FIN 331 in a Nutshell Financial Management I Review 331NS-1 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 Index 331NS-2 Financial Statements, Cash
Flow, and Taxes Key Financial Statements Index Balance sheet Income statements Statement of cash flows 331NS-3 The Annual Report Balance sheet Income statement
Snapshot of a firms financial position at a point in time Summarizes a firms revenues and expenses over a given period of time Statement of cash flows Index Reports the impact of a firms activities on cash flows over a given period of time 331NS-4 Sample Balance Sheet Allied Food Products Balance Sheets Assets = Liabilities + Owners Equity Index ASSETS Cash & Equivalents Accounts receivable Inventories Total current assets
Net plant & equipment TOTAL ASSETS 2005 $ 10 $ 375 $ 615 $ 1,000 $ 1,000 $ 2,000 2004 $ 80 $ 315 $ 415 $ 810 $ 870 $ 1,680 LIABILITIES & EQUITY Accounts payable
Notes payable Accruals Total current liabilities Long-term bonds Total liabilities Common stock (50,000,000 shares) Retained earnings Total common equity Total Liabilities & Equity 2008 $ 60 $ 110 $ 140 $ 310 $ 750 $ 1,060 $ 130 $ 810 $ 940 $ 2,000
2007 $ 30 $ 60 $ 130 $ 220 $ 580 $ 800 $ 130 $ 750 $ 880 $ 1,680 331NS-5 Sample Income Statement Allied Food Products INCOME STATEMENTS 2005 Net sales
$ 3,000.0 Operating costs $ 2,616.2 Gross profit (EBITDA) $ 383.8 Depreciation $ 100.0 Operating Income (EBIT) $ 283.8 Interest expense $ 88.0 Pretax income (EBT) $ 195.8 Taxes (40%) $ 78.3 NET INCOME $ 117.5 Common dividends Addtion to retained earnings
Index $ $ 57.5 60.0 $ $ $ $ $ $ $ $ $ 2004 2,850.0 2,497.0 353.0 90.0 263.0 60.0 203.0 81.2 121.8
$ $ 53.0 56.0 Net income=Dividends + Retained earnings 331NS-6 Allied Food Products Allied Food Products Per Share Data Common stock price Earnings per share Dividends per share Book value per share Cash Flow per share Index $23.00 $2.35 $1.15 $18.80 $4.35 $26.00 $2.44
$1.06 $17.60 $4.24 331NS-7 Allied 2005 Per-Share Ratios Ratio Earnings per Share (EPS) Dividends per Share (DPS) Book Value per Share (BVPS) Cash flow per Share (CFPS) Index Formula & Calculation Net Income $117 .5 $2.35 Shares Outstanding 50 Common dividends $57.5 $1.15 Shares Outstanding
50 Shareholde r Equity $940.00 $18.80 Shares Outstanding 50 Operating Cash Flow $217.5 $4.35 Shares Outstanding 50 331NS-8 Statement of Cash Flows Index Provides information about cash inflows and outflows during an accounting period Required since 1988 Developed from Balance Sheet and Income Statement data 331NS-9
Statement of Cash Flows Allied Food Products Balance Sheets ASSETS 2005 Cash & Equivalents $ 10 Accounts receivable $ 375 Inventories $ 615 Total current assets $ 1,000 Net plant & equipment $ 1,000 TOTAL ASSETS $ 2,000 2004 $ 80 $ 315 $ 415
$ 810 $ 870 $ 1,680 Reconciles the change in Cash & Equivalents Index 331NS-10 Allied Food Products: Statement of Cash Flows 2005 I Operating Activities Net Income before dividends Adjustments Additions Increase in accounts payable Increase in accruals Depreciation Subtractions Increase in accounts receivable Increase in inventories Net cash provided by operating activities II Long-term Investing activities Cash used to acquire fixed assets
III Financing Activities Increase in notes payable Increase in bonds Payment of dividends Net cash provided by financing activities Net change in cash & equivalents Cash & equivalents at beginning of year IV Cash & equivalents at end of year Index $117.5 $30.0 $10.0 $100.0 ($60.0) ($200.0) ($2.5) ($230.0) $50.0 $170.0 ($57.5) $162.5 ($70.0) $80.0 $10.0
331NS-11 Statement of Cash Flows Why is it important??? Reconciles the Income Statement and Balance Sheet to the flow of cash Index The Matching Principle requires estimates and accruals to prepare Financial statements Financial Analysis is concerned with Cash Flow 331NS-12 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 Index 331NS-13 Allied Food Products: Statement of Cash Flows 2005 I Operating Activities Net Income before dividends Adjustments Additions Increase in accounts payable Increase in accruals Depreciation Subtractions Increase in accounts receivable Increase in inventories Net cash provided by operating activities II Long-term Investing activities Cash used to acquire fixed assets III Financing Activities Increase in notes payable Increase in bonds Payment of dividends
Net cash provided by financing activities Net change in cash & equivalents Cash & equivalents at beginning of year IV Cash & equivalents at end of year Index $117.5 $30.0 $10.0 $100.0 ($60.0) ($200.0) ($2.5) Deficits ($230.0) $50.0 $170.0 ($57.5) $162.5 ($70.0) $80.0 Covered by new debt and
cash $10.0 331NS-14 Net Operating Working Capital ASSETS Cash & Equivalents Accounts receivable Inventories Total current assets Current Operating Assets 2005 $ 10 $ 375 $ 615 $ 1,000 $ 1,000 Allied Food Products Balance Sheets 2004 LIABILITIES & EQUITY $ 80
Accounts payable $ 315 Notes payable $ 415 Accruals $ 810 Total current liabilities $ 810 Current Operating Liabilities $ $ $ $ $ 2008 60 110 140 310 200 $ $
