FIN 331 in a Nutshell

FIN 331 in a NutshellFinancial Management I Reviewfor FIN 431

Time Value of MoneyTimelinesFuture ValuePresent ValuePresent Value of Uneven Cash Flows

Time Lines: Timing of Cash FlowsTick marks occur at the end of periods Time 0 = todayTime 1 = the end of the first period or the beginning of the second periodCF0CF1CF3CF20123I%+CF = Cash INFLOW -CF = Cash OUTFLOW PMT = Constant CF

Basic DefinitionsPresent Value (PV)The current value of future cash flows discounted at the appropriate discount rateValue at t=0 on a time lineFuture Value (FV)The amount an investment is worth after one or more periods.Later money on a time line

Future Value: General FormulaFV = future valuePV = present valueI = period interest rate, expressed as a decimalN = number of periodsFuture value interest factor = (1 + I)NNote: yx key on your calculatorFV = PV(1 + I)N

Texas Instruments BA-II PlusFV = future valuePV = present valuePMT = periodic paymentI/Y = period interest rate N = number of periodsOne of these MUST be negativeN I/Y PV PMT FV

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

TVM Functions

EXCEL TVM FUNCTIONS

N5

I/Y10%

PV$(100.00)

PMT0

FV$161.05=FV(B3,B2,B5,B4)

N5

I/Y10%

PV($100.00)=PV(B12,B11,B14,B15)

PMT0

FV$161.05

N5

I/Y10%=RATE(B16,B19,B18,B20)

PV$(100.00)

PMT0

FV$161.05

N5.00=NPER(B24,B26,B25,B27)

I/Y10%

PV$(100.00)

PMT0

FV$161.05

UnEven CFs-1

Rate12%

PeriodCash FlowPresent ValueFormula

1$200.00($178.57)=PV($B$3,A6,0,B6)

2$400.00($318.88)=PV($B$3,A7,0,B7)

3$600.00($427.07)=PV($B$3,A8,0,B8)

4$800.00($508.41)=PV($B$3,A9,0,B9)

Total PV =($1,432.93)=SUM(C6:C9)

($1,432.93)=-NPV(B3,B6:B9)

The functions require a PMT = 0.

Case_Solutions_1

NI/YPVPMTFVFunction

FV of $100 for 3 years at 10%:30.10-$100.00$0.00$133.10=FV(F2,E2,H2,G2)

PV of $100 in 3 years at 10%:30.10-$75.13$0.00$100.00=PV(F4,E4,H4,I4)

Rate for 3 years to grow $100 to $125.97:30.08-$100.00$0.00$125.97=RATE(E6,H6,G6,I6)

N to double if rate = 20%:3.800.20-$1.00$0.00$2.00=NPER(F8,H8,G8,I8)

Annuities

TypeNRatePVPMTFVFunction

END030.100-100$331.00=FV(D2,C2,F2,E2)

END030.10($248.69)1000=PV(D4,C4,F4,G4)

BEGIN130.100-100$364.10=FV(D6,C6,F6,E6,1)

BEGIN130.10($273.55)1000=PV(D8,C8,F8,G8,B8)

END050.10($379.08)1000=PV(D10,C10,F10,G10)

END0100.10($614.46)1000=PV(D12,C12,F12,G12)

END0250.10($907.70)1000=PV(D13,C13,F13,G13)

END0450.120-1095$1,487,261.89=FV(D15,C15,F15,E15)

END0250.120-1095$146,000.59=FV(D17,C17,F17,E17)

END0250.120($11,154.42)$1,487,261.89=PMT(D19,C19,E19,G19)

UnEven CFs (2)

Rate10%


000

1$100.00($90.91)=PV($B$3,A6,0,B6)

2$300.00($247.93)=PV($B$3,A7,0,B7)

3$300.00($225.39)=PV($B$3,A8,0,B8)

4($50.00)$34.15=PV($B$3,A9,0,B9)

Total PV =($530.09)=SUM(C6:C9)

($530.09)=-NPV(B3,B6:B9)


AMORT

AMORtBEG BALPMTINTPRINEND BAL

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

2$698$402$70$332$366

3$366$402$37$365$0

Total$1,206$206$1,000

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

Future Value Example Suppose you invest $100 for 5 years at 10%. How much would you have?Calculator Solution5 N 10 I/Y -100 PV0 PMTCPT FV = 161.05

Future Value:Important Relationship 1 For a given interest rate:The longer the time period, The higher the future valueFV = PV(1 + I)N

For a given I, as N increases, FV increases

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

Present ValuesThe current value of future cash flows discounted at the appropriate discount rateValue at t=0 on a time lineAnswers 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 Values FV = PV(1 + I)NRearrange 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 ExampleYou need $10,000 for the down payment on a new carYou 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(0.07,1,0,10000)PV = 10,000(1.07)-1 = 9,345.79

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

Present Value Important Relationship 2For a given time period: The higher the interest rate, The smaller the present valueFor a given N, as I increases, PV decreases

The Basic PV Equation - RefresherPV = FV / (1 + I)NThere are four parts to this equationPV, FV, I and NKnow any three, solve for the fourthIf you are using a financial calculator, be sure and remember the sign convention+CF = Cash INFLOW -CF = Cash OUTFLOW

Multiple Cash FlowsPresent ValueThe Basic FormulaThe TI BA II+Using the PV/FV keysUsing the Cash Flow WorksheetExcel

Multiple Uneven Cash Flows Present ValueYou 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?-1,432.93 = PV

Present Value of an Uneven Cash Flow Stream: Formula

Multiple Uneven Cash Flows PV Year 1 CF: 1 N; 12 I/Y; 200 FV; CPT PV = -178.57Year 2 CF: 2 N; 12 I/Y; 400 FV; CPT PV = -318.88Year 3 CF: 3 N; 12 I/Y; 600 FV; CPT PV = -427.07Year 4 CF: 4 N; 12 I/Y; 800 FV; CPT PV = -508.41Total PV = -$1,432.93

Multiple Uneven Cash Flows Using the TI BAIIs Cash Flow WorksheetClear all: Press CF Then 2nd And CLR WORK (above CE/C)CF0 is displayed and is 0Enter the Period 0 cash flowIf it is an outflow, hit +/- to change the signTo enter the figure in the cash flow register, press ENTER

TI BAII+: Uneven CFsPress 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 CFsRepeat for all cash flows, in order.To find NPV:Press NPV: I appears on the screenEnter the interest rate, press ENTER and the down arrow to display NPV.Press compute CPT

TI BAII+: Uneven Cash Flows CFC000 ENTER C01200 ENTER F011 ENTER C02400 ENTER F021 ENTER C03600 ENTER F031 ENTER C04800 ENTER F041 ENTER NPVI12 ENTER NPV CPT1432.93Cash Flows:CF0= 0CF1=200CF2=400CF3=600CF4=800

Excel PV of multiple uneven CFs

Sheet1

Rate12%


1$200.00($178.57)=PV($B$3,A6,0,B6)

2$400.00($318.88)=PV($B$3,A7,0,B7)

3$600.00($427.07)=PV($B$3,A8,0,B8)

4$800.00($508.41)=PV($B$3,A9,0,B9)

Total PV =($1,432.93)=SUM(C6:C9)

($1,432.93)=-NPV(B3,B6:B9)


TVM Functions

EXCEL TVM FUNCTIONS

N5

I/Y10%

PV$(100.00)

PMT0

FV$161.05=FV(B3,B2,B5,B4)

N5

I/Y10%

PV($100.00)=PV(B12,B11,B14,B15)

PMT0

FV$161.05

N5

I/Y10%=RATE(B16,B19,B18,B20)

PV$(100.00)

PMT0

FV$161.05

N5.00=NPER(B24,B26,B25,B27)

I/Y10%

PV$(100.00)

PMT0

FV$161.05

UnEven CFs-1

Rate12%


1$200.00($178.57)=PV($B$3,A6,0,B6)

2$400.00($318.88)=PV($B$3,A7,0,B7)

3$600.00($427.07)=PV($B$3,A8,0,B8)

4$800.00($508.41)=PV($B$3,A9,0,B9)

Total PV =($1,432.93)=SUM(C6:C9)

($1,432.93)=-NPV(B3,B6:B9)


Case_Solutions_1

NI/YPVPMTFVFunction

FV of $100 for 3 years at 10%:30.10-$100.00$0.00$133.10=FV(F2,E2,H2,G2)

PV of $100 in 3 years at 10%:30.10-$75.13$0.00$100.00=PV(F4,E4,H4,I4)

Rate for 3 years to grow $100 to $125.97:30.08-$100.00$0.00$125.97=RATE(E6,H6,G6,I6)

