevance theory states
that dividend policy has no effect on the
value of the firm orCHYits common stock. 235
A clientele based explanation
• [意思是. ..] Investors may form
clienteles based upon their tax
brackets.
• Investors in high tax brackets may
invest in stocks which do not pay
dividends & those in low tax brackets
may invest in dividend paying stocks.
• 倒沒有說多發現金股利不好，得看
想要滿足甚麼樣的投資人需求
CHY
236
–(a) Older investors were more likely
to hold high dividend stocks, &
–(b) Poorer investors tended to hold
high dividend stocks
CHY
237
A clientele based explanation
(c) If stockholders like dividends as a source
of current income => Higher dividends
(d) If stockholders like stable dividend levels
=> Avoid cutting dividends
(e) If stockholders like stable dividend payout
=> Maintain the target payout ratio
(f) If cash dividends serve as an Uncertainty
resolution => Higher dividends
CHY
238
【釋例】 Which of the following
theories about dividend policy is most
closely associated with the clientele
effect？
A. The bird-in-the-hand theory.
B. The tax preference theory.
C. The dividend irrelevance theory.
D. The MM theory.
• (B)Investors (clientele) in low tax brackets
may prefer higher payout ratios than
239
investors in high taxCHYbrackets.
B. THE RESIDUAL DIVIDEND
MODEL [2004-10-08]
• Determine the optimal capital budget.
• Based on the target capital structure,
determine the amount of equity capital
required to finance the optimal capital
budget.
• To the extent possible, use internally
generated retained earnings as the
primary source of meeting the equity
capital requirement.
Page 109
CHY
240
• Pay dividends only to the extent that
funds are left over after meeting the
financing needs of the capital budget,
taking into consideration other
constraining factors, such as bond
indenture constraints, preferred stock
restrictions, the availability of cash, tax
penalties on excess retained earnings,
capital impairment restrictions, & so
forth.
CHY
241
• Avoid cutting dividends at all costs,
because this sends the wrong signal to
investors.
• Therefore, do not apply this residual
dividend model on a year-by-year basis;
rather, apply it over a 5-10 year time
horizon.
• In other words, the residual dividend
model should be used to set long-run
target payout ratios, based on 5-10 year
free cash flow projections.
CHY
242
• A residual dividend policy:
– Net income (projected) = $200M
– D/E (target) = 2/3 (E/V = 60%; D/V = 40%)
– Capital budget (planned) = $260M
– Maximum capital spending with no outside equity:
.60  C = $200M C = $333.33M
– Therefore, a dividend will be paid
– New equity needed= .60  $260M = $156M
New debt needed
= .40  $260M = $104M
CHY
– Dividend = $200M - $156M
= $44M
243
C. REPURCHASING COMMON
STOCK AS AN ALTERNATIVE TO
PAYING DIVIDENDS
1. Advantages of Repurchasing
Common Shares [買回庫藏股票] Instead
of Paying Dividends
a. Signaling that mgt believe the shares
are undervalued 〔感覺便宜才會買進
〕
b. Only the shareholders who choose to
sell their shares are subject to a tax
CHY
244
c. Cash dividends, once declared, cannot
be cut without adversely affecting the
price of the common stocks. In contrast,
repurchase programs can be “on and
off” 〔自由實施〕
d. Buybacks helps shifting in a firm’s
target capital structure policy (DebtEquity Ratio UP)
CHY
245
An alternative to paying additional dividends
： Repurchasing common shares
• 【買回庫藏股票，可以拉高每股盈餘、省
現金股利稅、有訊號效果】
CHY
246
Disadvantages of Repurchasing
Common Shares Instead of
Paying Dividends ～
a. Buybacks may imply mgt uncertainty about the
trend of Free Cash Flow 〔否則就發現金
股利〕
b. The selling shareholders may not be fully
aware of all of the implications of a buyback
program 〔現有股東未必知道是否應該出
售〕
c. If the firm buys back shares at an inflated
price, it wastes money. 〔也許買價過高
CHY
247
〕
Calculating the Price Effect of a Stock
Repurchase [買回庫藏股票會. . .]
E.g., Net Income = $150M;
• #Issued Shares = # Outstanding Shares= 50M
• Current P/E = $75/ $3 = 25x
• If the amount to be allocated = $60M
• => 800,000 shares can be repurchased
• EPS after the repurchase =
$150M / (50M – 0.80M) = $3.05
CHY
248
每股盈餘(Earnings per Share )
Earnings Attributable to Ordinary Shareholders
Number of Outstanding Ordinary (Common) Shares
淨利
特別股利
=
Net Income －
Preferred Dividends
Number of Issued Shares－ Number of Treasury Shares
發行數
庫藏數
(現金股利↑時，每股盈餘會?) 不變
【Q】Would a company’s EPS increase or decrease as it
declares & pays cash dividends?
CHY
249
(股票股利↑時，每股盈餘會?) ↓
【Q】Would a company’s EPS ↑ or ↓ as it declares &
distributes stock dividends (股票股利)?
(買回庫藏股票時，每股盈餘會?) ↑
【Q】【Treasury Stock Transaction】Would a
company’s earnings per share ↑ or ↓ as it buys back
shares?
(重行賣出庫藏股票時，每股盈餘會?) ↓
【Q】【Decrease in Treasury Stocks】Would a
company’s EPS ↑ or ↓ as it resells its Treasury Stocks?
CHY
250
現金股利 (Cash Dividend) versus a 庫藏股
買回 (Share Repurchase) 的衝擊
• Assume no taxes, commissions, or other market
imperfections
• Consider a firm with 50,000 shares outstanding
and the following balance sheet
Balance Sheet
Cash
$ 100,000
Other Assets
900,000
Total
$1,000,000
CHY
$
0
1,000,000
Debt
Equity
$1,000,000
Total
251
• Price per share is $20
($1,000,000/50,000)
Net income is $100,000, so EPS = $2.00
=> The P/E ratio is 10
• The firm is considering;
– 1)
paying a $1 per share cash
dividend, or
– 2) repurchasing 2,500 shares at $20 a
CHY
share
252
現金股利 (Cash Dividend) versus a 庫藏股買
回 (Share Repurchase) 的衝擊
• 1.Choose 現金股利 (cash dividend)
(all stockholders get $1 per share)
Balance Sheet
Cash
$ 50,000 $
0
Other Assets900,000 950,000
Total
$ 950,000 $ 950,000
Debt
Equity
Total
• Price per share is $19 ($950,000/50,000)
Net income is still $100,000, so EPS = $2.00
The P/E ratio becomes CHY
9.5
253
現金股利 (Cash Dividend) versus a庫藏
股買回 (Share Repurchase) 的衝擊
• 2. Choose 庫藏股買回 (repurchase)
(2,500 shares are repurchased at $20 a share)
Balance Sheet
Cash
$ 50,000 $
0
Other Assets900,000 950,000
Total $ 950,000 $ 950,000
Debt
Equity
Total
• Price per share remains $20 ($950,000/47,500)
Net income is still $100,000, so EPS = $2.10
CHY
The P/E ratio is 9.5
254
【釋例】Repurchasing common shares (買
回庫藏股票) is an alternative to paying
additional dividends that:
A. Can boost the price of the shares if
investors interpret the purchases as a
signal that management believes the
shares are undervalued.
B. Has tax advantages for high-income
shareholders.
C. Is disadvantageous to the Company if the
shares are overpriced.
D. All of the above statements are true.
CHY
255
• 解析: D A stock repurchase plan can
signal that management believes its shares
are
undervalued.
• Repurchase plans can benefit high-income
shareholders as the lower capital gains
tax 【證所稅】 is paid by only the investors
who choose to sell
their shares.
• A disadvantage of are repurchase plan is
that the price at which the stock is
repurchased may be too high.
CHY
256
STOCK DIVIDENDS, SPLITS, &
REVERSE SPLITS
1. Empirical Evidence ~ STOCK
DIVIDENDS, SPLITS, & REVERSE
SPLITS do not change the value of
firms, nor the wealth of their
shareholders.