$ $ $ 2007 30 60 130 220 160 Net Operating Working Capital = Current Operating Assets - Current Operating Liabilities Net Operating Working Capital (2005) $ 800 Net Operating Working Capital (2004) $ 650 r Net Operating Working Capital $ 150 If the Asset side had included Short-term investments they would have been excluded as well. Index 331NS-15 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 Index 331NS-16 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 Index 331NS-17 Free Cash Flow (FCF) for 2005 FCF EBIT(1 T) Deprec & Amort Capital Expenditures NOWCNOWC OCF - Investment in Operating Capital EBIT = $283.8 m T = 40% Depreciation = $100 m Capital Expenditures = rFA + Deprec = $130+$100 = $230 rNOWC = $800 - $650 = $150 m FCF Index = [$283.8(1-.4)+$100] [$230-$150] = -$109.7 m 331NS-18 Analysis of Financial Statements
Index Ratio Analysis Limitations of ratio analysis Qualitative factors 331NS-19 Five Major Categories of Ratios Liquidity Asset management
Inventory Turnover DSO Days sales outstanding FAT - Fixed Assets Turnover TAT - Total Assets Turnover Debt management Index CR - Current Ratio QR - Quick Ratio or Acid-Test Debt Ratio TIE Times interest earned EBITDA coverage (EC) 331NS-20 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 Index P/E Price-Earnings ratio P/CF Price cash flow ratio M/B Market to book 331NS-21 Liquidity Ratios CR = Current Ratio = CA/CL
QR = Quick Ratio or Acid-Test = (CA-INV)/CL Index 331NS-22 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 Index 331NS-23 Debt Management Ratios Debt Ratio = Total Liabilities/Total Assets TIE EBITDA coverage = EC = Times interest earned = EBIT/Interest (EBITDA + lease pmts) . (Interest + principal pmts + lease pmts)
Index 331NS-24 Profitability Ratios Index PM = = BEP = = ROA = = ROE = = Profit margin on sales NI/Sales Basic earning power
EBIT/Total Assets Return on total assets NI/Total Assets Return on common equity NI/Common Equity 331NS-25 Market Value Metrics P/E = Price-Earnings ratio = Price per share/Earnings per share P/CF = Pricecash flow ratio = Price per share/Cash flow per share M/B = Market to book = Market price per share Book value per share Index 331NS-26
The 5 Major Categories of Ratios and What Questions They Answer Ratio Category Liquidity Questions Answered Can we make required payments? Asset Management Right amount of assets vs. sales? Debt Management Right mix of debt and equity? Profitability Market Value Index Do sales prices exceed unit costs Are sales high enough as reflected in PM, ROE, and ROA? Do investors like what they see as reflected in P/E and M/B ratios 331NS-27 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 Index 331NS-28 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
Index Difficult to tell, on balance, whether a company is in a strong or weak financial condition 331NS-29 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? Index 331NS-30
Financial Planning and Forecasting Index Forecasting sales Projecting the assets and internally generated funds Projecting outside funds needed Deciding how to raise funds 331NS-31 The AFN Formula If ratios are expected to remain constant: AFN = (A*/S0)S - (L*/S0)S - M(S1)(RR) Required Assets Spontaneously Liabilities Index Retained
Earnings 331NS-32 Variables in the AFN Formula A* = Assets tied directly to sales S0 = Last years sales S1 = Next years projected sales S = Increase in sales; (S1-S0) L* = Liabilities that spontaneously increase with sales Index 331NS-33 Variables in the AFN Formula
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 Index 331NS-34 Key Factors in AFN S A*/S0 = =
Sales Growth Capital Intensity Ratio L*/S0 = Spontaneous Liability Ratio M RR = = Profit Margin Retention Ratio Index
331NS-35 Time Value of Money Timelines Future Value Present Value Present Value of Uneven Cash Flows Index 331NS-36 Time Lines: Timing of Cash Flows 0 1 2 3 CF1 CF2
CF3 I% CF0 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 OUTFLOW Index PMT = Constant CF 331NS-37 Basic Definitions Present Value The current value of future cash flows
discounted at the appropriate discount rate Value at t=0 on a time line Future Value Index (PV) (FV) The amount an investment is worth after one or more periods. Later money on a time line 331NS-38 Future Value: General Formula FV = PV(1 + I)N
Index 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 331NS-39 Texas Instruments BA-II Plus One of these MUST FV = future value be negative PV = present value PMT = periodic payment I/Y = period interest rate N = number of periods N Index I/Y PV PMT
FV 331NS-40 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 (x) when you cant remember the exact formula Index 331NS-41 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 Index 331NS-42 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 = 161.05 Index 331NS-43
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 Index 331NS-44 Future Value Important 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 Index 331NS-45
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: Index 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? 331NS-46
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 Index 331NS-47 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?