N to double if rate = 20%:3.800.20-$1.00$0.00$2.00=NPER(F8,H8,G8,I8)

Annuities

TypeNRatePVPMTFVFunction

END030.100-100$331.00=FV(D2,C2,F2,E2)

END030.10($248.69)1000=PV(D4,C4,F4,G4)

BEGIN130.100-100$364.10=FV(D6,C6,F6,E6,1)

BEGIN130.10($273.55)1000=PV(D8,C8,F8,G8,B8)

END050.10($379.08)1000=PV(D10,C10,F10,G10)

END0100.10($614.46)1000=PV(D12,C12,F12,G12)

END0250.10($907.70)1000=PV(D13,C13,F13,G13)

END0450.120-1095$1,487,261.89=FV(D15,C15,F15,E15)

END0250.120-1095$146,000.59=FV(D17,C17,F17,E17)

END0250.120($11,154.42)$1,487,261.89=PMT(D19,C19,E19,G19)

UnEven CFs (2)

Rate10%


000

1$100.00($90.91)=PV($B$3,A6,0,B6)

2$300.00($247.93)=PV($B$3,A7,0,B7)

3$300.00($225.39)=PV($B$3,A8,0,B8)

4($50.00)$34.15=PV($B$3,A9,0,B9)

Total PV =($530.09)=SUM(C6:C9)

($530.09)=-NPV(B3,B6:B9)


AMORT

AMORtBEG BALPMTINTPRINEND BAL

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

2$698$402$70$332$366

3$366$402$37$365$0

Total$1,206$206$1,000

CHAPTER 3Financial Statements, Cash Flow, and TaxesKey Financial Statements Balance sheet Income statements Statement of cash flows

The Annual ReportBalance sheet Snapshot of a firms financial position at a point in timeIncome statement Summarizes a firms revenues and expenses over a given period of timeStatement of cash flows Reports the impact of a firms activities on cash flows over a given period of time

Sample Balance SheetAssets =Liabilities +Owners Equity

BS-new

Allied Food Products

Balance Sheets

ASSETS20052004

Cash & Equivalents$10$80

Accounts receivable$375$315

Inventories$615$415

Total current assets$1,000$810

Net plant & equipment$1,000$870

TOTAL ASSETS$2,000$1,680

LIABILITIES & EQUITY20082007

Accounts payable$60$30

Notes payable$110$60

Accruals$140$130

Total current liabilities$310$220

Long-term bonds$750$580

Total liabilities$1,060$800

Common stock (50,000,000 shares)$130$130

Retained earnings$810$750

Total common equity$940$880

Total Liabilities & Equity$2,000$1,680

IS-NEW

INCOME STATEMENTS

2008% of Sales2007

Net sales$3,000.0$2,850.0

Operating costs$2,616.287.21%$2,497.0

Gross profit$383.812.79%$353.0

Depreciation$100.03.33%$86.7

Other Operating Expenses$2.00.07%$9.0

Operating Income$281.89.39%$257.3

Interest expense$82.02.73%$60.0

Pretax income$199.86.66%$197.3

Taxes (40%)$79.92.66%$81.2

NET INCOME$119.94.00%$116.1

Common dividends$63.953.3%$60.151.8%

Addtion to retained earnings$56.046.7%$56.048.3%

SCF-new

Statement of Cash Flows

Cash Provided or Used

Operating Activities

Net Income$119.9

Adjustments

Noncash adjustments

Depreciation$100.0

Due to changes in working capital

Increase in accounts receivable($60.0)

Increase in inventories($200.0)

Increase in accounts payable$30.0

Increase in accruals$10.0

Net cash provided by operating activities($0.1)

Long-term Investing activities

Cash used to acquire fixed assets($230.0)

Financing Activities

Sale of short-term investments$65.0

Increase in notes payable$50.0

Increase in bonds outstanding$174.0

Payment of common dividends($63.9)

Net cash provided by financing activities$225.1($5.0)

Summary

Net change in cash($5.0)

Cash at beginning of year$15.0

Cash at end of year$10.0

Sample Income StatementNet income=Dividends + Retained earnings

BS-new


Balance Sheets

ASSETS20052004



Inventories$615$415







Accruals$140$130








IS-NEW


INCOME STATEMENTS

2005% of Sales2004

Net sales$3,000.0$2,850.0

Operating costs$2,616.287.21%$2,497.0

Gross profit (EBITDA)$383.812.79%$353.0


Operating Income (EBIT)$283.89.46%$263.0


Pretax income (EBT)$195.86.53%$203.0

Taxes (40%)$78.32.61%$81.2

NET INCOME$117.53.92%$121.8

Common dividends$57.553.3%$53.0

Addtion to retained earnings$60.051.1%$56.0

Per Share Data

Common stock price$23.00$26.00

Earnings per share$2.35$2.44

Dividends per share$1.15$1.06

Book value per share$18.80$17.60

Cash Flow per share$4.35$4.24

SCF-new




Net Income$117.5

Adjustments

Noncash adjustments

Depreciation$100.0















Summary





BS-new


Balance Sheets

ASSETS20052004



Inventories$615$415







Accruals$140$130








IS-NEW


INCOME STATEMENTS

2005% of Sales2004

Net sales$3,000.0$2,850.0

Operating costs$2,616.287.21%$2,497.0






Taxes (40%)$78.32.61%$81.2

NET INCOME$117.53.92%$121.8



Per Share Data






SCF-new




Net Income$117.5

Adjustments

Noncash adjustments

Depreciation$100.0















Summary




Allied 2005 Per-Share Ratios

Statement of Cash FlowsProvides information about cash inflows and outflows during an accounting period Required since 1988Developed from Balance Sheet and Income Statement data

Statement of Cash FlowsReconciles the change in Cash & Equivalents

BS-new


Balance Sheets

ASSETS20052004



Inventories$615$415







Accruals$140$130








IS-NEW


INCOME STATEMENTS

2005% of Sales2004

Net sales$3,000.0$2,850.0

Operating costs$2,616.287.21%$2,497.0






Taxes (40%)$78.32.61%$81.2

NET INCOME$117.53.92%$121.8



Per Share Data






SCF-new

Allied Food Products: Statement of Cash Flows

2005

IOperating Activities

Net Income before dividends$117.5

Adjustments

Additions



Depreciation$100.0

Subtractions




IILong-term Investing activities


IIIFinancing Activities


Increase in bonds$170.0

Payment of dividends($57.5)

Net cash provided by financing activities$162.5

Net change in cash & equivalents($70.0)

Cash & equivalents at beginning of year$80.0

IVCash & equivalents at end of year$10.0

BS-new


Balance Sheets

ASSETS20052004



Inventories$615$415







Accruals$140$130








IS-NEW


INCOME STATEMENTS

2005% of Sales2004

Net sales$3,000.0$2,850.0

Operating costs$2,616.287.21%$2,497.0






Taxes (40%)$78.32.61%$81.2

NET INCOME$117.53.92%$121.8



Per Share Data






SCF-new


2005



Adjustments

Additions



Depreciation$100.0

Subtractions














Statement of Cash FlowsReconciles the Income Statement and Balance Sheet to the flow of cashThe Matching Principle requires estimates and accruals to prepare Financial statementsFinancial Analysis is concerned with Cash FlowWhy is it important???

Statement of Cash FlowsA 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

DeficitsCovered by new debt and cash

BS-new


Balance Sheets

ASSETS20052004



Inventories$615$415







Accruals$140$130








IS-NEW


INCOME STATEMENTS

2005% of Sales2004

Net sales$3,000.0$2,850.0

Operating costs$2,616.287.21%$2,497.0






Taxes (40%)$78.32.61%$81.2

NET INCOME$117.53.92%$121.8



Per Share Data






SCF-new


2005



Adjustments

Additions



Depreciation$100.0

Subtractions














Net Operating Working Capital

Allied_BS


Balance Sheets

ASSETS20052004



Inventories$615$415







Accruals$140$130








Allied_IS


INCOME STATEMENTS

2005% of Sales2004

Net sales$3,000.0$2,850.0

Operating costs$2,616.287.21%$2,497.0






Taxes (40%)$78.32.61%$81.2

NET INCOME$117.53.92%$121.8



Per Share Data






Allied_SCF


2005



Adjustments

Additions



Depreciation$100.0

Subtractions














Allied_SRE


Statement of Retained Earnings

2005

Balance of retained earnings, Dec 31, 2004$750.0

Add: Net Income, 2005$117.5

Less: Dividends to common shareholders($57.5)