2. Rationale ~ SPLITS & STOCK
DIVIDENDS讓單價降下來, 降至
Optimal Trading Range 以內
CHY
257
Irrelevance of Stock Dividends
: Example
Shimano USA has 2 million shares currently
outstanding at $15 per share. The company
declares a 50% stock dividend. How many
shares will be outstanding after the dividend is
paid?
A 50% stock dividend will increase the number
of shares by 50%:
2 million
×
1.5 = 3 million shares
CHY
258
Irrelevance of Stock Dividends
•
•
•
•
[Pizza 多片]
After the stock dividend what is the new price
per share and what is the new value of the
firm?
The value of the firm was
2 Mil × $15 per share = $30 Mil.
After the dividend, the value will remain the
same.
Price per share
= $30Mil / 3Mil shares = $10 per share
CHY
259
Cash Dividend Policy is Also Irrelevant
[還記得Homemade Dividends?]
• Since investors do not need dividends to convert shares to
cash, dividend policy will have no impact on the value of
the firm.
• In the above example, Bob Investor began with total wealth
of $3,360:
$42
$3,360  80 shares 
share
 After a $3 dividend, his total wealth is still $3,360:
$39
$3,360  80 shares 
 $240
share
 After a $2 dividend, and sale of 2 ex-dividend shares,his
total wealth is still $3,360:
$40
$3,360  78 shares 
 $160  $80
CHY
260
share
【Corporate Finance 釋例】
1. Bay Corp. generated net income of $105
million and a return on equity (ROE) of 10%
during the year-ended 2005.
Assuming a
dividend payout rate of 45% and that the ROE
above is consistent with management’s long-term
expectations, the expected sustainable growth
rate （最高可維持成長率）of dividends is:
a. 10.0%
b. 5.5%
c.
2.5%
d. 1.25%
P121
CHY
261
【擬答】(B)
g = ROE (1 – Dividend Payout Rate)
＊
=> 10%(1-45%) = 5.5%
最高內部成長率 (Internal Growth Rate) 與最
高可維持成長率(Sustainable Growth Rate)
CHY
262
• 1. 當企業無法 發行新股增資、也無法增加借
貸 時 (When External Debt and Equity
Financing = 0)
• Internal Growth Rate
=
(ROA)
× (1- Dividend Payout Ratio)
• 2. 當企業無法發行新股增資、但是她能夠增加
借 貸 時
(When External Equity
Financing = 0
最 高 可 維 持 成 長 率 (Sustainable Growth
Rate) ~ Less stringent
• Sustainable Growth Rate =
(ROE) × (1- Dividend CHY
Payout Ratio)
263
Optimal capital structure
2. Which of the following statements best describes
the optimal capital structure?
a. The optimal capital structure is the mix of debt,
equity, & preferred stock that maximizes the
company’s earnings per share (EPS).
b. The optimal capital structure is the mix of debt,
equity, & preferred stock that maximizes the
company’s stock price.
c. The optimal capital structure is the mix of debt,
equity, & preferred stock that minimizes the
company’s weighted average cost of capital
(WACC).
CHY
d. Statements b & c are correct.
【擬答】 (D) E 264
Leverage & capital structure
3. Which of the following is likely to encourage a
company to use more debt in its capital
structure?
a. An increase in the corporate tax rate.
b. An increase in the personal tax rate.
c. Changes in the bankruptcy code make
bankruptcy less costly to corporations
d. Statements a & c are correct.
【擬答】(D)
P122
CHY
265
Capital structure & WACC
4. Which of the following statements is most correct?
a. Since debt financing raises the firm’s financial
risk, increasing a company’s debt ratio will always
increase the company’s WACC.
b. Since debt financing is cheaper than equity
financing, increasing a company’s debt ratio will
always reduce the company’s WACC.
c. Increasing a company’s debt ratio will typically
reduce the marginal costs of both debt & equity
financing; however, it still may raise the
company’s WACC.
d. None of the statements above is correct.
【擬答】 (D) E266
CHY
Operating & financial leverage
5. Which of the following statements is most
correct?
a. Firms whose sales are very sensitive to
changes in the business cycle are more
likely to rely on debt financing.
b. Firms with large tax loss carry forwards are
more likely to rely on debt financing.
c. Firms with a high operating leverage are
more likely to rely on debt financing.
d. None of the statements above is correct.
CHY
【擬答】(D) M
267
Stock repurchases
6. Which of the following statements is most correct?
a.
One advantage of stock repurchases is that
they are generally taxed more favorably than
dividend payments.
b.
Stock repurchases make sense if a company
is interested in increasing its equity ratio.
c.
Stock repurchases make sense if a
company believes that its stock is overvalued
& that it has a lot of profitable projects to fund over
the next year.
d.
If a company announces a 2-for-1 stock split
& the overall value of the firm remains unchanged,
the company’s stock price must have doubled.
CHY
268
【擬答】(A) E
Dividend theory
7. Which of the following statements is most
correct?
a. The tax preference theory states that, all
else equal, investors prefer stocks that
pay low dividends because retained
earnings can lead to capital gains that are
taxed at a lower rate.
b. An increase in the cost of equity capital
(ks) when a company announces an
increase in its dividend per share, would
be consistent with the bird-in-the-hand
theory.
CHY
269
c. An increase in the stock price when
a company decreases its dividend
is consistent with the signaling
theory.
d. A dividend policy that involves paying
a consistent percentage of net
income is the best policy if the
“clientele effect” is correct.
【擬答】(A) M
P123
CHY
270
Dividends & repurchases
8. Which of the following statements is most
correct?
a. In general, stock repurchases are taxed the
same way as dividends.
b. On average, companies send a negative signal
to the marketplace when they announce an
increase in their dividend.
c. In the real world, we find that dividends usually
exhibit greater stability than earnings.
d. All statements are correct.
CHY
【擬答】(C) E
271
Stock split
9. A stock split will cause a change in the total
dollar amounts shown in which of the
following balance sheet accounts?
a.
b.
c.
d.
e.
Cash.
Common stock.
Paid-in capital.
Retained earnings.
None of the statements above is correct.
【擬答】 (E) E
CHY
272
NPV profiles
10. Project A & Project B are mutually exclusive
projects with equal risk. Project A has an internal
rate of return of 12 percent, while Project B has
an internal rate of return of 15 percent.
The two projects have the same net present value
when the cost of capital is 7 percent. (In other
words, the “crossover rate” is 7 percent.)
Assume each project has an initial cash outflow
followed by a series of inflows. Which of the
following statements is most correct?
CHY
273
NPV
($)
A
B
k (%)
0
7%
12%
CHY
15%
274
a. If the cost of capital is 10 percent, each
project will have a positive net present
value.
b. If the cost of capital is 6 percent, Project B
has a higher net present value than Project
A.
c. If the cost of capital is 13 percent, Project B
has a higher net present value than Project
A.
d. Statements a & c are correct.
CHY
P124
275
【擬答】(D) E
Since both projects have an IRR > the
10% cost of capital, both will have a positive
NPV. Therefore, statement a is true. At 6
percent, the cost of capital is less than the
crossover rate & Project A has a higher NPV
than B. Therefore, statement b is false. If the
cost of capital is 13 percent, then the cost of
capital is greater than the crossover rate & B
would have a higher NPV than A. Therefore,
statement c is true.
CHY
276
NPV profiles
11. O’Leary Lumber Company is considering two
mutually exclusive projects, Project X &
Project Y. The two projects have normal cash
flows (an up-front cost followed by a series of
positive cash flows), the same risk, & the
same 10 percent WACC. However, Project X
has an IRR of 16 percent, while Project Y has
an IRR of 14 percent. Which of the following
statements is most correct?
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277
a. Project X’s NPV must be positive.
b. Project X’s NPV must be higher than Project
Y’s NPV.
c. If Project X has a lower NPV than Project Y,
then this means that Project X must be a
larger project.
d. Statements a & c are correct.
CHY
278
解析:(A).IRR of Project X > weighted average cost
of capital; therefore, the project has a positive
net present value. Statement b is incorrect; we
do not know where the crossover point is (if one
exists) for these two projects. Statement c is
also incorrect; if anything, existing information
would suggest that Project X was the smaller
project. In addition, the lower NPV could be the
product of the timing of cash flows or the length
of the project’s life.
