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

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fin 331 in a nutshell

FIN 331 in a Nutshell

Financial Management I Review

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

Click on the selected topic to go directly to that section

financial statements cash flow and taxes

Financial Statements, Cash Flow, and Taxes

Key Financial Statements

Balance sheet

Income statements

Statement of cash flows

Index

the annual report
The Annual Report
  • Balance sheet
    • Snapshot of a firm’s financial position at a point in time
  • Income statement
    • Summarizes a firm’s revenues and expenses over a given period of time
  • Statement of cash flows
    • Reports the impact of a firm’s activities on cash flows over a given period of time
sample balance sheet
Sample Balance Sheet

Assets =

Liabilities +

Owner’s Equity

sample income statement
Sample Income Statement

Net income=Dividends + Retained earnings

statement of cash flows
Statement of Cash Flows
  • Provides information about cash inflows and outflows during an accounting period
  • Required since 1988
  • Developed from Balance Sheet and Income Statement data
statement of cash flows1
Statement of Cash Flows

Reconciles the change in Cash & Equivalents

statement of cash flows2
Statement of Cash Flows
  • Reconciles the Income Statement and Balance Sheet to the flow of cash
    • The Matching Principle requires estimates and accruals to prepare Financial statements
    • Financial Analysis is concerned with Cash Flow

Why is it important???

statement of cash flows3
Statement of Cash Flows

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

slide14

Deficits

Covered by new debt and cash

net operating working capital
Net Operating Working Capital

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

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

= NOWC + Net fixed assets

  • Operating Capital
    • (2005) = $800 + $1,000 = $1,800 million
    • (2004) = $650 + $870 = $1,520 million
  • Net Investment in Operating Capital

= Op Cap (2005) – Op Cap (2004)

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

net operating profit after taxes nopat operating cash flow
NOPAT = EBIT(1 - Tax rate)

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

OCF05 = NOPAT + Deprec + Amort

= $170.3 + $100

= $270.3

Net Operating Profit after Taxes (NOPAT) & Operating Cash Flow
free cash flow fcf for 2005
EBIT = $283.8 m T = 40% Depreciation = $100 m

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

NOWC = $800 - $650 = $150 m

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

= -$109.7 m

Free Cash Flow (FCF) for 2005
analysis of financial statements

Analysis of Financial Statements

Ratio Analysis

Limitations of ratio analysis

Qualitative factors

Index

five major categories of ratios
Five Major Categories of Ratios
  • Liquidity
    • CR - Current Ratio
    • QR - Quick Ratio or “Acid-Test”
  • Asset management
    • Inventory Turnover
    • DSO – Days sales outstanding
    • FAT - Fixed Assets Turnover
    • TAT - Total Assets Turnover
  • Debt management
    • Debt Ratio
    • TIE – Times interest earned
    • EBITDA coverage (EC)
five major categories of ratios1
Five Major Categories of Ratios
  • Profitability
    • PM - Profit margin on sales
    • BEP – Basic earning power
    • ROA – Return on total assets
    • ROE – Return on common equity
  • Market value
    • P/E – Price-Earnings ratio
    • P/CF – Price – cash flow ratio
    • M/B – Market to book
liquidity ratios
Liquidity Ratios
  • CR = Current Ratio

= CA/CL

  • QR = Quick Ratio or “Acid-Test”

= (CA-INV)/CL

asset management ratios
Asset Management Ratios
  • Inventory Turnover = Sales/Inventories
  • DSO = Days sales outstanding

= Receivables /(Annual sales/365)

  • FAT = Fixed Assets Turnover

= Sales/Net Fixed Assets

  • TAT = Total Assets Turnover

= Sales/Total Assets

debt management ratios
Debt Management Ratios
  • Debt Ratio = Total Liabilities/Total Assets
  • TIE = Times interest earned

= EBIT/Interest

  • EBITDA coverage = EC

(EBITDA + lease pmts) .