Index 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) 331NS-48 Present Value: Important Relationship 1 For a given interest rate: The longer the time period, The lower the present value FV PV N ( 1 I )
For a given I, as N increases, PV decreases Index 331NS-49 Present Value Important Relationship 2 For a given time period: The higher the interest rate, The smaller the present value FV PV N ( 1 I ) For a given N, as I increases, PV decreases Index 331NS-50 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 Index 331NS-51 Multiple Cash Flows Present Value The Basic Formula The TI BA II+ Index Using the PV/FV keys Using the Cash Flow Worksheet Excel
331NS-52 Multiple Uneven Cash Flows Present Value You are offered an investment that will pay Index $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? 331NS-53 What is the PV of this uneven cash flow stream? 0
1 2 3 4 200 400 600 800 12% -178.57 -318.88 -427.07 -508.41 -1,432.93 = PV Index 331NS-54 Present Value of an Uneven
Cash Flow Stream: Formula N 1 PV CFt 1 I t 1 N PV CFt 1 I t t t 1 Index 331NS-55 Multiple Uneven Cash Flows PV Year Year Year Year Index
1 2 3 4 CF: CF: CF: CF: 1 2 3 4 N; N; N; N; 12 12 12 12 I/Y; I/Y; I/Y;
I/Y; 200 400 600 800 FV; CPT PV FV; CPT PV FV; CPT PV FV; CPT PV Total PV = = = = = -178.57 -318.88 -427.07 -508.41 -$1,432.93 331NS-56 Multiple Uneven Cash Flows Using the TI BAIIs 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 Index 331NS-57 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. Index 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. 331NS-58 TI BAII+: Uneven CFs Repeat for all cash flows, in order. To find NPV: Press NPV: I appears on the screen
Index Enter the interest rate, press ENTER and the down arrow to display NPV. Press compute CPT 331NS-59 TI BAII+: Uneven Cash Flows Cash Flows: Index CF0 = 0 CF1 = 200 CF2 =
400 CF3 = 600 CF4 = 800 C00 C01 F01 C02 F02 C03 F03 C04 F04 I NPV CF 0 ENTER 200 ENTER
1 ENTER 400 ENTER 1 ENTER 600 ENTER 1 ENTER 800 ENTER 1 ENTER NPV 12 ENTER CPT 1432.93 331NS-60 Excel PV of multiple uneven CFs Rate Period 1 2 3 4 12% Cash Flow $ $ $ $ 200.00 400.00
600.00 800.00 Total PV = Present Value ($178.57) ($318.88) ($427.07) ($508.41) =PV($B$3,A6,0,B6) =PV($B$3,A7,0,B7) =PV($B$3,A8,0,B8) =PV($B$3,A9,0,B9) ($1,432.93) ($1,432.93) =SUM(C6:C9) =-NPV(B3,B6:B9) Formula The functions require a PMT = 0. Index
331NS-61 Bonds and Their Valuation Index Interest rates Bond valuation Measuring yield 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 rRF
= Rate on Treasury securities Proxied by T-bill or T-bond rate Index 331NS-63 r = r* + IP + DRP + LP + MRP Here: r rRF Index r* = IP DRP LP MRP =Required rate of return on a debt security = Real risk-free rate = Inflation premium =
Default risk premium = Liquidity premium = Maturity risk premium 331NS-64 Premiums Added to r* for Different Types of Debt Debt Instrument IP DRP MRP LP ST Treasury ST IP LT Treasury LT IP ST Corporate ST IP DRP
LT Corporate LT IP DRP Index MRP LP MRP LP 331NS-65 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 Index 331NS-66 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 Index 331NS-67 The Bond-Pricing Equation 1 1 (1 YTM) t Bond Value C YTM
F t (1 YTM) PV(lump sum) PV(Annuity) C = Coupon payment; F = Face value Index 331NS-68 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 Index I/Y PV PMT FV 331NS-69 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) Index 331NS-70 Pricing Specific Bonds 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) Index Settlement and maturity need to be actual dates Redemption and Pr need to given as % of par value 331NS-71 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 Index 331NS-72 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: INT INT M VB ... 1 N N (1 rd ) (1 rd ) (1 rd ) 90 90 1,000 $887 ...
1 10 10 (1 rd ) (1 rd ) (1 rd ) Index 331NS-73 Using a financial calculator to solve for the YTM YTM =10.91% Bond sells at a discount because YTM > coupon rate INPUTS 10 N OUTPUT Index I/YR
- 887 90 1000 PV PMT FV 10.91 331NS-74 Solving for YTM YTM on a 10-year, 9% annual coupon, $1,000 par value bond selling for $887 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 = 10.91 =RATE(10,90,-887,1000) Index 331NS-75 Find YTM, if the bond price is $1,134.20 YTM = 7.08% Bond sells at a premium because YTM < coupon rate INPUTS 10 N OUTPUT Index I/YR -1134.2 90 1000 PV PMT FV 7.08 331NS-76 Solving for YTM YTM on a 10-year, 9% annual coupon, $1,000 par value bond selling for $1,134.20 Coupon rate = 9%
Annual coupons Par = $1,000 Maturity = 10 years Price = $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) Index 331NS-77 Semiannual bonds 2. Multiply years by 2: number of periods = 2N. Divide nominal rate by 2: periodic rate (I/YR) = r d / 2. 3. Divide annual coupon by 2: PMT = ann cpn / 2. 1.