Balance of retained earnings, Dec 31, 2005$810.0

Allied_BS_2


Balance Sheets

ASSETS20052004LIABILITIES & EQUITY20082007

Cash & Equivalents$10$80Accounts payable$60$30

Accounts receivable$375$315Notes payable$110$60

Inventories$615$415Accruals$140$130

Total current assets$1,000$810Total current liabilities$310$220

Current Operating Assets$1,000$810Current Operating Liabilities$200$160

Net Operating Working Capital = Current Operating Assets - Current Operating Liabilities

Net Operating Working Capital (2005)$800

Net Operating Working Capital (2004)$650

$150

Operating Capital (also called Total Net Operating Capital)Operating Capital= NOWC + Net fixed assetsOperating Capital(2005) = $800 + $1,000 = $1,800 million(2004) = $650 + $870 = $1,520 millionNet Investment in Operating Capital = Op Cap (2005) Op Cap (2004) = $1,800 - $1,520 = $280 million

Net Operating Profit after Taxes (NOPAT) & Operating Cash FlowNOPAT = EBIT(1 - Tax rate)NOPAT05= $283.8(1 - 0.4) = $170.3 mOCF05 = NOPAT + Deprec + Amort= $170.3 + $100= $270.3

Free Cash Flow (FCF) for 2005EBIT = $283.8 m T = 40% Depreciation = $100 mCapital Expenditures = FA + Deprec = $130+$100 = $230NOWC = $800 - $650 = $150 m

FCF = [$283.8(1-.4)+$100] [$230-$150] = -$109.7 m

CHAPTER 4Analysis of Financial StatementsRatio AnalysisLimitations of ratio analysisQualitative factors

Five Major Categories of RatiosLiquidity CR - Current RatioQR - Quick Ratio or Acid-Test Asset managementInventory TurnoverDSO Days sales outstandingFAT - Fixed Assets TurnoverTAT - Total Assets TurnoverDebt management Debt RatioTIE Times interest earnedEBITDA coverage (EC)

Five Major Categories of RatiosProfitabilityPM - Profit margin on salesBEP Basic earning powerROA Return on total assetsROE Return on common equityMarket valueP/E Price-Earnings ratioP/CF Price cash flow ratioM/B Market to book

Liquidity RatiosCR = Current Ratio = CA/CL

QR = Quick Ratio or Acid-Test = (CA-INV)/CL

Asset Management RatiosInventory Turnover = Sales/InventoriesDSO = Days sales outstanding = Receivables /(Annual sales/365)FAT = Fixed Assets Turnover = Sales/Net Fixed AssetsTAT= Total Assets Turnover = Sales/Total Assets

Debt Management RatiosDebt Ratio = Total Liabilities/Total Assets

TIE = Times interest earned = EBIT/Interest

EBITDA coverage = EC

(EBITDA + lease pmts) .(Interest + principal pmts + lease pmts)

Profitability RatiosPM = Profit margin on sales = NI/SalesBEP = Basic earning power = EBIT/Total AssetsROA = Return on total assets = NI/Total AssetsROE = Return on common equity = NI/Common Equity

Market Value MetricsP/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

The 5 Major Categories of Ratios and What Questions They Answer

Potential Problems and Limitations of Ratio AnalysisComparison with industry averages is difficult if the firm operates many different divisionsAverage performance necessarily goodSeasonal factors can distort ratiosWindow dressing techniques

Problems and Limitations (Continued)Different accounting and operating practices can distort comparisonsSometimes difficult to tell if a ratio value is good or badDifferent ratios give different signals Difficult to tell, on balance, whether a company is in a strong or weak financial condition

Qualitative FactorsRevenues 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?

CHAPTER 16Financial Planning and ForecastingForecasting salesProjecting the assets and internally generated fundsProjecting outside funds neededDeciding how to raise funds

The AFN FormulaIf ratios are expected to remain constant:

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

Required AssetsSpontaneously Liabilities Retained Earnings

Variables in the AFN FormulaA* = Assets tied directly to salesS0 = Last years salesS1 = Next years projected salesS = Increase in sales; (S1-S0)L* = Liabilities that spontaneously increase with sales

Variables in the AFN FormulaA*/S0: assets required to support sales; Capital Intensity RatioL*/S0: spontaneous liabilities ratioM: profit margin (Net income/sales)RR: retention ratio; percent of net income not paid as dividend

Key Factors in AFNS=Sales GrowthA*/S0=Capital Intensity RatioL*/S0=Spontaneous Liability RatioM=Profit MarginRR=Retention Ratio

CHAPTER 6Interest Rates

Nominal vs. Real ratesr= 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 securitiesProxied by T-bill or T-bond rate

r = r* + IP + DRP + LP + MRPHere: r=Required rate of return on a debt security r*= Real risk-free rate IP= Inflation premiumDRP= Default risk premium LP= Liquidity premiumMRP= Maturity risk premiumrRF =

Premiums Added to r* for Different Types of DebtST Treasury ST IPLT Treasury LT IP MRP

ST Corporate ST IP DRP LPLT Corporate LT IP DRP MRP LPDebt Instrument IP DRP MRP LP

CHAPTER 7Bonds and Their ValuationBond valuationMeasuring yield

Discount Rate = YTMThe discount rate (YTM) is: The opportunity cost of capitalThe rate that could be earned on alternative investments of equal riskRequired returnFor debt securities:YTM = r* + IP + LP + MRP + DRP

Bond ValueBond 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 EquationPV(Annuity)PV(lump sum)C = Coupon payment; F = Face value

Texas Instruments BA-II PlusFV = future value/face value/par valuePV = present value=bond value/priceI/Y = period interest rate = YTMN = number of periods to maturityPMT = coupon payment

Spreadsheet FunctionsFV(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 TI BA II+Bond Worksheet [2nd] BONDSDT CPN RDT RV ACT 2/Y YLD PRIExcel:PRICE(Settlement,Maturity,Rate,Yld,Redemption, Frequency,Basis)YIELD(Settlement,Maturity,Rate,Pr,Redemption, Frequency,Basis)Settlement and maturity need to be actual datesRedemption and Pr need to given as % of par value

Yield to Maturity (YTM)The market required rate of return for bonds of similar risk and maturityThe discount rate used to value a bondReturn earned if bond held to maturityUsually = coupon rate at issueQuoted as an APRThe IRR of a bond

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 YTMYTM =10.91%Bond sells at a discount because YTM > coupon rateINPUTSOUTPUTNI/YRPMTPVFV1010.91901000- 887

Solving for YTMCoupon rate = 9%Annual couponsPar = $1,000Maturity = 10 yearsPrice = $887Using the calculator:N = 10 PV = -887PMT = 90FV = 1000CPT I/Y = 10.91=RATE(10,90,-887,1000)YTM on a 10-year, 9% annual coupon, $1,000 par value bond selling for $887

Find YTM, if the bond price is $1,134.20YTM = 7.08% Bond sells at a premium because YTM < coupon rateINPUTSOUTPUTNI/YRPMTPVFV107.08901000-1134.2

Solving for YTMCoupon rate = 9%Annual couponsPar = $1,000Maturity = 10 yearsPrice = $1,134.20Using the calculator:N = 10 PV = -1134.20PMT = 90FV = 1000CPT I/Y = 7.08=RATE(10,90,-1134.20,1000)YTM on a 10-year, 9% annual coupon, $1,000 par value bond selling for $1,134.20

Semiannual bondsMultiply 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.INPUTSOUTPUTNI/YRPMTPVFV2Nrd / 2cpn / 2OKOK

What is the value of a 10-year, 10% semiannual coupon bond, if rd = 13%?Multiply years by 2 : N = 2 * 10 = 20Divide nominal rate by 2 : I/YR = 13 / 2 = 6.5Divide annual coupon by 2 : PMT = 100 / 2 = 50INPUTSOUTPUTNI/YRPMTPVFV206.5501000- 834.72

Valuing a Semiannual BondCoupon rate = 10%Annual couponsPar = $1,000Maturity = 10 yearsYTM = 13% Using the formula:Using the calculator:N = 20 I/Y = 6.5PMT = 50FV = 1000CPT PV = -834.72=PV(0.065, 10, 50, 1000)

YTM with Semiannual CouponsSuppose 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 CouponsSuppose 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 = 50FV = 1000CPT I/Y = 4% YTM = 4%*2 = 8% Result = YTM

NOTE: Solving a semi-annual payer for YTM will result in a 6-month YTM answerCalculator solves what you enter.