(Interest + principal pmts + lease pmts)

profitability ratios
Profitability Ratios
  • PM = Profit margin on sales

= NI/Sales

  • BEP = Basic earning power

= EBIT/Total Assets

  • ROA = Return on total assets

= NI/Total Assets

  • ROE = Return on common equity

= NI/Common Equity

market value metrics
Market Value Metrics
  • P/E = Price-Earnings ratio

= Price per share/Earnings per share

  • P/CF = Price–cash flow ratio

= Price per share/Cash flow per share

  • M/B = Market to book

= Market price per share

Book value per share

potential problems and limitations of ratio analysis
Potential Problems and Limitations of Ratio Analysis
  • Comparison with industry averages is difficult if the firm operates many different divisions
  • “Average” performance ≠ necessarily good
  • Seasonal factors can distort ratios
  • Window dressing techniques
problems and limitations continued
Problems and Limitations (Continued)
  • Different accounting and operating practices can distort comparisons
  • Sometimes difficult to tell if a ratio value is “good” or “bad”
  • Different ratios give different signals
    • Difficult to tell, on balance, whether a company is in a strong or weak financial condition
qualitative factors
Qualitative Factors
  • Revenues tied to a single customer?
  • Revenues tied to a single product?
  • Reliance on a single supplier?
  • Percentage of business generated overseas?
  • Competitive situation?
  • Legal and regulatory environment?
financial planning and forecasting

Financial Planning and Forecasting

Forecasting sales

Projecting the assets and internally generated funds

Projecting outside funds needed

Deciding how to raise funds

Index

the afn formula
The AFN Formula

If ratios are expected to remain constant:

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

Required  Assets

 Retained Earnings

Spontaneously  Liabilities

variables in the afn formula
Variables in the AFN Formula
  • A* = Assets tied directly to sales
  • S0 = Last year’s sales
  • S1 = Next year’s projected sales
  • ∆S = Increase in sales; (S1-S0)
  • L* = Liabilities that spontaneously increase with sales
variables in the afn formula1
Variables in the AFN Formula
  • A*/S0: assets required to support sales;

“Capital Intensity Ratio”

  • L*/S0: spontaneous liabilities ratio
  • M: profit margin (Net income/sales)
  • RR: retention ratio; percent of net

income not paid as dividend

key factors in afn
Key Factors in AFN
  • ∆S = Sales Growth
  • A*/S0 = Capital Intensity Ratio
  • L*/S0 = Spontaneous Liability Ratio
  • M = Profit Margin
  • RR = Retention Ratio
time value of money
Time Value of Money
  • Timelines
  • Future Value
  • Present Value
  • Present Value of Uneven Cash Flows
time lines timing of cash flows
Time Lines: Timing of Cash Flows

0

1

2

3

I%

CF0

CF1

CF2

CF3

  • Tick marks occur at the end of periods
    • Time 0 = today
    • Time 1 = the end of the first period or the beginning of the second period

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

basic definitions
Basic Definitions

Present Value(PV)

  • The current value of future cash flows discounted at the appropriate discount rate
  • Value at t=0 on a time line

Future Value(FV)

  • The amount an investment is worth after one or more periods.
  • “Later” money on a time line
future value general formula
Future Value: General Formula
  • FV = future value
  • PV = present value
  • I = period interest rate, expressed
  • as a decimal
  • N = number of periods
  • Future value interest factor = (1 + I)N
    • Note: “yx” key on your calculator

FV = PV(1 + I)N

texas instruments ba ii plus
Texas Instruments BA-II Plus

FV = future value

PV = present value

PMT = periodic payment

I/Y = period interest rate

N = number of periods

One of these MUST be negative

N I/Y PV PMT FV

excel spreadsheet functions
Excel Spreadsheet Functions

=FV(rate,nper,pmt,pv)

=PV(rate,nper,pmt,fv)

=RATE(nper,pmt,pv,fv)

=NPER(rate,pmt,pv,fv)

  • Use the formula icon (ƒx) when you can’t remember the exact formula
future values example
Future Values – Example

Suppose you invest $100 for 5 years at 10%

How much would you have?

