CHY1 Future value Present value Rates of return Amortization Chapter 1 Time Value of Money

CHY 1

• Future value

• Present value

• Rates of return

• Amortization

Chapter 1Time Value of Money

CHY 2

Time lines show timing of cash flows.

CF0 CF1 CF3CF2

0 1 2 3i%

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 3

Time line for a $100 lump sum due at the end of Year 2.

100

0 1 2 Yeari%

CHY 4

Time line for an ordinary annuity of $100 for 3 years.

100 100100

0 1 2 3i%

CHY 5

Time line for uneven CFs: -$50 at t = 0 and $100, $75, and $50 at the end of Years 1

through 3.

100 50 75

0 1 2 3i%

-50

CHY 6

What’s the FV of an initial $100 after 3 years if i = 10%?

FV = ?

0 1 2 310%

Finding FVs (moving to the righton a time line) is called compounding.

100

CHY 7

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 8

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 9

Three Ways to Find FVs

• Solve the equation with a regular calculator.

• Use a financial calculator.

• Use a spreadsheet.

CHY 10

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 11

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 12

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 13

Financial calculators solve this equation:

There are 4 variables. If 3 are known, the calculator will solve for the 4th.

.0n

i1PVnFV

Financial Calculator Solution

CHY 14

3 10 -100 0N I/YR PV PMT FV

133.10

Here’s the setup to find FV:

Clearing automatically sets everything to 0, but for safety enter PMT = 0.

Set: P/YR = 1, END.

INPUTS

OUTPUT

CHY 15

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 16

10%

What’s the PV of $100 due in 3 years if i = 10%?

Finding PVs is discounting, and it’s the reverse of compounding.

100

0 1 2 3

PV = ?

CHY 17

Solve FVn = PV(1 + i )n for PV:

PV =

FV

1+ i = FV

11+ i

nn n

n

PV = $100

11.10

= $100 0.7513 = $75.13.

3

CHY 18


3 10 0 100N I/YR PV PMT FV

-75.13

Either PV or FV must be negative. HerePV = -75.13. Put in $75.13 today, take out $100 after 3 years.

INPUTS

OUTPUT

CHY 19


• Use the PV function: see spreadsheet.– = PV(Rate, Nper, Pmt, FV)– = PV(0.10, 3, 0, 100) = -75.13

CHY 20

Finding the Time to Double

20%

2

0 1 2 ?

-1 FV = PV(1 + i)n

$2 = $1(1 + 0.20)n

(1.2)n = $2/$1 = 2nLN(1.2) = LN(2) n = LN(2)/LN(1.2) n = 0.693/0.182 = 3.8.

CHY 21

20 -1 0 2N I/YR PV PMT FV

3.8

INPUTS

OUTPUT

Financial Calculator

CHY 22


• Use the NPER function: see spreadsheet. – = NPER(Rate, Pmt, PV, FV)– = NPER(0.10, 0, -1, 2) = 3.8

CHY 23

Finding the Interest Rate

?%

2

0 1 2 3

-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 24

3 -1 0 2N I/YR PV PMT FV

25.99

INPUTS

OUTPUT

Financial Calculator

CHY 25


• Use the RATE function: – = RATE(Nper, Pmt, PV, FV)– = RATE(3, 0, -1, 2) = 0.2599

CHY 26

Ordinary Annuity

PMT PMTPMT

0 1 2 3i%

PMT PMT

0 1 2 3i%

PMT

Annuity Due

What’s the difference between an ordinary annuity and an annuity due?

PV FV

CHY 27

What’s the FV of a 3-year ordinary annuity of $100 at

10%?

100 100100

0 1 2 310%

110 121FV = 331

CHY 28

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:

.33110.

100

0.10

1)0(1

i

1i)(1PMT

3

n

CHY 29

Financial calculators solve this equation:

There are 5 variables. If 4 are known, the calculator will solve for the 5th.

.0i

1ni)(1PMTn

i1PVnFV

Financial Calculator Formula for Annuities

CHY 30

3 10 0 -100

331.00N I/YR PV PMT FV


Have payments but no lump sum PV, so enter 0 for present value.

INPUTS

OUTPUT

CHY 31


• Use the FV function: see spreadsheet.– = FV(Rate, Nper, Pmt, Pv)– = FV(0.10, 3, -100, 0) = 331.00

CHY 32

What’s the PV of this ordinary annuity?

100 100100

0 1 2 310%

90.91

82.64

75.13248.69 = PV

CHY 33

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:

69.24810.

100

0.10)0(1

11-

ii)(1

11-

PMT

3

n

CHY 34

Have payments but no lump sum FV, so enter 0 for future value.

3 10 100 0N I/YR PV PMT FV

-248.69

INPUTS

OUTPUT


CHY 35


• Use the PV function: see spreadsheet.– = PV(Rate, Nper, Pmt, Fv)– = PV(0.10, 3, 100, 0) = -248.69

CHY 36

Find the FV and PV if theannuity were an annuity due.

100 100

0 1 2 3

10%

100

CHY 37

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 38

3 10 100 0

-273.55 N I/YR PV PMT FV

Switch from “End” to “Begin”.Then enter variables to find PVA3 = $273.55.

Then enter PV = 0 and press FV to findFV = $364.10.

INPUTS

OUTPUT

CHY 39

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 40

What is the PV of this uneven cash

flow stream?0

100

1

300

2

300

310%

-50

4

90.91247.93225.39-34.15

530.08 = PV

CHY 41

• Input in “CFLO” register:CF0 = 0

CF1 = 100

CF2 = 300

CF3 = 300

CF4 = -50

• Enter I = 10%, then press NPV button to get NPV = 530.09. (Here NPV = PV.)