CHAPTER 8Risk and Rates of ReturnStand-alone RiskPortfolio RiskRisk & Return: CAPM / SML

The Expected Rate of Returnr hat = expected returnri = expected return in ith state of the economyPi = Probability of ith state occurring

Calculating the Expected Return

Return and STD

Portfolio Return

Portfolio %50%50%Portfolio

EconomyProbHTCollPortfolioReturn

Recession0.1-27%27%0.0%0.0%

Below Avg0.2-7%13%3.0%0.6%

Average0.415%0%7.5%3.0%

Above Avg0.230%-11%9.5%1.9%

Boom0.145%-21%12.0%1.2%

E(R )12.4%1.0%6.7%

Portfolio Standard Deviation

Squared

EconomyProbPortfolioDeviation

Recession0.10.0%0.00045

Below Avg0.23.0%0.00027

Average0.47.5%0.00003

Above Avg0.29.5%0.00016

Boom0.112.0%0.00028

E(R )6.7%0.00119Variance

=3.44%

Recap

HTCOLLPortfolio

E(R )12.40%1.00%6.7%

Std Dev20.00%13.20%3.4%

CV1.613.20.51

Pf Std

WStd DevVarianceCov

HT50%20.00%0.0400-0.0264-1.00

Coll50%13.20%0.0174

ijfor n=2

110.0100

12(0.0066)

21(0.0066)

220.0044

0.00116Variance

3.40%Std Dev

STD DEV

Deviation

EconomyProbHTDeviationSquaredx Prob

Recession0.1-27%-39%15.5%1.6%

Below Avg0.2-7%-19%3.8%0.8%

Average0.415%3%0.1%0.0%

Above Avg0.230%18%3.1%0.6%

Boom0.145%33%10.6%1.1%

E(R )12.4%Variance4.0%

Std Dev20.0%

COvariance

EconomyProbHTCollHT DevColl DevHT x Collx Prob

Recession0.1-27%27%-39.4%26.0%-10.244%-0.0102

Below Avg0.2-7%13%-19.4%12.0%-2.328%-0.0047

Average0.415%0%2.6%-1.0%-0.026%-0.0001

Above Avg0.230%-11%17.6%-12.0%-2.112%-0.0042

Boom0.145%-21%32.6%-22.0%-7.172%-0.0072

E(R )12.4%1.0%COV(HT,Coll) =-0.0264

HTColl

Std Dev20.0%13.2%

Cov-0.0264

Correlation-1.000

Coefficient

Sheet1

EconomyProbHTProb x HT

Recession0.1-27%-2.7%

Below Avg0.2-7%-1.4%

Average0.415%6.0%

Above Avg0.230%6.0%

Boom0.145%4.5%

E(R )12.4%

Return and STD (2)

Portfolio Return



Recession0.1-27%27%0.0%0.0%

Below Avg0.2-7%13%3.0%0.6%

Average0.415%0%7.5%3.0%

Above Avg0.230%-11%9.5%1.9%

Boom0.145%-21%12.0%1.2%

E(R )12.4%1.0%6.7%


Squared


Recession0.10.0%0.00045

Below Avg0.23.0%0.00027

Average0.47.5%0.00003

Above Avg0.29.5%0.00016

Boom0.112.0%0.00028


=3.44%

MBD0031B52F.unknown

MBD0030B13F.unknown

The Standard Deviation of Returns = Standard deviation = Variance = 2

Standard deviation for each investment

Standard Deviation of HTs Returns

Return and STD

Portfolio Return



Recession0.1-27%27%0.0%0.0%

Below Avg0.2-7%13%3.0%0.6%

Average0.415%0%7.5%3.0%

Above Avg0.230%-11%9.5%1.9%

Boom0.145%-21%12.0%1.2%

E(R )12.4%1.0%6.7%


Squared


Recession0.10.0%0.00045

Below Avg0.23.0%0.00027

Average0.47.5%0.00003

Above Avg0.29.5%0.00016

Boom0.112.0%0.00028


=3.44%

Recap

HTCOLLPortfolio

E(R )12.40%1.00%6.7%

Std Dev20.00%13.20%3.4%

CV1.613.20.51

Pf Std

WStd DevVarianceCov

HT50%20.00%0.0400-0.0264-1.00

Coll50%13.20%0.0174

ijfor n=2

110.0100

12(0.0066)

21(0.0066)

220.0044

0.00116Variance

3.40%Std Dev

STD DEV

Deviation

EconomyProbHTDeviationSquaredx Prob

Recession0.1-27%-39.4%15.5%1.6%

Below Avg0.2-7%-19.4%3.8%0.8%

Average0.415%2.6%0.1%0.0%

Above Avg0.230%17.6%3.1%0.6%

Boom0.145%32.6%10.6%1.1%

E(R )12.4%Variance4.0%

Std Dev20.0%

COvariance


Recession0.1-27%27%-39.4%26.0%-10.244%-0.0102

Below Avg0.2-7%13%-19.4%12.0%-2.328%-0.0047

Average0.415%0%2.6%-1.0%-0.026%-0.0001

Above Avg0.230%-11%17.6%-12.0%-2.112%-0.0042

Boom0.145%-21%32.6%-22.0%-7.172%-0.0072

E(R )12.4%1.0%COV(HT,Coll) =-0.0264

HTColl

Std Dev20.0%13.2%

Cov-0.0264

Correlation-1.000

Coefficient

Sheet1

EconomyProbHTProb x HT

Recession0.1-27%-2.7%

Below Avg0.2-7%-1.4%

Average0.415%6.0%

Above Avg0.230%6.0%

Boom0.145%4.5%

E(R )12.4%

Return and STD (2)

Portfolio Return



Recession0.1-27%27%0.0%0.0%

Below Avg0.2-7%13%3.0%0.6%

Average0.415%0%7.5%3.0%

Above Avg0.230%-11%9.5%1.9%

Boom0.145%-21%12.0%1.2%

E(R )12.4%1.0%6.7%


Squared


Recession0.10.0%0.00045

Below Avg0.23.0%0.00027

Average0.47.5%0.00003

Above Avg0.29.5%0.00016

Boom0.112.0%0.00028


=3.44%

MBD0031B52F.unknown

MBD0030B13F.unknown

Risk versus Return:Do we know enough now?^

Coefficient of Variation (CV)CV = Standard deviation/expected return = Risk per unit of return =

Portfolio Expected Returnrp = weighted average wi = % of portfolio in stock i ri = return on stock i^

Portfolio Expected ReturnAssume 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 ReturnPortfolio = (50% x HT) + (50% x Coll)Portfolio Return = Prob x Portfolio

Sheet1

Portfolio Return



Recession0.1-27%27%0.0%0.0%

Below Avg0.2-7%13%3.0%0.6%

Average0.415%0%7.5%3.0%

Above Avg0.230%-11%9.5%1.9%

Boom0.145%-21%12.0%1.2%

E(R )12.4%1.0%6.7%


Squared


Recession0.10.0%0.00045

Below Avg0.23.0%0.00027

Average0.47.5%0.00003

Above Avg0.29.5%0.00016

Boom0.112.0%0.00028


=3.44%

Sheet2

Sheet3

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

Calculating portfolio standard deviation and CV


Sheet1

Portfolio Return



Recession0.1-27%27%0.0%0.0%

Below Avg0.2-7%13%3.0%0.6%

Average0.415%0%7.5%3.0%

Above Avg0.230%-11%9.5%1.9%

Boom0.145%-21%12.0%1.2%

E(R )12.4%1.0%6.7%


Squared


Recession0.10.0%0.00045

Below Avg0.23.0%0.00027

Average0.47.5%0.00003

Above Avg0.29.5%0.00016

Boom0.112.0%0.00028


=3.4%

Sheet2

Sheet3

Portfolio Risk & Returnp = 3.4% is much lower than the of either stock p = 3.4% is lower than the weighted average of HT and Coll.s (16.6%)The portfolio provides the average return of component stocks, but lower than the average riskWhy? Negative correlation between stocks

Return and STD

Portfolio Return



Recession0.1-27%27%0.0%0.0%

Below Avg0.2-7%13%3.0%0.6%

Average0.415%0%7.5%3.0%

Above Avg0.230%-11%9.5%1.9%

Boom0.145%-21%12.0%1.2%

E(R )12.4%1.0%6.7%


Squared


Recession0.10.0%0.00045

Below Avg0.23.0%0.00027

Average0.47.5%0.00003

Above Avg0.29.5%0.00016

Boom0.112.0%0.00028


=3.44%

Recap

HTCOLLPortfolio

E(R )12.40%1.00%6.7%

Std Dev20.00%13.20%3.4%

CV1.613.20.51

Sheet4

WStd DevVarianceCovCorr Coeff

HT50%20.00%0.0400-0.0264-1.00

Coll50%13.20%0.0174

ijfor n=2

110.0100

12(0.0066)

21(0.0066)

220.0044

0.00116

3.40%

Sheet1 (2)


