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FIN 331 in a Nutshell. Financial Management I Review. FIN 331 in a Nutshell - Index. Financial Statements, Ratios, & AFN Time Value of Money Bond Valuation Risk & Return (SML/CAPM) Stock Valuation WACC NPV, IRR, MIRR Cash Flow Estimation.

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Fin 331 in a nutshell

FIN 331 in a Nutshell

Financial Management I Review


Fin 331 in a nutshell index
FIN 331 in a Nutshell - Index

  • Financial Statements, Ratios, & AFN

  • Time Value of Money

  • Bond Valuation

  • Risk & Return (SML/CAPM)

  • Stock Valuation

  • WACC

  • NPV, IRR, MIRR

  • Cash Flow Estimation

Click on the selected topic to go directly to that section


Financial statements cash flow and taxes

Financial Statements, Cash Flow, and Taxes

Key Financial Statements

Balance sheet

Income statements

Statement of cash flows

Index


The annual report
The Annual Report

  • Balance sheet

    • Snapshot of a firm’s financial position at a point in time

  • Income statement

    • Summarizes a firm’s revenues and expenses over a given period of time

  • Statement of cash flows

    • Reports the impact of a firm’s activities on cash flows over a given period of time


Sample balance sheet
Sample Balance Sheet

Assets =

Liabilities +

Owner’s Equity


Sample income statement
Sample Income Statement

Net income=Dividends + Retained earnings




Statement of cash flows
Statement of Cash Flows

  • Provides information about cash inflows and outflows during an accounting period

  • Required since 1988

  • Developed from Balance Sheet and Income Statement data


Statement of cash flows1
Statement of Cash Flows

Reconciles the change in Cash & Equivalents


Statement of cash flows2
Statement of Cash Flows

  • Reconciles the Income Statement and Balance Sheet to the flow of cash

    • The Matching Principle requires estimates and accruals to prepare Financial statements

    • Financial Analysis is concerned with Cash Flow

Why is it important???


Statement of cash flows3
Statement of Cash Flows

“A positive net income on the income statement is ultimately insignificant unless a company can translate its earnings into cash, and the only source in financial statement data for learning about the generation of cash from operations is the statement of cash flows”


Deficits

Covered by new debt and cash


Net operating working capital
Net Operating Working Capital

If the Asset side had included “Short-term investments” they would have been excluded as well.


Operating capital also called total net operating capital
Operating Capital (also called Total Net Operating Capital)

  • Operating Capital

    = NOWC + Net fixed assets

  • Operating Capital

    • (2005) = $800 + $1,000 = $1,800 million

    • (2004) = $650 + $870 = $1,520 million

  • Net Investment in Operating Capital

    = Op Cap (2005) – Op Cap (2004)

    = $1,800 - $1,520 = $280 million


Net operating profit after taxes nopat operating cash flow

NOPAT = EBIT(1 - Tax rate)

NOPAT05 = $283.8(1 - 0.4) = $170.3 m

OCF05 = NOPAT + Deprec + Amort

= $170.3 + $100

= $270.3

Net Operating Profit after Taxes (NOPAT) & Operating Cash Flow


Free cash flow fcf for 2005

EBIT = $283.8 m T = 40% Depreciation = $100 m

Capital Expenditures = FA + Deprec = $130+$100 = $230

NOWC = $800 - $650 = $150 m

FCF = [$283.8(1-.4)+$100] –[$230-$150]

= -$109.7 m

Free Cash Flow (FCF) for 2005


Analysis of financial statements

Analysis of Financial Statements

Ratio Analysis

Limitations of ratio analysis

Qualitative factors

Index


Five major categories of ratios
Five Major Categories of Ratios

  • Liquidity

    • CR - Current Ratio

    • QR - Quick Ratio or “Acid-Test”

  • Asset management

    • Inventory Turnover

    • DSO – Days sales outstanding

    • FAT - Fixed Assets Turnover

    • TAT - Total Assets Turnover

  • Debt management

    • Debt Ratio

    • TIE – Times interest earned

    • EBITDA coverage (EC)


Five major categories of ratios1
Five Major Categories of Ratios

  • Profitability

    • PM - Profit margin on sales

    • BEP – Basic earning power

    • ROA – Return on total assets

    • ROE – Return on common equity

  • Market value

    • P/E – Price-Earnings ratio

    • P/CF – Price – cash flow ratio

    • M/B – Market to book


Liquidity ratios
Liquidity Ratios

  • CR = Current Ratio

    = CA/CL

  • QR = Quick Ratio or “Acid-Test”

    = (CA-INV)/CL


Asset management ratios
Asset Management Ratios

  • Inventory Turnover = Sales/Inventories

  • DSO = Days sales outstanding

    = Receivables /(Annual sales/365)

  • FAT = Fixed Assets Turnover

    = Sales/Net Fixed Assets

  • TAT = Total Assets Turnover

    = Sales/Total Assets


Debt management ratios
Debt Management Ratios

  • Debt Ratio = Total Liabilities/Total Assets

  • TIE = Times interest earned

    = EBIT/Interest

  • EBITDA coverage = EC

    (EBITDA + lease pmts) .