CHY 42


Excel Formula in cell A3:

=NPV(10%,B2:E2)

A B C D E

1 0 1 2 3 4

2 100 300 300 -50

3 530.09

CHY 43

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 44

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 45

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 morefrequent than once a year--for example, semiannually, quarterly,or daily--interest is earned on interestmore often.

CHY 46

FV Formula with Different Compounding Periods (e.g., $100

at a 12% nominal rate with semiannual compounding for 5

years)

= $100(1.06)10 = $179.08.

FV = PV 1 .+ imnNom

mn

FV = $100 1 + 0.12

25S

2x5

CHY 47

FV of $100 at a 12% nominal rate for 5 years with different

compoundingFV(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 48

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 49

• 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 50

How do we find EFF% for a nominal rate of 12%, compounded

semiannually?

EFF% = - 1(1 + )iNom

m

m

= - 1.0(1 + )0.122

2

= (1.06)2 - 1.0 = 0.1236 = 12.36%.

CHY 51

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 52

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 53

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 54

When is each rate used?

iNom: Written into contracts, quoted by banks and brokers. Not used in calculations or shownon time lines.

CHY 55

iPer: Used in calculations, shown on time lines.

If iNom has annual compounding,then iPer = iNom/1 = iNom.

CHY 56

(Used for calculations if and only ifdealing with annuities where payments don’t match interest compounding periods.)

EAR = EFF%: Used to compare returns on investments with different payments per year.

CHY 57

Amortization

Construct an amortization schedulefor a $1,000, 10% annual rate loanwith 3 equal payments.

CHY 58

Step 1: Find the required payments.

PMT PMTPMT

0 1 2 310%

-1,000

3 10 -1000 0

INPUTS

OUTPUT

N I/YR PV FVPMT

402.11

CHY 59

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 60

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 3to complete the amortization table.

CHY 61

Interest declines. Tax implications.

BEG PRIN ENDYR BAL PMT INT PMT BAL

1 $1,000 $402 $100 $302 $698

2 698 402 70 332 366

3 366 402 37 366 0

TOT 1,206.34 206.34 1,000

CHY 62

$

0 1 2 3

402.11Interest

302.11

Level payments. Interest declines because outstanding balance declines. Lender earns10% on loan outstanding, which is falling.

Principal Payments

CHY 63

• 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

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.

FV=?

0 1 2 273

0.031054%

-100

Note: % in calculator, decimal in equation.

FV = $100 1.00031054 = $100 1.08846 = $108.85.

273273

CHY

273 -100 0

108.85

INPUTS

OUTPUT

N I/YR PV FVPMT

iPer = iNom/m= 11.33463/365= 0.031054% per day.

Enter i in one step.Leave data in calculator.

CHY 67

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

100

2 35%

4 5 6 6-mos. periods

100 100

CHY 68

• Payments occur annually, but compounding occurs each 6 months.

• So we can’t use normal annuity valuation techniques.

CHY 69

1st Method: Compound Each CF

0 1

100

2 35%

4 5 6

100 100.00110.25121.55331.80

FVA3 = $100(1.05)4 + $100(1.05)2 + $100= $331.80.

CHY 70

Could you find the FV with afinancial calculator?

Yes, by following these steps:

a. Find the EAR for the quoted rate:

2nd Method: Treat as an Annuity

EAR = (1 + ) - 1 = 10.25%. 0.10

22

CHY 71

3 10.25 0 -100

INPUTS

OUTPUT N I/YR PV FVPMT

331.80

b. Use EAR = 10.25% as the annual rate in your calculator:

CHY 72

What’s the PV of this stream?

0

100

15%

2 3

100 100

90.7082.2774.62

247.59

CHY

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

3 Ways to Solve:

1. Greatest future wealth: FV2. Greatest wealth today: PV3. Highest rate of return: Highest EFF%

iPer = 0.018538% per day.

1,000

0 365 456 days

-850

CHY

1. Greatest Future Wealth

Find FV of $850 left in bank for15 months and compare withnote’s FV = $1,000.

FVBank = $850(1.00018538)456

= $924.97 in bank.

Buy the note: $1,000 > $924.97.

CHY

456 -850 0

924.97

INPUTS

OUTPUT

N I/YR PV FVPMT

Calculator Solution to FV:

iPer = iNom/m= 6.76649%/365= 0.018538% per day.

Enter iPer in one step.

CHY

2. Greatest Present Wealth

Find PV of note, and comparewith its $850 cost:

PV = $1,000/(1.00018538)456

= $918.95.

CHY

456 .018538 0 1000

-918.95

INPUTS

OUTPUT

N I/YR PV FVPMT

6.76649/365 =

PV of note is greater than its $850 cost, so buy the note. Raises your wealth.

CHY

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.

3. Rate of Return

CHY

456 -850 0 1000

0.035646% per day

INPUTS

OUTPUT

N I/YR PV FVPMT

Convert % to decimal:

Decimal = 0.035646/100 = 0.00035646.

EAR = EFF% = (1.00035646)365 - 1 = 13.89%.

CHY

Using interest conversion:

P/YR = 365NOM% = 0.035646(365) = 13.01 EFF% = 13.89

Since 13.89% > 7.0% opportunity cost,buy the note.