CHY
279
NPV profiles
12. Cherry Books is considering two mutually
exclusive projects. Project A has an internal
rate of return of 18 percent, while Project B
has an internal rate of return of 30 percent.
The two projects have the same risk, the
same cost of capital, & the timing of the cash
flows is similar. Each has an up-front cost
followed by a series of positive cash flows.
One of the projects, however, is much larger
than the other. If the cost of capital is 16
percent, the two projects have the same net
present value (NPV); otherwise, their NPVs
are different. Which of the following
statements is most correct?
CHY
p125
280
a.If the cost of capital is 12 percent,
Project B will have a higher NPV.
b.If the cost of capital is 17 percent,
Project B will have a higher NPV.
c.Project B is larger than Project A.
d.Statements a & c are correct.
CHY
281
【擬答】:
NPV
($)
A
B
0
16% 17%
18%
CHY
30%
Discount
rate (%)
282
(B) E
Draw the NPV profiles using the information
given in the problem. It is clear that Project A will
have a higher NPV when the cost of capital is 12
percent. Therefore, statement a is false. At a 17
percent cost of capital, Project B will have a
higher NPV than Project A. Therefore, statement
b is true. If the cost of capital were 0, then the
NPV of the projects would be the simple sum of
all the cash flows. In order for statement c to be
true, B’s NPV at a 0 cost of capital would have to
be higher than A’s. From the diagram we see that
this is clearly incorrect. So, statement c is false.
CHY
283
NPV & IRR
13. Which of the following statements is most
correct?
a. If a project’s internal rate of return (IRR)
exceeds the cost of capital, then the
project’s net present value (NPV) must be
positive.
b. If Project A has a higher IRR than Project B,
then Project A must also have a higher NPV.
c. The IRR calculation implicitly assumes that
all cash flows are reinvested at a rate of
return equal to the cost of capital.
d. Statements a & c are correct.
CHY
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284
【擬答】: (A) E
If the projects are mutually exclusive,
then project B may have a higher NPV
even though Project A has a higher IRR.
IRR is calculated assuming cash flows are
reinvested at the IRR, not the cost of
capital.
CHY
285
NPV & IRR
14. Project A has an internal rate of return (IRR) of
15 percent. Project B has an IRR of 14 percent.
Both projects have a cost of capital of 12 percent.
Which of the following statements is most correct?
a. Both projects have a positive net present value
(NPV).
b. Project A must have a higher NPV than Project B.
c. If the cost of capital were less than 12 percent,
Project B would have a higher IRR than Project A.
d. Statements a & c are correct.
e. All of the statements above are correct.
CHY
286
【擬答】: (A) E
Projects with IRRs > the cost of
capital will have a positive NPV.
Statement b is false because you know
nothing about the relative magnitudes of
the projects. (C) is false because the
IRR is independent of the cost of
capital.
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287
NPV, IRR, & MIRR
15. A project has an up-front cost of $100,000.
The project’s WACC is 12 percent & its net
present value is $10,000. Which of the
following statements is most correct?
a. The project should be rejected since its return
is less than the WACC.
b. The project’s internal rate of return is greater
than 12 percent.
c. The project’s modified internal rate of return
is less than 12 percent.
d. All of the statements above are correct.
CHY
288
【擬答】: (B) E
If the NPV > 0, then IRR > 12%. (C)
is false; if NPV > 0, then MIRR >
WACC.
CHY
289
NPV, IRR, MIRR, & payback
16. A proposed project has normal cash flows.
In other words, there is an up-front cost
followed over time by a series of positive cash
flows. The project’s internal rate of return is
12 percent & its WACC is 10 percent. Which
of the following statements is most correct?
a. The project’s NPV is positive.
b. The project’s MIRR is greater than 10 percent
but less than 12 percent.
c. The project’s payback period is greater than
its discounted payback period.
d. Statements a & b are correct.
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290
【擬答】: (D) E
(A) is true because the IRR exceeds the
WACC. Statement b is also true because the
MIRR assumes that the inflows are reinvested at
the WACC, which is less than the IRR.
Statement c is false. For a normal project, the
discounted payback is always longer than the
regular payback because it takes longer for the
discounted cash flows to cover the purchase
price.
CHY
291
NPV & expected return
17. Stock C has a beta of 1.2, while Stock D
has a beta of 1.6. Assume that the stock
market is efficient. Which of the following
statements is most correct?
a. The required rates of return of the two stocks
should be the same.
b. The expected rates of return of the two stocks
should be the same.
c. Each stock should have a required rate of
return equal to zero.
d. The NPV of each stock should equal its
expected return.
e. The NPV of each stock should equal zero.
CHY
292
【擬答】: (E) E
If the stock is correctly priced, i.e., the
stock market is efficient, the NPV of this
project should be zero.
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293
NPV & project selection
18. Moynihan Motors has a cost of capital of 10
percent. The firm has two normal projects of
equal risk. Project A has an internal rate of
return of 14 percent, while Project B has an
internal rate of return of 12 percent. Which
of the following statements is most correct?
a. Both projects have a positive net present
value.
b. If the projects are mutually exclusive, the
firm should always select Project A.
d. Statements a & b are correct
e. Statements a & b are incorrect.
【擬答】:(A) E
CHY
294
IRR
19. Project A has an IRR of 15 percent. Project
B has an IRR of 18 percent. Both projects
have the same risk. Which of the following
statements is most correct?
a. If the WACC is 10 percent, both projects will
have a positive NPV, & the NPV of Project
B will exceed the NPV of Project A.
b. If the WACC is 15 percent, the NPV of
Project B will exceed the NPV of Project A.
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295
c. If the WACC < 18 percent, Project B will
always have a shorter payback than Project
A.
d. If the WACC > 18 percent, Project B will
always have a shorter payback than Project
A.
e. If the WACC increases, the IRR of both
projects will decline.
CHY
296
【擬答】:(B) E
Project A’s IRR is 15%, at a WACC of 15%
NPVA = 0; however, Project B would still have a
positive NPV. Given the information in a, we
can’t conclude which project’s NPV is going to
be greater at a cost of capital of 10%. Since we
are given no details about each project’s cash
flows we cannot conclude anything about
payback. Finally, IRR is independent of the
discount rate, that is, IRR stays the same no
matter what the WACC is.
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297
Post-audit
20. The post-audit is used to
a. Improve cash flow forecasts.
b. Stimulate management to improve
operations & bring results into line with
forecasts.
c. Eliminate potentially profitable but
risky projects.
d. Statements a & b are correct.
【擬答】:(D) E
CHY
298
NPV profiles
21. Projects L & S each have an initial cost of
$10, followed by a series of positive cash
inflows. Project L has total, undiscounted
cash inflows of $16, while S has total
undiscounted inflows of $15. Further, at a
discount rate of 10%, the two projects have
identical NPVs. Which project’s NPV will be
more sensitive to changes in the discount
rate?
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299
a. Project S.
b. Project L.
c. Both projects are equally sensitive to
changes in the discount rate since their NPVs
are equal at all costs of capital.
d. Neither project is sensitive to changes in the
discount rate, since both have NPV profiles
which are horizontal.
e. The solution cannot be determined unless the
timing of the cash flows is known.
【擬答】:(B) M
CHY
300
NPV profiles
22. Two mutually exclusive projects each have
a cost of $10,000. The total, undiscounted
cash flows for Project L are $15,000, while
the undiscounted cash flows for Project S
total $13,000. Their NPV profiles cross at a
discount rate of 10 percent. Which of the
following statements best describes this
situation?
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301
a. The NPV & IRR methods will select the same
project if the cost of capital is greater than 10
percent; for example, 18 percent.
b. The NPV & IRR methods will select the same
project if the cost of capital is less than 10
percent; for example, 8 percent.
c. To determine if a ranking conflict will occur
between the two projects the cost of capital is
needed as well as an additional piece of
information.
d. Project L should be selected at any cost of
capital, because it has a higher IRR.