Recession0.1-27%27%-39.4%26.0%-10.244%-0.0102

Below Avg0.2-7%13%-19.4%12.0%-2.328%-0.0047

Average0.415%0%2.6%-1.0%-0.026%-0.0001

Above Avg0.230%-11%17.6%-12.0%-2.112%-0.0042

Boom0.145%-21%32.6%-22.0%-7.172%-0.0072

E(R )12.4%1.0%COV(HT,Coll) =-0.0264

HTColl

Std Dev20.0%13.2%

Cov-0.0264

Correlation-1.000

Coefficient

MBD0031B52F.unknown

MBD0030B13F.unknown

Covariance of ReturnsMeasures how much the returns on two risky assets move together

Covariance vs. Variance of Returns

CovarianceCovariance (HT:Coll) = -0.0264

Return and STD

Portfolio Return



Recession0.1-27%27%0.0%0.0%

Below Avg0.2-7%13%3.0%0.6%

Average0.415%0%7.5%3.0%

Above Avg0.230%-11%9.5%1.9%

Boom0.145%-21%12.0%1.2%

E(R )12.4%1.0%6.7%


Squared


Recession0.10.0%0.00045

Below Avg0.23.0%0.00027

Average0.47.5%0.00003

Above Avg0.29.5%0.00016

Boom0.112.0%0.00028


=3.44%

Recap

HTCOLLPortfolio

E(R )12.40%1.00%6.70%

Std Dev20.00%13.20%3.44%

CV1.613.20.51

Sheet1 (2)


Recession0.1-27%27%-39.4%26.0%-10.244%-0.0102

Below Avg0.2-7%13%-19.4%12.0%-2.328%-0.0047

Average0.415%0%2.6%-1.0%-0.026%-0.0001

Above Avg0.230%-11%17.6%-12.0%-2.112%-0.0042

Boom0.145%-21%32.6%-22.0%-7.172%-0.0072

E(R )12.4%1.0%COV(HT,Coll) =-0.0264

MBD0030B13F.unknown

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

Two-Stock PortfoliosIf r = -1.0Two stocks can be combined to form a riskless portfolio If r = +1.0 No risk reduction at all In general, stocks have r 0.35Risk is lowered but not eliminatedInvestors typically hold many stocks

s of n-Stock PortfolioSubscripts denote stocks i and jri,j = Correlation between stocks i and j i and j =Standard deviations of stocks i and jij = Covariance of stocks i and j

Portfolio Risk-n Risky Assetsi jfor n=211w1w111 = w121212w1w21221w2w12122w2w222 = w2222 p2 = w1212 + w2222 + 2w1w2 12

Portfolio Risk-2 Risky Assets

Return and STD

Portfolio Return



Recession0.1-27%27%0.0%0.0%

Below Avg0.2-7%13%3.0%0.6%

Average0.415%0%7.5%3.0%

Above Avg0.230%-11%9.5%1.9%

Boom0.145%-21%12.0%1.2%

E(R )12.4%1.0%6.7%


Squared


Recession0.10.0%0.00045

Below Avg0.23.0%0.00027

Average0.47.5%0.00003

Above Avg0.29.5%0.00016

Boom0.112.0%0.00028


=3.44%

Recap

HTCOLLPortfolio

E(R )12.40%1.00%6.7%

Std Dev20.00%13.20%3.4%

CV1.613.20.51

Pf Std

WStd DevVarianceCov

HT50%20.00%0.0400-0.0264-1.00

Coll50%13.20%0.0174

ijfor n=2

110.0100

12(0.0066)

21(0.0066)

220.0044

0.00116Variance

3.40%Std Dev

Sheet1 (2)


Recession0.1-27%27%-39.4%26.0%-10.244%-0.0102

Below Avg0.2-7%13%-19.4%12.0%-2.328%-0.0047

Average0.415%0%2.6%-1.0%-0.026%-0.0001

Above Avg0.230%-11%17.6%-12.0%-2.112%-0.0042

Boom0.145%-21%32.6%-22.0%-7.172%-0.0072

E(R )12.4%1.0%COV(HT,Coll) =-0.0264

HTColl

Std Dev20.0%13.2%

Cov-0.0264

Correlation-1.000

Coefficient

MBD0031B52F.unknown

MBD0030B13F.unknown

Capital Asset Pricing Model (CAPM)Links risk and required returns Security Market Line (SML):A stocks required return equals the risk-free return (rRF) plus a risk premium (RPM x ) that reflects the stocks risk after diversificationPrimary conclusion: The relevant riskiness of a stock is its contribution to the riskiness of a well-diversified portfolio.

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

rRF = Risk-free rateRPM = Market risk premium = rM rRF

The Market Risk Premium (rM rRF = RPM)Additional return over the risk-free rate to compensate investors for assuming an average amount of riskSize depends on:Perceived risk of the stock market Investors degree of risk aversionVaries from year to yearEstimates suggest a range between 4% and 8% per year

Required Rates of ReturnAssume: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 ReturnsRequired by the marketExpected by YOU

Illustrating the Security Market Line..Coll..HTT-bills.USRSMLrM = 10.5

rRF = 5.5-1 0 1 2.SML: ri = 5.5% + (5.0%) i ri (%)Risk, i

Portfolio Beta

Where:wi = weight (% dollars invested in asset i)i = Beta of asset i p = Portfolio Beta

CHAPTER 9Stocks and Their Valuation

Constant growth stockDividends expected to grow forever at a constant rate, g:

D1 = D0 (1+g)1D2 = D0 (1+g)2Dt = D0 (1+g)t

Dividend growth formula converges to:

Constant Growth ModelNeeded data:D0 = Dividend just paidD1 = Next expected dividendg = constant growth raters = required return on the stock

Expected Value at time tValue at t=0Value at t

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

Constant growth model no longer applicableBut - growth constant after 3 years

Valuing common stock with nonconstant growth$P^

Corporate Value Model= Free Cash Flow methodValue of the firm = present value of the firms expected future free cash flows

Free cash flow =after-tax operating income less net capital investmentFCF = NOPAT Net capital investment

Applying the corporate value modelMarket value of firm: (MVF) = PV(future FCFs)MV of common stock:= MVF MV of debtIntrinsic stock value:= MVCS /# shares

Issues regarding the corporate value modelOften preferred to the dividend growth modelFirms that dont pay dividends Dividends hard to forecastAssumes at some point free cash flow growth rate will be constant Terminal value (TVN) = value of firm at the point that growth becomes constant

Firms Intrinsic ValueLong-run gFCF = 6%WACC = 10%

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 millionValue per share= MV of equity / # of shares= $376.94 / 10= $37.69

Firm multiples methodOften used by analysts to value stocksP / EPrice-earning P / CFPrice-cash flowP / SalesPrice-salesMethod: Estimate appropriate ratio based on comparable firmsMultiply estimate by expected metric to estimate stock price

CHAPTER 10The Cost of CapitalCost of equityWACCAdjusting for risk

WACCWeighted Average Cost of CapitalWACC = wdrd(1-T) + wprp + wcrs

Where:

wD = % of debt in capital structurewP= % of preferred stock in capital structurewC= % of common equity in capital structurerD = firms cost of debtrP= firms cost of preferred stockrC= firms cost of equityT = firms corporate tax rateWeightsComponent costs

Three ways to determine the cost of equity, rs: 1.DCF: rs = D1/P0 + g2.CAPM: rs= rRF + (rM - rRF)i= rRF + (RPM)i3.Own-Bond-Yield-Plus-Risk Premium:rs = rd + Bond RP

DCF Approach: InputsCurrent stock price (P0)Current dividend (D0)Growth rate (g)

Four Mistakes to AvoidCurrent (YTM) vs. historical (Coupon rate) cost of debtMixing current and historical measures to estimate the market risk premiumBook weights vs. Market WeightsUse Target weightsUse market value of equityBook value of debt = reasonable proxy for market value.Incorrect cost of capital componentsOnly investor provided funding

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 projectDifferent divisions/projects may have different risksDivision or project WACC should be adjusted to reflect appropriate risk

Divisional and Project Costs of CapitalUsing the WACC as the discount rate is only appropriate for projects that are the same risk as the firms current operationsIf considering a project that is NOT of the same risk as the firm, then an appropriate discount rate for that project is neededDivisions also often require separate discount rates

Using WACC for All Projects - ExampleWhat would happen if we use the WACC for all projects regardless of risk?Assume the WACC = 15%

Sheet1

Required

Return

20%

15%WACC

10%

5%

05%10%15%20%IRR

Sheet2

RequiredExpectedDecision

ProjectReturnReturnIf 15%Risk Adj

A20%17%AcceptReject

B15%18%AcceptAccept

C10%12%RejectAccept

Sheet3

Divisional Risk and the Cost of Capital Rate of Return (%) WACC Rejection Region Acceptance Region Risk WACCH WACCL WACCF 0 RiskL RiskH Acceptance RegionRejection Region

Subjective ApproachConsider the projects risk relative to the firm overallIf project risk > firm risk project discount rate > WACCIf project risk < firm risk project discount rate < WACC

Subjective Approach - Example

CHAPTER 11The Basics of Capital BudgetingShould we build thisplant?