CHY 82

OVERVIEW AND THE COST OF

CAPITAL [ 公司理財與資金成

本 ]

Page 17

CHY 83

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 84

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 85

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 86

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 87

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 88

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〕

Page 13

CHY 89

– 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 90

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〕

CHY 91

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

CHY 92

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]

CHY 93


• The Cost of Debt 〔負債〕　 Capital

rafter-tax = (1-t)rD

CHY 94

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 capitalafter-tax cost of debt capital for the firm?

Answer:

rafter-tax = (1-t)rD =(1-0.35)(7%) =4.55%4.55%

[ 如果同時看到 coupon 與 Yield to Maturity, 請用YTM]

CHY 95


2. The Cost of Preferred Stock [ 特別股 ]

Capital

PS

pp P

DIVr

CHY 96

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

CHY 97


3. The Cost of Retained Earnings 〔保留盈餘〕 (Common equity)

a. The Capital Asset Pricing Model (CAPM)Capital Asset Pricing Model (CAPM) Approach [ Approach [ 資本資產定價模型資本資產定價模型 ]:]:

rCE = rF + βCS(rM – rF)

CHY 98

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%

CHY 99


3. The Cost of Retained Earnings 〔保留盈餘〕(Common equity)

b. The Dividend-YieldDividend-Yield-Plus-Growth-Growth- Rate Rate ( or Implied Return) Approach:

DIVCS

CE gP

DIVr 1

CHY 100

Example: 　　 The Ajax Company currentlycurrently （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 estimate Ajax’s cost of retained earnings capital.retained earnings capital.

Answer:

%4.13%525$

)05.1(2$

)1(0

DIVCS

DIVCE g

P

gDIVr

CHY 101


3. The Cost of Retained Earnings 〔保留盈餘〕 (Common equity)c. The Bond-Yield-Plus-Risk-Premium Approach

ERPDCE rrr

CHY 102

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:

%3.10%4%3.6 ERPDCE rrr

CHY 103


4. Cost of Newly IssuedNewly Issued Common Stock [ 新的普通股　有發行成本 flotation costs]

(Also Called the Cost of External Equity)

DIVCS

newCE gfP

DIVr

)1(1

CHY 104

Example: 　　 The XYZ Corporation’s common shares are trading at $40. The Company currentlycurrently 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).

%65.1104.

)15.1(40$

)04.1(50.2$

)1(

10

DIVCS

DIVnewCE g

fP

gDIVr

Answer:

CHY 105

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 capitaltarget capital structurestructure 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 weighted-average cost of capital

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WACC

• 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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CHY 108

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 $1,000 million

CHY 109

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%

CHY 110

Example continued… The prevailing financial market conditions are as follows:

Quality Yields on Newly Issued BondsBonds by QltyAaa 6.9%Aa 7.0A 7.2Baa 7.5

Quality Yields on Newly Issued PreferredPreferred Stocks Stocks by Quality

A 7.5%B 8.0C 8.9

Risk-free rate……………………………… 　 6.5%Equity risk premium over bonds …………. 2.7Expected return on stock market index…… 9.5

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Example continued…What is the company’s weighted-average cost of weighted-average cost of capitalcapital 　　〔〔加權平均資金成本加權平均資金成本〕〕 ??

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.

Continue on next page

CHY 112

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=rF+CS(rm-rF) = 6.5% +1.07(9.5-6.5) =9.7%*

*%7.9%0.6%7.3

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DIVr

CHY 113

Therefore, the weighted-average cost of capital　〔加權平均資金成本　〕 of the firm under these conditions is:

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CHY 114

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.

CHY 115

＝＞ 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〕

CHY 116

Answer:The firm’s marginal cost of this last $100 million unit of capital is 10%, which is calculated as follows:

Source Capital Struc. Weight Component W. Cost Cost

Debt $50 million 50% 6% 0.5(6%) =3%

Equity 50 million 50% 14% 0.5(14%) = 7%

=10%

CHY 117

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 ]

CHY 118

THE BASICS OF CAPITAL BUDGETING

CHY 119

I. INTRODUCTION

Capital budgeting is the process of analyzing projects in order to decide which ones should be undertaken.

CHY 120

II. RANKING CAPITAL PROJECTS

A. FOUR METHODS AND THEIR CALCULATION1.Payback Period

2.Discounted Payback Period

3.Net Present Value (NPV)

4.Internal Rate of Return (IRR)

CHY 121

3. Net Present Value (NPV)Example:

Calculate the net present value of the above project whose cost of capital is 10%.

Answer:Year Cash Flow P.V. of Cash Flow 0 $(100,000) $(100,000)

1 20,000 18,1822 40,000 33,0583 60,000 45,0794 30,000 20,4905 10,000 6,209

$ 23,018

CHY 122

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.

CHY 123

4. Internal Rate of Return (IRR)

Example:

What is the internal rate of return for the project in the previous problem?

CHY 124


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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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%

CHY 126

a. Modified Internal Rate of Return (MIRR)

CHY 127

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

CHY 128

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 C0 $(50,000) $(120,000) $(20,000)1 40,000 (50,000) 2,0002 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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Answer:1. The NPVS of the projects are:Yr NPV of Proj A NPV of Proj B NPV of Proj C

@15% @15% @15%0 $(50,000) $(120,000) $(20,000)1 34,783 (43,478) 1,7392 15,123 113,422 11,3423 6,575 49,314 9,863

$ 6,481 $ (742) $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.

CHY 130


• 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.

CHY 131

• 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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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.