【擬答】: (A) M
CHY
302
NPV profiles
23. A company is comparing two mutually
exclusive projects with normal cash flows.
Project P has an IRR of 15 percent, while
Project Q has an IRR of 20 percent. If the
WACC is 10 percent, the two projects have
the same NPV. Which of the following
statements is most correct?
a. If the WACC is 12 percent, both projects
would have a positive NPV.
b. If the WACC is 12 percent, Project Q would
have a higher NPV than Project P.
c. If the WACC is 8 percent, Project Q would
have a lower NPV than Project P.
d. All of the statements above are correct.
CHY
303
【擬答】: (D) M
The diagram above can be drawn from
the statements in this question
NPV
($)
P
Q
k (%)
0
10%
15%
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20%
304
NPV & IRR
24. Assume that you are comparing two mutually
exclusive projects. Which of the following
statements is most correct?
a. The NPV & IRR rules will always lead to the
same decision unless one or both of the
projects are “non-normal” in the sense of
having only one change of sign in the cash
flow stream, that is, one or more initial cash
outflows (the investment) followed by a series
of cash inflows.
P130
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305
b. If a conflict exists between the NPV & the
IRR, the conflict can always be eliminated
by dropping the IRR & replacing it with the
MIRR.
c. There will be a meaningful (as opposed to
irrelevant) conflict only if the projects’ NPV
profiles cross, & even then, only if the cost
of capital is to the left of (or lower than) the
discount rate at which the crossover occurs.
d. All of the statements above are correct.
【擬答】： (C) M
CHY
306
NPV & IRR
25. Which of the following statements is
incorrect?
a.Assuming a project has normal cash
flows, the NPV will be positive if the IRR
is less than the cost of capital.
b.If the multiple IRR problem does not
exist, any independent project
acceptable by the NPV method will also
be acceptable by the IRR method.
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307
c.If IRR = k (the cost of capital), then NPV =
0.
d.NPV can be negative if the IRR is positive.
e.The NPV method is not affected by the
multiple IRR problem.
【擬答】 (A) M
NPV is positive if IRR is greater than
the cost of capital.
CHY
308
NPV & IRR
26. Project J has the same internal rate of
return as Project K. Which of the following
statements is most correct?
a. If the projects have the same size (scale) they
will have the same NPV, even if the two
projects have different levels of risk.
b. If the two projects have the same risk they will
have the same NPV, even if the two projects
are of different size.
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309
c.If the two projects have the same
size (scale) they will have the same
discounted payback, even if the two
projects have different levels of risk.
d. None of the statements above is
correct.
CHY
310
【擬答】(D) M
(A) is false: The projects could easily have
different NPVs based on different cash flows &
costs of capital. (B): NPV is dependent upon the
size of the project. Think about the NPV of a $3
project versus the NPV of a $3 million project.
Statement c is false. NPV is dependent on a
project’s risk.
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311
NPV, IRR, & MIRR
27. Which of the following statements is most
correct?
a. If a project with normal cash flows has an IRR
that exceeds the cost of capital, then the
project must have a positive NPV.
b. If the IRR of Project A exceeds the IRR of
Project B, then Project A must also have a
higher NPV.
c. The modified internal rate of return (MIRR)
can never exceed the IRR.
d. Statements a & c are correct.
CHY
312
P131
【擬答】(A) M
The IRR is the discount rate at which a
project’s NPV is zero. If a project’s IRR exceeds
the firm’s cost of capital, then its NPV must be
positive, since NPV is calculated using the firm’s
cost of capital to discount project cash flows.
CHY
313
NPV, IRR, & MIRR
28. Which of the following statements is most
correct?
a. The MIRR method will always arrive at the
same conclusion as the NPV method.
b. The MIRR method can overcome the multiple
IRR problem, while the NPV method cannot.
c. The MIRR method uses a more reasonable
assumption about reinvestment rates than the
IRR method.
d. Statements a & c are correct.
CHY
314
【擬答】(C) M
MIRR & NPV can conflict for mutually
exclusive projects if the projects differ in
size. NPV does not suffer from the
multiple IRR problem.
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315
NPV, IRR, & payback
29. Project X has an internal rate of return of
20 percent. Project Y has an internal rate of
return of 15 percent. Both projects have a
positive net present value. Which of the
following statements is most correct?
a. Project X must have a higher net present
value than Project Y.
b. If the two projects have the same WACC,
Project X must have a higher net present
value.
c. Project X must have a shorter payback than
Project Y.
d. None of the statements
above
is
correct.
CHY
316
【擬答】(D) M
Statement a is false; the two
projects’ NPV profiles could cross,
consequently, a higher IRR doesn’t
guarantee a higher NPV. Statement b is
false; if the two projects’ NPV profiles
cross, Y could have a higher NPV.
Statement c is false; we don’t have
enough information.
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317
IRR
30. A capital investment’s internal rate of return
a. Changes when the cost of capital changes.
b. Is equal to the annual net cash flows
divided by one half of the project’s cost
when the cash flows are an annuity.
c. Must exceed the cost of capital in order for
the firm to accept the investment.
d. Is similar to the yield to maturity on a bond.
e. Statements c & d are correct.
【擬答】(E) M
P132
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318
MIRR
31. Which of the following statements is most
correct? The modified IRR (MIRR)
method:
a. Always leads to the same ranking decision
as NPV for independent projects.
b. Overcomes the problem of multiple internal
rates of return.
c. Compounds cash flows at the cost of capital.
d. Overcomes the problems of cash flow timing
& project size that lead to criticism of the
regular IRR method.
e. Statements b & c are correct
【擬答】(E) M
CHY
319
Ranking methods
32. Which of the following statements is
correct?
a. Because discounted payback takes account
of the cost of capital, a project’s discounted
payback is normally shorter than its regular
payback.
b. The NPV & IRR methods use the same basic
equation, but in the NPV method the discount
rate is specified & the equation is solved for
NPV, while in the IRR method the NPV is set
equal to zero & the discount rate is found.
c. If the cost of capital is less than the crossover
rate for two mutually exclusive projects’ NPV
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320
profiles, a NPV/IRR conflict
will not occur.
d. If you are choosing between two projects that
have the same life, & if their NPV profiles
cross, then the smaller project will probably
be the one with the steeper NPV profile.
e. If the cost of capital is relatively high, this will
favor larger, longer-term projects over
smaller, shorter-term alternatives because it
is good to earn high rates on larger amounts
over longer periods.
【擬答】(B) M
Statement (B) reflects exactly the difference
between the NPV & IRR methods.
CHY
321
Project selection
33. A company estimates that its weighted
average cost of capital (WACC) is 10
percent. Which of the following independent
projects should the company accept?
a. Project A requires an up-front expenditure of
$1,000,000 & generates a net present value
of $3,200.
b. Project B has a modified internal rate of
return of 9.5 percent.
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322
c. Project C requires an up-front expenditure of
$1,000,000 & generates a positive internal
rate of return of 9.7 percent.
d. Project D has an internal rate of return of 9.5
percent.
【擬答】(A) M
Project A is the only project with either a
positive NPV or an IRR that exceeds the cost
of capital.
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323
Miscellaneous concepts
34. Which of the following is most correct?
a. The NPV & IRR rules will always lead to the
same decision in choosing between mutually
exclusive projects, unless one or both of the
projects are “nonnormal” in the sense of
having only one change of sign in the cash
flow stream.
b. The Modified Internal Rate of Return (MIRR)
compounds cash outflows at the cost of
capital.
c. Conflicts between NPV & IRR rules arise in
choosing between two
CHYmutually exclusive
projects
324
(that each have normal cash flows) when
the cost of capital exceeds the
crossover rate (that is, the discount rate
at which the NPV profiles cross).
d.The discounted payback method
overcomes the problems that the
payback method has with cash flows
occurring after the payback period.
e.None of the statements above is
correct.
【擬答】(E) M
CHY
325
IRR can lead to conflicting decisions with
NPV even with normal cash flows if the
projects are mutually exclusive. Cash
outflows are discounted at the cost of capital
with the MIRR method, while cash inflows are
compounded at the cost of capital. Conflicts
between NPV & IRR arise when the cost of
capital is less than the crossover rate. The
discounted payback method corrects the
problem of ignoring the time value of money,
but it still does not consider cash flows that
occur beyond the payback period.
