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331NS-1 FIN 331 in a Nutshell Financial Management I Review for FIN 338.

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1 331NS-1 FIN 331 in a Nutshell Financial Management I Review for FIN 338

2 331NS-2 Time Value of Money  Timelines  Future Value  Present Value  Present Value of Uneven Cash Flows

3 331NS-3 Time Lines: Timing of Cash Flows  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 0 CF 1 CF 3 CF I% +CF = Cash INFLOW -CF = Cash OUTFLOW PMT = Constant CF

4 331NS-4 Basic Definitions  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

5 331NS-5 FV = PV(1 + I) N Future Value: General Formula  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: “y x ” key on your calculator

6 331NS-6 Texas Instruments BA-II Plus  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

7 331NS-7 Excel Spreadsheet Functions =FV(rate,nper,pmt,pv) =PV(rate,nper,pmt,fv) =RATE(nper,pmt,pv,fv) =NPER(rate,pmt,pv,fv )  Use the formula icon (ƒ x ) when you can’t remember the exact formula

8 331NS-8 Future Values – Example  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

9 331NS-9 Future Value – Example  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 =

10 331NS-10 Future Value: Important 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

11 331NS-11 Future Value Important Relationship 2 For a given time period: The higher the interest rate, The larger the future value For a given N, as I increases, FV increases FV = PV(1 + I ) N

12 331NS-12 Present Values  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?

13 331NS-13 Present Values 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

14 331NS-14 Present Value: One 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; FV; CPT PV = =PV(0.07,1,0,10000) PV = 10,000(1.07) -1 = 9,345.79

15 331NS-15 Present Value: Important 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

16 331NS-16 Present Value Important 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

17 331NS-17 The Basic PV Equation - Refresher 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

18 331NS-18 Multiple Cash Flows Present Value  The Basic Formula  The TI BA II+ Using the PV/FV keys Using the Cash Flow Worksheet  Excel

19 331NS-19 Multiple Uneven Cash Flows Present 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 4 th year.  You can earn 12% on similar investments.  What is the most you should pay for this investment?

20 331NS-20 What is the PV of this uneven cash flow stream? % , = PV

21 331NS-21 Present Value of an Uneven Cash Flow Stream: Formula

22 331NS-22 Multiple Uneven Cash Flows – PV Year 1 CF: 1 N; 12 I/Y; 200 FV; CPT PV = Year 2 CF: 2 N; 12 I/Y; 400 FV; CPT PV = Year 3 CF: 3 N; 12 I/Y; 600 FV; CPT PV = Year 4 CF: 4 N; 12 I/Y; 800 FV; CPT PV = Total PV = -$1,432.93

23 331NS-23  Clear all: Press CF Then 2 nd And CLR WORK (above CE/C)  CF 0 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 Multiple Uneven Cash Flows – Using the TI BAII’s Cash Flow Worksheet

24 331NS-24 TI BAII+: Uneven CFs  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.

25 331NS-25 TI BAII+: Uneven CFs  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”

26 331NS-26 TI BAII+: Uneven Cash Flows CF C000 ENTER  C01200 ENTER  F011 ENTER  C02400 ENTER  F021 ENTER  C03600 ENTER  F031 ENTER  C04800 ENTER  F041 ENTER  NPV I12 ENTER  NPV CPT Cash Flows: CF0= 0 CF1=200 CF2=400 CF3=600 CF4=800

27 331NS-27 Excel – PV of multiple uneven CFs

28 331NS-28 CHAPTER 3 Financial Statements, Cash Flow, and Taxes  Key Financial Statements Balance sheet Income statements Statement of cash flows

29 331NS-29 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

30 331NS-30 Sample Balance Sheet Assets = Liabilities + Owner’s Equity

31 331NS-31 Sample Income Statement Net income=Dividends + Retained earnings

32 331NS-32 Allied Food Products

33 331NS-33 Allied 2005 Per-Share Ratios RatioFormula & Calculation Earnings per Share (EPS) Dividends per Share (DPS) Book Value per Share (BVPS) Cash flow per Share (CFPS)

34 331NS-34 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

35 331NS-35 Statement of Cash Flows Reconciles the change in Cash & Equivalents

36 331NS-36

37 331NS-37 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???