Steps to capital budgetingEstimate CFs (inflows & outflows)Assess riskiness of CFsDetermine appropriate cost of capitalFind NPV and/or IRRAccept if NPV>0 and/or IRR>WACC

Independent versus Mutually Exclusive ProjectsIndependent:The cash flows of one are unaffected by the acceptance of the otherMutually Exclusive:The acceptance of one project precludes acceptance of the other

NPV: Sum of the PVs of all cash flows.Cost often is CF0 and is negativeNOTE: t=0

TI BAII+: Uneven Cash FlowsCFC00100 +/- ENTER C0110 ENTER F011 ENTER C0260 ENTER F021 ENTER C0380 ENTER F031 ENTER NPVI10 ENTER NPV CPT$18.78Cash Flows:CF0= -100CF1=10CF2=60CF3=80

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 registerPress IRR:

NPV vs IRRIRR: Enter NPV = 0, solve for IRRNPV: Enter r, solve for NPV

Modified Internal Rate of Return (MIRR)MIRR = discount rate which causes the PV of a projects terminal value (TV) to equal the PV of costsTV = inflows compounded at WACCMIRR assumes cash inflows reinvested at WACC

Normal vs. Non-normal Cash FlowsNormal Cash Flow Project:Cost (negative CF) followed by a series of positive cash inflowsOne change of signsNon-normal Cash Flow Project:Two or more changes of signsMost common: Cost (negative CF), then string of positive CFs, then cost to close projectFor example, nuclear power plant or strip mine

Multiple IRRsDescartes Rule of Signs

Polynomial of degree nn roots1 real root per sign changeRest = imaginary (i2 = -1)

012-800,0005,000,000-5,000,000PV outflows @ 10% = -4,932,231.40TV inflows @ 10% = 5,500,000.00MIRR = 5.6%The Pavillion Project:Non-normal CFs and MIRR

MIRR versus IRRMIRR 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 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

Sheet1

Project

LS

NPV$18.79$19.98

IRR18.13%23.56%

MIRR16.50%16.89%

PB2.3751.600

DPB2.701.88

0123

-100705020

20

55

84.7

-100159.7

16.89%

0123

-100705020

63.636363636441.322314049615.026296018

-36.36363636364.958677686

1.88

Sheet2

A1BCD

2Project Expected

3Net Cash Flows

4YearLS

50($100)($100)

611070

726050

838020

9NPV$18.78$19.98

10IRR18.13%23.56%

11MIRR16.50%16.89%

12

13=NPV(0.1,C6:C8)+C5

14=IRR(C5:C8)

15=MIRR(C5:C8,0.1,0.1)

Sheet3

CHAPTER 12

Cash Flow Estimation and Risk Analysis

Relevant Cash Flows:Incremental Cash Flow for a ProjectProjects incremental cash flow is:

Corporate cash flow with the projectMinus Corporate cash flow without the project

Relevant Cash FlowsChanges in Net Working CapitalYInterest/Dividends ....NSunk Costs ..NOpportunity Costs .YExternalities/Cannibalism ..YTax Effects ....Y

Tax Effect on Salvage Net Salvage Cash Flow = SP - (SP-BV)(T)

Where:SP = Selling PriceBV = Book ValueT = Corporate tax rate

Including inflation when estimating cash flowsNominal r > real rThe cost of capital, r, includes a premium for inflationNominal CF > real CF Nominal cash flows incorporate inflationIf you discount real CF with the higher nominal r, then your NPV estimate is too low

INFLATIONReal vs. Nominal Cash flowsNominalReal

INFLATIONReal vs. Nominal Cash flows2 Ways to adjust

Adjust WACCCash Flows = RealAdjust WACC to remove inflation

Adjust Cash Flows for InflationUse Nominal WACC

Sensitivity AnalysisShows how changes in an input variable affect NPV or IRREach variable is fixed except oneChange one variable to see the effect on NPV or IRRAnswers what if questions

Sensitivity Analysis

Scenario

Scenario Analysis

BaseLowerUpper

Units6,0005,5006,500

Price/unit$80.00$75.00$85.00

Variable cost/unit$60.00$58.00$62.00

Fixed cost/year$50,000$45,000$55,000

BASEBESTWORST

Initial investment$200,000

Depreciated to salvage value of 0 over 5 years

Deprec/yr$40,000

Project Life5years

Tax rate34%

Required return12%

BASEWORSTBEST

Units6,0005,5006,500

Price/unit$80.00$75.00$85.00


Fixed Cost$50,000$55,000$45,000

Sales$480,000$412,500$552,500

Variable Cost360,000341,000377,000

Fixed Cost50,00055,00045,000

Depreciation40,00040,00040,000

EBIT30,000(23,500)90,500

Taxes10,200(7,990)30,770

Net Income19,800(15,510)59,730

+ Deprec40,00040,00040,000

TOTAL CF59,80024,49099,730

NPV15,566(111,719)159,504

IRR15.1%-14.4%40.9%

NOTE:Note in WORST CASE, tax credit for negative earnings

$(200,000)$(200,000)$(200,000)

59,80024,49099,730

59,80024,49099,730

59,80024,49099,730

59,80024,49099,730

59,80024,49099,730

PV$215,566$88,281$359,504

NPV15,566(111,719)159,504

Sensitivity


BaseUnitsFixed CostVar Cost

Units6,0006,6006,0006,000

Price/unit$80808080

Variable cost/unit$60606054

Fixed cost/year$50,00050,00055,00050,000



Deprec/yr$40,000

Tax rate40%

Required Return10%

BASEUNITSFCVC

Units6,0006,6006,0006,000

Price/unit$80$80$80$80

Variable cost/unit$60$60$60$54

Fixed cost$50,000$50,000$55,000$50,000

Sales$480,000$528,000$480,000$480,000

Variable Cost360,000396,000360,000324,000

Fixed Cost50,00050,00055,00050,000

Depreciation40,00040,00040,00040,000UNITSFCVC

EBIT30,00042,00025,00066,000-30%$(62,015)$53,983$265,509

Taxes12,00016,80010,00026,400-20%$(34,722)$42,610$183,628

Net Income18,00025,20015,00039,600-10%$(7,428)$31,238$101,747

+ Deprec40,00040,00040,00040,000BASE$19,866$19,866$19,866

10%$47,159$8,493$(62,015)

TOTAL CF58,00065,20055,00079,60020%$74,453$(2,879)$(143,896)

30%$101,747$(14,251)$(225,777)

NPV$19,866$47,159$8,493$101,747

% Change in NPV137.4%-57.2%412.2%

% Change in Variable10.0%10.0%-10.0%

SENSITIVITY RATIO13.74-5.72-41.22

DIRECTINVERSEINVERSE

Sensitivity Ratio = (% Change in NPV)/% Change in Variable

Positive = Direct relationship

Negative = Inverse relationship

$(200,000)$(200,000)$(200,000)$(200,000)

58,00065,20055,00079,600

58,00065,20055,00079,600

58,00065,20055,00079,600

58,00065,20055,00079,600

58,00065,20055,00079,600

PV$219,866$247,159$208,493$301,747

NPV$19,866$47,159$8,493$101,747

Sensitivity

Units

FC

VC

Scenario

Scenario Analysis

BaseLowerUpper

Units6,0005,5006,500

Price/unit$80.00$75.00$85.00


Fixed cost/year$50,000$45,000$55,000

BASEBESTWORST



Deprec/yr$40,000

Project Life5years

Tax rate34%

Required return12%

BASEWORSTBEST

Units6,0005,5006,500

Price/unit$80.00$75.00$85.00


Fixed Cost$50,000$55,000$45,000

Sales$480,000$412,500$552,500

Variable Cost360,000341,000377,000

Fixed Cost50,00055,00045,000


EBIT30,000(23,500)90,500

Taxes10,200(7,990)30,770

Net Income19,800(15,510)59,730

+ Deprec40,00040,00040,000

TOTAL CF59,80024,49099,730

NPV15,566(111,719)159,504

IRR15.1%-14.4%40.9%


$(200,000)$(200,000)$(200,000)