CHY
326
Miscellaneous concepts
35. Which of the following statements is most
correct?
a. The IRR method is appealing to some
managers because it produces a rate of
return upon which to base decisions rather
than a dollar amount like the NPV method.
b. The discounted payback method solves all
the problems associated with the payback
method.
c. For independent projects, the decision to
accept or reject will always be the same using
either the IRR method or the NPV method.
d. Statements a & c are correct.
P134
CHY
327
【擬答】(D) M
The discounted payback method still
ignores cash flows that occur after the
payback period.
(A) 如殖利率報價
CHY
328
Miscellaneous concepts
(A) M
36. Which of the following statements is most
correct?
a. One of the disadvantages of choosing
between mutually exclusive projects on the
basis of the discounted payback method is
that you might choose the project with the
faster payback period but with the lower total
return.
b. Multiple IRRs can occur in cases when
project cash flows are normal, but they are
more common in cases where project cash
flows are nonnormal.
CHY
329
c.
When choosing between mutually
exclusive projects, managers should accept all
projects with IRRs greater than the weighted
average cost of capital.
d.
Statements a & b are correct.
【擬答】(A) M
Multiple IRRs can occur only for projects with
nonnormal cash flows. Mutually exclusive
projects imply that only one project should be
chosen. The project with the highest NPV
should be chosen.
CHY
330
Miscellaneous concepts
37. Normal projects C & D are mutually exclusive.
Project C has a higher net present value if the
WACC is less than 12 percent, whereas
Project D has a higher net present value if the
WACC exceeds 12 percent. Which of the
following statements is most correct?
a. Project D has a higher internal rate of return.
b. Project D is probably larger in scale than
Project C.
c. Project C probably has a faster payback.
d. Statements a & c are correct.
e. All of the statements above are correct.
【擬答】(A) M
CHY
331
【擬答】(A) M
Sketch the profiles. From the
information given, D has the higher IRR.
The project’s scale cannot be
determined from the information given.
As C’s NPV declines more rapidly with
an increase in rates, this implies that
more of the cash flows are coming later
on. So C would have a slower payback
than D.
CHY
332
NPV profiles
38. Your assistant has just completed an
analysis of two mutually exclusive projects.
You must now take her report to a board of
directors meeting & present the alternatives
for the board’s consideration. To help you
with your presentation, your assistant also
constructed a graph with NPV profiles for the
two projects. However, she forgot to label the
profiles, so you do not know which line
applies to which project. Of the following
statements regarding the profiles, which one
is most reasonable?
P135
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333
a. If the two projects have the same investment
cost, & if their NPV profiles cross once in the
upper right quadrant, at a discount rate of 40
percent, this suggests that a NPV versus IRR
conflict is not likely to exist.
b. If the two projects’ NPV profiles cross once, in
the upper left quadrant, at a discount rate of
minus 10 percent, then there will probably not
be a NPV versus IRR conflict, irrespective of
the relative sizes of the two projects, in any
meaningful, practical sense (that is, a conflict
that will affect the actual investment decision).
CHY
334
c.If one of the projects has a NPV profile
that crosses the X-axis twice, hence the
project appears to have two IRRs, your
assistant must have made a mistake.
d.Whenever a conflict between NPV &
IRR exist, then, if the two projects have
the same initial cost, the one with the
steeper NPV profile probably has less
rapid cash flows. However, if they have
identical cash flow patterns, then the
one with the steeper profile probably
has the lower initial cost.
CHY
335
e. If the two projects both have a
single outlay at t = 0, followed by a
series of positive cash inflows, & if
their NPV profiles cross in the lower
left quadrant, then one of the projects
should be accepted, & both would be
accepted if they were not mutually
exclusive.
【擬答】(B) Diff: T
CHY
336
NPV, IRR, & MIRR
39. Which of the following statements is most
correct?
a. When dealing with independent projects,
discounted payback (using a payback
requirement of 3 or less years), NPV, IRR, &
modified IRR always lead to the same
accept/reject decisions for a given project.
b. When dealing with mutually exclusive
projects, the NPV & modified IRR methods
always rank projects the same, but those
rankings can conflict with rankings produced
by the discounted payback & the regular IRR
methods.
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337
c.Multiple rates of return are possible with
the regular IRR method but not with the
modified IRR method, & this fact is one
reason given by the textbook for favoring
MIRR (or modified IRR) over IRR.
d.Statements a & c are correct.
【擬答】(C) Diff: T
CHY
338
NPV, IRR, & MIRR
40. Which of the following statements is
correct?
a. There can never be a conflict between NPV &
IRR decisions if the decision is related to a
normal, independent project, that is, NPV will
never indicate acceptance if IRR indicates
rejection.
b. To find the MIRR, we first compound CFs at
the regular IRR to find the TV, & then we
discount the TV at the cost of capital to find
the PV.
c. The NPV & IRR methods both assume that
cash flows are reinvested at the cost of
capital. However, the MIRR method
assumes reinvestment
CHY at the MIRR itself.
339
P130
d. If you are choosing between two projects
that have the same cost, & if their NPV
profiles cross, then the project with the
higher IRR probably has more of its cash
flows coming in the later years.
e. A change in the cost of capital would
normally change both a project’s NPV & its
IRR.
【擬答】 (A) Diff: T
CHY
340
Sketch out a NPV profile for a normal,
independent project, which means that only
one NPV profile will appear on the graph. If
WACC < IRR, then IRR says accept. But in
that case, NPV > 0, so NPV will also say
accept. Statement d is false. Here is the
reasoning:
1. For the NPV profiles to cross, then one
project must have a higher NPV at k = 0 than
the other project, that is, their vertical axis
intercepts will be different.
2. A second condition for NPV profiles to cross
is that one have a higher IRR than the other.
.
CHY
341
3. The third condition necessary for profiles to
cross is that the project with the higher NPV
at k = 0 will have the lower IRR
One can sketch out two NPV profiles on a
graph to see that these three conditions are
indeed required.
4. The project with the higher NPV at k = 0
must have more cash inflows, because it has
the higher NPV when cash flows are not
discounted, which is the situation if k = 0.
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5. If the project with more total cash inflows also
had its cash flows come in earlier, it would
dominate the other project--its NPV would be
higher at all discount rates, & its IRR would
also be higher, so the profiles would not
cross. The only way the profiles can cross is
for the project with more total cash inflows to
get a relatively high percentage of those
inflows in distant years, so that their PVs are
low when discounted at high rates. Most
students either grasp this intuitively or else
just guess at the question!
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Choosing among mutually exclusive
projects
41. Project A has an internal rate of return
of 18 percent, while Project B has an
internal rate of return of 16 percent.
However, if the company’s cost of
capital (WACC) is 12 percent, Project B
has a higher net present value. Which
of the following statements is most
correct?
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a. The crossover rate for the two projects
is less than 12 percent.
b. Assuming the timing of the two
projects is the same, Project A is
probably of larger scale than Project
B.
c. Assuming that the two projects have
the same scale, Project A probably
has a faster payback than Project B.
d. Statements a & b are correct.
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345
【擬答】(C) Diff: T
Draw out the NPV profiles of these two
projects. As B’s NPV declines more rapidly
with an increase in discount rates, this
implies that more of the cash flows are
coming later on. Therefore, Project A has
a faster payback than Project B.
CHY
346
Capital components
42. Which of the following statements is most
correct?
a. In the weighted average cost of capital
calculation, we must adjust the cost of
preferred stock for the tax exclusion of 70
percent of dividend income.
b. We ideally would like to use historical
measures of the component costs from prior
financings in estimating the appropriate
weighted average cost of capital.
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c. The cost of a new equity issuance (ke) could
possibly be lower than the cost of retained
earnings (ks) if the market risk premium &
risk-free rate decline by a substantial amount.
d. None of the statements above is correct.