38 331NS-38 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”

39 331NS-39 Deficits Covered by new debt and cash

40 331NS-40 Net Operating Working Capital

41 331NS-41 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

42 331NS-42 Net Operating Profit after Taxes (NOPAT) & Operating Cash Flow NOPAT = EBIT(1 - Tax rate) NOPAT 05 = $283.8( ) = $170.3 m OCF 05 = NOPAT + Deprec + Amort = $ $100 = $270.3

43 331NS-43 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

44 331NS-44 CHAPTER 4 Analysis of Financial Statements  Ratio Analysis  Limitations of ratio analysis  Qualitative factors

45 331NS-45 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)

46 331NS-46 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

47 331NS-47 Liquidity Ratios CR = Current Ratio = CA/CL QR = Quick Ratio or “Acid-Test” = (CA-INV)/CL

48 331NS-48 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

49 331NS-49 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)

50 331NS-50 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

51 331NS-51 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

52 331NS-52 The 5 Major Categories of Ratios and What Questions They Answer Ratio CategoryQuestions Answered LiquidityCan we make required payments? Asset ManagementRight amount of assets vs. sales? Debt ManagementRight mix of debt and equity? ProfitabilityDo sales prices exceed unit costs Are sales high enough as reflected in PM, ROE, and ROA? Market ValueDo investors like what they see as reflected in P/E and M/B ratios

53 331NS-53 Potential Problems and Limitations of Ratio Analysis  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

54 331NS-54 Problems and Limitations (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

55 331NS-55 Qualitative Factors  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?

56 331NS-56 CHAPTER 16 Financial Planning and Forecasting  Forecasting sales  Projecting the assets and internally generated funds  Projecting outside funds needed  Deciding how to raise funds

57 331NS-57 The AFN Formula If ratios are expected to remain constant: AFN = (A*/S 0 )∆S - (L*/S 0 )∆S - M(S 1 )(RR) Required  Assets Spontaneously  Liabilities  Retained Earnings

58 331NS-58 Variables in the AFN Formula  A* = Assets tied directly to sales  S 0 = Last year’s sales  S 1 = Next year’s projected sales  ∆S = Increase in sales; (S 1 -S 0 )  L* = Liabilities that spontaneously increase with sales

59 331NS-59 Variables in the AFN Formula  A*/S 0 : assets required to support sales; “Capital Intensity Ratio”  L*/S 0 : spontaneous liabilities ratio  M: profit margin (Net income/sales)  RR: retention ratio; percent of net income not paid as dividend

60 331NS-60 Key Factors in AFN  ∆S=Sales Growth  A*/S 0 =Capital Intensity Ratio  L*/S 0 =Spontaneous Liability Ratio  M=Profit Margin  RR=Retention Ratio

61 331NS-61 CHAPTER 6 Interest Rates

62 331NS-62 “Nominal” vs. “Real” rates r= Any nominal rate r*= The “real” risk-free rate ≈ T-bill rate with no inflation Typically ranges from 1% to 4% per year r RF = Rate on Treasury securities Proxied by T-bill or T-bond rate

63 331NS-63 r = r* + IP + DRP + LP + MRP Here: 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 RF =

64 331NS-64 Premiums Added to r* for Different Types of Debt  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

65 331NS-65 CHAPTER 7 Bonds and Their Valuation  Bond valuation  Measuring yield

66 331NS-66 Discount Rate = YTM  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

67 331NS-67 Bond Value  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

68 331NS-68 The Bond-Pricing Equation PV(Annuity) PV(lump sum) C = Coupon payment; F = Face value

69 331NS-69 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 N I/Y PV PMT FV

70 331NS-70 Spreadsheet Functions 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)

71 331NS-71 Pricing Specific Bonds  TI BA II+ Bond Worksheet [2 nd ] 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

72 331NS-72 Yield to Maturity (YTM)  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