CHY 133

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

CHY 134

CASH FLOW ESTIMATION AND OTHER CAPITAL BUDGETING

TOPICS

CHY 135

I. INTRODUCTIONA. CASH FLOW VS. ACCOUNTING PROFIT

B. DEFINITIONSa. 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 analyzed.

CHY 136

• 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).

CHY 137

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 5-year 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:

CHY 138

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 AdditionalWorking Capital Outlay

$ 40,000 (2)

CHY 139

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.

CHY 140

Example continued:

• In addition, it is assumed that a terminal-year 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.

CHY 141

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

CHY 142

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.

CHY 143

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.

CHY 144

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

CHY 145

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 ProjectedPro Forma (Free) Cash Income Flows

Sales $600,000 $600,000Direct Expenses 300,000 300,000Depreciation 100,000 100,000Selling Expenses and Externalities 16,000 16,000EBIT $184,000 $184,000Interest Expense 35,700Pretax Income $148,300Income Tax Expense @40% 59,320 73,600(40% of EBIT)Net Income $ 88,980

EBIT(1-t) $110,400Plus: Depreciation 100,000Less: Capital Expenditures 0Less: Required Additional

Working Capital Outlay 40,000Incremental Cash Flow in the

Operating Years $170,400

CHY 146

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

CHY 147

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.

CHY 148

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

CHY 149

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.

CHY 150

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 151

(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

CHY 152

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%

CHY 153

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 154

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 155

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 Cash Flow PV of Cash Flow @14.6% 0 $(512,000) $(512,000) 1 170,400 148,691 2 170,400 129,748 3 170,400 113,218 4 170,400 98,794 5 170,400 86,208 6 48,800 21,543

$ 86,202Since 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.

CHY 156

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. The firm’s cost of capital is 15% and its marginal income tax rate is 40%.

CHY 157

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 OutlayCost of New Machine $90,000

Less: Sale of Old Machine 5,000Less: Tax Savings on Sale of Old Machine 800 【 0.40×$2,000

loss 】Initial Investment Outlay $84,200

CHY 158

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:

Cash Flow After-tax reduction in cash operating costs $24,000 (1)Depreciation on new machine $18,000Depreciation on old machine 10,000Increase in depreciation $ 8,000Tax savings on increase in depreciation 3,200 (2)Less: Increase in required working capital 3,000Operating cash flow $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

CHY 159

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

CHY 160

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 Cash Flow PV of Cash Flow @15% 0 $(84,200) $(84,200) 1 24,200 21,299 2 24,200 18,299 3 24,200 15,912 4 24,200 13,836 5 24,200 14,020

NPV $(1,090)Answer:

The old machine should not be replaced because the NPV of the project is negative.

CHY 161

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 162

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.

• Which machine should purchased?

CHY 163

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 164

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 Machine A P.V. of A Machine B P.V of B Operating Operating Operating Operating

Cash Flows CF @14% CF CF @14%

0 $(600,000) $(600,000) $ (700,000) $(700,000)

1 300,000 263,158 200,000 175,439

2 300,000 230,840 200,000 153,894

3 300,000 202,491 200,000 134,994

4 200,000 118,416

5 200,000 103,874

6 200,000 91,117

$ 96,489 $ 77,734

CHY 165

Machine A Machine B

PV = 96,489 PV =77,734n = 3 n = 6i = 14 i = 14FV = 0 FV = 0

EAA = PMT = $41,561 EAA = PMT = $19,990

The decision is to buy Machine A because it has the algebraically higher equivalent annual annuity per year.

CHY 166

公司財務研討 I

In Class Question P57

CHY 167

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 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 life of six years.

CHY 169

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 life of six years.

CHY 170

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?

CHY 171

2. The Replacement Chain (Common Life) Approach

• The replacement chain (Common Life) methodreplacement chain (Common Life) method solves the problem by equalizing the lives of the two machines.

• This is done by extending the life of Machine Aextending 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 appear as follows:

CHY 172

2. The Replacement Chain (Common Life) Approach @ 14% continued…

Year Machine A P.V. of Machine B P.V of Operating Machine A Operating Machine B Cash Flows Operating Cash Flows Cash Flows

0 $(600,000) $(600,000) $ (700,000) $(700,000)1 300,000 263,158 200,000 175,4392 300,000 230,840 200,000 153,8943 (300,000)(*))(*) (202,491) 200,000 134,9944 300,000 177,624 200,000 118,4165 300,000 155,811 200,000 103,8746 300,000 136,767 200,000 91,117

$ 161,618 $ 77,734

CHY 173

(*) 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 174

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

CHY 175

CAPITAL BUDGETING RISK ANALYSIS

I. TYPES OF RISK

• Stand-alone Risk

• Corporate (Within-firm) Risk

• Market Risk (Beta)

CHY 176

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 they are about its market risk.

CHY 177

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 aremore concerned with market risk than with corporate risk.

CHY 178

MeasuringMeasuring Stand-alone Risk Stand-alone Risk

Scenario AnalysisScenario Analysis• The probabilities assigned to each scenarioprobabilities assigned to each scenario are

subjective.• ““Outlier” scenariosOutlier” 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 179

Sensitivity Analysis

NPV NPV 結果對那個變數最敏感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　考慮到特殊事件　 (Outliers)(Outliers)

　但是　但是 : : 變數的分配要主觀認定變數的分配要主觀認定 , , 且操作且操作複雜複雜

CHY 180

Measuring Measuring Market riskMarket risk THE SECURITY MARKET LINE

r = rF +β （ rM-rF ）

• USING A MARKET (SYSTEMATIC; MARKET (SYSTEMATIC; BETA) RISK MEASUREBETA) RISK MEASURE TO DETERMINE THE REQUIRED RETURN ON A CAPITAL PROJECT FINANCED WITH EQUITY CAPITAL

CHY 181

Using the SML to Estimate the Risk-Adjusted Cost of Equity

Capital

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.

