Chapter 1 Time Value of Money

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

Time lines show timing of cash flows.
1 2 3 i% CF0 CF1 CF2 CF3 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

Time line for a $100 lump sum due at the end of Year 2.
1 2 Year i% 100 CHY

Time line for an ordinary annuity of $100 for 3 years.
1 2 3 i% 100 100 100 CHY

Time line for uneven CFs: -$50 at t = 0 and $100, $75, and $50 at the end of Years 1 through 3.
1 2 3 i% -50 100 75 50 CHY

What’s the FV of an initial $100 after 3 years if i = 10%?
1 2 3 10% 100 FV = ? Finding FVs (moving to the right on a time line) is called compounding. CHY

FV2 = FV1(1+i) = PV(1 + i)(1+i) = PV(1+i)2 = $100(1.10)2 = $121.00.
After 1 year: FV1 = PV + INT1 = PV + PV (i) = PV(1 + i) = $100(1.10) = $ After 2 years: FV2 = FV1(1+i) = PV(1 + i)(1+i) = PV(1+i)2 = $100(1.10)2 = $ CHY

FV3 = FV2(1+i)=PV(1 + i)2(1+i) = PV(1+i)3 = $100(1.10)3 = $133.10.
After 3 years: FV3 = FV2(1+i)=PV(1 + i)2(1+i) = PV(1+i)3 = $100(1.10)3 = $ In general, FVn = PV(1 + i)n. CHY

Solve the equation with a regular calculator.
Three Ways to Find FVs Solve the equation with a regular calculator. Use a financial calculator. Use a spreadsheet. CHY

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

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

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

Financial Calculator Solution
Financial calculators solve this equation: There are 4 variables. If 3 are known, the calculator will solve for the 4th. CHY

Here’s the setup to find FV:
INPUTS N I/YR PV PMT FV 133.10 OUTPUT Clearing automatically sets everything to 0, but for safety enter PMT = 0. Set: P/YR = 1, END. CHY

Use the FV function: see spreadsheet in Ch 02 Mini Case.xls.
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) = CHY

What’s the PV of $100 due in 3 years if i = 10%?
Finding PVs is discounting, and it’s the reverse of compounding. 1 2 3 10% PV = ? 100 CHY

  Solve FVn = PV(1 + i )n for PV: 1   PV = $100     1.10 =
3 1   PV = $100     1.10 = $100  0.7513  = $75.13. CHY

N I/YR PV PMT FV -75.13 INPUTS OUTPUT Either PV or FV must be negative. Here PV = Put in $75.13 today, take out $100 after 3 years. CHY

Use the PV function: see spreadsheet.
Spreadsheet Solution Use the PV function: see spreadsheet. = PV(Rate, Nper, Pmt, FV) = PV(0.10, 3, 0, 100) = CHY

Finding the Time to Double
1 2 ? 20% -1 2 FV = PV(1 + i)n $2 = $1( )n (1.2)n = $2/$1 = 2 nLN(1.2) = LN(2) n = LN(2)/LN(1.2) n = 0.693/0.182 = 3.8. CHY

Financial Calculator INPUTS N I/YR PV PMT FV 3.8 OUTPUT CHY

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

Finding the Interest Rate
1 2 3 ?% -1 2 FV = PV(1 + i)n $2 = $1(1 + i)3 (2)(1/3) = (1 + i) = (1 + i) i = = 25.99%. CHY

Financial Calculator INPUTS N I/YR PV PMT FV 25.99 OUTPUT CHY

Spreadsheet Solution Use the RATE function: = RATE(Nper, Pmt, PV, FV)
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What’s the difference between an ordinary annuity and an annuity due?
1 2 3 i% PMT PMT PMT Annuity Due 1 2 3 i% PMT PMT PMT PV FV CHY

What’s the FV of a 3-year ordinary annuity of $100 at 10%?
1 2 3 10% 100 100 100 110 121 FV = 331 CHY

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: CHY

Financial Calculator Formula
for Annuities Financial calculators solve this equation: There are 5 variables. If 4 are known, the calculator will solve for the 5th. CHY

INPUTS 331.00 N I/YR PV PMT FV OUTPUT Have payments but no lump sum PV, so enter 0 for present value. CHY

Use the FV function: see spreadsheet.
Spreadsheet Solution Use the FV function: see spreadsheet. = FV(Rate, Nper, Pmt, Pv) = FV(0.10, 3, -100, 0) = CHY

What’s the PV of this ordinary annuity?
1 2 3 10% 100 100 100 90.91 82.64 75.13 = PV CHY

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: CHY

INPUTS N I/YR PV PMT FV OUTPUT Have payments but no lump sum FV, so enter 0 for future value. CHY

Use the PV function: see spreadsheet.
Spreadsheet Solution Use the PV function: see spreadsheet. = PV(Rate, Nper, Pmt, Fv) = PV(0.10, 3, 100, 0) = CHY

Find the FV and PV if the annuity were an annuity due.
1 2 3 10% 100 100 100 CHY

PV and FV of Annuity Due vs. Ordinary Annuity
PV of annuity due: = (PV of ordinary annuity) (1+i) = (248.69) ( ) = FV of annuity due: = (FV of ordinary annuity) (1+i) = (331.00) ( ) = 364.1 CHY

Switch from “End” to “Begin”.
Then enter variables to find PVA3 = $ INPUTS N I/YR PV PMT FV OUTPUT Then enter PV = 0 and press FV to find FV = $ CHY

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

What is the PV of this uneven cash flow stream?
1 2 3 4 10% 100 300 300 -50 90.91 247.93 225.39 -34.15 = PV CHY

Input in “CFLO” register:
Enter I = 10%, then press NPV button to get NPV = (Here NPV = PV.) CHY

Spreadsheet Solution A B C D E 1 0 1 2 3 4 2 100 300 300 -50 3 530.09
Excel Formula in cell A3: =NPV(10%,B2:E2) CHY

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

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 = %. CHY

Will the FV of a lump sum be larger or smaller if we compound more often, holding the stated I% constant? Why? LARGER! If compounding is more frequent than once a year--for example, semiannually, quarterly, or daily--interest is earned on interest more often. CHY

FV Formula with Different Compounding Periods (e. g
FV Formula with Different Compounding Periods (e.g., $100 at a 12% nominal rate with semiannual compounding for 5 years) mn i   FV = PV  + Nom  n   m 2x5 0.12   FV = $100  1 +  5S   2 = $100(1.06)10 = $ CHY

FV of $100 at a 12% nominal rate for 5 years with different compounding
FV(Annual)= $100(1.12)5 = $ FV(Semiannual)= $100(1.06)10=$ FV(Quarterly)= $100(1.03)20 = $ FV(Monthly)= $100(1.01)60 = $ FV(Daily) = $100(1+(0.12/365))(5x365) = $ CHY

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 = 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

Banks say “interest paid daily.” Same as compounded daily.
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

How do we find EFF% for a nominal rate of 12%, compounded semiannually?
( ) iNom m ( ) 2 0.12 2 = = (1.06) = = 12.36%. CHY

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

EAR (or EFF%) for a Nominal Rate of of 12%
EARAnnual = 12%. EARQ = ( /4)4 - 1 = %. EARM = ( /12) = %. EARD(365) = ( /365) = %. CHY

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

When is each rate used? iNom:
Written into contracts, quoted by banks and brokers. Not used in calculations or shown on time lines. CHY

Used in calculations, shown on time lines.
iPer: Used in calculations, shown on time lines. If iNom has annual compounding, then iPer = iNom/1 = iNom. CHY

(Used for calculations if and only if
EAR = EFF%: Used to compare returns on investments with different payments per year. (Used for calculations if and only if dealing with annuities where payments don’t match interest compounding periods.) CHY

Amortization Construct an amortization schedule
for a $1,000, 10% annual rate loan with 3 equal payments. CHY

Step 1: Find the required payments.
1 2 3 10% -1,000 PMT PMT PMT INPUTS N I/YR PV PMT FV OUTPUT 402.11 CHY

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 = $ $100 = $ CHY

Step 4: Find ending balance after Year 1.
End bal = Beg bal - Repmt = $1,000 - $ = $ Repeat these steps for Years 2 and 3 to complete the amortization table. CHY

Interest declines. Tax implications.
BEG PRIN END YR BAL PMT INT PMT BAL 1 $1,000 $402 $100 $302 $698 TOT 1, ,000 Interest declines. Tax implications. CHY