    (Interest + principal pmts + lease pmts)


Profitability ratios
Profitability Ratios

  • PM = Profit margin on sales

    = NI/Sales

  • BEP = Basic earning power

    = EBIT/Total Assets

  • ROA = Return on total assets

    = NI/Total Assets

  • ROE = Return on common equity

    = NI/Common Equity


Market value metrics
Market Value Metrics

  • P/E = Price-Earnings ratio

    = Price per share/Earnings per share

  • P/CF = Price–cash flow ratio

    = Price per share/Cash flow per share

  • M/B = Market to book

    = Market price per share

    Book value per share



Potential problems and limitations of ratio analysis
Potential Problems and Limitations of Ratio Analysis Answer

  • Comparison with industry averages is difficult if the firm operates many different divisions

  • “Average” performance ≠ necessarily good

  • Seasonal factors can distort ratios

  • Window dressing techniques


Problems and limitations continued
Problems and Limitations Answer(Continued)

  • Different accounting and operating practices can distort comparisons

  • Sometimes difficult to tell if a ratio value is “good” or “bad”

  • Different ratios give different signals

    • Difficult to tell, on balance, whether a company is in a strong or weak financial condition


Qualitative factors
Qualitative Factors Answer

  • Revenues tied to a single customer?

  • Revenues tied to a single product?

  • Reliance on a single supplier?

  • Percentage of business generated overseas?

  • Competitive situation?

  • Legal and regulatory environment?


Financial planning and forecasting

Financial Planning and Forecasting Answer

Forecasting sales

Projecting the assets and internally generated funds

Projecting outside funds needed

Deciding how to raise funds

Index


The afn formula
The AFN Formula Answer

If ratios are expected to remain constant:

AFN = (A*/S0)∆S - (L*/S0)∆S - M(S1)(RR)

Required  Assets

 Retained Earnings

Spontaneously  Liabilities


Variables in the afn formula
Variables in the AFN Formula Answer

  • A* = Assets tied directly to sales

  • S0 = Last year’s sales

  • S1 = Next year’s projected sales

  • ∆S = Increase in sales; (S1-S0)

  • L* = Liabilities that spontaneously increase with sales


Variables in the afn formula1
Variables in the AFN Formula Answer

  • A*/S0: assets required to support sales;

    “Capital Intensity Ratio”

  • L*/S0: spontaneous liabilities ratio

  • M: profit margin (Net income/sales)

  • RR: retention ratio; percent of net

    income not paid as dividend


Key factors in afn
Key Factors in AFN Answer

  • ∆S = Sales Growth

  • A*/S0 = Capital Intensity Ratio

  • L*/S0 = Spontaneous Liability Ratio

  • M = Profit Margin

  • RR = Retention Ratio


Time value of money
Time Value of Money Answer

  • Timelines

  • Future Value

  • Present Value

  • Present Value of Uneven Cash Flows


Time lines timing of cash flows
Time Lines: Timing of Cash Flows Answer

0

1

2

3

I%

CF0

CF1

CF2

CF3

  • Tick marks occur at the end of periods

    • Time 0 = today

    • Time 1 = the end of the first period or the beginning of the second period

+CF = Cash INFLOW-CF = Cash OUTFLOWPMT = Constant CF


Basic definitions
Basic Definitions Answer

Present Value(PV)

  • The current value of future cash flows discounted at the appropriate discount rate

  • Value at t=0 on a time line

    Future Value(FV)

  • The amount an investment is worth after one or more periods.

  • “Later” money on a time line


Future value general formula
Future Value: General Formula Answer

  • FV = future value

  • PV = present value

  • I = period interest rate, expressed

  • as a decimal

  • N = number of periods

  • Future value interest factor = (1 + I)N

    • Note: “yx” key on your calculator

FV = PV(1 + I)N


Texas instruments ba ii plus
Texas Instruments BA-II Plus Answer

FV = future value

PV = present value

PMT = periodic payment

I/Y = period interest rate

N = number of periods

One of these MUST be negative

N I/Y PV PMT FV


Excel spreadsheet functions
Excel Spreadsheet Functions Answer

=FV(rate,nper,pmt,pv)

=PV(rate,nper,pmt,fv)

=RATE(nper,pmt,pv,fv)

=NPER(rate,pmt,pv,fv)

  • Use the formula icon (ƒx) when you can’t remember the exact formula


Future values example
Future Values – Example Answer

Suppose you invest $100 for 5 years at 10%

How much would you have?

Formula Solution:

FV =PV(1+I)N

=100(1.10)5

=100(1.6105)

=161.05


Future value example
Future Value – Example Answer

Suppose you invest $100 for 5 years at 10%. How much would you have?

Calculator Solution

  • 5 N

  • 10 I/Y

  • -100 PV

  • 0 PMT

  • CPT FV = 161.05


Future value important relationship 1
Future Value: AnswerImportant Relationship 1

For a given interest rate:

  • The longer the time period,

  • The higher the future value

    FV = PV(1 + I)N

For a given I, as N increases, FV increases


Future value important relationship 2
Future Value AnswerImportant Relationship 2

For a given time period:

  • The higher the interest rate,

  • The larger the future value

FV = PV(1 + I)N

For a given N, as I increases, FV increases


Present values
Present Values Answer

  • The current value of future cash flows discounted at the appropriate discount rate

  • Value at t=0 on a time line

  • Answers the questions:

    • How much do I have to invest today to have some amount in the future?

    • What is the current value of an amount to be received in the future?


Present values1
Present Values Answer

FV = PV(1 + I)N

  • Rearrange to solve for PV

    PV = FV / (1+I)N

    PV = FV(1+I)-N

  • “Discounting” = finding the present value of one or more future amounts


Present value one period example
Present Value: AnswerOne Period Example

  • You need $10,000 for the down payment on a new car

  • You can earn 7% annually.

  • How much do you need to invest today?