Formula Solution:

FV =PV(1+I)N

=100(1.10)5

=100(1.6105)

=161.05

future value example
Future Value – Example

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

Calculator Solution

  • 5 N
  • 10 I/Y
  • -100 PV
  • 0 PMT
  • CPT FV = 161.05
future value important relationship 1
Future Value: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

future value important relationship 2
Future ValueImportant Relationship 2

For a given time period:

  • The higher the interest rate,
  • The larger the future value

FV = PV(1 + I)N

For a given N, as I increases, FV increases

present values
Present Values
  • The current value of future cash flows discounted at the appropriate discount rate
  • Value at t=0 on a time line
  • Answers the questions:
    • How much do I have to invest today to have some amount in the future?
    • What is the current value of an amount to be received in the future?
present values1
Present Values

FV = PV(1 + I)N

  • Rearrange to solve for PV

PV = FV / (1+I)N

PV = FV(1+I)-N

  • “Discounting” = finding the present value of one or more future amounts
present value one period example
Present Value: One Period Example
  • You need $10,000 for the down payment on a new car
  • You can earn 7% annually.
  • How much do you need to invest today?
  • 1 N;
  • 7 I/Y;
  • 0 PMT;
  • 10000 FV;
  • CPT PV = -9345.79

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

=PV(0.07,1,0,10000)

present value important relationship 1
Present Value: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 2
Present ValueImportant Relationship 2

For a given time period:

  • The higher the interest rate,
  • The smaller the present value

For a given N, as I increases, PV decreases

the basic pv equation refresher
The Basic PV Equation - Refresher

PV = FV / (1 + I)N

There are four parts to this equation

    • PV, FV, I and N
    • Know any three, solve for the fourth
  • If you are using a financial calculator, be sure and remember the sign convention

+CF = Cash INFLOW-CF = Cash OUTFLOW

multiple cash flows present value
Multiple Cash FlowsPresent Value
  • The Basic Formula
  • The TI BA II+
    • Using the PV/FV keys
    • Using the Cash Flow Worksheet
  • Excel
multiple uneven cash flows present value
Multiple Uneven Cash Flows Present Value
  • You are offered an investment that will pay
    • $200 in year 1,
    • $400 the next year,
    • $600 the following year, and
    • $800 at the end of the 4th year.
    • You can earn 12% on similar investments.
    • What is the most you should pay for this investment?
what is the pv of this uneven cash flow stream

4

0

1

2

3

12%

200

400

600

800

-178.57

-318.88

-427.07

-508.41

What is the PV of this uneven cash flow stream?

-1,432.93 = PV

multiple uneven cash flows pv
Multiple Uneven Cash Flows – PV

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

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

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

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

Total PV = -$1,432.93

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

Clear all:

  • Press CF
  • Then 2nd
  • And CLR WORK (above CE/C)

CF0 is displayed and is 0

Enter the Period 0 cash flow

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

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

ti baii uneven cfs
TI BAII+: Uneven CFs
  • Press the down arrow () to move to the next cash flow register.
  • Enter the cash flow amount, press ENTER and then down arrow to move to the cash flow counter (Fn).
  • The default counter value is “1”.
    • To accept the value of “1”, press the down arrow again.
    • To change the counter, enter the correct count, press ENTER and then the down arrow.
ti baii uneven cfs1
TI BAII+: Uneven CFs
  • Repeat for all cash flows, in order.
  • To find NPV:
    • Press NPV: I appears on the screen
    • Enter the interest rate, press ENTER and the down arrow to display NPV.
    • Press compute “CPT”
ti baii uneven cash flows
TI BAII+: Uneven Cash Flows

CF

C000ENTER

C01200 ENTER

F011 ENTER

C02400 ENTER 

F021 ENTER 

C03600 ENTER

F031 ENTER

C04 800 ENTER 

F04 1 ENTER  NPV

I12 ENTER 

NPV CPT

1432.93

Cash Flows:

CF0 = 0

CF1 = 200

CF2 = 400

CF3 = 600

CF4 = 800

bonds and their valuation

Bonds and Their Valuation

Interest rates

Bond valuation

Measuring yield

Index

nominal vs real rates
“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

r r ip drp lp mrp
Here:

r = Required rate of return on a debt security

r* = Real risk-free rate

IP = Inflation premium

DRP = Default risk premium

LP = Liquidity premium

MRP = Maturity risk premium

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

rRF=

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

ST Treasury ST IP

LT Treasury LT IP MRP

ST Corporate ST IP DRP LP

LT Corporate LT IP DRP MRP LP

Debt Instrument IP DRP MRP LP

discount rate ytm
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

bond value
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
the bond pricing equation
The Bond-Pricing Equation

PV(lump sum)

PV(Annuity)