10% on loan outstanding, which is falling.
$ 402.11 Interest 302.11 Principal Payments 1 2 3 Level payments. Interest declines because outstanding balance declines. Lender earns 10% on loan outstanding, which is falling. CHY

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 %, 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 = $100 1.00031054
1 2 273 % -100 FV=? FV = $100 ( ) 273 273 = $100 ( ) = $ Note: % in calculator, decimal in equation. CHY

Leave data in calculator.
iPer = iNom/m = /365 = % per day. INPUTS 108.85 N I/YR PV PMT FV OUTPUT Enter i in one step. Leave data in calculator. CHY

What’s the value at the end of Year 3 of the following CF stream if the quoted interest rate is 10%, compounded semiannually? 1 2 3 4 5 6 6-mos. periods 5% 100 100 100 CHY

Payments occur annually, but compounding occurs each 6 months.
So we can’t use normal annuity valuation techniques. CHY

1st Method: Compound Each CF
1 2 3 4 5 6 5% 100 100 100.00 110.25 121.55 331.80 FVA3 = $100(1.05)4 + $100(1.05)2 + $100 = $ CHY

Could you find the FV with a financial calculator?
2nd Method: Treat as an Annuity Could you find the FV with a financial calculator? Yes, by following these steps: a. Find the EAR for the quoted rate: EAR = ( ) - 1 = 10.25%. 0.10 2 2 CHY

b. Use EAR = 10.25% as the annual rate in your calculator:
INPUTS N I/YR PV PMT FV OUTPUT 331.80 CHY

What’s the PV of this stream?
1 2 3 5% 100 100 100 90.70 82.27 74.62 247.59 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 % nominal rate, with 365 daily compounding, which is a daily rate of % 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

1. Greatest future wealth: FV 2. Greatest wealth today: PV
iPer = % per day. 365 456 days -850 1,000 3 Ways to Solve: 1. Greatest future wealth: FV 2. Greatest wealth today: PV 3. Highest rate of return: Highest EFF% CHY

1. Greatest Future Wealth
Find FV of $850 left in bank for 15 months and compare with note’s FV = $1,000. FVBank = $850( )456 = $ in bank. Buy the note: $1,000 > $ CHY

Calculator Solution to FV:
iPer = iNom/m = %/365 = % per day. INPUTS 924.97 N I/YR PV PMT FV OUTPUT Enter iPer in one step. CHY

2. Greatest Present Wealth
Find PV of note, and compare with its $850 cost: PV = $1,000/( )456 = $ CHY

/365 = INPUTS N I/YR PV PMT FV OUTPUT PV of note is greater than its $850 cost, so buy the note. Raises your wealth. CHY

3. Rate of Return Find the EFF% on note and compare with 7.0% bank pays, which is your opportunity cost of capital: FVn = PV(1 + i)n $1,000 = $850(1 + i)456 Now we must solve for i. CHY

Convert % to decimal: Decimal = 0.035646/100 = 0.00035646.
INPUTS % per day N I/YR PV PMT FV OUTPUT Convert % to decimal: Decimal = /100 = EAR = EFF% = ( ) = 13.89%. CHY

Using interest conversion: P/YR = 365 NOM% = 0.035646(365) = 13.01
EFF% = 13.89 Since 13.89% > 7.0% opportunity cost, buy the note. CHY

OVERVIEW AND THE COST OF CAPITAL [公司理財與資金成本] Page 17
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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

經理人應該 . . . 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〕. 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

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

Fund all worthwhile investment opportunities. [不要為發放股利犧牲好方案]
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

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

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

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

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

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

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

A. THE COST OF A FIRM’S CAPITAL COMPONENTS
The Cost of Debt 〔負債〕 Capital rafter-tax = (1-t)rD CHY

rafter-tax = (1-t)rD =(1-0.35)(7%) =4.55%
Example:　　A firm’s bonds are rated Baa. Currently, new Baa bonds are being issued with a coupon of 7%. Assuming a corporate income tax rate of 35%, what is the after-tax cost of debt capital for the firm? Answer: rafter-tax = (1-t)rD =(1-0.35)(7%) =4.55% [如果同時看到coupon 與Yield to Maturity, 請用YTM] CHY

2. The Cost of Preferred Stock [特別股] Capital CHY

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

3. The Cost of Retained Earnings 〔保留盈餘〕(Common equity) a. The Capital Asset Pricing Model (CAPM) Approach [資本資產定價模型]: rCE = rF + βCS(rM – rF) CHY

rCE = rF + βCS(rM – rF) = 4% + 1.2(10% -4%) = 11.2%
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

3. The Cost of Retained Earnings 〔保留盈餘〕 (Common equity) b. The Dividend-Yield-Plus-Growth- Rate ( or Implied Return) Approach: CHY

Example: The Ajax Company currently （小心這是關鍵字）pays a dividend of $2
Example:　　The Ajax Company currently （小心　這是關鍵字）pays a dividend of $2.00 per share on its common shares. The long-term dividend growth rate is expected to be 5% per year. If Ajax common shares are currently selling at $25 per share, estimate Ajax’s cost of retained earnings capital. Answer: CHY

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

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: CHY

4. Cost of Newly Issued Common Stock [新的普通股　有發行成本flotation costs] (Also Called the Cost of External Equity) CHY

Example: The XYZ Corporation’s common shares are trading at $40
Example:　　The XYZ Corporation’s common shares are trading at $40. The Company currently is paying a dividend of $2.50 per share on its common stock. If it were to sell additional common shares, its flotation cost　〔發行成本〕 would be 15%. If the Company has a 4% long-term growth rate in dividends per share, calculate its cost of newly issued common stock (external equity). Answer: CHY

B. DETERMINING A FIRM’S OPTIMUM CAPITAL STRUCTURE
The optimal capital structure (最適資本結構) of a firm is defined as that mix of capital sources that will maximize the value of a firm taken as a whole. One of the important issues in finance is how a management should determine what its optimal capital structure should be. Once determined, this is target capital structure that the firm should seek to maintain. CHY

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 CHY

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. CHY

Example: Consider a company with the following capital structure:
Book Value 帳面值 Market Value市值 Debt $100 million $106 million Preferred Stock Common Equity 　842 Total Invested Capital $500 million $1,000 million CHY

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

Risk-free rate……………………………… 6.5%
Example continued… The prevailing financial market conditions are as follows: Quality Yields on Newly Issued Bonds by Qlty Aaa % Aa A Baa Quality Yields on Newly Issued Preferred Stocks by Quality A % B C Risk-free rate………………………………　 6.5% Equity risk premium over bonds …………. 2.7 Expected return on stock market index…… 9.5 CHY

Example continued… What is the company’s weighted-average cost of capital　〔加權平均資金成本〕?
Answer: From these data we can find each of the component costs and, subsequently, the weighted-average cost of capital. The cost of debt is 7.0% on a pretax basis, as this is the cost of newly issued bonds of equal quality (Aa rating). The cost of preferred stock is 7.5%, which is equal to the cost of newly issued preferred stocks of similar quality. CHY Continue on next page

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+bCS(rm-rF) = 6.5% +1.07( ) =9.7%* CHY

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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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% % Equity 400 million 50% % 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

＝＞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

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 % 6% 0.5(6%) =3% Equity 50 million % 14% 0.5(14%) = 7% =10% CHY

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

THE BASICS OF CAPITAL BUDGETING
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I. INTRODUCTION Capital budgeting is the process of analyzing projects in order to decide which ones should be undertaken. CHY

II. RANKING CAPITAL PROJECTS
A. FOUR METHODS AND THEIR CALCULATION Payback Period Discounted Payback Period Net Present Value (NPV) Internal Rate of Return (IRR) CHY

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 $(100,000) $(100,000) , ,182 , ,058 , ,079 , ,490 , ,209 $ 23,018 CHY

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

4. Internal Rate of Return (IRR)
Example: What is the internal rate of return for the project in the previous problem? CHY

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) ,000 ,000 ,000 ,000 ,000 CHY

Answer continued: HP12C TIBA2+ 1000【CHS】【g】【CF0】【CF】1000 【+/-】【ENTER】【↓】【g】【CFj】【ENTER】【↓】【g】【CFj】【ENTER】【↓】【g】【CFj】【ENTER】【↓】【g】【CFj】【ENTER】【↓】【g】【CFj】【f】【IRR】 100 【ENTER】【IRR】【CPT】 The answer is: 18.91% CHY

a. Modified Internal Rate of Return (MIRR)
CHY

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

Example: Three projects, each with a cost of 15%, have the following free cash flows: Year Project A Project B Project C 0 $(50,000) $(120,000) $(20,000) , (50,000) 2,000 , , ,000 10, , ,000 If the projects are independent, which one(s) should be undertaken? If the projects are mutually exclusive, which one should be undertaken? CHY