INPUTS 2N rd / 2 OK cpn / 2 OK N I/YR PV PMT FV OUTPUT Index 331NS-78 What is the value of a 10-year, 10% semiannual coupon bond, if rd = 13%?
1. 2. 3. 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 INPUTS OUTPUT Index 20 6.5 N I/YR PV 50 1000 PMT FV
- 834.72 331NS-79 Valuing a Semiannual Bond Coupon rate = 10% Annual coupons Par = $1,000 Maturity = 10 years YTM = 13% Using the formula: 1 1 (1.065 )20 B 50 0.065
Using the calculator: N = 20 I/Y = 6.5 PMT = 50 FV = 1000 CPT PV = -834.72 1000 20 (1.065 ) =PV(0.065, 10, 50, 1000) Index 331NS-80 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 $1197.93.
Index Is the YTM more or less than 10%? What is the semiannual coupon payment? How many periods are there? 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 $1197.93. N = 40 PV = -1197.93 NOTE: Solving a semiPMT = 50 annual payer for YTM FV = 1000 will result in a 6-month CPT I/Y = 4% YTM answer YTM = 4%*2 = 8% Result = YTM Index
Calculator solves what you enter. 331NS-82 Risk and Rates of Return Index Stand-alone Risk Portfolio Risk Risk & Return: CAPM / SML 331NS-83 The Expected Rate of Return n r ri Pi i 1 r hat = expected return ri = expected return in ith state of the economy Pi = Probability of ith state occurring Index
331NS-84 Calculating the Expected Return ^ r expected rate of return ^ N r ri Pi i 1 Economy Recession Below Avg Average Above Avg Boom Prob 0.1 0.2 0.4 0.2 0.1 HT
-27% -7% 15% 30% 45% E(R ) Prob x HT -2.7% -1.4% 6.0% 6.0% 4.5% 12.4% ^ r HT (-27%) (0.1) (-7%) (0.2) (15%) (0.4) (30%) (0.2) (45%) (0.1) 12.4% Index 331NS-85 The Standard Deviation of Returns = Standard deviation = Variance = 2 n
( r r i ) Pi 2 i 1 Index 331NS-86 Standard deviation for each investment N ^ (ri r )2 Pi i 1
2 T bills (5.5 - 5.5) (0.1) (5.5 - 5.5) (0.2) 2 2 (5.5 - 5.5) (0.4) (5.5 - 5.5) (0.2) (5.5 - 5.5)2 (0.1) T bills 0.0% HT 20.0% Index 2 1 2 Coll 13.2% USR 18.8% M 15.2% 331NS-87
Standard Deviation of HTs Returns Economy Recession Below Avg Average Above Avg Boom Index Prob 0.1 0.2 0.4 0.2 0.1 E(R ) Deviation HT Deviation Squared -27% -39.4% 15.5% -7% -19.4% 3.8% 15%
2.6% 0.1% 30% 17.6% 3.1% 45% 32.6% 10.6% 12.4% Variance Std Dev x Prob 1.6% 0.8% 0.0% 0.6% 1.1% 4.0% 20.0% 331NS-88 Risk versus Return: Do we know enough now? Security Expected return, ^
r Risk, 5.5% 0.0% HT 12.4% 20.0% Coll 1.0% 13.2% USR 9.8% 18.8% 10.5% 15.2%
T-bills Market Index 331NS-89 Coefficient of Variation (CV) CV = Standard deviation/expected return = Risk per unit of return = / r Standarddeviation CV Expectedreturn r Index 331NS-90 Portfolio Expected Return ^ rp = weighted average wi = % of portfolio in stock i ri = return on stock i
n rp w i ri i 1 Index 331NS-91 Portfolio Expected Return Assume a two-stock portfolio is created with $50,000 invested in both HT and Collections n rp w i ri i 1 ^rp = 0.5(12.4%) + 0.5(1.0%) = 6.7% Index 331NS-92 Portfolio Return Portfolio Return Portfolio % Economy Prob Recession
0.1 Below Avg 0.2 Average 0.4 Above Avg 0.2 Boom 0.1 E(R ) 50% HT -27% -7% 15% 30% 45% 12.4% 50% Coll 27% 13% 0% -11% -21% 1.0%
Portfolio Portfolio Return 0.0% 0.0% 3.0% 0.6% 7.5% 3.0% 9.5% 1.9% 12.0% 1.2% 6.7% Portfolio = (50% x HT) + (50% x Coll) Portfolio Return = Prob x Portfolio Index 331NS-93 Portfolio Risk Portfolio Standard deviation is NOT a weighted average of the standard deviations of the component assets Index 331NS-94
Calculating portfolio standard deviation and CV 2 0.10 (0.0 - 6.7) 2 0.20 (3.0 - 6.7) p 0.40 (7.5 - 6.7) 2 0.20 (9.5 - 6.7) 2 2 0.10 (12.0 - 6.7) 1 2 3.4% 3.4% CVp 0.51 6.7% Index
331NS-95 Portfolio Standard Deviation Portfolio Standard Deviation Economy Recession Below Avg Average Above Avg Boom Index Prob 0.1 0.2 0.4 0.2 0.1 E(R ) Squared Portfolio Deviation 0.0% 0.00045 3.0% 0.00027 7.5% 0.00003
9.5% 0.00016 12.0% 0.00028 6.7% 0.00119 Variance = 3.4% 331NS-96 Portfolio Risk & Return E(R ) Std Dev CV HT 12.40% 20.00% 1.6 COLL 1.00% 13.20% 13.2 Portfolio 6.7% 3.4% 0.51
p = 3.4% is much lower than the of either stock = 3.4% is lower than the weighted average of p HT and Coll.s (16.6%) The portfolio provides the average return of component stocks, but lower than the average risk Index 331NS-97 Covariance of Returns Measures how much the returns on two risky assets move together Cov (a , b ) ab ab rai ra rbi rb Pi i
Index 331NS-98 Covariance vs. Variance of Returns Cov (a , b ) ab ab rai ra rbi rb Pi i Var (a ) aa 2 a a2 rai ra rai ra Pi
i Index 331NS-99 Covariance Cov (a , b ) ab ab ra ra rb rb Pi i Economy Recession Below Avg Average Above Avg Boom i Prob 0.1