【擬答】(D) M
Unlike interest expense on debt, preferred
dividends are not deductible, hence there are
no tax savings associated with the use of
preferred stock. The component costs of
WACC should reflect the costs of new
financing, not historical measures. The cost of
issuing new equity is always greater than the
cost of retained earnings.
CHY
348
Capital components
43. Which of the following statements is most
correct?
a. The cost of retained earnings is the rate of
return stockholders require on a firm’s
common stock.
b. The component cost of preferred stock is
expressed as kp(1 - T), because preferred
stock dividends are treated as fixed charges,
similar to the treatment of debt interest.
c. The bond-yield-plus-risk-premium approach
to estimating a firm’s cost of common equity
involves adding a subjectively determined risk
premium to the market
risk-free bond rate. 349
CHY
d. The higher the firm’s flotation cost for new
common stock, the more likely the firm is to
use preferred stock, which has no flotation
cost.
【擬答】(A) M
Preferred stock dividends are not tax
deductible; therefore, the cost of preferred
stock is only kp. The risk premium in the
bond-yield-plus-risk premium approach would
be added to the firm’s cost of debt, not the
risk-free rate. Preferred stock also has
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350
flotation costs.
Cost of capital estimation
44. Which of the following statements is
correct?
a. The cost of capital used to evaluate a project
should be the cost of the specific type of
financing used to fund that project.
b. The cost of debt used to calculate the
weighted average cost of capital is based on
an average of the cost of debt already issued
by the firm & the cost of new debt.
P131
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c. One problem with the CAPM approach in
estimating the cost of equity capital is that if a
firm’s stockholders are, in fact, not well
diversified, beta may be a poor measure of
the firm’s true investment risk.
d. The bond-yield-plus-risk-premium approach
is the most sophisticated & objective method
of estimating a firm’s cost of equity capital.
e. The cost of equity capital is generally easier
to measure than the cost of debt, which
varies daily with interest rates, or the cost of
preferred stock since preferred stock is
issued infrequently.
【擬答】(C) M
CHY
352
Cost of equity estimation
45. Which of the following statements is
correct?
a. Although some methods of estimating the
cost of equity capital encounter severe
difficulties, the CAPM is a simple & reliable
model that provides great accuracy &
consistency in estimating the cost of equity
capital.
b. The DCF model is preferred over other
models to estimate the cost of equity because
of the ease with which a firm’s growth rate is
obtained.
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c. The bond-yield-plus-risk-premium approach
to estimating the cost of equity is not always
accurate but its advantages are that it is a
standardized & objective model.
d. Depreciation-generated funds are an
additional source of capital and, in fact,
represent the largest single source of funds
for some firms.
【擬答】(D) M
CHY
354
CAPM cost of equity estimation
46. In applying the CAPM to estimate the cost
of equity capital, which of the following
elements is not subject to dispute or
controversy?
a. The expected rate of return on the market,
kM.
b. The stock’s beta coefficient, bi.
c. The risk-free rate, kRF.
d. The market risk premium (RPM).
e. All of the above are subject to dispute.
【擬答】 (E) M
CHY
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CAPM & DCF estimation
47. Which of the following statements is most
correct?
a. Beta measures market risk, but if a firm’s
stockholders are not well diversified, beta
may not accurately measure stand-alone
risk.
b. If the calculated beta underestimates the
firm’s true investment risk, then the CAPM
method will overestimate ks.
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c. The discounted cash flow method of
estimating the cost of equity can’t be used
unless the growth component, g, is constant
during the analysis period.
d. An advantage shared by both the DCF &
CAPM methods of estimating the cost of
equity capital, is that they yield precise
estimates & require little or no judgement.
e. None of the statements above is correct.
【擬答】(A) M
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357
WACC
48. Which of the following statements is most
correct?
a. The weighted average cost of capital for a
given capital budget level is a weighted
average of the marginal cost of each relevant
capital component that makes up the firm’s
target capital structure.
b. The weighted average cost of capital is
calculated on a before-tax basis.
c. An increase in the risk-free rate is likely to
increase the marginal costs of both debt &
equity financing.
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d. Statements a & c are correct.
e. All of the statements above are correct.
【擬答】 (D) M
Both statements a & c are true; therefore,
statement d is the correct choice.
Statement a recites the definition of the
weighted average cost of capital.
Statement c is correct because
• kd = kRF + LP + MRP + DRP while
ks = kRF + (kM - kRF)b. If kRF increases
then the values for kd & ks will increase.
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359
49. Which of the following statements is correct?
a. The WACC should include only after-tax
component costs. Therefore, the required rates of
return (or “market rates”) on debt, preferred, &
common equity (kd, kp, & ks) must be adjusted to
an after-tax basis before they are used in the
WACC equation.
b. The cost of retained earnings is generally higher
than the cost of new common stock.
c. Preferred stock is riskier to investors than is debt.
Therefore, if someone told you that the market
rates showed kd > kp for a given company, that
person must have made a mistake.
d. If a company with a debt ratio of 50 percent were
suddenly exempted from all future income taxes,
then, all other things held constant, this would
cause its WACC to increase.
CHY
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【擬答】
(D) M
If a firm paid no income taxes, its cost of
debt would not be adjusted downward, hence
the component cost of debt would be higher
than if T were greater than 0. With a higher
component cost of debt, the WACC would
increase. Of course, the company would have
higher earnings, & its cash flows from a given
project would be high, so the higher WACC
would not impede its investments, that is, its
capital budget would be larger than if it were
taxed.
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WACC
50. Which of the following statements is most
correct?
a. An increase in flotation costs incurred in
selling new stock will increase the cost of
retained earnings.
b. The WACC should include only after-tax
component costs. Therefore, the required
rates of return (or “market rates”) on debt,
preferred, & common equity (kd, kp, & ks)
must be adjusted to an after-tax basis before
they are used in the WACC equation.
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c. An increase in a firm’s corporate tax rate will
increase the firm’s cost of debt capital, as
long as the yield to maturity on the company’s
bonds remains constant or falls.
d. Statements b & c are correct.
e. None of the statements above is correct.
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【擬答】 (E) M
An increase in flotation costs has no effect
on the cost of retained earnings. Since interest
is tax deductible, while preferred & common
dividends are not, only the cost of debt used in
the WACC equation must be adjusted by
multiplying by (1 - T). An increase in the firm’s
corporate tax rate reduces the after-tax
component cost of debt.
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Risk-adjusted cost of capital
51. If a company uses the same cost of capital
for evaluating all projects, which of the
following results is likely?
a. Accepting poor, high-risk projects.
b. Rejecting good, low-risk projects.
c. Accepting only good, low-risk projects.
d. Accepting no projects.
e. Answers a & b are correct.
【擬答】 (E) M
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365
Risk-adjusted cost of capital
52. If a typical U.S. company uses the same
cost of capital to evaluate all projects, the firm
will most likely become
a. Riskier over time, & its value will decline.
b. Riskier over time, & its value will rise.
c. Less risky over time, & its value will rise.
d. Less risky over time, & its value will decline.
e. There is no reason to expect its risk position
or value to change over time as a result of its
use of a single discount rate.
【擬答】 (A) M
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Division WACCs & risk
53. Pearson Plastics has two equal-sized
divisions, Division A & Division B. The
company estimates that if the divisions
operated as independent companies Division
A would have a cost of capital of 8 percent,
while Division B would have a cost of capital
of 12 percent.
Since the two divisions are the same size,
Pearson’s composite weighted average cost
of capital (WACC) is 10 percent.
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367
In the past, Pearson has assigned separate
hurdle rates to each division based on their
relative risk. Now, however, Pearson has
chosen to use the corporate WACC, which is
currently 10 percent, for both divisions. Which of
the following is likely to occur as a result of this
change? Assume that this change is likely to
have no effect on the average risk of each
division & market conditions remain unchanged.
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a. Over time, the overall risk of the company will
increase.
b. Over time, Division B will become a larger part of
the overall company.
c. Over time, the company’s corporate WACC will
increase.
d. All of the statements above are correct.
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【擬答】 (D) M
If the company uses the 10 percent
WACC, it will turn down all projects with a
return of less than 10 percent but more than 8
percent. Thus, these “safer” projects will no
longer be taken, & the company will increase
the proportion of risky projects it undertakes.