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) , (43,478) ,739 , , ,342 , , ,863 $ 6, $ (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

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

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. CHY

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

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

CASH FLOW ESTIMATION AND OTHER CAPITAL BUDGETING TOPICS
CHY

I. INTRODUCTION A. CASH FLOW VS. ACCOUNTING PROFIT B. DEFINITIONS
a. The incremental free cash flow of a project should be calculated before financing costs, because the method of financing an asset’s purchase has no bearing on the value of the asset. b. The cost of capital used as the discount rate in determining the present value of the net free cash flows is an after-tax cost (as it is in the conventional WACC formulation). . Sunk costs are costs that would be incurred regardless of whether or not an investment is made in the asset or project being evaluated. d. Opportunity costs are cash flows that could be generated from assets already owned by a firm if they were not used for the target project. e. Externalities are the positive or negative changes in the cash flows of projects (other than the target project) that are attributable to the target project. f. Shipping and installation costs associated with a target project should be included as part of its incremental net free cash flows to be analyzed. CHY

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

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

Example continued: Incremental Annual Effects of the Widget Project
Sales $ 600,000 Direct Expenses ,000 Depreciation ,000 Selling Expenses and Externalities ,000 Administrative Expenses (1) EBIT $ 184,000 Interest Expense ,700 Pretax Income $ 148,300 Income Tax ,320 Net Income $ 88,980 Required Additional Working Capital Outlay $ 40,000 (2) CHY

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

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

Example continued: The capital structure of the Company is as follows:
Book Value Market Value Negotiated Debt $10,000,000 $11,000,000 Preferred Stock 5,000, ,000,000 Common Equity ,000, ,000,000 Total Invested Capital $85,000,000 $100,000,000 CHY

Bond Yields………………………..7.0% Preferred Stock Yields…………….6.0
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

Calculating the initial investment outlay for the widget project.
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

Answer: 1. Calculating the initial investment outlay (Year 0)
Cost of the Widget-making Machine $510,000 Additional Working Capital ,000 Initial Investment Outlay $512,000 CHY

2. Calculating the incremental cash flows during the operating years (Years 1-5):
The table below shows how the pro forma income and additional working capital information is used to determine the incremental cash flows during the operating years: Projected Projected Pro Forma (Free) Cash Income Flows Sales $600,000 $600,000 Direct Expenses , ,000 Depreciation , ,000 Selling Expenses and Externalities , ,000 EBIT $184, $184,000 Interest Expense ,700 Pretax Income $148,300 Income Tax , ,600(40% of EBIT) Net Income $ 88,980 EBIT(1-t) $110,400 Plus: Depreciation ,000 Less: Capital Expenditures Less: Required Additional Working Capital Outlay ,000 Incremental Cash Flow in the Operating Years $170,400 CHY

FCFF = EBIT(1-t) + DEPR –CAPX –ΔWC
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

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

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

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

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, $10,000--(1) Plus: Cash from Collection of Receivables and sale of unsold inventory , ,000—(2) Less: Closing expenses, net of taxes , ,200—(3) Terminal-year cash flow , ,000 CHY

Net Closing Expense = $2,000(1-0.4) = $1,200
(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

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)/ = 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) (83,000,000/100,000,000) = 14.6% CHY

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

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

Year Cash Flow PV of Cash Flow @14.6% 0 $(512,000) $(512,000)
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 0 $(512,000) $(512,000) , ,691 , ,748 , ,218 , ,794 , ,208 , ,543 $ 86,202 Since the NPV of the free cash flows to the firm generated by the project is positive, the expected return on the project is greater than the firm’s cost of capital. Therefore, the widget project should be undertaken. CHY

B. ANALYZING A REPLACEMENT PROJECT
Example: A company is thinking of replacing a machine and buying a new one. The annual cash operating expenses associated with the current machine are $100,000. the machine is being depreciated by $10,000 per year (straight line). It has a useful life of five additional years and, if sold today, it could fetch $5,000 in the used machine market, which is $2,000 below its book value. The new machine would probably be used for 5 years, at which time it would be fully depreciated. However, it could be sold for $7,000 at the end of Year 5(which is an estimate and not a “salvage value” for purposes of computing depreciation from a tax perspective). The cash operating expenses required to operate the new machine are only $60,000 per year, but it would also require an additional working capital each year of $3,000. The price of the new machine is $90,000. The firm’s cost of capital is 15% and its marginal income tax rate is 40%. CHY

Example continued: Calculate the initial investment outlay for the analysis: The initial investment outlay in Year 0 is the cost of the new machine, less the cash received from selling the old machine and the tax savings that accrues to the benefit of the Company because it sells the old machine at a loss: Cash Outlay Cost of New Machine $90,000 Less: Sale of Old Machine ,000 Less: Tax Savings on Sale of Old Machine 【0.40×$2, loss】 Initial Investment Outlay $84,200 CHY

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 $18,000 Depreciation on old machine ,000 Increase in depreciation $ 8,000 Tax savings on increase in depreciation ,200 (2) Less: Increase in required working capital ,000 Operating 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

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 ,000 Less: Tax on gain from sale of machine ,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

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 $(84,200) $(84,200) , ,299 , ,299 , ,912 , ,836 , ,020 NPV $(1,090) Answer: The old machine should not be replaced because the NPV of the project is negative. CHY

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

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

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

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 0 $(600,000) $(600,000) $ (700,000) $(700,000) , , , ,439 , , , ,894 , , , ,994 , ,416 , ,874 , ,117 $ 96, $ 77,734 CHY

Machine A Machine B PV = 96,489 PV =77,734 n = 3 n = 6 i = 14 i = 14
FV = 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

公司財務研討 I In Class Question
P57 CHY

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

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

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

2. The Replacement Chain (Common Life) Approach
The replacement chain (Common Life) method solves the problem by equalizing the lives of the two machines. This is done by extending the life of Machine A until it equals that of Machine B by treating the problem as if Machine A 陸續接力【 at the end of Year 3, 續用 Machine A 】 In that case, the operating cash flows of the two machines & their associated present values would appear as follows: CHY

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) , , , ,439 , , , ,894 3 (300,000)(*) (202,491) , ,994 , , , ,416 , , , ,874 , , , ,117 $ 161, $ 77,734 CHY

(*) 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 = $ (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

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

CAPITAL BUDGETING RISK ANALYSIS
I. TYPES OF RISK Stand-alone Risk Corporate (Within-firm) Risk Market Risk (Beta) CHY

釋例 Which of the following statements is true?
Stand-alone risk is the best way for a conglomerate to analyze the risk associated with a potential new acquisition. Corporate risk measures do not take into account the principle that diversification reduces risk. 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

解析: C A is false because corporate or market risk should be the way for a conglomerate to analyze a new acquisition since diversification may reduce　overall risk relative to the acquisition’s stand-alone risk. B is false because corporate risk does take into account the principle that　diversification reduces risk. D is false because diversified investors are more concerned with market risk than with corporate risk. CHY

Measuring Stand-alone Risk
Scenario Analysis The probabilities assigned to each scenario are subjective. “Outlier” scenarios (war, famine, & pestilence), which represent the largest risks to the viability of a project, do occur from time to time. Yet, such scenarios are not often included in the analysis because they are very unlikely. The tendency to ignore highly improbable, yet very costly, scenarios results in an underestimation of project risk. CHY

Monte Carlo Simulation
Sensitivity Analysis NPV 結果對那個變數最敏感? Monte Carlo Simulation Simulating probable events & generate estimated returns & risk indexes 考慮到特殊事件　(Outliers) 　但是: 變數的分配要主觀認定, 且操作複雜 CHY

Measuring Market risk THE SECURITY MARKET LINE
r = rF +β（rM-rF） USING A MARKET (SYSTEMATIC; BETA) RISK MEASURE TO DETERMINE THE REQUIRED RETURN ON A CAPITAL PROJECT FINANCED WITH EQUITY CAPITAL CHY

Using the SML to Estimate the Risk-Adjusted Cost of Equity Capital
Good projects 30% 2.5 A B C Project IRR Bad projects 5% Firm’s risk (beta) An all-equity firm should accept a project whose IRR exceeds the cost of equity capital & reject projects whose IRRs fall short of the cost of capital. CHY