73 331NS-73 What is the YTM on a 10-year, 9% annual coupon, $1,000 par value bond, selling for $887?  Must find the r d that solves this model:

74 331NS-74 Using a financial calculator to solve for the YTM  YTM =10.91%  Bond sells at a discount because YTM > coupon rate INPUTS OUTPUT NI/YRPMTPVFV

75 331NS-75  Coupon rate = 9%  Annual coupons  Par = $1,000  Maturity = 10 years  Price = $887 Using the calculator: N = 10 PV = -887 PMT = 90 FV = 1000 CPT I/Y = Solving for YTM =RATE(10,90,-887,1000) YTM on a 10-year, 9% annual coupon, $1,000 par value bond selling for $887

76 331NS-76 Find YTM, if the bond price is $1,  YTM = 7.08%  Bond sells at a premium because YTM < coupon rate INPUTS OUTPUT NI/YRPMTPVFV

77 331NS-77  Coupon rate = 9%  Annual coupons  Par = $1,000  Maturity = 10 years  Price = $1, Using the calculator: N = 10 PV = PMT = 90 FV = 1000 CPT I/Y = 7.08 Solving for YTM =RATE(10,90, ,1000) YTM on a 10-year, 9% annual coupon, $1,000 par value bond selling for $1,134.20

78 331NS-78 Semiannual bonds 1. Multiply years by 2 : number of periods = 2N. 2. Divide nominal rate by 2 : periodic rate (I/YR) = r d / Divide annual coupon by 2 : PMT = ann cpn / 2. INPUTS OUTPUT NI/YRPMTPVFV 2Nr d / 2cpn / 2OK

79 331NS-79 What is the value of a 10-year, 10% semiannual coupon bond, if r d = 13%? 1. Multiply years by 2 : N = 2 * 10 = Divide nominal rate by 2 : I/YR = 13 / 2 = Divide annual coupon by 2 : PMT = 100 / 2 = 50 INPUTS OUTPUT NI/YRPMTPVFV

80 331NS-80 Valuing a Semiannual Bond  Coupon rate = 10%  Annual coupons  Par = $1,000  Maturity = 10 years  YTM = 13% Using the formula: Using the calculator: N = 20 I/Y = 6.5 PMT = 50 FV = 1000 CPT PV = =PV(0.065, 10, 50, 1000)

81 331NS-81 YTM with Semiannual Coupons  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 $ Is the YTM more or less than 10%? What is the semiannual coupon payment? How many periods are there?

82 331NS-82 YTM with Semiannual Coupons  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 $ N = 40 PV = 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.

83 331NS-83 CHAPTER 8 Risk and Rates of Return  Stand-alone Risk  Portfolio Risk  Risk & Return: CAPM / SML

84 331NS-84 The Expected Rate of Return r “hat” = expected return r i = expected return in “i th ” state of the economy P i = Probability of “i th ” state occurring

85 331NS-85 Calculating the Expected Return

86 331NS-86 The Standard Deviation of Returns σ = Standard deviation σ = √ Variance = √ σ 2

87 331NS-87 Standard deviation for each investment

88 331NS-88 Standard Deviation of HT’s Returns

89 331NS-89 Risk versus Return: Do we know enough now? SecurityExpected return, r Risk, σ T-bills5.5%0.0% HT12.4%20.0% Coll1.0%13.2% USR 9.8%18.8% Market10.5%15.2% ^

90 331NS-90 Coefficient of Variation (CV)  CV = Standard deviation/expected return = Risk per unit of return =

91 331NS-91 r p = weighted average w i = % of portfolio in stock i r i = return on stock i ^ Portfolio Expected Return

92 331NS-92 Portfolio Expected Return Assume a two-stock portfolio is created with $50,000 invested in both HT and Collections r p = 0.5(12.4%) + 0.5(1.0%) = 6.7% ^

93 331NS-93 Portfolio Return “Portfolio” = (50% x HT) + (50% x Coll) “Portfolio Return” = Prob x “Portfolio”

94 331NS-94 Portfolio Risk  Portfolio Standard deviation is NOT a weighted average of the standard deviations of the component assets