  • 1 N;

  • 7 I/Y;

  • 0 PMT;

  • 10000 FV;

  • CPT PV = -9345.79

PV = 10,000(1.07)-1 = 9,345.79

=PV(0.07,1,0,10000)


Present value important relationship 1
Present Value: AnswerImportant Relationship 1

For a given interest rate:

  • The longer the time period,

  • The lower the present value

For a given I, as N increases, PV decreases


Present value important relationship 2
Present Value AnswerImportant Relationship 2

For a given time period:

  • The higher the interest rate,

  • The smaller the present value

For a given N, as I increases, PV decreases


The basic pv equation refresher
The Basic PV Equation - Refresher Answer

PV = FV / (1 + I)N

There are four parts to this equation

  • PV, FV, I and N

  • Know any three, solve for the fourth

  • If you are using a financial calculator, be sure and remember the sign convention

  • +CF = Cash INFLOW-CF = Cash OUTFLOW


    Multiple cash flows present value
    Multiple Cash Flows AnswerPresent Value

    • The Basic Formula

    • The TI BA II+

      • Using the PV/FV keys

      • Using the Cash Flow Worksheet

    • Excel


    Multiple uneven cash flows present value
    Multiple Uneven Cash Flows AnswerPresent Value

    • You are offered an investment that will pay

      • $200 in year 1,

      • $400 the next year,

      • $600 the following year, and

      • $800 at the end of the 4th year.

      • You can earn 12% on similar investments.

      • What is the most you should pay for this investment?


    What is the pv of this uneven cash flow stream

    4 Answer

    0

    1

    2

    3

    12%

    200

    400

    600

    800

    -178.57

    -318.88

    -427.07

    -508.41

    What is the PV of this uneven cash flow stream?

    -1,432.93 = PV



    Multiple uneven cash flows pv
    Multiple Uneven Cash Flows Answer – PV

    Year 1 CF: 1 N; 12 I/Y; 200 FV; CPT PV = -178.57

    Year 2 CF: 2 N; 12 I/Y; 400 FV; CPT PV = -318.88

    Year 3 CF: 3 N; 12 I/Y; 600 FV; CPT PV = -427.07

    Year 4 CF: 4 N; 12 I/Y; 800 FV; CPT PV = -508.41

    Total PV = -$1,432.93


    Multiple uneven cash flows using the ti baii s cash flow worksheet
    Multiple Uneven Cash Flows – AnswerUsing the TI BAII’s Cash Flow Worksheet

    Clear all:

    • Press CF

    • Then 2nd

    • And CLR WORK (above CE/C)

      CF0 is displayed and is 0

      Enter the Period 0 cash flow

    • If it is an outflow, hit “+/-” to change the sign

      To enter the figure in the cash flow register, press ENTER


    Ti baii uneven cfs
    TI BAII+: Uneven CFs Answer

    • Press the down arrow () to move to the next cash flow register.

    • Enter the cash flow amount, press ENTER and then down arrow to move to the cash flow counter (Fn).

    • The default counter value is “1”.

      • To accept the value of “1”, press the down arrow again.

      • To change the counter, enter the correct count, press ENTER and then the down arrow.


    Ti baii uneven cfs1
    TI BAII+: Uneven CFs Answer

    • Repeat for all cash flows, in order.

    • To find NPV:

      • Press NPV: I appears on the screen

      • Enter the interest rate, press ENTER and the down arrow to display NPV.

      • Press compute “CPT”


    Ti baii uneven cash flows
    TI BAII+: Uneven Cash Flows Answer

    CF

    C000ENTER

    C01200 ENTER

    F011 ENTER

    C02400 ENTER 

    F021 ENTER 

    C03600 ENTER

    F031 ENTER

    C04 800 ENTER 

    F04 1 ENTER  NPV

    I12 ENTER 

    NPV CPT

    1432.93

    Cash Flows:

    CF0 = 0

    CF1 = 200

    CF2 = 400

    CF3 = 600

    CF4 = 800


    Excel pv of multiple uneven cfs
    Excel – AnswerPV of multiple uneven CFs


    Bonds and their valuation

    Bonds and Their Valuation Answer

    Interest rates

    Bond valuation

    Measuring yield

    Index


    Nominal vs real rates
    “Nominal” vs. “Real” rates Answer

    r = Any nominal rate

    r* = The “real” risk-free rate

    ≈ T-bill rate with no inflation

    Typically ranges from 1% to 4% per year

    rRF = Rate on Treasury securities

    Proxied by T-bill or T-bond rate


    R r ip drp lp mrp

    Here: Answer

    r = Required rate of return on a debt security

    r* = Real risk-free rate

    IP = Inflation premium

    DRP = Default risk premium

    LP = Liquidity premium

    MRP = Maturity risk premium

    r = r* + IP + DRP + LP + MRP

    rRF=


    Premiums added to r for different types of debt
    Premiums Added to r* for Different Types of Debt Answer

    ST Treasury ST IP

    LT Treasury LT IP MRP

    ST Corporate ST IP DRP LP

    LT Corporate LT IP DRP MRP LP

    Debt Instrument IP DRP MRP LP


    Discount rate ytm
    Discount Rate = YTM Answer

    The discount rate (YTM) is:

    • The opportunity cost of capital

    • The rate that could be earned on alternative investments of equal risk

    • Required return

      For debt securities:

      YTM = r* + IP + LP + MRP + DRP


    Bond value
    Bond Value Answer

    • Bond Value = PV(coupons) + PV(par)

    • Bond Value = PV(annuity) + PV(lump sum)

    • Remember:

      • As interest rates increase present values decrease – as YTM ↑ → PV ↓

      • As interest rates increase, bond prices decrease and vice versa


    The bond pricing equation
    The Bond-Pricing Equation Answer

    PV(lump sum)

    PV(Annuity)