Pro

ject

IRR

Firm’s risk (beta)

SML

5%

Good projects

Bad projects

30%

2.5

A

B

C

CHY 182

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.

CHY 183

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 184

• 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 185

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 ）= 5%+1.5(10-5)=12.5%

CHY 186

MEASURING THE BETA OF A PROJECT

• The Pure Play Method ~ 找 Single Product Company (Pure Player) 看她的Beta

CHY 187

INCLUDING A RISK ADJUSTMENT

• Certainty Equivalent ApproachCertainty 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 RateRisk-Adjusted Discount Rate ~ cash flows not scaled down, 但是以 Risk-Adjusted Cost of Equity Capital 折現

CHY 188

CAPITAL STRUCTURE &

LEVERAGE

Page 83

CHY 189

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 190

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 %∆Sales EBIT 息前稅前盈餘

CHY 191

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 riskthe 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 CapitalDebt/Total Capital or Debt/EquityDebt/Equity ratios.

CHY 192

• However, a more useful measure of financial leverage is the degree of financial leveragedegree of financial leverage 【【財財務槓桿務槓桿】】 (( DFL),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 193

• DFL =

%ΔPretax Income%ΔPretax Income

%ΔEBIT

= EBIT / Pretax Income

= EBIT / (EBIT-INTEREST)

CHY 194

Degree of Total Leverage 【【總槓桿總槓桿】】

• DTL 【【總槓桿總槓桿】】　= DOL 【【營業槓桿營業槓桿】】　 × DFL 【【財務槓桿財務槓桿】】

• %ΔPretax Income%ΔPretax Income = ΔPretax Income

Pretax Income

= DOL × DFL x % ΔSales

CHY 195

• %ΔEPS = DOL × DFL x %ΔSales

• EPS2006

= EPS2005 (1 + DOL × DFL x %ΔSales)

• DOL & DFL 像是擴大器

CHY 196

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 employed.

CHY 197

Financial Leverage 財務槓桿財務槓桿 , EPS 每股盈餘 & EBIT 息前稅前盈

餘

EBIT ($ millions, no taxes)

EPS ($)

0 0.2 0.4 0.6 0.8 1

3

2.5

2

1.5

1

0.5

0

– 0.5

– 1

D/E = 1　Levered Firm

D/E = 0 Un-leveraged Firm

CHY 198

• 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 199

【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 lower earnings per share than leveraged

CHY 200

• 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 201

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 future cash flows

CHY 202

CAPITAL STRUCTURE THEORIESA. 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〕

• EBIT is not affected by the use of debt.

CHY 203

MM with Taxes

1.1. The Effect of Taxes 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 Costs2. The Effect of Bankruptcy Costs [實務上破產成本驚人 , 故企業不敢借太兇 ]

CHY 204

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 debt isis beneficial to a firm beneficial to a firm, but only up to a point.only up to a point.

• In contrast to the Modigliani-Miller irrelevance proposition, an optimal capital structure does exist [[ 存在最適資本結構存在最適資本結構 ]]. It is that mix of debt, mix of debt, preferred stock, & common equity that minimizes preferred stock, & common equity that minimizes the firm’s weighted average cost of capital.the firm’s weighted average cost of capital.

CHY 205

CHY 206

CHY 207

【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 208

CHY 209

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 210

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 common equity was significantly overvaluedovervalued.

• The announcement of a stock offering is generally taken by the market to be a signal signal that management believesmanagement believes that its firm’s stockstock is overpriced relative to the firm’s future overpriced relative to the firm’s future prospectsprospects.

CHY 211

【融資順位理論】 Pecking Order Theory

• 有好消息的企業：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：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

CHY 212

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 213

【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 high debt-to-equity ratios.

CHY 214

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 215

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 216

Corporate FinanceImportant Equations

The Cost of Debt Capital

rafter-tax = (1-t)rD

The Cost of Preferred Stock Capital

PS

PP P

DIVr

CHY 217

The Capital Asset Pricing Model (CAPM) Approach:

rCE = rF + βCS(rM – rF)

The Dividend-Yield-Plus-Growth-Rate ( or Implied Return) Approach

DIVCS

CE gP

DIVr 1

CHY 218

The Bond-Yield-Plus-Risk-Premium Approach

rCE = rD+ rERP

Cost of Newly Issued Common Stock Cost of Newly Issued Common Stock (Also Called the Cost of External (Also Called the Cost of External

Equity)Equity)

DIVCS

newCE gfP

DIVr

)1(1

CHY 219

The weighted-average cost of capitalThe weighted-average cost of capital

rw = (1-t)rD (VD/ VA) + rP (VP/ VA) + rCE (VCE/ VA)