95 331NS-95 Calculating portfolio standard deviation and CV

96 331NS-96 Portfolio Standard Deviation

97 331NS-97 Portfolio Risk & Return σ p = 3.4% is much lower than the σ of either stock σ p = 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 

98 331NS-98 Covariance of Returns  Measures how much the returns on two risky assets move together

99 331NS-99 Covariance vs. Variance of Returns

100 331NS-100 Covariance Covariance (HT:Coll) =

101 331NS-101 Correlation Coefficient  Correlation Coefficient = ρ (rho)  Scales covariance to [-1,+1] -1 = Perfectly negatively correlated 0 = Uncorrelated; not related +1 = Perfectly positively correlated

102 331NS-102 Two-Stock Portfolios  If  = -1.0 Two stocks can be combined to form a riskless portfolio  If  = +1.0 No risk reduction at all  In general, stocks have  ≈ 0.35 Risk is lowered but not eliminated  Investors typically hold many stocks

103 331NS-103  of n-Stock Portfolio  Subscripts denote stocks i and j  i,j = Correlation between stocks i and j  σ i and σ j =Standard deviations of stocks i and j  σ ij = Covariance of stocks i and j

104 331NS-104 Portfolio Risk-n Risky Assets i jfor n=2 11w 1 w 1  11 = w 1 2  w 1 w 2  12 21w 2 w 1  21 22w 2 w 2  22 = w 2 2  2 2  p 2 = w 1 2  w 2 2  w 1 w 2  12

105 331NS-105 Portfolio Risk-2 Risky Assets

106 331NS-106 Capital Asset Pricing Model (CAPM)  Links risk and required returns  Security Market Line (SML): A stock’s required return equals the risk- free return (r RF ) plus a risk premium (RP M 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.

107 331NS-107 The SML and Required Return  The Security Market Line (SML) is part of the Capital Asset Pricing Model (CAPM)  r RF = Risk-free rate  RP M = Market risk premium = r M – r RF

108 331NS-108 The Market Risk Premium (r M – r RF = RP M )  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

109 331NS-109 Required Rates of Return Assume:r RF = 5.5%RP M = 5%  r HT = 5.5% + (5.0%)(1.32) = 5.5% + 6.6%= 12.10%  r M = 5.5% + (5.0%)(1.00)= 10.50%  r USR = 5.5% + (5.0%)(0.88)= 9.90%  r T-bill = 5.5% + (5.0%)(0.00)= 5.50%  r Coll = 5.5% + (5.0%)(-0.87)= 1.15%

110 331NS-110 Expected vs Required Returns ExpectedRequired Return HT Undervalued Market Fairly valued USR Overvalued T-bills 5.50 Fairly valued Coll Overvalued “Required” by the market “Expected” by YOU

111 331NS-111 Illustrating the Security Market Line.. Coll.. HT T-bills. USR SML r M = 10.5 r RF = SML: r i = 5.5% + (5.0%)  i r i (%) Risk,  i

112 331NS-112 Portfolio Beta Where: w i = weight (% dollars invested in asset i) β i = Beta of asset i β p = Portfolio Beta

113 331NS-113 CHAPTER 9 Stocks and Their Valuation

114 331NS-114 Constant growth stock  Dividends expected to grow forever at a constant rate, g: D 1 = D 0 (1+g) 1 D 2 = D 0 (1+g) 2 D t = D 0 (1+g) t  Dividend growth formula converges to:

115 331NS-115 Constant Growth Model Needed data: D 0 = Dividend just paid D 1 = Next expected dividend g = constant growth rate r s = required return on the stock

116 331NS-116 Expected Value at time t Value at t=0 Value at t

117 331NS-117 Supernormal Growth  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

118 331NS-118 Valuing common stock with nonconstant growth r s = 13% g = 30% g = 6%  P  0.06 $   = P 0 ^ D 0 =

119 331NS-119 Corporate Value Model  = 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

120 331NS-120 Applying the corporate value model  Market value of firm: (MV F ) = PV(future FCFs)  MV of common stock: = MV F – MV of debt  Intrinsic stock value: = MV CS /# shares