0.2 0.4 0.2 0.1 E(R ) i HT -27% -7% 15% 30% 45% 12.4% Coll 27% 13% 0% -11% -21% 1.0% HT Dev -39.4% -19.4% 2.6% 17.6%
32.6% Coll Dev HT x Coll 26.0% -10.244% 12.0% -2.328% -1.0% -0.026% -12.0% -2.112% -22.0% -7.172% COV(HT,Coll) = x Prob -0.0102 -0.0047 -0.0001 -0.0042 -0.0072 -0.0264 Covariance (HT:Coll) = -0.0264 Index 331NS-100 Correlation Coefficient
Correlation Coefficient = (rho) Scales covariance to [-1,+1] -1 = Perfectly negatively correlated 0 = Uncorrelated; not related +1 = Perfectly positively correlated ab ab a b Index 331NS-101 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 Index 331NS-102 of n-Stock Portfolio 2 p n n w i w j i j ij i 1 j 1 n ab ab a b n 2p w i w j ij i 1 j 1
Index Subscripts denote stocks i and j i,j = Correlation between stocks i and j i and j =Standard deviations of stocks i and j ij = Covariance of stocks i and j 331NS-103 Portfolio Risk-n Risky Assets 2 p n n w i w j ij i 1 j 1 i j 1 1 2 2
for n=2 1 w1w111 = w1212 2 w1w212 1 w2w121 2 w2w222 = w2222 p2 = w1212 + w2222 + 2w1w2 12 Index 331NS-104 Portfolio Risk-2 Risky Assets 2 p n n w i w j i j ij i 1 j 1 HT Coll
i 1 1 2 2 Index j 1 2 1 2 W 50% 50% Std Dev Variance 20.00% 0.0400 13.20% 0.0174 Cov -0.0264
-1.00 for n=2 0.0100 (0.0066) (0.0066) 0.0044 0.00116 Variance 3.40% Std Dev 331NS-105 Capital Asset Pricing Model (CAPM) Links risk and required returns Security Market Line (SML): A stocks required return equals the riskfree return (rRF) plus a risk premium (RPM x ) that reflects the stocks risk after diversification Primary conclusion:
Index The relevant riskiness of a stock is its contribution to the riskiness of a welldiversified portfolio. 331NS-106 The SML and Required Return The Security Market Line (SML) is part of the Capital Asset Pricing Model (CAPM) ri rRF rM rRF i ri rRF RPM i Index rRF = Risk-free rate RPM = Market risk premium = rM rRF 331NS-107 The Market Risk Premium
(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 Index Estimates suggest a range between 4% and 8% per year 331NS-108 Required Rates of Return Assume:
rRF = 5.5% RPM = 5% rHT = 5.5% + (5.0%)(1.32) rM = 5.5% + 6.6% = 5.5% + (5.0%)(1.00) = 12.10% = 10.50% rUSR = 5.5% + (5.0%)(0.88) = 9.90% rT-bill = 5.5% + (5.0%)(0.00)
= 5.50% rColl Index = 5.5% + (5.0%)(-0.87) = 1.15% 331NS-109 Expected vs Required Returns Expected by YOU Index Required by the market Expected Required Return
Return HT 12.40 12.10 Undervalued Market 10.50 10.50 Fairly valued USR 9.80 9.90 Overvalued T-bills 5.50
5.50 Fairly valued Coll 1.00 1.15 Overvalued 331NS-110 Illustrating the Security Market Line SML: ri = 5.5% + (5.0%) i ri (%) SML . .. HT rM = 10.5 rRF = 5.5 -1 Index
. Coll. . T-bills 0 USR 1 2 Risk, i 331NS-111 Portfolio Beta n p w i i i 1 Where: wi = weight (% dollars invested in asset i) i = Beta of asset i p = Portfolio Beta
Index 331NS-112 Stocks and Their Valuation Index Constant growth stock valuation Non-constant growth stock valuation Corporate value model 331NS-113 Constant growth stock 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: D0 (1 g) D1
P0 rs - g rs - g ^ Index 331NS-114 Constant Growth Model D0 (1 g) D1 P0 rs - g rs - g ^ Needed data: D0 = Dividend just paid D1 = Next expected dividend g = constant growth rate rs = required return on the stock Index 331NS-115
Expected Value at time t D1 P0 rs g D t 1 Pt rs g Index Value at t=0 Value at t 331NS-116 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 Index 331NS-117 Valuing common stock with nonconstant growth 0 r = 13% 1 s g = 30% D0 = 2.00 4.394 2.301 2 g = 30% 2.600 3 g = 30% 4
... g = 6% 3.380 4.658 2.647 3.045 4.658 46.114 54.107 Index = P0 P 0.13 0.06 $66.54 331NS-118 Corporate Value Model = Free Cash Flow method Value of the firm = present value of the
firms expected future free cash flows Free cash flow =after-tax operating income less net capital investment FCF = NOPAT Net capital investment Index 331NS-119 Applying the corporate value model Market value of firm: (MVF) = PV(future FCFs) MV of common stock: = MVF MV of debt Intrinsic stock value: Index
= MVCS /# shares 331NS-120 Issues regarding the corporate value model Often preferred to the dividend growth model Firms that dont 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 Index 331NS-121
Firms Intrinsic Value Long-run gFCF = 6% 0 r = 10% 1 -5 -4.545 8.264 15.026 398.197 416.942 Index 2 10 WACC = 10% 3 20 4 g = 6% ... 21.20