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

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

Expected stock market return 10.00% Grocery industry market beta 0.85
Risk-free rate % Expected stock market return % Grocery industry market beta Airline industry market beta 　 Greenhouse grocery’s WACC　 8.00%　 Market return on unleveraged investments 9.00% a. 8.00% b. 9.00% c. 9.25% d % CHY

r = rF +βairlines（rM-rF） = 5%+1.5(10-5)=12.5%
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

MEASURING THE BETA OF A PROJECT
The Pure Play Method ~ 找Single Product Company (Pure Player) 看她的Beta CHY

INCLUDING A RISK ADJUSTMENT
Certainty Equivalent Approach ~ All cash flows not known with certainty are scaled down. (e.g., 都乘以0.8, 然後以rF 折現) Risk-Adjusted Discount Rate ~ cash flows not scaled down, 但是以Risk-Adjusted Cost of Equity Capital 折現 CHY

CAPITAL STRUCTURE & LEVERAGE
Page 83 CHY

Business Risk (純資產的產銷風險) Tax Position (Tax Shield 稅盾)
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

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 =　 CF固定成本 %∆Sales EBIT 息前稅前盈餘 CHY

2-2 ANALYZING FINANCIAL RISK 【財務風險】
Financial leverage refers to using fixed-cost sources of investment capital, such as debt, to finance a firm. Financial risk is the extra risk to shareholders that results from using financial leverage. [買聯電股票的風險 >買聯電晶圓廠的風險 ] Financial risk can be measured by standard measures of financial leverage, such as the Debt/Total Capital or Debt/Equity ratios. CHY

However, a more useful measure of financial leverage is the degree of financial leverage 【財務槓桿】( DFL), defined as the percent change in pretax income that occurs every time there is a one-percent change in EBIT. (DFL) can be calculated in a number of ways that are mathematically equivalent.　　~ 當EBIT變動1% , 稅前淨利變動的百分比 CHY

= EBIT / (EBIT-INTEREST)
DFL = %ΔPretax Income %ΔEBIT = EBIT / Pretax Income = EBIT / (EBIT-INTEREST) CHY

Degree of Total Leverage 【總槓桿】
DTL 【總槓桿】 = DOL【營業槓桿】 × DFL【財務槓桿】 %ΔPretax Income = ΔPretax Income Pretax Income = DOL × DFL x % ΔSales CHY

%ΔEPS = DOL × DFL x %ΔSales
CHY

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

Financial Leverage財務槓桿, EPS每股盈餘& EBIT息前稅前盈餘
D/E = 1　Levered Firm 3 2.5 2 1.5 1 0.5 – 0.5 – 1 D/E = 0 Un-leveraged Firm EBIT ($ millions, no taxes) CHY

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

【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

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

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

There are no brokerage costs. There are no taxes.
CAPITAL STRUCTURE THEORIES A. MODIGLIANI & MILLER’S CAPITAL STRUCTURE IRRELEVANCE PROPOSITION [MM 資本結構無關企業價值理論] Assumptions There are no brokerage costs. There are no taxes. There are no bankruptcy costs. Investors & corporation can borrow at the same rate. All investors have the same information about the firm’s future investment opportunities as the firm’s management.　〔企業不需要用高負債來顯示其看好未來獲利〕 EBIT is not affected by the use of debt. CHY

MM with 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 Costs [實務上破產成本驚人, 故企業不敢借太兇] CHY

B. THE TRADE-OFF THEORY The optimal capital structure for a firm is one that will maximize the value of its assets (or minimize its weighted average cost of capital 〔最低之加權平均資金成本〕) debt is beneficial to a firm, but only up to a point. In contrast to the Modigliani-Miller irrelevance proposition, an optimal capital structure does exist [存在最適資本結構]. It is that mix of debt, preferred stock, & common equity that minimizes the firm’s weighted average cost of capital. CHY

【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

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

C. SIGNALING THEORY [訊號理論]
〔發行新股籌資顯示企業認為股價高於真實價值〕Management would want to raise capital by selling common equity if it believed that the firm’s common equity was significantly overvalued. The announcement of a stock offering is generally taken by the market to be a signal that management believes that its firm’s stock is overpriced relative to the firm’s future prospects. CHY

【融資順位理論】Pecking Order Theory
有好消息的企業：先以自有資金融資 => 短期債融資 =>長期債融資 =>可轉債融資 => 股票融資有壞消息的企業：最後才是自有資金融資 => 短期債融資 =>長期債融資 =>可轉債融資 => 股票融資 CHY

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

【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

D. MM Theorem is more realistic than the static trade-off theory.
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

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

Corporate Finance Important Equations
The Cost of Debt Capital rafter-tax = (1-t)rD The Cost of Preferred Stock Capital CHY

The Dividend-Yield-Plus-Growth-Rate ( or Implied Return) Approach
The Capital Asset Pricing Model (CAPM) Approach: rCE = rF + βCS(rM – rF) The Dividend-Yield-Plus-Growth-Rate ( or Implied Return) Approach CHY

The Bond-Yield-Plus-Risk-Premium Approach
rCE = rD+ rERP Cost of Newly Issued Common Stock (Also Called the Cost of External Equity) CHY

The weighted-average cost of capital
rw = (1-t)rD (VD/ VA) + rP (VP/ VA) + rCE (VCE/ VA) Free Cash Flow from an Expansion Project FCFF = EBIT(1-t) + DEPR –CAPX –ΔWC CHY

Degree of Operating Leverage Degree of Financial Leverage
DFL = %ΔEBIT = 1+CF %Δsales EBIT Degree of Financial Leverage CHY

Quantifying Total Company Risk
CHY

DIVIDEND POLICY 【股利政策】
I. Dividend 【股利】 & Cash Buyout [庫藏股買回] II. DETERMINING A FIRM’S OPTIMUM DIVIDEND POLICY　【股利政策】　　　　　　　　　　　　　　　　Page 101 CHY

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

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. -t … … $P $P - div The price drops by the amount of the cash dividend Ex-dividend Date 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

A. THREE THEORIES ON DIVIDEND POLICY
MM: Dividend Irrelevance Theory (MM股利無關企業價值論) This dividend irrelevance theory suggests that the dividend payout ratio & dividend policy is irrelevant on determining the value of firms. CHY

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〕. This summarizes the MM argument for why dividend policy is irrelevant. Generally, firms that pay too much in dividends lose value because they cannot take value-creating projects that they should. In the MM world, this cost is eliminated by assuming that these firms can raise the capital (with no transactions costs & no frictions) to take these projects. Investors who receive dividends often face a much larger tax bill than investors who get capital gains. This is eliminated by assuming that there are no tax disadvantages associated with dividends. CHY

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 Dividends(自己發自己現金股利) CHY

Homemade Dividends (自己發自己現金股利)
Bianchi Inc. stock Price=$42 about to pay a $2 cash dividend. [當然配息以後股價理論上會跌$2] Bob Investor owns 80 shares and prefers $3 cash dividend. Bob’s homemade dividend strategy: Sell 2 shares ex-dividend homemade dividends Cash from dividend ($D x 80) $160 Cash from selling stock $80 Total Cash $240 Value of Stock Holdings $40 × 78　股＝$3,120 $3 Dividend $240 $0 $39 × 80　股＝　$3,120 CHY

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

【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

2. The Bird-in-the –Hand [一鳥在手] Theory
Higher Div Payout => Better CHY

x Expected EPS at period 1 ÷ (r – g)
PRICE cs = DIV1 / (r – g) = Div Payout Ratio x Expected EPS at period 1 ÷ (r – g) CHY

3. The Tax Preference Theory
The tax preference theory suggests that high dividend payout policies reduce the value of common shares and, hence, the value of the firm. CHY

In the presence of personal taxes:
A firm should not issue stock to pay a dividend. 2. Managers have an incentive to seek alternative uses for funds to reduce dividends. 3. Personal taxes mitigate against the payment of dividends CHY

4. A Summary of the Three Theories
The bird-in-the-hand theory [一鳥在手] suggests that the higher the payout ratio, the higher will be the value of the firm & its common stock. The tax preference theory states that the higher the payout ratio, the lower will be the value of the firm & its common stock. The dividend irrelevance theory states that dividend policy has no effect on the value of the firm or its common stock. CHY

A clientele based explanation
[意思是. ..] Investors may form clienteles based upon their tax brackets. Investors in high tax brackets may invest in stocks which do not pay dividends & those in low tax brackets may invest in dividend paying stocks. 倒沒有說多發現金股利不好，得看想要滿足甚麼樣的投資人需求 Investors buy stock in companies which have dividend policies that they like. This self-selection process creates dividend clienteles that each firm caters to. As long as there are sufficient investors in each clientele, having a high dividend or no dividend, by itself, should not affect value. If an imbalance occurs between supply & demand in any clientele, there can be an effect on stock prices. CHY