121 331NS-121 Issues regarding the corporate value model  Often preferred 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 (TV N ) = value of firm at the point that growth becomes constant

122 331NS-122 Firm’s Intrinsic Value g = 6% r = 10% = = TV Long-run g FCF = 6%WACC = 10%

123 331NS-123 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 = $ $40 = $ million  Value per share= MV of equity / # of shares = $ / 10 = $37.69

124 331NS-124 Firm multiples method  Often used by analysts to value stocks P / EPrice-earning P / CFPrice-cash flow P / SalesPrice-sales  Method: Estimate appropriate ratio based on comparable firms Multiply estimate by expected metric to estimate stock price

125 331NS-125 CHAPTER 10 The Cost of Capital  Cost of equity  WACC  Adjusting for risk

126 331NS-126 WACC Weighted Average Cost of Capital Where: w D = % of debt in capital structure w P = % of preferred stock in capital structure w C = % of common equity in capital structure r D = firm’s cost of debt r P = firm’s cost of preferred stock r C = firm’s cost of equity T = firm’s corporate tax rate Weights Component costs WACC = w d r d (1-T) + w p r p + w c r s

127 331NS-127 Three ways to determine the cost of equity, r s : 1.DCF: r s = D 1 /P 0 + g 2.CAPM: r s = r RF + (r M - r RF )β i = r RF + (RP M )β i 3.Own-Bond-Yield-Plus-Risk Premium: r s = r d + Bond RP

128 331NS-128 DCF Approach: Inputs 1.Current stock price (P 0 ) 2.Current dividend (D 0 ) 3.Growth rate (g)

129 331NS-129 Four Mistakes to Avoid  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

130 331NS-130  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 Should the company use the composite WACC as the hurdle rate for each of its projects?

131 331NS-131 Divisional and Project Costs of Capital  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 separate discount rates

132 331NS-132 Using WACC for All Projects - Example  What would happen if we use the WACC for all projects regardless of risk?  Assume the WACC = 15%

133 331NS-133 Divisional Risk and the Cost of Capital Rate of Return (%) WACC Rejection Region Acceptance Region Risk WACC H L F 0 Risk L H Acceptance Region Rejection Region

134 331NS-134 Subjective Approach  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

135 331NS-135 Subjective Approach - Example Risk LevelDiscount Rate Very Low RiskWACC – 8% 7% Low RiskWACC – 3% 12% Same Risk as FirmWACC 15% High RiskWACC + 5% 20% Very High RiskWACC + 10% 25%

136 331NS-136 CHAPTER 11 The Basics of Capital Budgeting Should we build this plant?

137 331NS-137 Steps to capital budgeting 1. Estimate CFs (inflows & outflows) 2. Assess riskiness of CFs 3. Determine appropriate cost of capital 4. Find NPV and/or IRR 5. Accept if NPV>0 and/or IRR>WACC

138 331NS-138 Independent versus Mutually Exclusive 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

139 331NS-139 NPV: Sum of the PVs of all cash flows. Cost often is CF 0 and is negative NPV = ∑ n t = 0 CF t (1 + r) t. NPV = ∑ n t = 1 CF t (1 + r) t - CF 0 NOTE: t=0

140 331NS-140 TI BAII+: Uneven Cash Flows CF C /- 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

141 331NS-141 Internal Rate of Return (IRR)  IRR = the discount rate that forces PV of inflows equal to cost, and the NPV = 0:  Solving for IRR with a financial calculator: Enter CFs in CFLO register Press IRR:

142 331NS-142 NPV vs IRR IRR: Enter NPV = 0, solve for IRR = NPV ∑ n t = 0 CF t (1 + r) t = 0 ∑ n t = 0 CF t (1 + IRR) t NPV: Enter r, solve for NPV

143 331NS-143 Modified Internal Rate of Return (MIRR)  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

144 331NS-144 Normal vs. Non-normal Cash Flows  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, nuclear power plant or strip mine

145 331NS-145 Multiple IRRs  Descartes Rule of Signs  Polynomial of degree n → n roots 1 real root per sign change Rest = imaginary (i 2 = -1)