21.20 530 = 0.10 - 0.06 = TV3 331NS-122 If the firm has $40 million in debt and has 10 million shares of stock, what is the firms 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
Index 331NS-123 Firm multiples method 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 Index
331NS-124 The Cost of Capital Index Cost of equity WACC Adjusting for risk 331NS-125 WACC Weighted Average Cost of Capital WACC = wdrd(1-T) + wprp + wcrs Where: Weights wD = % of debt in capital structure wP= % of preferred stock in capital structure wC= % of common equity in capital structure Component costs
rD = firms cost of debt rP= firms cost of preferred stock rC= firms cost of equity T = firms corporate tax rate Index 331NS-126 Three ways to determine the cost of equity, rs: 1. DCF: rs = D1/P0 + g 2. CAPM: rs = rRF + (rM - rRF)i = rRF + (RPM)i 3. Own-Bond-Yield-Plus-Risk Premium: rs = rd + Bond RP Index 331NS-127
DCF Approach: Inputs 1. Current stock price (P0) 2. Current dividend (D0) 3. Growth rate (g) Index 331NS-128 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 Index 331NS-129 Should the company use the composite WACC as the hurdle rate for each of its projects? NO! A firms composite WACC reflects the risk of an average project WACC = hurdle rate for an average risk project Different divisions/projects may have
different risks Index Division or project WACC should be adjusted to reflect appropriate risk 331NS-130 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 firms 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
Index 331NS-131 Using WACC for All Projects - Example What would happen if we use the WACC for all projects regardless of risk? Assume the WACC = 15% Project A B C Index Required Expected Return Return 20% 17% 15% 18% 10% 12%
Decision If 15% Risk Adj Accept Reject Accept Accept Reject Accept 331NS-132 Divisional Risk and the Cost of Capital Rate of Return (%) Acceptance Region WACC WACC H Acceptance Region Rejection Region WACC F Rejection Region
WACC L 0 Index Risk L Risk H Risk 331NS-133 Subjective Approach Consider the projects risk relative to the firm overall Index If project risk > firm risk project discount rate > WACC If project risk < firm risk project discount rate < WACC 331NS-134 Subjective Approach - Example Risk Level Discount Rate Very Low Risk WACC 8% 7% Low Risk WACC 3% 12% Same Risk as Firm WACC High Risk WACC + 5% 20%
Very High Risk WACC + 10% 25% Index 15% 331NS-135 The Basics of Capital Budgeting Independent vs. mutually exclusive CFs Normal vs. non-normal CFs NPV IRR MIRR PB DPB
Index 331NS-136 Steps to capital budgeting 1. 2. 3. 4. 5. Index 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 331NS-137 Independent vs. Mutually Exclusive Projects Independent:
The cash flows of one are unaffected by the acceptance of the other Mutually Exclusive: Index The acceptance of one project precludes acceptance of the other 331NS-138 NPV: Sum of the PVs of all cash flows. n NPV = t=0 CFt . (1 + r)t NOTE: t=0 Cost often is CF0 and is negative n
NPV = t=1 Index CFt (1 + r)t - CF0 331NS-139 TI BAII+: Uneven Cash Flows Cash Flows: Index CF0 = -100 CF1 = 10
CF2 = 60 CF3 = 80 C00 C01 F01 C02 F02 C03 F03 I NPV CF 100 +/- ENTER 10 ENTER 1 ENTER 60 ENTER 1 ENTER
80 ENTER 1 ENTER NPV 10 ENTER CPT $18.78 331NS-140 Internal Rate of Return (IRR) IRR = discount rate that forces PV of inflows equal to cost, and NPV = 0: N 0 t 0 CFt t ( 1 IRR ) Solving for IRR with a financial calculator: Index Enter CFs in CFLO register Press IRR
331NS-141 NPV vs IRR NPV: Enter r, solve for NPV n CF t = NPV (1 + r)t t=0 IRR: Enter NPV = 0, solve for IRR n t=0 Index CFt =0 (1 + IRR)t 331NS-142 Modified Internal Rate of Return (MIRR) MIRR = discount rate which causes the PV of a projects terminal value
(TV) to equal the PV of costs TV = inflows compounded at WACC MIRR assumes cash inflows reinvested at WACC Index 331NS-143 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:
Index 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 331NS-144 Multiple IRRs Descartes Rule of Signs n CFt 0 t t 0 ( 1 IRR ) Polynomial of degree nn roots Index
1 real root per sign change Rest = imaginary (i2 = -1) 331NS-145 The Pavillion Project: Non-normal CFs and MIRR 0 -800,000 1 5,000,000 2 -5,000,000 PV outflows @ 10% = -4,932,231.40 TV inflows @ 10% = 5,500,000.00 MIRR = 5.6% Index 331NS-146 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 Index 331NS-147 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 outflows @ 10% = -$4,932.2314. TV of inflows @ 10% = $5,500. MIRR = 5.6%.