Therefore, statement a is true. If Division A’s
projects have lower returns than Division B’s
because they have less risk, fewer & fewer
projects will be accepted from Division A &
more projects will be accepted from Division
B.
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Therefore, Division B will grow & Division A
will shrink. Therefore, statement b is true. If the
company becomes riskier, then its cost of equity
will increase causing WACC to increase.
Therefore, statement c is true.
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WACC
54. An analyst has collected the following
information regarding Christopher Co.:
• The company’s capital structure is 70 percent
equity & 30 percent debt.
• The yield to maturity on the company’s bonds
is 9 percent.
• The company’s year-end dividend is
forecasted to be $0.80 a share.
• The company expects that its dividend will
grow at a constant rate of 9 percent a year.
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• The company’s stock price is $25.
• The company’s tax rate is 40 percent.
• The company anticipates that it will need to
raise new common stock this year, & total
flotation costs will equal 10 percent of the
amount issued.
Assume the company accounts for flotation
costs by adjusting the cost of capital. Given
this information, calculate the company’s
WACC.
a. 10.41%
b.
12.56%
c. 10.78%
d.
13.55%
CHY
e. 9.29%
373
【擬答】 (A) E
WACC = wdkd(1 - T) + wcke. kd is given =
9%. Find ke:
ke= D1/[P0(1 - F)] + g
= $0.8/[$25(1 - 0.1)] + 0.09
= 0.125556.
WACC = (0.3)(0.09)(0.6) + (0.7)(0.125556) =
10.41%
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374
55. Flaherty Electric has a capital structure that
consists of 70 percent equity & 30 percent
debt. The company’s long-term bonds have a
before-tax yield to maturity of 8.4 percent.
The company uses the DCF approach to
determine the cost of equity. Flaherty’s
common stock currently trades at $45 per
share. The year-end dividend (D1) is
expected to be $2.50 per share, & the
dividend is expected to grow forever at a
constant rate of 7 percent a year.
The company estimates that it will have to issue
new common stock to help fund this year’s
projects.
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The flotation cost on new common stock issued
is 10 percent, & the company’s tax rate is
40 percent. What is the company’s
weighted average cost of capital, WACC?
a. 10.73%
b. 10.30%
c. 11.31%
d. 7.48%
e. 9.89%
【擬答】 (A) E
WACC = [0.3  0.084  (1 - 0.4)] + [0.7 
($2.5/($45  (1 - 0.1)) + 0.07)]= 10.73%.
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WACC
56. Billick Brothers is estimating its WACC. The
company has collected the following
information:
• Its capital structure consists of 40 percent
debt & 60 percent common equity.
• The company has 20-year bonds outstanding
with a 9 percent annual coupon that are
trading at par.
• The company’s tax rate is 40 percent.
• The risk-free rate is 5.5 percent.
• The market risk premium is 5 percent.
• The stock’s beta is 1.4.
P137
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|What is the company’s WACC?
a.
9.71% b.
9.66%
c.
8.31% d. 11.18% e. 11.10%
【擬答】 (B) E
WACC = wdkd(1 - T) + wcks.
ks = kRF + RPM(b)
ks = 5.5% + 5%(1.4)
ks = 5.5% + 7% = 12.5%.
WACC = wdkd(1 - T) + wcks
WACC = 0.4(9%)(1 - 0.4) + (0.6)12.5%
WACC = 9.66%.
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Agency
57. Which of the following statements is most
correct?
a. Compensating managers with stock can
reduce the agency problem between
stockholders & managers.
b. Restrictions are included in credit agreements
to protect bondholders from the agency
problem that exists between bondholders &
stockholders.
c. The threat of a takeover can reduce the
agency problem between bondholders &
stockholders.
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d. Statements a & b are correct.
P137
【擬答】: (D) E
The threat of a takeover alleviates
the agency problem between
managers & stockholders, not
between
bondholders
&
stockholders.
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Agency
58. Which of the following work to reduce agency
conflicts between stockholders &
bondholders?
a. Including restrictive covenants in the
company’s bond contract.
b. Providing managers with a large number of
stock options.
c.
The passage of laws that make it easier for
companies to resist hostile takeovers.
d. Statements b & c are correct.
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【擬答】:(A) E
Restrictive covenants resolve differences
between bondholders & stockholders.
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Agency
59. Which of the following actions are likely to
reduce
agency
conflicts
between
stockholders & managers?
a. Paying managers a large fixed salary.
b. Increasing the threat of corporate
takeover.
c. Placing restrictive covenants in debt
agreements.
d. All of the statements above are correct.
CHY
383
【擬答】: (B) E
Corporate takeovers are most likely to occur
when a firm is underperforming. Managers
who fear losing their jobs will try to
maximize shareholder wealth. The other
statements are false. Statement a will
exacerbate the agency conflict, while
statement c reduces the agency conflict
between stockholders & bondholders.
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Agency
60. Which of the following actions are likely to
reduce the agency problem between
stockholders & managers?
a. Congress passes a law that severely restricts
hostile takeovers.
b.A manager receives a lower salary but receives
additional shares of the company’s stock.
c. The board of directors has become more vigilant
in its oversight [ 董 事 會 盯 更 緊 ] of the
company’s management.
d.Statements b & c are correct.
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擬答: (D) E
Statement a will serve to increase the
agency problems by preventing
takeovers. Both statements b & c
will reduce agency problems.
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Financial policy & cash flows
61. Which of the following statements is most
correct?
a. The optimal dividend policy is the one that satisfies
the shareholders because they supply the firm’s
capital.
b. The use of debt financing has no effect on cash
flow or stock price.
c. The riskiness of projected cash flows depends
upon how the firm is financed.
d. Stock price is dependent on the projected cash
flows & the use of debt, but not on the timing of the
cash flow stream.
CHY
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【擬答】(C) M
P139
Corporate goals & control
62. Which of the following statements is
most correct?
a.The proper goal of the financial manager
should be to maximize the firm’s
expected cash flow, because this will add
the most wealth to each of the individual
shareholders (owners) of the firm.
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b. One way to state the decision framework
most useful for carrying out the firm’s
objective is as follows: “The financial
manager should seek that combination of
assets, liabilities, & capital that will
generate the largest expected projected
after-tax income over the relevant time
horizon.”
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c.The riskiness inherent in a firm’s
earnings per share (EPS) depends on
the characteristics of the projects the
firm selects, which means it depends
upon the firm’s assets, but EPS does
not depend on the manner in which
those assets are financed.
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d. Since large, publicly-owned firms are controlled by
their management teams, & typically, ownership is
widely dispersed, managers have great freedom
in managing the firm. Managers may operate in
stockholders’ best interests, but they may also
operate in their own personal best interests. As
long as managers stay within the law, there simply
aren’t any effective controls over managerial decisions in such situations.
e. Agency problems exist between stockholders &
managers, & between stockholders & creditors.
【擬答】 (E) M
CHY
391
Split
63. Which of the following statements is
false?
a.
A good reason for a firm to initiate a
reverse split is to get the price of the
shares up to some minimum
requirement for listing on a national
exchange.
b.
Stock dividends do not change the
value of firms, but reverse splits do
change form value.CHY
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c.
When the number of shares of a stock
doubles because of a stock split, trading
volume tends to increase by less than 100
percent.
d. When a stock undergoes a reverse split,
effective trading activity tends to increase.
平均每元交易成本降低〕
〔
【擬答】(B)
Stock dividends, splits, and reverse splits have
no effect on firm value.
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Capital Structure & Leverage
64. Assume the following facts for Lowry’s
Manufacturing
Company’s
two
operating divisions at 20X2:
Division A: sales = $1,000,000; variable
costs = $400,000; units sold = 10,000
Division B: sales = $ 800,000; variable
costs = $600,000; units sold = 4,000
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Based on fixed costs of $500,000
divided
equally
between
the
two
divisions, the pre-tax operating profit (EBIT)
during 20X2 for Division A and Division B,
respectively, was?
a.
b.
c.
d.