146 331NS ,0005,000,000-5,000,000 PV 10% = -4,932, TV 10% = 5,500, MIRR = 5.6% The Pavillion Project: Non-normal CFs and MIRR

147 331NS-147 MIRR versus IRR  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

148 331NS-148 When to use the MIRR instead of the IRR? Accept Project P?  When there are nonnormal CFs and more than one IRR, use MIRR. PV of 10% = -$4, TV of 10% = $5,500. MIRR = 5.6%.  Do not accept Project P. NPV = -$ < 0. MIRR = 5.6% < WACC = 10%.

149 331NS-149 Excel Functions

150 331NS-150 CHAPTER 12 Cash Flow Estimation and Risk Analysis

151 331NS-151 Relevant Cash Flows: 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

152 331NS-152 Relevant Cash Flows  Changes in Net Working Capital……Y  Interest/Dividends …………..…………..N  “Sunk” Costs ………………………… ……….. N  Opportunity Costs ………………………….Y  Externalities/Cannibalism ……………..Y  Tax Effects ………………………..…………..Y

153 331NS-153 Tax Effect on Salvage Net Salvage Cash Flow = SP - (SP-BV)(T) Where: SP = Selling Price BV = Book Value T = Corporate tax rate

154 331NS-154 Including inflation when estimating cash flows  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

155 331NS-155 INFLATION Real vs. Nominal Cash flows Nominal Real

156 331NS-156 INFLATION Real vs. Nominal Cash flows  2 Ways to adjust Adjust WACC  Cash Flows = Real  Adjust WACC to remove inflation Adjust Cash Flows for Inflation  Use Nominal WACC

157 331NS-157 Sensitivity Analysis  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

158 331NS-158 Sensitivity Analysis

159 331NS-159

160 331NS-160 Sensitivity Analysis

161 331NS-161 Sensitivity Graph Unit Sales Variable Cost Fixed Cost

162 331NS-162 Sensitivity Ratio  %NPV = (New NPV - Base NPV)/Base NPV  %VAR = (New VAR - Base VAR)/Base VAR If SR>0  Direct relationship If SR<0  Inverse relationship

163 331NS-163 Sensitivity Ratio -30%$ -62$54$ %NPV (-62-20)/20 (54-20)/20 (266-20)/ % 1.7% 12.3% %VAR -30% -30% -30% SR Change from Resulting NPV (000s) Base LevelUnit Sales FC VC

164 331NS-164 Sensitivity Graph Unit Sales Variable Cost Fixed Cost -5.72

165 331NS-165 Results of Sensitivity Analysis  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.

166 331NS-166 Sensitivity Analysis: 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

167 331NS-167 Sensitivity Analysis: Strengths  Provides indication of stand-alone risk  Identifies dangerous variables  Gives some breakeven information

168 331NS-168 Scenario Analysis  Examines several possible situations, usually: Worst case Base case or most likely case, and Best case  Provides a range of possible outcomes

169 331NS-169 Scenario Example

170 331NS-170

171 331NS-171 Problems with Scenario Analysis  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

172 331NS-172 Monte Carlo Simulation Analysis  Computerized version of scenario analysis using continuous probability distributions  Computer selects values for each variable based on given probability distributions

173 331NS-173 Monte Carlo Simulation Analysis  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

174 331NS-174 Histogram of Results

175 331NS-175 Advantages of Simulation Analysis  Reflects the probability distributions of each input  Shows range of NPVs, the expected NPV, σ NPV, and CV NPV  Gives an intuitive graph of the risk situation

176 331NS-176 Disadvantages of Simulation Analysis  Difficult to specify probability distributions and correlations  If inputs are bad, output will be bad: “Garbage in, garbage out”

177 331NS-177 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

178 331NS-178 Real Options  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

179 331NS-179 Types of Real Options  Investment timing options  Growth options Expansion of existing product line New products New geographic markets  Abandonment options Contraction Temporary suspension  Flexibility options

180 331NS-180 FIN 331 in a Nutshell Financial Management I Review for FIN 338


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