Do not accept Project P. Index NPV = -$386.78 < 0. MIRR = 5.6% < WACC = 10%. 331NS-148 Excel Functions A1 B 2 3 4 5 6 7 8 9 10 11 Year 0 1
2 3 NPV IRR MIRR C D Project Expected Net Cash Flows L S ($100) ($100) 10 70 60 50 80 20 $18.78 $19.98 18.13% 23.56% 16.50% 16.89%
12 13 14 Index 15 =NPV(0.1,C6:C8)+C5 =IRR(C5:C8) =MIRR(C5:C8,0.1,0.1) 331NS-149 Cash Flow Estimation and Risk Analysis Index Relevant cash flows Net salvage value Inflation Sensitivity analysis Scenario analysis
Real options 331NS-150 Relevant Cash Flows: Incremental Cash Flow for a Project Projects incremental cash flow is: Corporate cash flow with the project Minus Corporate cash flow without the project Index 331NS-151 Relevant Cash Flows Changes in Net Working CapitalY Interest/Dividends .... N Sunk Costs .. N Opportunity Costs .Y Externalities/Cannibalism .. Y
Tax Effects .... Y Index 331NS-152 Tax Effect on Salvage Net Salvage Cash Flow = SP - (SP-BV)(T) Where: SP = Selling Price BV = Book Value T = Corporate tax rate Index 331NS-153 Including inflation when estimating cash flows Nominal r > real r Nominal CF > real CF
The cost of capital, r, includes a premium for inflation Nominal cash flows incorporate inflation If you discount real CF with the higher nominal r, then your NPV estimate is too low Index 331NS-154 INFLATION Real vs. Nominal Cash flows n CFt NPV t t 0 1 WACC Real Nominal Index
331NS-155 INFLATION Real vs. Nominal Cash flows 2 Ways to adjust Adjust WACC Adjust Cash Flows for Inflation Index Cash Flows = Real Adjust WACC to remove inflation Use Nominal WACC 331NS-156 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 Index 331NS-157 Sensitivity Analysis Sensitivity Analysis Units Price/unit Variable cost/unit Fixed cost/year Base 6,000 $
80 $ 60 $ 50,000 Units Fixed Cost 6,600 6,000 80 80 60 60 50,000 55,000 Var Cost 6,000 80 54 50,000 Initial investment $ 200,000 Depreciated to salvage value of 0 over 5 years Deprec/yr $ 40,000
Tax rate 40% Required Return 10% Index 331NS-158 Units Price/unit Variable cost/unit Fixed cost Sales Variable Cost Fixed Cost Depreciation EBIT Taxes Net Income + Deprec BASE 6,000 $ 80 $ 60 $
50,000 UNITS 6,600 $ 80 $ 60 $ 50,000 $ $ $ $ $ $ TOTAL CF NPV % Change in NPV % Change in Variable SENSITIVITY RATIO Index
480,000 360,000 50,000 40,000 30,000 12,000 18,000 40,000 58,000 $ 19,866 528,000 396,000 50,000 40,000 42,000 16,800 25,200 40,000 65,200 $ 47,159 137.4% 10.0%
13.74 DIRECT FC 6,000 80 60 55,000 480,000 360,000 55,000 40,000 25,000 10,000 15,000 40,000 $ $ $ $ 55,000 $ 8,493 -57.2% 10.0%
-5.72 INVERSE VC 6,000 80 54 50,000 480,000 324,000 50,000 40,000 66,000 26,400 39,600 40,000 79,600 $ 101,747 412.2% -10.0% -41.22 INVERSE 331NS-159 Sensitivity Analysis UNITS
FC VC -30% $ (62,015) $ 53,983 $ 265,509 -20% $ (34,722) $ 42,610 $ 183,628 -10%
$ (7,428) $ 31,238 $ 101,747 BASE $ 19,866 $ 19,866 $ 19,866 10% $
47,159 $ 8,493 $ (62,015) 20% $ 74,453 $ (2,879) $ (143,896) 30% $ 101,747 $
(14,251) $ (225,777) Index 331NS-160 Sensitivity Graph $300,000 Variable Cost $200,000 $100,000 $- Unit Sales Fixed Cost -30% -20% -10%
BASE 10% 20% 30% $(100,000) $(200,000) $(300,000) Units Index FC VC 331NS-161 14-162 Sensitivity Ratio %NPV = (New NPV - Base NPV)/Base NPV %VAR = (New VAR - Base VAR)/Base VAR
%NPV SR %VAR If SR>0 Direct relationship If SR<0 Inverse relationship Index 331NS-162 14-163 Sensitivity Ratio Change from Base Level -30% 0 %NPV %VAR SR Index Resulting NPV (000s) Unit Sales FC $ -62 20 $54 20 VC $266 20 (-62-20)/20 (54-20)/20 (266-20)/20 -4.1% 1.7% 12.3% -30% -30% -30% 13.74 -5.72 -41.22 331NS-163 Sensitivity Graph $300,000 Variable Cost
$200,000 $100,000 $- Fixed Cost Unit Sales -41.22 13.74 -5.72 -30% -20% -10% BASE 10% 20% 30%
$(100,000) $(200,000) $(300,000) Units Index FC VC 331NS-164 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. Index
331NS-165 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 wont fall Ignores relationships among variables Index 331NS-166 Sensitivity Analysis: Strengths
Provides indication of stand-alone risk Identifies dangerous variables Gives some breakeven information Index 331NS-167 Scenario Analysis Examines several possible situations, usually: Worst case Base case or most likely case, and Best case Provides a range of possible outcomes Index 331NS-168