(a) Older investors were more likely to hold high dividend stocks, &
(b) Poorer investors tended to hold high dividend stocks CHY

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

【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

B. THE RESIDUAL DIVIDEND MODEL [2004-10-08]
Determine the optimal capital budget. Based on the target capital structure, determine the amount of equity capital required to finance the optimal capital budget. To the extent possible, use internally generated retained earnings as the primary source of meeting the equity capital requirement Page 109 CHY

Pay dividends only to the extent that funds are left over after meeting the financing needs of the capital budget, taking into consideration other constraining factors, such as bond indenture constraints, preferred stock restrictions, the availability of cash, tax penalties on excess retained earnings, capital impairment restrictions, & so forth. CHY

Avoid cutting dividends at all costs, because this sends the wrong signal to investors.
Therefore, do not apply this residual dividend model on a year-by-year basis; rather, apply it over a 5-10 year time horizon. In other words, the residual dividend model should be used to set long-run target payout ratios, based on 5-10 year free cash flow projections. CHY

A residual dividend policy: Net income (projected) = $200M
D/E (target) = 2/3 (E/V = 60%; D/V = 40%) Capital budget (planned) = $260M Maximum capital spending with no outside equity: .60  C = $200M C = $333.33M Therefore, a dividend will be paid New equity needed= .60  $260M = $156M New debt needed = .40  $260M = $104M Dividend = $200M - $156M = $44M CHY

C. REPURCHASING COMMON STOCK AS AN ALTERNATIVE TO PAYING DIVIDENDS
Advantages of Repurchasing Common Shares [買回庫藏股票] Instead of Paying Dividends a. Signaling that mgt believe the shares are undervalued　〔感覺便宜才會買進〕 b. Only the shareholders who choose to sell their shares are subject to a tax CHY

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

【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】
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

Disadvantages of Repurchasing Common Shares Instead of Paying Dividends　～
a. Buybacks may imply mgt uncertainty about the trend of Free Cash Flow　〔否則就發現金股利〕 b. The selling shareholders may not be fully aware of all of the implications of a buyback program　〔現有股東未必知道是否應該出售〕 c. If the firm buys back shares at an inflated price, it wastes money.　〔也許買價過高〕 CHY

Calculating the Price Effect of a Stock Repurchase [買回庫藏股票會. . .]
E.g., Net Income = $150M; #Issued Shares = # Outstanding Shares= 50M Current P/E = $75/ $3 = 25x If the amount to be allocated = $60M => 800,000 shares can be repurchased EPS after the repurchase = $150M / (50M – 0.80M) = $3.05 CHY

每股盈餘(Earnings per Share )
Earnings Attributable to Ordinary Shareholders Number of Outstanding Ordinary (Common) Shares 　　　　　　淨利　　　　　　　特別股利 = Net Income －　　　　Preferred Dividends　　　 Number of Issued Shares－ Number of Treasury Shares 　　　　　　發行數　　　　　　庫藏數 (現金股利↑時，每股盈餘會?)　不變【Q】Would a company’s EPS increase or decrease as it declares & pays cash dividends? CHY

(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

現金股利 (Cash Dividend) versus a 庫藏股買回 (Share Repurchase) 的衝擊
Assume no taxes, commissions, or other market imperfections Consider a firm with 50,000 shares outstanding and the following balance sheet Balance Sheet Cash 　　　　$ 100,000　　　$ 　0 　Debt Other Assets　　900, 　　1,000,000 　Equity 　　　　Total　 $1,000,000　　　$1,000,000 　Total CHY

The firm is considering; 1) paying a $1 per share cash dividend, or
Price per share is $20 ($1,000,000/50,000) Net income is $100,000, so EPS = $ => The P/E ratio is 10 The firm is considering; 1) paying a $1 per share cash dividend, or 2) repurchasing 2,500 shares at $20 a share CHY

現金股利 (Cash Dividend) versus a 庫藏股買回 (Share Repurchase) 的衝擊
1. Choose 現金股利 (cash dividend) (all stockholders get $1 per share) 　　　　　Balance Sheet Cash 　　$ 50,000 $ Debt Other Assets 900, ,000 Equity Total $ 950,000 $ 950,000 Total Price per share is $19 ($950,000/50,000) Net income is still $100,000, so EPS = $2.00 The P/E ratio becomes 9.5 CHY

現金股利 (Cash Dividend) versus a庫藏股買回 (Share Repurchase) 的衝擊
2. Choose 庫藏股買回 (repurchase) (2,500 shares are repurchased at $20 a share) Balance Sheet Cash $ 50,000 $ Debt Other Assets 900, ,000 Equity Total $ 950,000 $ 950,000 Total Price per share remains $20 ($950,000/47,500) Net income is still $100,000, so EPS = $2.10 The P/E ratio is 9.5 CHY

B. Has tax advantages for high-income shareholders.
【釋例】Repurchasing common shares (買回庫藏股票) is an alternative to paying additional dividends that: A. Can boost the price of the shares if investors interpret the purchases as a signal that management believes the shares are undervalued. B. Has tax advantages for high-income shareholders. C. Is disadvantageous to the Company if the shares are overpriced. D. All of the above statements are true. CHY

解析: D A stock repurchase plan can signal that management believes its shares are undervalued.
Repurchase plans can benefit high-income shareholders as the lower capital gains tax 【證所稅】 is paid by only the investors who choose to sell their shares. A disadvantage of are repurchase plan is that the price at which the stock is repurchased may be too high. CHY

STOCK DIVIDENDS, SPLITS, & REVERSE SPLITS
Empirical Evidence ~ STOCK DIVIDENDS, SPLITS, & REVERSE SPLITS do not change the value of firms, nor the wealth of their shareholders. Rationale ~ SPLITS & STOCK DIVIDENDS讓單價降下來,　降至Optimal Trading Range 以內 CHY

Irrelevance of Stock Dividends : Example
Shimano USA has 2 million shares currently outstanding at $15 per share. The company declares a 50% stock dividend. How many shares will be outstanding after the dividend is paid? A 50% stock dividend will increase the number of shares by 50%: 2 million　×　1.5 = 3 million shares CHY 12

Irrelevance of Stock Dividends [Pizza 多片]
After the stock dividend what is the new price per share and what is the new value of the firm? The value of the firm was 　2 Mil × $15 per share = $30 Mil. After the dividend, the value will remain the same. Price per share = $30Mil / 3Mil shares = $10 per share CHY

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: After a $3 dividend, his total wealth is still $3,360: After a $2 dividend, and sale of 2 ex-dividend shares,his total wealth is still $3,360: CHY 19

【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 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

【擬答】(B) g = ROE (1 – Dividend Payout Rate)＊ => 10%(1-45%) = 5.5%
最高內部成長率 (Internal Growth Rate) 與最高可維持成長率(Sustainable Growth Rate) CHY

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

Optimal capital structure
2. Which of the following statements best describes the optimal capital structure? a. The optimal capital structure is the mix of debt, equity, & preferred stock that maximizes the company’s earnings per share (EPS). b. The optimal capital structure is the mix of debt, equity, & preferred stock that maximizes the company’s stock price. c. The optimal capital structure is the mix of debt, equity, & preferred stock that minimizes the company’s weighted average cost of capital (WACC). Statements b & c are correct. 【擬答】 (D) E CHY

Leverage & capital structure
3. Which of the following is likely to encourage a company to use more debt in its capital structure? a. An increase in the corporate tax rate. b. An increase in the personal tax rate. c. Changes in the bankruptcy code make bankruptcy less costly to corporations Statements a & c are correct. 【擬答】(D) P122 CHY

Capital structure & WACC
4. Which of the following statements is most correct? a. Since debt financing raises the firm’s financial risk, increasing a company’s debt ratio will always increase the company’s WACC. b. Since debt financing is cheaper than equity financing, increasing a company’s debt ratio will always reduce the company’s WACC. 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. None of the statements above is correct. 【擬答】 (D) E CHY

None of the statements above is correct.
Operating & financial leverage 5. Which of the following statements is most correct? Firms whose sales are very sensitive to changes in the business cycle are more likely to rely on debt financing. Firms with large tax loss carry forwards are more likely to rely on debt financing. Firms with a high operating leverage are more likely to rely on debt financing. None of the statements above is correct. 【擬答】(D) M CHY