    C = Coupon payment; F = Face value


    Texas instruments ba ii plus1

    N I/Y PV PMT FV Answer

    Texas Instruments BA-II Plus

    • FV = future value/face value/par value

    • PV = present value=bond value/price

    • I/Y = period interest rate = YTM

    • N = number of periods to maturity

    • PMT = coupon payment


    Spreadsheet functions
    Spreadsheet Functions Answer

    FV(Rate,Nper,Pmt,PV,0/1)

    PV(Rate,Nper,Pmt,FV,0/1)

    RATE(Nper,Pmt,PV,FV,0/1)

    NPER(Rate,Pmt,PV,FV,0/1)

    PMT(Rate,Nper,PV,FV,0/1)

    • Inside parens: (RATE,NPER,PMT,PV,FV,0/1)

    • “0/1”Ordinary annuity = 0 (default)

      • Annuity Due = 1 (must be entered)


    Pricing specific bonds
    Pricing Specific Bonds Answer

    • TI BA II+

      • Bond Worksheet [2nd] BOND

      • SDT CPN RDT RV ACT 2/Y YLD PRI

    • Excel:

      • PRICE(Settlement,Maturity,Rate,Yld,Redemption, Frequency,Basis)

      • YIELD(Settlement,Maturity,Rate,Pr,Redemption, Frequency,Basis)

        • Settlement and maturity need to be actual dates

        • Redemption and Pr need to given as % of par value


    Yield to maturity ytm
    Yield to Maturity (YTM) Answer

    • The market required rate of return for bonds of similar risk and maturity

    • The discount rate used to value a bond

    • Return earned if bond held to maturity

    • Usually = coupon rate at issue

    • Quoted as an APR

    • The IRR of a bond


    What is the ytm on a 10 year 9 annual coupon 1 000 par value bond selling for 887
    What is the YTM on a 10-year, 9% annual coupon, $1,000 par value bond, selling for $887?

    • Must find the rd that solves this model:


    Using a financial calculator to solve for the ytm
    Using a financial calculator to solve for the YTM value bond, selling for $887?

    • YTM =10.91%

    • Bond sells at a discount because YTM > coupon rate

    10

    - 887

    90

    1000

    INPUTS

    N

    I/YR

    PV

    PMT

    FV

    OUTPUT

    10.91


    Solving for ytm
    Solving for YTM value bond, selling for $887?

    • Coupon rate = 9%

    • Annual coupons

    • Par = $1,000

    • Maturity = 10 years

    • Price = $887

    YTM on a 10-year, 9% annual coupon, $1,000 par value bond selling for $887

    • Using the calculator:

      • N = 10

      • PV = -887

      • PMT = 90

      • FV = 1000

      • CPT I/Y = 10.91

    =RATE(10,90,-887,1000)


    Find ytm if the bond price is 1 134 20
    Find YTM, value bond, selling for $887?if the bond price is $1,134.20

    • YTM = 7.08%

    • Bond sells at a premium because YTM < coupon rate

    10

    -1134.2

    90

    1000

    INPUTS

    N

    I/YR

    PV

    PMT

    FV

    OUTPUT

    7.08


    Solving for ytm1
    Solving for YTM value bond, selling for $887?

    • Coupon rate = 9%

    • Annual coupons

    • Par = $1,000

    • Maturity = 10 years

    • Price = $1,134.20

    YTM on a 10-year, 9% annual coupon, $1,000 par value bond selling for $1,134.20

    • Using the calculator:

      • N = 10

      • PV = -1134.20

      • PMT = 90

      • FV = 1000

      • CPT I/Y = 7.08

    =RATE(10,90,-1134.20,1000)


    Semiannual bonds
    Semiannual bonds value bond, selling for $887?

    • Multiply years by 2: number of periods = 2N.

    • Divide nominal rate by 2: periodic rate (I/YR) = rd / 2.

    • Divide annual coupon by 2: PMT = ann cpn / 2.

    2N

    rd / 2

    OK

    cpn / 2

    OK

    INPUTS

    N

    I/YR

    PV

    PMT

    FV

    OUTPUT


    What is the value of a 10 year 10 semiannual coupon bond if r d 13
    What is the value of a 10-year, 10% semiannual coupon bond, if rd = 13%?

    • Multiply years by 2 : N = 2 * 10 = 20

    • Divide nominal rate by 2 : I/YR = 13 / 2 = 6.5

    • Divide annual coupon by 2 : PMT = 100 / 2 = 50

    20

    6.5

    50

    1000

    INPUTS

    N

    I/YR

    PV

    PMT

    FV

    OUTPUT

    - 834.72


    Valuing a semiannual bond
    Valuing a Semiannual Bond if r

    • Coupon rate = 10%

    • Annual coupons

    • Par = $1,000

    • Maturity = 10 years

    • YTM = 13%

    • Using the calculator:

      • N = 20

      • I/Y = 6.5

      • PMT = 50

      • FV = 1000

      • CPT PV = -834.72

    Using the formula:

    =PV(0.065, 10, 50, 1000)


    Ytm with semiannual coupons
    YTM with Semiannual Coupons if r

    • Suppose a bond with a 10% coupon rate and semiannual coupons, has a face value of $1000, 20 years to maturity and is selling for $1197.93.

      • Is the YTM more or less than 10%?

      • What is the semiannual coupon payment?

      • How many periods are there?


    Ytm with semiannual coupons1
    YTM with Semiannual Coupons if r

    • Suppose a bond with a 10% coupon rate and semiannual coupons, has a face value of $1000, 20 years to maturity and is selling for $1197.93.