C = Coupon payment; F = Face value

texas instruments ba ii plus1

N I/Y PV PMT FV

Texas Instruments BA-II Plus
  • FV = future value/face value/par value
  • PV = present value=bond value/price
  • I/Y = period interest rate = YTM
  • N = number of periods to maturity
  • PMT = coupon payment
spreadsheet functions
Spreadsheet Functions

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

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

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

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

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

  • Inside parens: (RATE,NPER,PMT,PV,FV,0/1)
  • “0/1”Ordinary annuity = 0 (default)
    • Annuity Due = 1 (must be entered)
pricing specific bonds
Pricing Specific Bonds
  • TI BA II+
    • Bond Worksheet [2nd] BOND
    • SDT CPN RDT RV ACT 2/Y YLD PRI
  • Excel:
    • PRICE(Settlement,Maturity,Rate,Yld,Redemption, Frequency,Basis)
    • YIELD(Settlement,Maturity,Rate,Pr,Redemption, Frequency,Basis)
      • Settlement and maturity need to be actual dates
      • Redemption and Pr need to given as % of par value
yield to maturity ytm
Yield to Maturity (YTM)
  • The market required rate of return for bonds of similar risk and maturity
  • The discount rate used to value a bond
  • Return earned if bond held to maturity
  • Usually = coupon rate at issue
  • Quoted as an APR
  • The IRR of a bond
what is the ytm on a 10 year 9 annual coupon 1 000 par value bond selling for 887
What is the YTM on a 10-year, 9% annual coupon, $1,000 par value bond, selling for $887?
  • Must find the rd that solves this model:
using a financial calculator to solve for the ytm
Using a financial calculator to solve for the YTM
  • YTM =10.91%
  • Bond sells at a discount because YTM > coupon rate

10

- 887

90

1000

INPUTS

N

I/YR

PV

PMT

FV

OUTPUT

10.91

solving for ytm
Solving for YTM
  • Coupon rate = 9%
  • Annual coupons
  • Par = $1,000
  • Maturity = 10 years
  • Price = $887

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

  • Using the calculator:
      • N = 10
      • PV = -887
      • PMT = 90
      • FV = 1000
      • CPT I/Y = 10.91

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

find ytm if the bond price is 1 134 20
Find YTM, if the bond price is $1,134.20
  • YTM = 7.08%
  • Bond sells at a premium because YTM < coupon rate

10

-1134.2

90

1000

INPUTS

N

I/YR

PV

PMT

FV

OUTPUT

7.08

solving for ytm1
Solving for YTM
  • Coupon rate = 9%
  • Annual coupons
  • Par = $1,000
  • Maturity = 10 years
  • Price = $1,134.20

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

  • Using the calculator:
      • N = 10
      • PV = -1134.20
      • PMT = 90
      • FV = 1000
      • CPT I/Y = 7.08

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

semiannual bonds
Semiannual bonds
  • Multiply years by 2: number of periods = 2N.
  • Divide nominal rate by 2: periodic rate (I/YR) = rd / 2.
  • Divide annual coupon by 2: PMT = ann cpn / 2.

2N

rd / 2

OK

cpn / 2

OK

INPUTS

N

I/YR

PV

PMT

FV

OUTPUT

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

20

6.5

50

1000

INPUTS

N

I/YR

PV

PMT

FV

OUTPUT

- 834.72

valuing a semiannual bond
Valuing a Semiannual Bond
  • Coupon rate = 10%
  • Annual coupons
  • Par = $1,000
  • Maturity = 10 years
  • YTM = 13%
  • Using the calculator:
    • N = 20
    • I/Y = 6.5
    • PMT = 50
    • FV = 1000
    • CPT PV = -834.72

Using the formula:

=PV(0.065, 10, 50, 1000)

ytm with semiannual coupons
YTM with Semiannual Coupons
  • Suppose a bond with a 10% coupon rate and semiannual coupons, has a face value of $1000, 20 years to maturity and is selling for $1197.93.
    • Is the YTM more or less than 10%?
    • What is the semiannual coupon payment?
    • How many periods are there?
ytm with semiannual coupons1
YTM with Semiannual Coupons
  • Suppose a bond with a 10% coupon rate and semiannual coupons, has a face value of $1000, 20 years to maturity and is selling for $1197.93.