6. Which of the following statements is most correct?
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

Dividend theory 7. Which of the following statements is most correct? a. The tax preference theory states that, all else equal, investors prefer stocks that pay low dividends because retained earnings can lead to capital gains that are taxed at a lower rate. b. An increase in the cost of equity capital (ks) when a company announces an increase in its dividend per share, would be consistent with the bird-in-the-hand theory. CHY

c. An increase in the stock price when a company decreases its dividend is consistent with the signaling theory. 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

Dividends & repurchases
8. Which of the following statements is most correct? a. In general, stock repurchases are taxed the same way as dividends. b. On average, companies send a negative signal to the marketplace when they announce an increase in their dividend. c. In the real world, we find that dividends usually exhibit greater stability than earnings. d. All statements are correct 【擬答】(C) E CHY

None of the statements above is correct. 【擬答】 (E) E
Stock split 9. A stock split will cause a change in the total dollar amounts shown in which of the following balance sheet accounts? a. Cash. b. Common stock. c. Paid-in capital. d. Retained earnings. None of the statements above is correct. 【擬答】 (E) E CHY

NPV profiles 10. Project A & Project B are mutually exclusive projects with equal risk. Project A has an internal rate of return of 12 percent, while Project B has an internal rate of return of 15 percent. The two projects have the same net present value when the cost of capital is 7 percent. (In other words, the “crossover rate” is 7 percent.) Assume each project has an initial cash outflow followed by a series of inflows. Which of the following statements is most correct? CHY

Statements a & c are correct. P124
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. Statements a & c are correct. P124 CHY

【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

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? CHY

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

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

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? p125 CHY

c. Project B is larger than Project A.
a. If the cost of capital is 12 percent, Project B will have a higher NPV. b. If the cost of capital is 17 percent, Project B will have a higher NPV. c. Project B is larger than Project A. d. Statements a & c are correct. CHY

【擬答】: CHY

(B) E Draw the NPV profiles using the information given in the problem. It is clear that Project A will have a higher NPV when the cost of capital is 12 percent. Therefore, statement a is false. At a 17 percent cost of capital, Project B will have a higher NPV than Project A. Therefore, statement b is true. If the cost of capital were 0, then the NPV of the projects would be the simple sum of all the cash flows. In order for statement c to be true, B’s NPV at a 0 cost of capital would have to be higher than A’s. From the diagram we see that this is clearly incorrect. So, statement c is false. CHY

NPV & IRR 13. Which of the following statements is most correct? a. If a project’s internal rate of return (IRR) exceeds the cost of capital, then the project’s net present value (NPV) must be positive. b. If Project A has a higher IRR than Project B, then Project A must also have a higher NPV. c. The IRR calculation implicitly assumes that all cash flows are reinvested at a rate of return equal to the cost of capital. Statements a & c are correct. P126 CHY

【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

a. Both projects have a positive net present value (NPV).
NPV & IRR 14. Project A has an internal rate of return (IRR) of 15 percent. Project B has an IRR of 14 percent. Both projects have a cost of capital of 12 percent. Which of the following statements is most correct? a. Both projects have a positive net present value (NPV). b. Project A must have a higher NPV than Project B. c. If the cost of capital were less than 12 percent, Project B would have a higher IRR than Project A. d. Statements a & c are correct. e. All of the statements above are correct. CHY

【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

b. The project’s internal rate of return is greater than 12 percent.
NPV, IRR, & MIRR 15. A project has an up-front cost of $100,000. The project’s WACC is 12 percent & its net present value is $10,000. Which of the following statements is most correct? a. The project should be rejected since its return is less than the WACC. b. The project’s internal rate of return is greater than 12 percent. c. The project’s modified internal rate of return is less than 12 percent. d. All of the statements above are correct. CHY

【擬答】: (B) E If the NPV > 0, then IRR > 12%. (C) is false; if NPV > 0, then MIRR > WACC. CHY

a. The project’s NPV is positive.
NPV, IRR, MIRR, & payback 16. A proposed project has normal cash flows. In other words, there is an up-front cost followed over time by a series of positive cash flows. The project’s internal rate of return is 12 percent & its WACC is 10 percent. Which of the following statements is most correct? a. The project’s NPV is positive. b. The project’s MIRR is greater than 10 percent but less than 12 percent. c. The project’s payback period is greater than its discounted payback period. d. Statements a & b are correct. P121 CHY

【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

a. The required rates of return of the two stocks should be the same.
NPV & expected return 17. Stock C has a beta of 1.2, while Stock D has a beta of 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

【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

NPV & project selection
18. Moynihan Motors has a cost of capital of 10 percent. The firm has two normal projects of equal risk. Project A has an internal rate of return of 14 percent, while Project B has an internal rate of return of 12 percent. Which of the following statements is most correct? a. Both projects have a positive net present value. b. If the projects are mutually exclusive, the firm should always select Project A. d. Statements a & b are correct Statements a & b are incorrect. 【擬答】:(A) E CHY

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. If the WACC is 15 percent, the NPV of Project B will exceed the NPV of Project A. P128 CHY

e. If the WACC increases, the IRR of both projects will decline.
c. If the WACC < 18 percent, Project B will always have a shorter payback than Project A. d. If the WACC > 18 percent, Project B will always have a shorter payback than Project A. e. If the WACC increases, the IRR of both projects will decline. CHY

【擬答】:(B) E Project A’s IRR is 15%, at a WACC of 15% NPVA = 0; however, Project B would still have a positive NPV. Given the information in a, we can’t conclude which project’s NPV is going to be greater at a cost of capital of 10%. Since we are given no details about each project’s cash flows we cannot conclude anything about payback. Finally, IRR is independent of the discount rate, that is, IRR stays the same no matter what the WACC is. CHY

20. The post-audit is used to a. Improve cash flow forecasts.
b. Stimulate management to improve operations & bring results into line with forecasts. c. Eliminate potentially profitable but risky projects. Statements a & b are correct. 【擬答】:(D) E CHY

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

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

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? P129 CHY

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. Project L should be selected at any cost of capital, because it has a higher IRR. 【擬答】: (A) M CHY

a. If the WACC is 12 percent, both projects would have a positive NPV.
NPV profiles 23. A company is comparing two mutually exclusive projects with normal cash flows. Project P has an IRR of 15 percent, while Project Q has an IRR of 20 percent. If the WACC is 10 percent, the two projects have the same NPV. Which of the following statements is most correct? a. If the WACC is 12 percent, both projects would have a positive NPV. b. If the WACC is 12 percent, Project Q would have a higher NPV than Project P. c. If the WACC is 8 percent, Project Q would have a lower NPV than Project P. d. All of the statements above are correct. CHY

【擬答】: (D) M The diagram above can be drawn from the statements in this question CHY

NPV & IRR 24. Assume that you are comparing two mutually exclusive projects. Which of the following statements is most correct? The NPV & IRR rules will always lead to the same decision unless one or both of the projects are “non-normal” in the sense of having only one change of sign in the cash flow stream, that is, one or more initial cash outflows (the investment) followed by a series of cash inflows. P130 CHY

All of the statements above are correct. 【擬答】： (C) M
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. All of the statements above are correct. 【擬答】： (C) M CHY

25. Which of the following statements is incorrect?
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

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

NPV & IRR 26. Project J has the same internal rate of return as Project K. Which of the following statements is most correct? a. If the projects have the same size (scale) they will have the same NPV, even if the two projects have different levels of risk. b. If the two projects have the same risk they will have the same NPV, even if the two projects are of different size. CHY

d. None of the statements above is correct.
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

【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

NPV, IRR, & MIRR 27. Which of the following statements is most correct? a. If a project with normal cash flows has an IRR that exceeds the cost of capital, then the project must have a positive NPV. b. If the IRR of Project A exceeds the IRR of Project B, then Project A must also have a higher NPV. c. The modified internal rate of return (MIRR) can never exceed the IRR. d. Statements a & c are correct. P131 CHY

【擬答】(A) M The IRR is the discount rate at which a project’s NPV is zero. If a project’s IRR exceeds the firm’s cost of capital, then its NPV must be positive, since NPV is calculated using the firm’s cost of capital to discount project cash flows. CHY

NPV, IRR, & MIRR 28. Which of the following statements is most correct? a. The MIRR method will always arrive at the same conclusion as the NPV method. b. The MIRR method can overcome the multiple IRR problem, while the NPV method cannot. c. The MIRR method uses a more reasonable assumption about reinvestment rates than the IRR method. d. Statements a & c are correct. CHY

【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

a. Project X must have a higher net present value than Project Y.
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