59,80024,49099,730

59,80024,49099,730

59,80024,49099,730

59,80024,49099,730

59,80024,49099,730

PV$215,566$88,281$359,504

NPV15,566(111,719)159,504

Sensitivity



Units6,0006,6006,0006,000

Price/unit$80808080


Fixed cost/year$50,00050,00055,00050,000



Deprec/yr$40,000

Tax rate40%

Required Return10%

BASEUNITSFCVC

Units6,0006,6006,0006,000



Fixed cost$50,000$50,000$55,000$50,000

Sales$480,000$528,000$480,000$480,000

Variable Cost360,000396,000360,000324,000

Fixed Cost50,00050,00055,00050,000


EBIT30,00042,00025,00066,000-30%$(62,015)$53,983$265,509

Taxes12,00016,80010,00026,400-20%$(34,722)$42,610$183,628

Net Income18,00025,20015,00039,600-10%$(7,428)$31,238$101,747

+ Deprec40,00040,00040,00040,000BASE$19,866$19,866$19,866

10%$47,159$8,493$(62,015)

TOTAL CF58,00065,20055,00079,60020%$74,453$(2,879)$(143,896)

30%$101,747$(14,251)$(225,777)

NPV$19,866$47,159$8,493$101,747

% Change in NPV137.4%-57.2%412.2%







$(200,000)$(200,000)$(200,000)$(200,000)

58,00065,20055,00079,600

58,00065,20055,00079,600

58,00065,20055,00079,600

58,00065,20055,00079,600

58,00065,20055,00079,600

PV$219,866$247,159$208,493$301,747

NPV$19,866$47,159$8,493$101,747

Sensitivity

Units

FC

VC

Sensitivity GraphUnit SalesVariable CostFixed Cost

Chart3

-6201553983265509

-3472242610183628

-7428.032114050931238101747

19865.632625689919865.632625689919865.6326256899

471598493.2723174646-62015

74453-2879-143896

101747-14251-225777

Units

FC

VC

Scenario

Scenario Analysis

BaseLowerUpper

Units6,0005,5006,500

Price/unit$80.00$75.00$85.00


Fixed cost/year$50,000$45,000$55,000

BASEBESTWORST



Deprec/yr$40,000

Project Life5years

Tax rate34%

Required return12%

BASEWORSTBEST

Units6,0005,5006,500

Price/unit$80.00$75.00$85.00


Fixed Cost$50,000$55,000$45,000

Sales$480,000$412,500$552,500

Variable Cost360,000341,000377,000

Fixed Cost50,00055,00045,000


EBIT30,000(23,500)90,500

Taxes10,200(7,990)30,770

Net Income19,800(15,510)59,730

+ Deprec40,00040,00040,000

TOTAL CF59,80024,49099,730

NPV15,566(111,719)159,504

IRR15.1%-14.4%40.9%


$(200,000)$(200,000)$(200,000)

59,80024,49099,730

59,80024,49099,730

59,80024,49099,730

59,80024,49099,730

59,80024,49099,730

PV$215,566$88,281$359,504

NPV15,566(111,719)159,504

Sensitivity



Units6,0006,6006,0006,000

Price/unit$80808080


Fixed cost/year$50,00050,00055,00050,000



Deprec/yr$40,000

Tax rate40%

Required Return10%

BASEUNITSFCVC

Units6,0006,6006,0006,000



Fixed cost$50,000$50,000$55,000$50,000

Sales$480,000$528,000$480,000$480,000

Variable Cost360,000396,000360,000324,000

Fixed Cost50,00050,00055,00050,000


EBIT30,00042,00025,00066,000-30%$(62,015)$53,983$265,509

Taxes12,00016,80010,00026,400-20%$(34,722)$42,610$183,628

Net Income18,00025,20015,00039,600-10%$(7,428)$31,238$101,747

+ Deprec40,00040,00040,00040,000BASE$19,866$19,866$19,866

10%$47,159$8,493$(62,015)

TOTAL CF58,00065,20055,00079,60020%$74,453$(2,879)$(143,896)

30%$101,747$(14,251)$(225,777)

NPV$19,866$47,159$8,493$101,747

% Change in NPV137.4%-57.2%412.2%







$(200,000)$(200,000)$(200,000)$(200,000)

58,00065,20055,00079,600

58,00065,20055,00079,600

58,00065,20055,00079,600

58,00065,20055,00079,600

58,00065,20055,00079,600

PV$219,866$247,159$208,493$301,747

NPV$19,866$47,159$8,493$101,747

Sensitivity

Units

FC

VC

Sensitivity Ratio%NPV = (New NPV - Base NPV)/Base NPV%VAR = (New VAR - Base VAR)/Base VAR If SR>0 Direct relationship If SR

Sensitivity Ratio -30%$ -62$54$266 0202020%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 Change from Resulting NPV (000s) Base LevelUnit Sales FC VC14-*

Sensitivity GraphUnit Sales13.74Variable Cost-41.22Fixed Cost-5.72

Chart3

-6201553983265509

-3472242610183628

-7428.032114050931238101747

19865.632625689919865.632625689919865.6326256899

471598493.2723174646-62015

74453-2879-143896

101747-14251-225777

Units

FC

VC

Scenario

Scenario Analysis

BaseLowerUpper

Units6,0005,5006,500

Price/unit$80.00$75.00$85.00


Fixed cost/year$50,000$45,000$55,000

BASEBESTWORST



Deprec/yr$40,000

Project Life5years

Tax rate34%

Required return12%

BASEWORSTBEST

Units6,0005,5006,500

Price/unit$80.00$75.00$85.00


Fixed Cost$50,000$55,000$45,000

Sales$480,000$412,500$552,500

Variable Cost360,000341,000377,000

Fixed Cost50,00055,00045,000


EBIT30,000(23,500)90,500

Taxes10,200(7,990)30,770

Net Income19,800(15,510)59,730

+ Deprec40,00040,00040,000

TOTAL CF59,80024,49099,730

NPV15,566(111,719)159,504

IRR15.1%-14.4%40.9%


$(200,000)$(200,000)$(200,000)

59,80024,49099,730

59,80024,49099,730

59,80024,49099,730

59,80024,49099,730

59,80024,49099,730

PV$215,566$88,281$359,504

NPV15,566(111,719)159,504

Sensitivity



Units6,0006,6006,0006,000

Price/unit$80808080


Fixed cost/year$50,00050,00055,00050,000



Deprec/yr$40,000

Tax rate40%

Required Return10%

BASEUNITSFCVC

Units6,0006,6006,0006,000



Fixed cost$50,000$50,000$55,000$50,000

Sales$480,000$528,000$480,000$480,000

Variable Cost360,000396,000360,000324,000

Fixed Cost50,00050,00055,00050,000


EBIT30,00042,00025,00066,000-30%$(62,015)$53,983$265,509

Taxes12,00016,80010,00026,400-20%$(34,722)$42,610$183,628

Net Income18,00025,20015,00039,600-10%$(7,428)$31,238$101,747

+ Deprec40,00040,00040,00040,000BASE$19,866$19,866$19,866

10%$47,159$8,493$(62,015)

TOTAL CF58,00065,20055,00079,60020%$74,453$(2,879)$(143,896)

30%$101,747$(14,251)$(225,777)

NPV$19,866$47,159$8,493$101,747

% Change in NPV137.4%-57.2%412.2%







$(200,000)$(200,000)$(200,000)$(200,000)

58,00065,20055,00079,600

58,00065,20055,00079,600

58,00065,20055,00079,600

58,00065,20055,00079,600

58,00065,20055,00079,600

PV$219,866$247,159$208,493$301,747

NPV$19,866$47,159$8,493$101,747

Sensitivity

Units

FC

VC

Results of Sensitivity AnalysisSteeper 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:WeaknessesDoes not reflect diversificationSays nothing about the likelihood of change in a variablei.e. a steep sales line is not a problem if sales wont fallIgnores relationships among variables

Sensitivity Analysis:StrengthsProvides indication of stand-alone riskIdentifies dangerous variablesGives some breakeven information

Scenario AnalysisExamines several possible situations, usually:Worst case Base case or most likely case, and Best caseProvides a range of possible outcomes

Scenario Example

Scenario

Scenario Analysis

BaseLowerUpper

Units6,0005,5006,500

Price/unit$80.00$75.00$85.00


Fixed cost/year$50,000$45,000$55,000

BASEBESTWORST



Deprec/yr$40,000

Project Life5years

Tax rate34%

Required return12%

BASEWORSTBEST

Units6,0005,5006,500

Price/unit$80.00$75.00$85.00


Fixed Cost$50,000$55,000$45,000

Sales$480,000$412,500$552,500

Variable Cost360,000341,000377,000

Fixed Cost50,00055,00045,000


EBIT30,000(23,500)90,500

Taxes10,200(7,990)30,770

Net Income19,800(15,510)59,730

+ Deprec40,00040,00040,000

TOTAL CF59,80024,49099,730

NPV15,566(111,719)159,504

IRR15.1%-14.4%40.9%


$(200,000)$(200,000)$(200,000)