      N = 40

      PV = -1197.93

      PMT = 50

      FV = 1000

      CPT I/Y = 4%

      YTM = 4%*2 = 8%

       Result = ½ YTM

    NOTE: Solving a semi-annual payer for YTM will result in a 6-month YTM answer

    Calculator solves what you enter.


    Risk and rates of return

    Risk and Rates of Return if r

    Stand-alone Risk

    Portfolio Risk

    Risk & Return: CAPM / SML

    Index


    The expected rate of return
    The Expected Rate of Return if r

    r “hat” = expected return

    ri = expected return in “ith” state of the economy

    Pi = Probability of “ith” state occurring



    The standard deviation of returns
    The Standard Deviation of Returns if r

    σ = Standard deviation

    σ = √ Variance = √ σ2




    Risk versus return do we know enough now
    Risk versus Return: if rDo we know enough now?

    ^


    Coefficient of variation cv
    Coefficient of Variation (CV) if r

    CV = Standard deviation/expected return

    = Risk per unit of return

    =


    Portfolio expected return
    Portfolio Expected Return if r

    ^

    • rp = weighted average

      • wi = % of portfolio in stock i

      • ri = return on stock i


    Portfolio expected return1
    Portfolio Expected Return if r

    Assume a two-stock portfolio is created with

    $50,000 invested in both HT and Collections

    ^

    rp = 0.5(12.4%) + 0.5(1.0%) = 6.7%


    Portfolio return
    Portfolio Return if r

    “Portfolio” = (50% x HT) + (50% x Coll)

    “Portfolio Return” = Prob x “Portfolio”


    Portfolio risk
    Portfolio Risk if r

    Portfolio Standard deviation is NOT a weighted average of the standard deviations of the component assets




    Portfolio risk return
    Portfolio Risk & Return if r

    • σp = 3.4% is much lower than the σ of either stock

    • σp = 3.4% is lower than the weighted average of HT and Coll.’s σ (16.6%)

    • The portfolio provides the average return of component stocks, but lower than the average risk

    • Why? Negative correlation between stocks


    Covariance of returns
    Covariance of Returns if r

    Measures how much the returns on two risky assets move together



    Covariance
    Covariance if r

    Covariance (HT:Coll) = -0.0264


    Correlation coefficient
    Correlation Coefficient if r

    • Correlation Coefficient = ρ (rho)

    • Scales covariance to [-1,+1]

      • -1 = Perfectly negatively correlated

      • 0 = Uncorrelated; not related

      • +1 = Perfectly positively correlated


    Two stock portfolios
    Two-Stock Portfolios if r

    If r = -1.0

    • Two stocks can be combined to form a riskless portfolio

      If r = +1.0

    • No risk reduction at all

      In general, stocks have r≈ 0.35

    • Risk is lowered but not eliminated

      Investors typically hold many stocks


    S of n stock portfolio
    s if r of n-Stock Portfolio

    • Subscripts denote stocks i and j

    • ri,j = Correlation between stocks i and j

    • σi and σj=Standard deviations of stocks i and j

    • σij = Covariance of stocks i and j


    Portfolio risk n risky assets
    Portfolio Risk-n Risky Assets if r

    i j for n=2

    1 1 w1w111 = w1212

    1 2 w1w212

    2 1 w2w121

    2 2 w2w222 = w2222

    p2= w1212 + w2222 + 2w1w2 12



    Capital asset pricing model capm
    Capital Asset Pricing Model (CAPM) if r

    • Links risk and required returns

    • Security Market Line (SML):

      • A stock’s required return equals the risk-free return (rRF) plus a risk premium (RPM x ) that reflects the stock’s risk after diversification

    • Primary conclusion:

      • The relevant riskiness of a stock is its contribution to the riskiness of a well-diversified portfolio.


    The sml and required return
    The SML and if rRequired Return

    • The Security Market Line (SML) is part of the Capital Asset Pricing Model (CAPM)

    • rRF = Risk-free rate

    • RPM = Market risk premium = rM – rRF


    The market risk premium r m r rf rp m
    The Market Risk Premium if r (rM – rRF = RPM)

    • Additional return over the risk-free rate to compensate investors for assuming an average amount of risk

    • Size depends on:

      • Perceived risk of the stock market

      • Investors’ degree of risk aversion

    • Varies from year to year

      • Estimates suggest a range between 4% and 8% per year


    Required rates of return
    Required if r Rates of Return

    Assume: rRF = 5.5% RPM = 5%

    • rHT = 5.5% + (5.0%)(1.32)

      = 5.5% + 6.6% = 12.10%

    • rM = 5.5% + (5.0%)(1.00) = 10.50%

    • rUSR = 5.5% + (5.0%)(0.88) = 9.90%

    • rT-bill = 5.5% + (5.0%)(0.00) = 5.50%

    • rColl = 5.5% + (5.0%)(-0.87) = 1.15%


    Expected vs required returns
    Expected if r vs RequiredReturns

    “Required” by the market

    “Expected” by YOU


    Illustrating the security market line
    Illustrating the if rSecurity Market Line

    SML: ri = 5.5% + (5.0%) i

    ri (%)

    SML

    .

    HT

    .

    .

    rM = 10.5

    rRF = 5.5

    .

    USR

    T-bills

    .

    Risk, i

    -1 0 1 2

    Coll.