Division A = $100,000, Division B = $ (300,000)
Division A = $170,000, Division B = $ 100,000
Division A = $600,000, Division B = $ 200,000
Division A = $350,000, Division B = $ (50,000)
CHY
395
【擬答】(D)
The formula is :(sales-variable costs) – fixed
costs;
The altemate formula is: (per unit contribution
margin) (units sold) – fixed costs.
Choice D calculation:
Division A = ($1,000,000 - $400,000) $250,000 = $350,000
Division B = ($800,000 - $600,000) -$250,000
= $(50,000)
Alternate Formula:
Division A = ($100 - $40) (10,000)- $250,000
= $350,000
Division B = ($200 - $150)(4,000) -$250,000 =
$(50,000)
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(A) X. These are the results if each divisions’
fixed costs were $500,000.
(B) X. These are meaningless results.
(C) X. These are the operating profit
excluding fixed costs.
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65. The Simpson Corporation has a
degree of operating leverage of 2.0 and
a degree of financial leverage of 5.0.
Simpson’s degree of total leverage is:
a.
7.0
b.
10.0
c.
2.5
d.
0.4
CHY
398
【擬答】 (B)
Degree of Total Leverage (DTL)
= Degree of Operating Leverage (DOL) ×
Degree of Financial Leverage (DFL)
DTL = DOL × DFL = 2.0 ×5.0 =10.0
CHY
399
66. Which of the following is a true statement
regarding a company’s use of debt and its impact
on the cost of debt, the cost of equity capital, and
the weighted-average cost of capital?
a.
The cost of equity capital increases as the
debt-to-total capital ratio rises because the
required return on common equity should increase
with the higher risk.
b.
The cost of debt declines as the debt-to-total
capital ratio increases because the credit ratings
on the bond improve as the debt-to-total capital
ratio increases.
c.
Beta for a stock is constant at all levels of debtto-equity.
CHY
400
d.
All are true.
P141
【擬答】(A)
The cost of equity should rise as the debt-toequity. In effect, the additional risk results
in a higher beta.
(B) X. The cost of debt will likely increase as
the debt-to-equity ratio increases. As this
ratio increases, the firm’s credit ratings
should fall.
(C) X. See explanation for choice “a” as to
why beta is not constant.
Choice “d” is incorrect. Since both “b” and “c”
are incorrect, “d” is incorrect.
CHY
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67. An investor in a stock can create
his or her own dividend policy by:
a.
Selling off a portion of the shares
owned.
b.
Buying the stock on margin.
c.
Buying futures contracts on the
shares.
d.
All of the above techniques will
create an investor’s own dividend
policy.
CHY
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【擬答】
(A)
(A) V. By selling off shares funds are
raised as if a dividend was received.
Choice “b” and “c” are incorrect. These
choices increase leverage, but do not
constitute a dividend policy for a
shareholder.
CHY
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68. Which statement is most correct, based
on the clientele effect?
a.
If a company changed its dividend
policy from a low payout ratio to a high
payout ratio, it would likely lose its existing
investor base (its “clientele”) and the price
of the shares would fall.
b.
If a company changed its dividend
policy from a low payout ratio to a high
payout ratio, it would likely gain a new
“clientele” and the price of the shares
would rise.
CHY
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c. If a company changed its dividend policy
from a low payout ratio to a high payout
ratio, its investor base (clientele) would
change from growth-oriented investors to
income-oriented investors. But, in the long
run, there would probably be no significant
change in the price of the shares.
d. Investors prefer that the dividend that a
company pays be equal to the total
amount of the free cash flow that the firm
has generated for equity investors during
the most recent accounting period.
CHY
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【擬答】(C) According to the clientele
effect, a change in the dividend payout
probably has no effect on firm or
common stock values.
Choice “a” and “b” are incorrect. These
outcomes contradict the clientele effect.
Choice “d” is incorrect. Such a policy
would produce erratic dividends, which
investors dislike. This has nothing to do
with the clientele effect.
CHY
406
70. Proposition I of the Modigliani-Miller
Theorem (without taxes) suggests that if two
firms have the same total value:
a.
The one with the most debt will have the
highest equity value.
b.
The one with the most debt will have the
lowest equity value.
c.
The equity values of the two firms will be
equal in spite of the fact that one firm has more
debt than the other.
d.
The optimum capital structure would be
one with a modest amount of debt.
【擬答】(B)
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The value of a firm equals the sum
of the values of the debt and equity
portions of its capital structure.
Therefore, if the debt portion is large,
the
equity portion must be small
and vice versa.
CHY
408
Modigliani-Miller Theorem (without taxes)
Proposition I 任何Debt-Equity Ratio都可以;
Firm Value 不受影響
Proposition Cost
of Cost
of WACC不變
Debt不變
Equity
隨
II
Debt-Equity
Ratio 增 加 而
上升
CHY
409
Modigliani-Miller Theorem (with taxes)
Proposition I Debt-Equity Ratio越高越好
WACC隨
Cost of
Equity隨
Debt-Equity
Debt-Equity Ratio增加,
Ratio增加 稅盾愈多 而
而上升
減少
Debt- Equity Ratio有最合適水準
Proposition
Ⅱ
Cost of
Debt不變
Trade-off
Theory
Signaling
Theory
增加Equity之外部融資會有負面訊號
效果
CHY
410
71. Proposition Ⅱ of the Modigliani-Miller
Theorem (without taxes) suggests that if
there is no preferred stock in the capital
structure, as a firm’s debt-to-equity ration
increases:
a.
Its cost of common equity capital
decreases.
b. Its cost of common equity capital ↑.
c. Its cost of common equity capital remains
constant.
d. All of the above are possible.
CHY
P143
411
【擬答】 (B)
Proposition II states that the weighted
average cost of capital must remain
constant across all debt-to-equity
rations for a non-taxpaying firm => the
cost of debt is assumed to remain
constant over the entire range of debtto-equity ratios, so in the absence of
preferred equity, the cost of equity
capital must increase as the debt-toequity ratio rises.
CHY
412
72. According to Proposition Ⅱ of the
Modigliani-Miller Theorem (with taxes):
a.
As the debt-to-equity ratio ↑, WACC
will remain constant.
b.
As the debt-to-equity ratio↑, WACC will
↑.
c.
When the capital structure is
entirely comprised of debt, WACC = aftertax cost of debt capital.
d.
The value of the equity of a firm with
100﹪debt will be zero. [有稅盾價值]
【擬答】 (C)
CHY
413
73. Which statement is most correct？
a.
If a company changed its dividend
policy from a low payout ratio 【股利支付
比率】 to a high payout ratio, it would
likely lose its existing investor base (its
“clientele”) and the price of the shares
would fall.
b.
If a company changed its dividend
policy from a low payout ratio to a high
payout ratio, it would likely gain a new
“clientele” and the price of the shares
would rise.
CHY
414
c.
If a company changed its dividend policy
from a low payout ratio to a high payout ratio,
its investor base (clientele) would change
from growth oriented investors to income
oriented investors but, in the long run, there
would probably be no significant change in
the price of the shares.
d.
Investors prefer that the dividend that a
company pays be equal to the total amount of
the free cash flow that the firm has generated
for equity investors during the most recent
accounting period.
CHY
415
【擬答】 (C)
(D) X
because such a policy would
produce erratic dividends <= 投資人現金流
量不確定 =負面效果
CHY
416
Business risk
(C)
E
74. A decrease in the debt ratio will
generally have no effect on
a.
b.
c.
d.
e.
Financial risk.
Total risk.
Business risk.
Market risk.
None of the above is correct. (It will
affect each type of risk above.)
CHY
417
75. A capital project that is undertaken
primarily for the purpose of
increasing sales is called:
a.
An expansion project.
b.
A replacement project.
c.
An environmental project.
d.
A remediation project.
CHY
418
【擬答】 (A)
An expansion project is undertaken to
increase sales. This sales increase can
be accomplished by expanding into
existing or new markets.
(B)X
A replacement project is
undertaken
to
replace
existing
equipment.
Choices “c” & “d” are incorrect. Neither of
these are done to increase sales.
CHY
419