Free Cash Flow from an Expansion Free Cash Flow from an Expansion ProjectProject

FCFF = EBIT(1-t) + DEPR –CAPX –ΔWC

CHY 220

Degree of Operating Leverage

DFL = %ΔEBIT = 1+CF %Δsales EBIT

Degree of Financial LeverageDegree of Financial Leverage

INTEBIT

EBIT

etaxIncome

EBIT

EBIT

etaxIncomeDFL

Pr%

Pr%

CHY 221

Quantifying Total Company Risk

SalesDFLDOLIncomeetax

etaxIncomeIncomeetax

%

_Pr

Pr_Pr%

)%1(

%%

01 SalesDFLDOLEPSEPS

SalesDFLDOLEPS

DFLDOLDTL

CHY 222

DIVIDEND POLICY 【股利政策】

• I. Dividend 【股利　】 & Cash Buyout [Buyout [ 庫藏股買回庫藏股買回 ]]

• II. DETERMINING A FIRM’S OPTIMUM DIVIDEND POLICYOPTIMUM DIVIDEND POLICY　　【股利政策　　　　　　　　　　　　　　　　　　　　　　　　】　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　

　　　　　　　　　　 Page 101Page 101

CHY 223

Procedure for Cash Dividend Payment

25 Oct. 1 Nov. 2 Nov. 6 Nov. 7 Dec.

Declaration Date

Cum-dividend

Date

Ex-dividend

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 to be stockholders as of 6 November.

CHY 224

Price Behavior around the Ex-Dividend Date

• In a perfect world, the stock price will fall by the amount of the dividend on the ex-dividend date.

$P

$P - div

Ex-dividend

Date

The price drops by the amount of the cash dividend

-t … -2 -1 0 +1 +2 …

Taxes complicate things a bit. Empirically, the price drop is less than the dividend and occurs within the first few minutes of the ex-date.

CHY 225

A. THREE THEORIES ON DIVIDEND POLICY

1. MM: Dividend Irrelevance Theory (MM 股利無關企業價值論 )

This dividend irrelevance theorydividend irrelevance theory suggests that the dividend payout ratio & dividend policy is irrelevant on determining the value of value of firmsfirms.

CHY 226

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 　〔無代理人問題〕 .

CHY 227

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 Investors Can Create Homemade DividendsDividends( 自己發自己現金股利 )

CHY 228

Homemade Dividends 　( 自己發自己現金股利 )

• Bianchi Inc. stock Price=$42 about to 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 sharesInvestor owns 80 shares and prefers $3 cash dividendprefers $3 cash dividend.• Bob’s homemade dividend strategy:

– Sell 2 shares ex-dividend Sell 2 shares ex-dividend

homemade dividendsCash from dividend ($D x 80) $160Cash from selling stock $80Total Cash $240Value of Stock Holdings $40 × 78 　股

＝ $3,120

$3 Dividend$240

$0$240

$39 × 80　股＝　$3,120

CHY 229

f. 高 Dividend Payout % 者Internal Growth Rate 低　 [ 今

天多拿到 $ => 未來少拿到 $ ]

Where: ROE is the return on equity　（淨值報酬率） .

K is the payout ratio 　（股利支付率） .

Internal Growth Rate (g)

= ROE (1-k)

CHY 230

【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 231

2. The Bird-in-the –Hand [[一鳥在手一鳥在手 ]] Theory

Higher Div Payout => Better

ECEDIVCECS gr

KE

gr

DIVP

11

CHY 232

PRICE cs

= DIV1 / (r – g)

= Div Payout Ratio

x Expected EPS at period 1

÷ (r – g)

CHY 233

3. The Tax Preference Theory

The tax preference theorytax preference theory suggests that high high dividenddividend payout policies reduce the reduce the value of common sharesvalue of common shares and, hence, the value of the firmvalue of the firm..

CHY 234

• In the presence of personal taxespersonal taxes:

1. A firm should not issue stock to pay a should not issue stock to pay a dividend.dividend.

2. Managers have an incentive to seek alternative uses for funds to reduce alternative uses for funds to reduce dividendsdividends.

3. Personal taxes mitigate against the payment ersonal taxes mitigate against the payment of dividendsof dividends

CHY 235

4. A Summary of the Three Theories

• The bird-in-the-hand theorybird-in-the-hand theory [[一鳥在手一鳥在手 ]] suggests that the higher the payout ratiohigher the payout ratio, the higher will be the value of the firmhigher will be the value of the firm & its common stock.

• The tax preference theorytax preference theory states that the higher the payout ratio, the lower will be the lower will be the value of the firmvalue of the firm & its common stock.

• The dividend irrelevance theorydividend irrelevance theory states that dividend policy has no effect on the value of no effect on the value of the firm or its common stockthe firm or its common stock.

CHY 236

A clientele based explanation• [ 意思是 . ..] Investors may form

clienteles based upon their tax brackets. • Investors in high tax brackets may Investors in high tax brackets may

invest in stocks which do not pay invest in stocks which do not pay dividendsdividends & those in low tax brackets may invest in dividend paying stocks.

• 倒沒有說多發現金股利不好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 237

–(a) Older investors were more likely to hold high dividend stocks, &

–(b) Poorer investors tended to hold high dividend stocks

CHY 238

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 239

【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 investors in high tax brackets.

CHY 240

B. THE RESIDUAL DIVIDEND MODEL [2004-10-08]

• Determine the optimal capital budgetoptimal capital budget.

• Based on the target capital structuretarget capital structure, determine the amount of equity capital required to finance the optimal capital budget.

• To the extent possible, use internally internally generated retained earnings as the generated retained earnings as the primary sourceprimary source of meeting the equity capital requirement. Page 109Page 109

CHY 241

• Pay dividends only to the extent that Pay dividends only to the extent that funds are left overfunds 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 242

• Avoid 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 residual dividend model should be used to set long-run model should be used to set long-run target payout ratios,target payout ratios, based on 5-10 year based on 5-10 year free cash flow projections.free cash flow projections.