【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

30. A capital investment’s internal rate of return
IRR 30. A capital investment’s internal rate of return a. Changes when the cost of capital changes. b. Is equal to the annual net cash flows divided by one half of the project’s cost when the cash flows are an annuity. c. Must exceed the cost of capital in order for the firm to accept the investment. d. Is similar to the yield to maturity on a bond. Statements c & d are correct. 【擬答】(E) M P132 CHY

b. Overcomes the problem of multiple internal rates of return.
MIRR 31. Which of the following statements is most correct? The modified IRR (MIRR) method: a. Always leads to the same ranking decision as NPV for independent projects. b. Overcomes the problem of multiple internal rates of return. c. Compounds cash flows at the cost of capital. d. Overcomes the problems of cash flow timing & project size that lead to criticism of the regular IRR method. Statements b & c are correct 【擬答】(E) M CHY

32. Which of the following statements is correct?
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. CHY

d. If you are choosing between two projects that have the same life, & if their NPV profiles cross, then the smaller project will probably be the one with the steeper NPV profile. e. If the cost of capital is relatively high, this will favor larger, longer-term projects over smaller, shorter-term alternatives because it is good to earn high rates on larger amounts over longer periods. 【擬答】(B) M Statement (B) reflects exactly the difference between the NPV & IRR methods. CHY

Project B has a modified internal rate of return of 9.5 percent. P133
Project selection 33. A company estimates that its weighted average cost of capital (WACC) is 10 percent. Which of the following independent projects should the company accept? a. Project A requires an up-front expenditure of $1,000,000 & generates a net present value of $3,200. Project B has a modified internal rate of return of 9.5 percent. P133 CHY

d. Project D has an internal rate of return of 9.5 percent. 【擬答】(A) M
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. CHY

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

e. None of the statements above is correct.
(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

IRR can lead to conflicting decisions with NPV even with normal cash flows if the projects are mutually exclusive. Cash outflows are discounted at the cost of capital with the MIRR method, while cash inflows are compounded at the cost of capital. Conflicts between NPV & IRR arise when the cost of capital is less than the crossover rate. The discounted payback method corrects the problem of ignoring the time value of money, but it still does not consider cash flows that occur beyond the payback period. CHY

Miscellaneous concepts
35. Which of the following statements is most correct? a. The IRR method is appealing to some managers because it produces a rate of return upon which to base decisions rather than a dollar amount like the NPV method. b. The discounted payback method solves all the problems associated with the payback method. c. For independent projects, the decision to accept or reject will always be the same using either the IRR method or the NPV method. d. Statements a & c are correct. P134 CHY

【擬答】(D) M The discounted payback method still ignores cash flows that occur after the payback period. (A) 如殖利率報價 CHY

Miscellaneous concepts (A) M
36. Which of the following statements is most correct? a. One of the disadvantages of choosing between mutually exclusive projects on the basis of the discounted payback method is that you might choose the project with the faster payback period but with the lower total return. b. Multiple IRRs can occur in cases when project cash flows are normal, but they are more common in cases where project cash flows are nonnormal. CHY

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

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. All of the statements above are correct. 【擬答】(A) M CHY

【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

NPV profiles 38. Your assistant has just completed an analysis of two mutually exclusive projects. You must now take her report to a board of directors meeting & present the alternatives for the board’s consideration. To help you with your presentation, your assistant also constructed a graph with NPV profiles for the two projects. However, she forgot to label the profiles, so you do not know which line applies to which project. Of the following statements regarding the profiles, which one is most reasonable? P135 CHY

a. If the two projects have the same investment cost, & if their NPV profiles cross once in the upper right quadrant, at a discount rate of 40 percent, this suggests that a NPV versus IRR conflict is not likely to exist. b. If the two projects’ NPV profiles cross once, in the upper left quadrant, at a discount rate of minus 10 percent, then there will probably not be a NPV versus IRR conflict, irrespective of the relative sizes of the two projects, in any meaningful, practical sense (that is, a conflict that will affect the actual investment decision). CHY

c. If one of the projects has a NPV profile that crosses the X-axis twice, hence the project appears to have two IRRs, your assistant must have made a mistake. d. Whenever a conflict between NPV & IRR exist, then, if the two projects have the same initial cost, the one with the steeper NPV profile probably has less rapid cash flows. However, if they have identical cash flow patterns, then the one with the steeper profile probably has the lower initial cost. CHY

e. If the two projects both have a single outlay at t = 0, followed by a series of positive cash inflows, & if their NPV profiles cross in the lower left quadrant, then one of the projects should be accepted, & both would be accepted if they were not mutually exclusive. 【擬答】(B) Diff: T CHY

NPV, IRR, & MIRR 39. Which of the following statements is most correct? a. When dealing with independent projects, discounted payback (using a payback requirement of 3 or less years), NPV, IRR, & modified IRR always lead to the same accept/reject decisions for a given project. b. When dealing with mutually exclusive projects, the NPV & modified IRR methods always rank projects the same, but those rankings can conflict with rankings produced by the discounted payback & the regular IRR methods. CHY

d. Statements a & c are correct.
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

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. 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. P130 CHY

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. A change in the cost of capital would normally change both a project’s NPV & its IRR. 【擬答】 (A) Diff: T CHY

Sketch out a NPV profile for a normal, independent project, which means that only one NPV profile will appear on the graph. If WACC < IRR, then IRR says accept. But in that case, NPV > 0, so NPV will also say accept. Statement d is false. Here is the reasoning: 1. For the NPV profiles to cross, then one project must have a higher NPV at k = 0 than the other project, that is, their vertical axis intercepts will be different. 2. A second condition for NPV profiles to cross is that one have a higher IRR than the other. . CHY

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. CHY

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! CHY

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? CHY

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. Statements a & b are correct. P131 CHY

【擬答】(C) Diff: T Draw out the NPV profiles of these two projects. As B’s NPV declines more rapidly with an increase in discount rates, this implies that more of the cash flows are coming later on. Therefore, Project A has a faster payback than Project B. CHY

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. CHY

d. None of the statements above is correct. 【擬答】(D) M
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

Capital components 43. Which of the following statements is most correct? a. The cost of retained earnings is the rate of return stockholders require on a firm’s common stock. b. The component cost of preferred stock is expressed as kp(1 - T), because preferred stock dividends are treated as fixed charges, similar to the treatment of debt interest. c. The bond-yield-plus-risk-premium approach to estimating a firm’s cost of common equity involves adding a subjectively determined risk premium to the market risk-free bond rate. CHY

d. The higher the firm’s flotation cost for new common stock, the more likely the firm is to use preferred stock, which has no flotation cost. 【擬答】(A) M Preferred stock dividends are not tax deductible; therefore, the cost of preferred stock is only kp. The risk premium in the bond-yield-plus-risk premium approach would be added to the firm’s cost of debt, not the risk-free rate. Preferred stock also has flotation costs. CHY

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. The cost of debt used to calculate the weighted average cost of capital is based on an average of the cost of debt already issued by the firm & the cost of new debt. P131 CHY

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

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. CHY

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. 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

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

CAPM & DCF estimation 47. Which of the following statements is most correct? a. Beta measures market risk, but if a firm’s stockholders are not well diversified, beta may not accurately measure stand-alone risk. If the calculated beta underestimates the firm’s true investment risk, then the CAPM method will overestimate ks. P133 CHY

None of the statements above is correct. 【擬答】(A) M
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. None of the statements above is correct. 【擬答】(A) M CHY

WACC 48. Which of the following statements is most correct? a. The weighted average cost of capital for a given capital budget level is a weighted average of the marginal cost of each relevant capital component that makes up the firm’s target capital structure. b. The weighted average cost of capital is calculated on a before-tax basis. c. An increase in the risk-free rate is likely to increase the marginal costs of both debt & equity financing. CHY

d. Statements a & c are correct.
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. CHY

a. The WACC should include only after-tax component costs. Therefore, the required rates of return (or “market rates”) on debt, preferred, & common equity (kd, kp, & ks) must be adjusted to an after-tax basis before they are used in the WACC equation. b. The cost of retained earnings is generally higher than the cost of new common stock. c. Preferred stock is riskier to investors than is debt. Therefore, if someone told you that the market rates showed kd > kp for a given company, that person must have made a mistake. d. If a company with a debt ratio of 50 percent were suddenly exempted from all future income taxes, then, all other things held constant, this would cause its WACC to increase. CHY