    Portfolio beta
    Portfolio Beta if r

    Where:

    wi =weight (% dollars invested in asset i)

    βi = Beta of asset i

    βp=Portfolio Beta


    Stocks and their valuation

    Stocks and Their Valuation if r

    Constant growth stock valuation

    Non-constant growth stock valuation

    Corporate value model

    Index


    Constant growth stock
    Constant growth stock if r

    • Dividends expected to grow forever at a constant rate, g:

      D1 = D0 (1+g)1

      D2 = D0 (1+g)2

      Dt = D0 (1+g)t

    • Dividend growth formula converges to:


    Constant growth model
    Constant Growth Model if r

    Needed data:

    D0 = Dividend just paid

    D1 = Next expected dividend

    g = constant growth rate

    rs = required return on the stock


    Expected value at time t
    Expected Value at time t if r

    Value at t=0

    Value at t


    Supernormal growth
    Supernormal Growth if r

    • What if g = 30% for 3 years before achieving long-run growth of 6%?

    • Constant growth model no longer applicable

    • But - growth constant after 3 years


    Valuing common stock with nonconstant growth

    0 if r

    1

    2

    3

    4

    rs = 13%

    ...

    g = 30%

    g = 30%

    g = 30%

    g = 6%

    D0 = 2.00 2.600 3.380 4.394

    4.658

    2.301

    2.647

    3.045

    4.658

    =

    =

    $66.54

    46.114

    -

    0.13

    0.06

    54.107 = P0

    Valuing common stock with nonconstant growth

    $

    P


    Corporate value model
    Corporate Value Model if r

    • = Free Cash Flow method

      • Value of the firm = present value of the firm’s expected future free cash flows

      • Free cash flow =after-tax operating income less net capital investment

      • FCF = NOPAT – Net capital investment


    Applying the corporate value model
    Applying the corporate value model if r

    Market value of firm:

    • (MVF) = PV(future FCFs)

      MV of common stock:

    • = MVF – MV of debt

      Intrinsic stock value:

    • = MVCS /# shares


    Issues regarding the corporate value model
    Issues regarding the corporate value model if r

    • Oftenpreferred to the dividend growth model

      • Firms that don’t pay dividends

      • Dividends hard to forecast

    • Assumes at some point free cash flow growth rate will be constant

    • Terminal value (TVN) = value of firm at the point that growth becomes constant


    Firm s intrinsic value

    0 if r

    1

    2

    3

    4

    r = 10%

    ...

    g = 6%

    -5 10 20

    21.20

    -4.545

    8.264

    15.026

    21.20

    398.197

    530= = TV3

    0.10

    -

    0.06

    416.942

    Firm’s Intrinsic Value

    Long-run gFCF = 6% WACC = 10%


    If the firm has $40 million in debt and has 10 million shares of stock, what is the firm’s intrinsic value per share?

    • MV of equity = MV of firm – MV of debt

      = $416.94 - $40

      = $376.94 million

    • Value per share= MV of equity / # of shares

      = $376.94 / 10

      = $37.69


    Firm multiples method
    Firm multiples method shares of stock, what is the firm’s intrinsic value per share?

    • Often used by analysts to value stocks

      • P / E Price-earning

      • P / CF Price-cash flow

      • P / Sales Price-sales

    • Method:

      • Estimate appropriate ratio based on comparable firms

      • Multiply estimate by expected metric to estimate stock price


    The cost of capital

    The Cost of Capital shares of stock, what is the firm’s intrinsic value per share?

    Cost of equity

    WACC

    Adjusting for risk

    Index


    Wacc weighted average cost of capital
    WACC shares of stock, what is the firm’s intrinsic value per share?Weighted Average Cost of Capital

    WACC = wdrd(1-T) + wprp + wcrs

    Where:

    wD = % of debt in capital structure

    wP= % of preferred stock in capital structure

    wC= % of common equity in capital structure

    rD = firm’s cost of debt

    rP= firm’s cost of preferred stock

    rC= firm’s cost of equity

    T = firm’s corporate tax rate

    Weights

    Component costs


    Three ways to determine the cost of equity r s
    Three ways to determine shares of stock, what is the firm’s intrinsic value per share?the cost of equity, rs:

    1. DCF: rs = D1/P0 + g

    2. CAPM: rs = rRF + (rM - rRF)βi

    = rRF + (RPM)βi

    3. Own-Bond-Yield-Plus-Risk Premium:

    rs = rd + Bond RP


    Dcf approach inputs
    DCF Approach: Inputs shares of stock, what is the firm’s intrinsic value per share?

    • Current stock price (P0)

    • Current dividend (D0)

    • Growth rate (g)


    Four mistakes to avoid
    Four Mistakes to Avoid shares of stock, what is the firm’s intrinsic value per share?

    • Current (YTM) vs. historical (Coupon rate) cost of debt

    • Mixing current and historical measures to estimate the market risk premium

    • Book weights vs. Market Weights

      • Use Target weights

      • Use market value of equity

      • Book value of debt = reasonable proxy for market value.

    • Incorrect cost of capital components

      • Only investor provided funding


    Should the company use the composite wacc as the hurdle rate for each of its projects
    Should the company use the composite WACC as the hurdle rate for each of its projects?

    • NO!

    • A firm’s composite WACC reflects the risk of an average project

      • WACC = “hurdle rate” for an average risk project

    • Different divisions/projects may have different risks

      • Division or project WACC should be adjusted to reflect appropriate risk


    Divisional and project costs of capital
    Divisional and Project Costs of Capital for each of its projects?

    • Using the WACC as the discount rate is only appropriate for projects that are the same risk as the firm’s current operations

    • If considering a project that is NOT of the same risk as the firm, then an appropriate discount rate for that project is needed

    • Divisions also often require separatediscount rates


    Using wacc for all projects example
    Using WACC for All Projects - Example for each of its projects?

    • What would happen if we use the WACC for all projects regardless of risk?