CHY 243

• A A residualresidual dividend policy: dividend policy:

– Net income (projected) = $200M$200M

– D/E (target) = 2/3 (E/V = 60%;60%; D/V = 40%)

– Capital budget (planned) = $260M$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$156MNew debt needed = .40 $260M = $104M

– Dividend = $200M - $156M = $44M$44M

CHY 244

C. REPURCHASING COMMON STOCK AS AN ALTERNATIVE TO

PAYING DIVIDENDS1.1. Advantages Advantages of Repurchasing of Repurchasing

Common Shares 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 245

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 (Debt-Equity Ratio UP)

CHY 246

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 247

DisadvantagesDisadvantages of Repurchasing of Repurchasing Common SharesCommon 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 248

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$150M / (50M – 0.80M) = $3.05

CHY 249

每股盈餘 (Earnings per Share )

Earnings Attributable to Ordinary ShareholdersNumber 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 250

( 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 251

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 outstanding50,000 shares outstandingand the following balance sheet

Balance Sheet

Cash　　　　 $ 100,000 　　　 $ 　 0 　 DebtOther Assets 　　 900,000 　　 1,000,000 　 Equity

　　　　 Total 　$1,000,000 　　　 $1,000,000 　Total

CHY 252

• Price per share is $20 ($1,000,000/50,000)Net income is $100,000, so EPS = $2.00 => The P/E ratio is 10P/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 share

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• 1.Choose 現金股利 (cash dividend)(all stockholders get $1 per share)

　　　　　　　　　　　　　　　 Balance Sheet

Cash 　　 $ 50,000$ 0DebtOther Assets 900,000950,000Equity

Total $ 950,000$ 950,000Total

• Price per share is $19 ($950,000/50,000)Net income is still $100,000, so EPS = $2.00EPS = $2.00The P/E ratio becomes 9.5

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• 2. Choose 庫藏股買回 (repurchase)(2,500 shares are repurchased at $20 a share)

Balance Sheet

Cash $ 50,000 $ 0Debt

Other Assets 900,000 950,000Equity

Total $ 950,000 $ 950,000Total

• Price per share remains $20 ($950,000/47,500)Net income is still $100,000, so EPS = $2.10EPS = $2.10The P/E ratio is 9.5P/E ratio is 9.5

CHY 255

【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 advantagestax advantages for high-income shareholders.

C. Is disadvantageous to the Company if the disadvantageous to the Company if the shares are overpricedshares are overpriced.

D. All of the above statements are true.

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• 解析 : D A stock repurchase plan can signal that management believes its shares signal that management believes its shares are are undervaluedundervalued.

• Repurchase plans can benefit high-income shareholders as the lower capital gains the lower capital gains tax tax 【【證所稅證所稅　】　】 is paid by only the is paid by only the investors who choose to sellinvestors 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 257

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 258

Irrelevance of Stock DividendsStock 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 million2 million 　　 ×× 1.51.5 = = 3 million shares3 million shares

CHY 259

Irrelevance of Stock Dividends [Pizza 多片 ]

• After the stock dividend what is the new price the new price per share and what is the new value of the per share and what is the new value of the firm?firm?

• The value of thevalue of the firm was firm was

　　 2 Mil × $15 per share = $30 Mil. 2 Mil × $15 per share = $30 Mil.

• After the dividendAfter the dividend, the value will remain the same.

• Price per share Price per share

= $30Mil / 3Mil shares = $10 per share= $30Mil / 3Mil shares = $10 per share

CHY 260

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:

share

42$shares 80360,3$

240$share

39$shares 80360,3$

80$160$share

40$shares 78360,3$

After a $3 dividend, his total wealth is still $3,360:

After a $2 dividend, and sale of 2 ex-dividend shares,his shares,his total wealth is still $3,360:total wealth is still $3,360:

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【 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 262

【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)

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• 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 =

• 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 =

(ROA) × (1- Dividend Payout Ratio)

(ROE) × (1- Dividend Payout Ratio)

CHY 264

Optimal capital structure2. 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).

d. Statements b & c are correct. 【擬答】 (D) E

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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 corporationsd. Statements a & c are correct.

【擬答】 (D) P122

CHY 266

Capital structure & WACC4. 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)

E

CHY 267

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. 【擬答】 (D) M

CHY 268

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.

【擬答】 (A) E

CHY 269

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.

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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 271

Dividends & repurchases


a. In general, stock repurchases are taxed the taxed the samesame way as dividends.

b. On average, companies send a negative signalnegative signal to the marketplace when they announce an increase in their dividend.

c. In the real world, we find that dividends usually exhibit greatergreater stability than earnings.

d.All statements are correct. 【擬答】 (C) E

CHY 272

Stock split9. A stock split will cause a change in the total

dollar amounts shown in which of the following balance sheet accounts?

a. Cash.b. Common stock.c. Paid-in capital.d. Retained earnings.e. None of the statements above is correct.

【擬答】 (E) E

CHY 273

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?

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0 7% 15% 12%

A

NPV ($)

k (%)

B

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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.

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CHY 276

【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 277

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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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 279

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 280

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? p125p125

CHY 281

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.


CHY 282

【擬答】 :

　

0 16% 30% 18%

A

NPV ($)

Discount rate (%)

B

17%

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(B) EDraw 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 284

NPV & IRR13.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.