【擬答】 (D) M If a firm paid no income taxes, its cost of debt would not be adjusted downward, hence the component cost of debt would be higher than if T were greater than 0. With a higher component cost of debt, the WACC would increase. Of course, the company would have higher earnings, & its cash flows from a given project would be high, so the higher WACC would not impede its investments, that is, its capital budget would be larger than if it were taxed. CHY

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. CHY

d. Statements b & c are correct.
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. CHY

【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

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. Answers a & b are correct. 【擬答】 (E) M CHY

Risk-adjusted cost of capital
52. If a typical U.S. company uses the same cost of capital to evaluate all projects, the firm will most likely become a. Riskier over time, & its value will decline. b. Riskier over time, & its value will rise. c. Less risky over time, & its value will rise. d. Less risky over time, & its value will decline. e. There is no reason to expect its risk position or value to change over time as a result of its use of a single discount rate. 【擬答】 (A) M P135 CHY

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

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. CHY

a. Over time, the overall risk of the company will increase.
b. Over time, Division B will become a larger part of the overall company. c. Over time, the company’s corporate WACC will increase. d. All of the statements above are correct. CHY

【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. CHY

Therefore, Division B will grow & Division A will shrink
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. CHY

The yield to maturity on the company’s bonds is 9 percent.
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. P136 CHY

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 % b % c % d % e % CHY

WACC = wdkd(1 - T) + wcke. kd is given = 9%. Find ke:
【擬答】 (A) E WACC = wdkd(1 - T) + wcke. kd is given = 9%. Find ke: ke= D1/[P0(1 - F)] + g = $0.8/[$25( )] = WACC = (0.3)(0.09)(0.6) + (0.7)( ) = 10.41% CHY

55. Flaherty Electric has a capital structure that consists of 70 percent equity & 30 percent debt. The company’s long-term bonds have a before-tax yield to maturity of 8.4 percent. The company uses the DCF approach to determine the cost of equity. Flaherty’s common stock currently trades at $45 per share. The year-end dividend (D1) is expected to be $2.50 per share, & the dividend is expected to grow forever at a constant rate of 7 percent a year. The company estimates that it will have to issue new common stock to help fund this year’s projects. CHY

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 % b % c % d % 9.89% 【擬答】 (A) E WACC = [0.3   ( )] + [0.7  ($2.5/($45  ( )) )]= 10.73%. CHY

The company’s tax rate is 40 percent.
WACC 56. Billick Brothers is estimating its WACC. The company has collected the following information: Its capital structure consists of 40 percent debt & 60 percent common equity. The company has 20-year bonds outstanding with a 9 percent annual coupon that are trading at par. The company’s tax rate is 40 percent. The risk-free rate is 5.5 percent. The market risk premium is 5 percent. The stock’s beta is 1.4. P137 CHY

|What is the company’s WACC. a. 9. 71%. b. 9. 66%. c. 8. 31%. d. 11
|What is the company’s WACC? a % b % c % d % e % 【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%)( ) + (0.6)12.5% WACC = 9.66%. CHY

Agency 57. Which of the following statements is most correct? a. Compensating managers with stock can reduce the agency problem between stockholders & managers. b. Restrictions are included in credit agreements to protect bondholders from the agency problem that exists between bondholders & stockholders. c. The threat of a takeover can reduce the agency problem between bondholders & stockholders. Statements a & b are correct. P137 CHY

【擬答】: (D) E The threat of a takeover alleviates the agency problem between managers & stockholders, not between bondholders & stockholders. CHY

a. Including restrictive covenants in the company’s bond contract.
Agency 58. Which of the following work to reduce agency conflicts between stockholders & bondholders? a. Including restrictive covenants in the company’s bond contract. Providing managers with a large number of stock options. The passage of laws that make it easier for companies to resist hostile takeovers. d. Statements b & c are correct. CHY

【擬答】:(A) E Restrictive covenants resolve differences between bondholders & stockholders. CHY

a. Paying managers a large fixed salary.
Agency 59. Which of the following actions are likely to reduce agency conflicts between stockholders & managers? a. Paying managers a large fixed salary. Increasing the threat of corporate takeover. Placing restrictive covenants in debt agreements. All of the statements above are correct. CHY

【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. CHY

a. Congress passes a law that severely restricts hostile takeovers.
Agency 60. Which of the following actions are likely to reduce the agency problem between stockholders & managers? a. Congress passes a law that severely restricts hostile takeovers. b. A manager receives a lower salary but receives additional shares of the company’s stock. c. The board of directors has become more vigilant in its oversight [董事會盯更緊] of the company’s management. d. Statements b & c are correct. CHY

擬答: (D) E Statement a will serve to increase the agency problems by preventing takeovers. Both statements b & c will reduce agency problems. CHY

Financial policy & cash flows
61. Which of the following statements is most correct? a. The optimal dividend policy is the one that satisfies the shareholders because they supply the firm’s capital. b. The use of debt financing has no effect on cash flow or stock price. c. The riskiness of projected cash flows depends upon how the firm is financed. d. Stock price is dependent on the projected cash flows & the use of debt, but not on the timing of the cash flow stream. 【擬答】(C) M P139 CHY

Corporate goals & control
62. Which of the following statements is most correct? a. The proper goal of the financial manager should be to maximize the firm’s expected cash flow, because this will add the most wealth to each of the individual shareholders (owners) of the firm. CHY

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.” CHY

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. CHY

d. Since large, publicly-owned firms are controlled by their management teams, & typically, ownership is widely dispersed, managers have great freedom in managing the firm. Managers may operate in stockholders’ best interests, but they may also operate in their own personal best interests. As long as managers stay within the law, there simply aren’t any effective controls over managerial decisions in such situations. Agency problems exist between stockholders & managers, & between stockholders & creditors. 【擬答】 (E) M CHY

63. Which of the following statements is false?
Split 63. Which of the following statements is false? a. A good reason for a firm to initiate a reverse split is to get the price of the shares up to some minimum requirement for listing on a national exchange. b. Stock dividends do not change the value of firms, but reverse splits do change form value. CHY

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. CHY

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 P140 CHY

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

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

(B) X. These are meaningless results.
(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

65. The Simpson Corporation has a degree of operating leverage of 2
65. The Simpson Corporation has a degree of operating leverage of 2.0 and a degree of financial leverage of 5.0. Simpson’s degree of total leverage is: a. 7.0 b. 10.0 c. 2.5 d. 0.4 CHY

Degree of Total Leverage (DTL)
【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

c. Beta for a stock is constant at all levels of debt-to-equity.
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

(C) X. See explanation for choice “a” as to why beta is not constant.
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

a. Selling off a portion of the shares owned.
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

【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

68. Which statement is most correct, based on the clientele effect?
a. If a company changed its dividend policy from a low payout ratio to a high payout ratio, it would likely lose its existing investor base (its “clientele”) and the price of the shares would fall. b. If a company changed its dividend policy from a low payout ratio to a high payout ratio, it would likely gain a new “clientele” and the price of the shares would rise. CHY

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

【擬答】(C) According to the clientele effect, a change in the dividend payout probably has no effect on firm or common stock values. Choice “a” and “b” are incorrect. These outcomes contradict the clientele effect. Choice “d” is incorrect. Such a policy would produce erratic dividends, which investors dislike. This has nothing to do with the clientele effect. CHY

a. The one with the most debt will have the highest equity value.
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

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

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

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

a. Its cost of common equity capital decreases.
71. Proposition Ⅱ of the Modigliani-Miller Theorem (without taxes)　suggests that if there is no preferred stock in the capital structure, as a firm’s debt-to-equity ration increases: a. Its cost of common equity capital decreases. b. Its cost of common equity capital ↑. c. Its cost of common equity capital remains constant. d. All of the above are possible P143 CHY

【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

a. As the debt-to-equity ratio ↑, WACC will remain constant.
72. According to Proposition Ⅱ of the Modigliani-Miller Theorem (with taxes): a. As the debt-to-equity ratio ↑, WACC will remain constant. b. As the debt-to-equity ratio↑, WACC will ↑. c. When the capital structure is entirely comprised of debt, WACC = 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

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

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

【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

74. A decrease in the debt ratio will generally have no effect on
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. Market risk. None of the above is correct. (It will affect each type of risk above.) CHY

b. A replacement project. c. An environmental project.
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

【擬答】 (A) An expansion project is undertaken to increase sales. This sales increase can be accomplished by expanding into existing or new markets. (B)X 　A replacement project is undertaken to replace existing equipment. Choices “c” & “d” are incorrect. Neither of these are done to increase sales. CHY

Chapter 1 Time Value of Money

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