    • Assume the WACC = 15%


    Divisional risk and the cost of capital
    Divisional Risk and the Cost of Capital for each of its projects?

    Rate of Return

    (%)

    Acceptance Region

    WACC

    WACC

    H

    Acceptance Region

    Rejection Region

    WACC

    F

    Rejection Region

    WACC

    L

    Risk

    0

    Risk

    Risk

    L

    H


    Subjective approach
    Subjective Approach for each of its projects?

    • Consider the project’s risk relative to the firm overall

      • If project risk > firm risk  project discount rate > WACC

      • If project risk < firm risk  project discount rate < WACC


    Subjective approach example
    Subjective Approach - Example for each of its projects?


    The basics of capital budgeting

    The Basics of Capital Budgeting for each of its projects?

    Independent vs. mutually exclusive CFs

    Normal vs. non-normal CFs

    NPV

    IRR

    MIRR

    PB

    DPB

    Index


    Steps to capital budgeting
    Steps to capital budgeting for each of its projects?

    • Estimate CFs (inflows & outflows)

    • Assess riskiness of CFs

    • Determine appropriate cost of capital

    • Find NPV and/or IRR

    • Accept if NPV>0 and/or IRR>WACC


    Independent vs mutually exclusive projects
    Independent vs. Mutually Exclusive Projects for each of its projects?

    • Independent:

      • The cash flows of one are unaffected by the acceptance of the other

    • Mutually Exclusive:

      • The acceptance of one project precludes acceptance of the other


    Npv sum of the pvs of all cash flows

    n for each of its projects?

    CFt

    .

    NPV =

    (1 + r)t

    t = 0

    n

    CFt

    - CF0

    NPV =

    (1 + r)t

    t = 1

    NPV: Sum of the PVs of all cash flows.

    NOTE: t=0

    Cost often is CF0 and is negative


    Ti baii uneven cash flows1
    TI BAII+: Uneven Cash Flows for each of its projects?

    CF

    C00100 +/-ENTER

    C0110 ENTER

    F011 ENTER

    C0260 ENTER 

    F021 ENTER 

    C0380 ENTER

    F031 ENTER NPV

    I10 ENTER 

    NPV CPT

    $18.78

    Cash Flows:

    CF0 = -100

    CF1 = 10

    CF2 = 60

    CF3 = 80


    Internal rate of return irr
    Internal Rate of Return (IRR) for each of its projects?

    IRR = discount rate that forces PV of inflows equal to cost, and NPV = 0:

    Solving for IRR with a financial calculator:

    • Enter CFs in CFLO register

    • Press IRR


    Npv vs irr

    n for each of its projects?

    CFt

    = NPV

    (1 + r)t

    t = 0

    n

    CFt

    = 0

    (1 + IRR)t

    t = 0

    NPV vs IRR

    NPV: Enter r, solve for NPV

    IRR: Enter NPV = 0, solve for IRR


    Modified internal rate of return mirr
    Modified Internal Rate of Return (MIRR) for each of its projects?

    • MIRR = discount rate which causes the PV of a project’s terminal value (TV) to equal the PV of costs

      • TV = inflows compounded at WACC

    • MIRR assumes cash inflows reinvested at WACC


    Normal vs non normal cash flows
    Normal vs. Non-normal Cash Flows for each of its projects?

    Normal Cash Flow Project:

    • Cost (negative CF) followed by a series of positive cash inflows

    • One change of signs

      Non-normal Cash Flow Project:

    • Two or more changes of signs

    • Most common: Cost (negative CF), then string of positive CFs, then cost to close project

    • For example, strip mine


    Multiple irrs
    Multiple IRRs for each of its projects?

    • Descartes Rule of Signs

    • Polynomial of degree n→n roots

      • 1 real root per sign change

      • Rest = imaginary (i2 = -1)


    The Pavillion Project: for each of its projects?Non-normal CFs and MIRR

    1

    2

    0

    -800,000

    5,000,000

    -5,000,000

    PV outflows @ 10% = -4,932,231.40

    TV inflows @ 10% = 5,500,000.00

    MIRR = 5.6%


    Mirr versus irr
    MIRR versus IRR for each of its projects?

    • MIRR correctly assumes reinvestment at opportunity cost = WACC

    • MIRR avoids the multiple IRR problem

    • Managers like rate of return comparisons, and MIRR is better for this than IRR


    When to use the mirr instead of the irr accept project p
    When to use the MIRR instead of the IRR? Accept Project P? for each of its projects?

    • When there are nonnormal CFs and more than one IRR, use MIRR.

      • PV of outflows @ 10% = -$4,932.2314.

      • TV of inflows @ 10% = $5,500.

      • MIRR = 5.6%.

    • Do not accept Project P.

      • NPV = -$386.78 < 0.

      • MIRR = 5.6% < WACC = 10%.


    Excel functions
    Excel Functions for each of its projects?


    Cash flow estimation and risk analysis

    Cash Flow Estimation and Risk Analysis for each of its projects?

    Relevant cash flows

    Net salvage value

    Inflation

    Sensitivity analysis

    Scenario analysis

    Real options

    Index


    Relevant cash flows incremental cash flow for a project
    Relevant Cash Flows: for each of its projects?Incremental Cash Flow for a Project

    Project’s incremental cash flow is:

    Corporate cash flow with the project

    Minus

    Corporate cash flow without the project


    Relevant cash flows
    Relevant Cash Flows for each of its projects?

    Changes in Net Working Capital…… Y

    Interest/Dividends …………..………….. N

    “Sunk” Costs ………………………………….. N

    Opportunity Costs ………………………….Y

    Externalities/Cannibalism …………….. Y

    Tax Effects ………………………..………….. Y


    Tax effect on salvage
    Tax Effect on Salvage for each of its projects?