59,80024,49099,730

59,80024,49099,730

59,80024,49099,730

59,80024,49099,730

59,80024,49099,730

PV$215,566$88,281$359,504

NPV15,566(111,719)159,504

Sensitivity


BaseUnitsFixed Cost

Units6,0005,5006,000

Price/unit$808080


Fixed cost/year$50,00050,00055,000



Deprec/yr$40,000

Tax rate34%

Required Return12%

BASEUNITSFC

Units6,0005,5006,000

Price/unit$80$80$80

Variable cost/unit$60$60$60

Fixed cost$50,000$50,000$55,000

Sales$480,000$440,000$480,000

Variable Cost360,000330,000360,000

Fixed Cost50,00050,00055,000


EBIT30,00020,00025,000

Taxes10,2006,8008,500

Net Income19,80013,20016,500

+ Deprec40,00040,00040,000

TOTAL CF59,80053,20056,500

NPV$15,566$(8,226)$3,670

% Change in NPV-152.8%-76.4%

% Change in Variable-8.3%10.0%

SENSITIVITY RATIO18.34-7.64

DIRECTINVERSE




$(200,000)$(200,000)$(200,000)

59,80053,20056,500

59,80053,20056,500

59,80053,20056,500

59,80053,20056,500

59,80053,20056,500

PV$215,566$191,774$203,670

NPV$15,566$(8,226)$3,670

Scenario

Scenario Analysis

BaseLowerUpper

Units6,0005,5006,500

Price/unit$80.00$75.00$85.00


Fixed cost/year$50,000$45,000$55,000

BASEBESTWORST



Deprec/yr$40,000

Project Life5years

Tax rate34%

Required return12%

BASEWORSTBEST

Units6,0005,5006,500

Price/unit$80.00$75.00$85.00


Fixed Cost$50,000$55,000$45,000

Sales$480,000$412,500$552,500

Variable Cost360,000341,000377,000

Fixed Cost50,00055,00045,000


EBIT30,000(23,500)90,500

Taxes10,200(7,990)30,770

Net Income19,800(15,510)59,730

+ Deprec40,00040,00040,000

TOTAL CF59,80024,49099,730

NPV15,566(111,719)159,504

IRR15.1%-14.4%40.9%


$(200,000)$(200,000)$(200,000)

59,80024,49099,730

59,80024,49099,730

59,80024,49099,730

59,80024,49099,730

59,80024,49099,730

PV$215,566$88,281$359,504

NPV15,566(111,719)159,504

Sensitivity


BaseUnitsFixed Cost

Units6,0005,5006,000

Price/unit$808080


Fixed cost/year$50,00050,00055,000



Deprec/yr$40,000

Tax rate34%

Required Return12%

BASEUNITSFC

Units6,0005,5006,000

Price/unit$80$80$80

Variable cost/unit$60$60$60

Fixed cost$50,000$50,000$55,000

Sales$480,000$440,000$480,000

Variable Cost360,000330,000360,000

Fixed Cost50,00050,00055,000


EBIT30,00020,00025,000

Taxes10,2006,8008,500

Net Income19,80013,20016,500

+ Deprec40,00040,00040,000

TOTAL CF59,80053,20056,500

NPV$15,566$(8,226)$3,670

% Change in NPV-152.8%-76.4%

% Change in Variable-8.3%10.0%

SENSITIVITY RATIO18.34-7.64

DIRECTINVERSE




$(200,000)$(200,000)$(200,000)

59,80053,20056,500

59,80053,20056,500

59,80053,20056,500

59,80053,20056,500

59,80053,20056,500

PV$215,566$191,774$203,670

NPV$15,566$(8,226)$3,670

Problems with Scenario AnalysisOnly considers a few possible out-comesAssumes that inputs are perfectly correlatedAll bad values occur together and all good values occur togetherFocuses on stand-alone risk

Monte Carlo Simulation AnalysisComputerized version of scenario analysis using continuous probability distributionsComputer selects values for each variable based on given probability distributions

Monte Carlo Simulation AnalysisCalculates 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 valuesGenerally shown graphically

Histogram of Results

Advantages of Simulation AnalysisReflects the probability distributions of each inputShows range of NPVs, the expected NPV, NPV, and CVNPVGives an intuitive graph of the risk situation

Disadvantages of Simulation AnalysisDifficult to specify probability distributions and correlationsIf inputs are bad, output will be bad: Garbage in, garbage out

Disadvantages of Sensitivity, Scenario and Simulation AnalysisSensitivity, scenario, and simulation analyses do not provide a decision rule Do not indicate whether a projects expected return is sufficient to compensate for its riskSensitivity, 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 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 conditionsAlert managers always look for real options in projectsSmarter managers try to create real options

Types of Real OptionsInvestment timing optionsGrowth options Expansion of existing product lineNew productsNew geographic marketsAbandonment optionsContractionTemporary suspensionFlexibility options

FIN 331 in a NutshellFinancial Management I Reviewfor FIN 338

Its important to point out that there are many different ways to refer to the interest rate that we use in time value of money calculations. Students often get confused with the terminology, especially since they tend to think of an interest rate only in terms of loans and savings accounts.I am providing information on the Texas Instruments BA-II Plus other calculators are similar. If you recommend or require a specific calculator other than this one, you may want to make the appropriate changes.

Note: the more information students have to remember to enter the more likely they are to make a mistake. For this reason, I normally tell my students to set P/Y = 1 and leave it that way. Then I teach them to work on a period basis, which is consistent with using the formulas. If you want them to use the P/Y function, remind them that they will need to set it every time they work a new problem and that CLR TVM does not affect P/Y.

If students are having difficulty getting the correct answer, make sure they have done the following:Set decimal places to floating point (2nd Format, Dec = 9 enter) or show 4 to 5 decimal places if using and HPDouble check and make sure P/Y = 1Make sure to clear the TVM registers after finishing a problem (or before starting a problem) It is important to point out that CLR TVM clears the FV, PV, N, I/Y and PMT registers. C/CE and CLR Work DO NOT affect the TVM keys

The remaining slides will work the problems using the notation provided above for calculator keys. The formulas are presented in the notes section.Click on the tabs at the bottom of the worksheet to move between examples.It is important at this point to discuss the sign convention in the calculator. The calculator is programmed so that cash outflows are entered as negative and inflows are entered as positive. If you enter the PV as positive, the calculator assumes that you have received a loan that you will have to repay at some point. The negative sign on the future value indicates that you would have to repay 1276.28 in 5 years. Show the students that if they enter the 1000 as negative, the FV will compute as a positive number.

Also, you may want to point out the change sign key on the calculator. There seem to be a few students each semester that have never had to use it before.

Formula: FV = 1000(1.05)5 = 1000(1.27628) = 1276.28It is important at this point to discuss the sign convention in the calculator. The calculator is programmed so that cash outflows are entered as negative and inflows are entered as positive. If you enter the PV as positive, the calculator assumes that you have received a loan that you will have to repay at some point. The negative sign on the future value indicates that you would have to repay 1276.28 in 5 years. Show the students that if they enter the 1000 as negative, the FV will compute as a positive number.

Also, you may want to point out the change sign key on the calculator. There seem to be a few students each semester that have never had to use it before.

Formula: FV = 1000(1.05)5 = 1000(1.27628) = 1276.28Remember the sign convention.

Formulas: PV = 500 / (1.1)5 = 500(.620921323) = 310.46PV = 500 / (1.1)10 = 500(.385543289) = 192.77Formulas: PV = 500 / (1.1)5 = 500(.620921323) = 310.46PV = 500 / (1.15)5 = 500(.497176735) = 248.59Point out that the PV interest factor = 1 / (1 + r)tPoint out that the PV interest factor = 1 / (1 + r)tThe students can read the example in the book.

After carefully going over your budget, you have determined you can afford to pay $632 per month towards a new sports car. You call up your local bank and find out that the going rate is 1 percent per month for 48 months. How much can you borrow?

Note that the difference between the answer here and the one in the book is due to the rounding of the Annuity PV factor in the book.Remember the sign convention.

Formulas: PV = 500 / (1.1)5 = 500(.620921323) = 310.46PV = 500 / (1.1)10 = 500(.385543289) = 192.77Formulas: PV = 500 / (1.1)5 = 500(.620921323) = 310.46PV = 500 / (1.15)5 = 500(.497176735) = 248.59FV = 100(1.08)4 + 300(1.08)2 = 136.05 + 349.92 = 485.97Olympics balance sheet is pretty straightforward. Assets consist of cash and cash equivalents, short-term investments, accounts receivable and inventories under current assets plus net plant and equipment.Liabilities include accounts payable, notes payable, and accruals under current liabilities plus Olympic has long-term bonds outstanding.Shareh

FIN 331 in a Nutshell

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