Scenario Example Scenario Analysis Units Price/unit Variable cost/unit Fixed cost/year $ $ $ Base 6,000 80.00 $ 60.00 $ 50,000 $ BASE Lower 5,500 75.00 $ 58.00 $ 45,000 $ BEST Upper 6,500 85.00
62.00 55,000 WORST Initial investment $ 200,000 Depreciated to salvage value of 0 over 5 years Deprec/yr $ 40,000 Project Life 5 years Tax rate 34% Required return 12% Index 331NS-169 Scenario Analysis Units Price/unit Variable cost/unit Fixed cost/year $ $
$ Base 6,000 80.00 $ 60.00 $ 50,000 $ BASE Lower 5,500 75.00 $ 58.00 $ 45,000 $ BEST Upper 6,500 85.00 62.00 55,000 WORST Initial investment $ 200,000 Depreciated to salvage value of 0 over 5 years Deprec/yr $ 40,000 Project Life
5 years Tax rate 34% Required return 12% Index BASE 6,000 80.00 $ 60.00 $ 50,000 $ Units Price/unit Variable cost/unit Fixed Cost $ $ $ Sales Variable Cost Fixed Cost Depreciation EBIT Taxes
Net Income + Deprec $ 480,000 360,000 50,000 40,000 30,000 10,200 19,800 40,000 WORST 5,500 75.00 $ 62.00 $ 55,000 $ BEST 6,500 85.00 58.00 45,000 $ 412,500 $ 552,500 341,000 377,000 55,000 45,000
40,000 40,000 (23,500) 90,500 (7,990) 30,770 (15,510) 59,730 40,000 40,000 TOTAL CF 59,800 24,490 99,730 NPV 15,566 (111,719) 159,504 15.1%
-14.4% 40.9% IRR 331NS-170 Problems with Scenario Analysis Only considers a few possible outcomes Assumes that inputs are perfectly correlated All bad values occur together and all good values occur together Focuses on stand-alone risk Index 331NS-171
Monte Carlo Simulation Analysis Computerized version of scenario analysis using continuous probability distributions Computer selects values for each variable based on given probability distributions Index 331NS-172 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 Index 331NS-173 Histogram of Results Probability of NPV 12% 10% 8% 6% 4% 2% 0% NPV Index 331NS-174 Advantages of Simulation Analysis
Reflects the probability distributions of each input Shows range of NPVs, the expected NPV, NPV, and CVNPV Gives an intuitive graph of the risk situation Index 331NS-175 Disadvantages of Simulation Analysis Difficult to specify probability distributions and correlations If inputs are bad, output will be bad: Garbage in, garbage out Index 331NS-176 Disadvantages of Sensitivity, Scenario and Simulation Analysis
Sensitivity, scenario, and simulation analyses do not provide a decision rule Do not indicate whether a projects expected return is sufficient to compensate for its risk Sensitivity, scenario, and simulation analyses all ignore diversification Index Measure only stand-alone risk, which may not be the most relevant risk in capital budgeting 331NS-177 Real Options When managers can influence the size and risk of a projects cash flows by taking different actions during the
projects life in response to changing market conditions Alert managers always look for real options in projects Smarter managers try to create real options Index 331NS-178 Types of Real Options Investment timing options Growth options Abandonment options
Expansion of existing product line New products New geographic markets Contraction Temporary suspension Flexibility options Index 331NS-179 FIN 331 in a Nutshell Financial Management I Review Index 331NS-180
Dining Cryptographers Paper by David Chaum (1988) Presentation
Presentation by Glenn Fink ... Two fewer diffs Graph Theory Interpretation Persons=Nodes Keys=Edges Shared by nodes Anonymity Set: The set of nodes whose transmissions are indistinguishable Collusion Sharing keys to expose another person's transmissions Keys and Compromises A "key" is...Regional Service Planning Common Statewide Research Issues Update
Genevieve Burtchell, Ark-Tex COG / Linda Pugh Trans Dir. Dennis Wilde, Nortex Regional Planning Commission / Nora Hodges - Trans Dir. Chris Coffman / Johnny Smith, Panhandle Regional Planning Commission. ... and large buses and automobiles for 12 percent. Approximately...Engaging_Others_Knowing_Ourselves-Template_for_Book_Groups.pptx
An Invitation. This book invites us all into conversation by challenging us to reflect on our past, learn from our present, and envision the future to which God is calling us.The heart of the book is the real-life case studies...