    Net Salvage Cash Flow

    = SP - (SP-BV)(T)

    Where:

    SP = Selling Price

    BV = Book Value

    T = Corporate tax rate


    Including inflation when estimating cash flows
    Including inflation when estimating cash flows for each of its projects?

    Nominal r > real r

    The cost of capital, r, includes a premium for inflation

    Nominal CF > real CF

    Nominal cash flows incorporate inflation

    If you discount real CF with the higher nominal r, then your NPV estimate is too low


    INFLATION for each of its projects?

    Real vs. Nominal Cash flows

    Real

    Nominal


    2 Ways to adjust for each of its projects?

    Adjust WACC

    Cash Flows = Real

    Adjust WACC to remove inflation

    Adjust Cash Flows for Inflation

    Use Nominal WACC

    INFLATION

    Real vs. Nominal Cash flows


    Sensitivity analysis
    Sensitivity Analysis for each of its projects?

    Shows how changes in an input variable affect NPV or IRR

    Each variable is fixed except one

    Change one variable to see the effect on NPV or IRR

    Answers “what if” questions


    Sensitivity analysis1
    Sensitivity Analysis for each of its projects?


    Sensitivity analysis2
    Sensitivity Analysis for each of its projects?


    Sensitivity graph
    Sensitivity Graph for each of its projects?

    Variable Cost

    Unit Sales

    Fixed Cost


    Sensitivity ratio
    Sensitivity Ratio for each of its projects?

    %NPV = (New NPV - Base NPV)/Base NPV

    %VAR = (New VAR - Base VAR)/Base VAR

    14-162

    • If SR>0  Direct relationship

    • If SR<0  Inverse relationship


    Sensitivity ratio1
    Sensitivity Ratio for each of its projects?

    -30% $ -62 $54 $266

    0 20 20 20

    %NPV (-62-20)/20 (54-20)/20 (266-20)/20 -4.1% 1.7% 12.3%

    %VAR -30% -30% -30%

    SR 13.74 -5.72 -41.22

    14-163

    Change from Resulting NPV (000s)

    Base Level Unit Sales FCVC


    Sensitivity graph1
    Sensitivity Graph for each of its projects?

    Variable Cost

    -41.22

    Unit Sales

    13.74

    Fixed Cost

    -5.72


    Results of sensitivity analysis
    Results of Sensitivity Analysis for each of its projects?

    Steeper sensitivity lines = greater risk

    Small changes → large declines in NPV

    The Variable Cost line is steeper than unit sales or fixed cost so, for this project, the firm should focus on the accuracy of variable cost forecasts.


    Sensitivity analysis weaknesses
    Sensitivity Analysis: for each of its projects?Weaknesses

    Does not reflect diversification

    Says nothing about the likelihood of change in a variable

    i.e. a steep sales line is not a problem if sales won’t fall

    Ignores relationships among variables


    Sensitivity analysis strengths
    Sensitivity Analysis: for each of its projects?Strengths

    Provides indication of stand-alone risk

    Identifies dangerous variables

    Gives some breakeven information


    Scenario analysis
    Scenario Analysis for each of its projects?

    Examines several possible situations, usually:

    Worst case

    Base case or most likely case, and

    Best case

    Provides a range of possible outcomes


    Scenario example
    Scenario Example for each of its projects?


    Problems with scenario analysis
    Problems with Scenario Analysis for each of its projects?

    Only considers a few possible out-comes

    Assumes that inputs are perfectly correlated

    All “bad” values occur together and all “good” values occur together

    Focuses on stand-alone risk


    Monte carlo simulation analysis
    Monte Carlo Simulation Analysis for each of its projects?

    Computerized version of scenario analysis using continuous probability distributions

    Computer selects values for each variable based on given probability distributions


    Monte carlo simulation analysis1
    Monte Carlo Simulation Analysis for each of its projects?

    Calculates NPV and IRR

    Process is repeated many times (1,000 or more)

    End result: Probability distribution of NPV and IRR based on sample of simulated values

    Generally shown graphically


    Histogram of results
    Histogram of Results for each of its projects?


    Advantages of simulation analysis
    Advantages of Simulation Analysis for each of its projects?

    Reflects the probability distributions of each input

    Shows range of NPVs, the expected NPV, σNPV, and CVNPV

    Gives an intuitive graph of the risk situation


    Disadvantages of simulation analysis
    Disadvantages of Simulation Analysis for each of its projects?

    Difficult to specify probability distributions and correlations

    If inputs are bad, output will be bad:“Garbage in, garbage out”


    Disadvantages of sensitivity scenario and simulation analysis
    Disadvantages of Sensitivity, Scenario and Simulation Analysis

    Sensitivity, scenario, and simulation analyses do not provide a decision rule

    Do not indicate whether a project’s expected return is sufficient to compensate for its risk

    Sensitivity, scenario, and simulation analyses all ignore diversification

    Measure only stand-alone risk, which may not be the most relevant risk in capital budgeting


    Real options
    Real Options Analysis

    When managers can influence the size and risk of a project’s cash flows by taking different actions during the project’s life in response to changing market conditions

    Alert managers always look for real options in projects

    Smarter managers try to create real options


    Types of real options
    Types of Real Options Analysis

    Investment timing options

    Growth options

    Expansion of existing product line

    New products

    New geographic markets

    Abandonment options

    Contraction

    Temporary suspension

    Flexibility options


    Fin 331 in a nutshell1

    FIN 331 in a Nutshell Analysis

    Financial Management I Review

    Index


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