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CHY 285

【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 286

NPV & IRR14. 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 287

【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.

CHY 288

NPV, IRR, & MIRR15. 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 289

　【擬答】 : (B) E

If the NPV > 0, then IRR > 12%. (C) is false; if NPV > 0, then MIRR > WACC.

CHY 290

NPV, IRR, MIRR, & payback16. 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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CHY 291

　【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 292

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 293

【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.

CHY 294

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 correcte. Statements a & b are incorrect.【擬答】 :(A) E

CHY 295

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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CHY 296

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.

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【擬答】 :(B) EProject 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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Post-audit 20. The post-audit is used toa. 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 299

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?

CHY 300

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 301

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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CHY 302

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 303

NPV profiles23. 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.


CHY 304

【擬答】 : (D) M

The diagram above can be drawn from the statements in this question

Q

10% 20%15%

NPV($)

k (%)

P

0

CHY 305

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.

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CHY 306

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 307

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.

CHY 308

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 309

NPV & IRR26. 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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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 311

　【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.

CHY 312

NPV, IRR, & MIRR


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.


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CHY 313

　【擬答】 (A) MThe 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 314

NPV, IRR, & MIRR28. 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.


CHY 315

【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.

CHY 316

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 317

【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.

CHY 318

IRR30. A capital investment’s internal rate of returna. 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

CHY 319

MIRR 31. Which of the following statements is most

correct? The modified IRR (MIRR) methodThe 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 320

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 profiles, a NPV/IRR conflict will not occur.

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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.

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Project selection33. 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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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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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 mutually exclusive projects

CHY 325

(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 326

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.

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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

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　【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

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Miscellaneous concepts (A) M36. 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.

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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 331

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 332

　【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 333

NPV profiles38. 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?

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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).

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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.

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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

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NPV, IRR, & MIRR39. 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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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 339

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 at the MIRR itself.

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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 341

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.

.

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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. P131

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【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.

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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 349

Capital components43. 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.

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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 flotation costs.

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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.

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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 353

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 355

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 356

CAPM & DCF estimation47. 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

CHY 358

WACC48. 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.

CHY 359


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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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.

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【擬答】　 (D) MIf 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.

CHY 365

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

CHY 366

Risk-adjusted cost of capital52. 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 P135

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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.

CHY 368

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.


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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%

e. 9.29%

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【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%

CHY 375

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 expectedexpected 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) EWACC = [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. P137P137

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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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Agency57. Which of the following statements is most

correct? a. Compensating managers with stock can reduce

the agency problem between stockholders & stockholders & managersmanagers.

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.

d. Statements a & b are correct. P137

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【擬答】 : (D) E

The threat of a takeover alleviates the agency problem between managers & stockholders, not between bondholders & stockholders.

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Agency58. 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 384

【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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Agency60. Which of the following actions are likely to

reduce the agency problem between stockholders & managers?

a. Congress passes a law that severely restricts 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 flows61. 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.

【擬答】 (C) M P139

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Corporate goals & control


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 stockhold ers’ 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 deci sions in such situations.

e. Agency problems exist between stockholders & managers, & between stockholders & creditors.

【擬答　】 (E) M

CHY 392

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.

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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. Division A = $100,000, Division B = $ (300,000)b. Division A = $170,000, Division B = $ 100,000c. Division A = $600,000, Division B = $ 200,000d. Division A = $350,000, Division B = $ (50,000)

CHY 396

【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)

CHY 397

(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.

CHY 398

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 leveragedegree of total leverage is:

a. 7.0

b. 10.0

c. 2.5

d. 0.4

CHY 399

【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 400

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 debt-to-equity.

d. All are true. P141

CHY 401

【擬答】 (A)

The cost of equity should rise as the debt-to-equity. 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 402

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 403

【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 404

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 shares would rise.would rise.

CHY 405

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 406

【擬答】 (C) According to the clientele effect, a change in the dividend payout a change in the dividend payout probably has no effect on firm or probably has no effect on firm or common stock values.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 407

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) P142

CHY 408

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 409

Modigliani-Miller Theorem (without taxes)

Proposition I 任何 Debt-Equity Ratio 都可以 ; Firm Value 不受影響

Proposition II

Cost of Debt 不變

Cost of Equity 隨Debt-Equity Ratio 增加而上升

WACC 不變

CHY 410

Modigliani-Miller Theorem (with taxes)

Proposition I Debt-Equity Ratio越高越好

Proposition Ⅱ Cost of Debt 不變

Cost of Equity 隨Debt-Equity Ratio 增加而上升

WACC 隨Debt-Equity Ratio 增加 , 稅盾愈多而減少

Trade-off Theory

Debt- Equity Ratio 有最合適水準

Signaling Theory

增加 Equity 之外部融資會有負面訊號效果

CHY 411

71. Proposition of the Modigliani-Miller ⅡTheorem (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.

P143

CHY 412

【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 debt-to-equity ratios, so in the absence of preferred equity, the cost of equity capital must increase as the debt-to-equity ratio rises.

CHY 413

72. According to Proposition of the ⅡModigliani-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 = after-tax 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 414

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 415

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 416

【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 417

Business risk (C) E

74. A decrease in the debt ratio will generally have no effect on

a. Financial risk.

b. Total risk.

c. Business risk.

d. Market risk.

e. None of the above is correct. (It will affect each type of risk above.)

CHY 418

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 419

【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.

Documents

CHY1 Future value Present value Rates of return Amortization Chapter 1 Time Value of Money