N = 40

PV = -1197.93

PMT = 50

FV = 1000

CPT I/Y = 4%

YTM = 4%*2 = 8%

 Result = ½ YTM

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

Calculator solves what you enter.

risk and rates of return

Risk and Rates of Return

Stand-alone Risk

Portfolio Risk

Risk & Return: CAPM / SML

Index

the expected rate of return
The Expected Rate of Return

r “hat” = expected return

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

Pi = Probability of “ith” state occurring

the standard deviation of returns
The Standard Deviation of Returns

σ = Standard deviation

σ = √ Variance = √ σ2

coefficient of variation cv
Coefficient of Variation (CV)

CV = Standard deviation/expected return

= Risk per unit of return

=

portfolio expected return
Portfolio Expected Return

^

  • rp = weighted average
    • wi = % of portfolio in stock i
    • ri = return on stock i
portfolio expected return1
Portfolio Expected Return

Assume a two-stock portfolio is created with

$50,000 invested in both HT and Collections

^

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

portfolio return
Portfolio Return

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

“Portfolio Return” = Prob x “Portfolio”

portfolio risk
Portfolio Risk

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

portfolio risk return
Portfolio Risk & Return

  • σp = 3.4% is much lower than the σ of either stock
  • σp = 3.4% is lower than the weighted average of HT and Coll.’s σ (16.6%)
  • The portfolio provides the average return of component stocks, but lower than the average risk
  • Why? Negative correlation between stocks
covariance of returns
Covariance of Returns

Measures how much the returns on two risky assets move together

covariance
Covariance

Covariance (HT:Coll) = -0.0264

correlation coefficient
Correlation Coefficient
  • Correlation Coefficient = ρ (rho)
  • Scales covariance to [-1,+1]
    • -1 = Perfectly negatively correlated
    • 0 = Uncorrelated; not related
    • +1 = Perfectly positively correlated
two stock portfolios
Two-Stock Portfolios

If r = -1.0

  • Two stocks can be combined to form a riskless portfolio

If r = +1.0

  • No risk reduction at all

In general, stocks have r≈ 0.35

  • Risk is lowered but not eliminated

Investors typically hold many stocks

s of n stock portfolio
s of n-Stock Portfolio
  • Subscripts denote stocks i and j
  • ri,j = Correlation between stocks i and j
  • σi and σj=Standard deviations of stocks i and j
  • σij = Covariance of stocks i and j
portfolio risk n risky assets
Portfolio Risk-n Risky Assets

i j for n=2

1 1 w1w111 = w1212

1 2 w1w212

2 1 w2w121

2 2 w2w222 = w2222

p2= w1212 + w2222 + 2w1w2 12

capital asset pricing model capm
Capital Asset Pricing Model (CAPM)
  • Links risk and required returns
  • Security Market Line (SML):
    • A stock’s required return equals the risk-free return (rRF) plus a risk premium (RPM x ) that reflects the stock’s risk after diversification
  • Primary conclusion:
    • The relevant riskiness of a stock is its contribution to the riskiness of a well-diversified portfolio.
the sml and required return
The SML and Required Return
  • The Security Market Line (SML) is part of the Capital Asset Pricing Model (CAPM)
  • rRF = Risk-free rate
  • RPM = Market risk premium = rM – rRF
the market risk premium r m r rf rp m
The Market Risk Premium (rM – rRF = RPM)
  • Additional return over the risk-free rate to compensate investors for assuming an average amount of risk
  • Size depends on:
    • Perceived risk of the stock market
    • Investors’ degree of risk aversion
  • Varies from year to year
    • Estimates suggest a range between 4% and 8% per year
required rates of return
Required Rates of Return

Assume: rRF = 5.5% RPM = 5%

  • rHT = 5.5% + (5.0%)(1.32)

= 5.5% + 6.6% = 12.10%

  • rM = 5.5% + (5.0%)(1.00) = 10.50%
  • rUSR = 5.5% + (5.0%)(0.88) = 9.90%
  • rT-bill = 5.5% + (5.0%)(0.00) = 5.50%
  • rColl = 5.5% + (5.0%)(-0.87) = 1.15%
expected vs required returns
Expected vs RequiredReturns

“Required” by the market

“Expected” by YOU

illustrating the security market line
Illustrating the Security Market Line

SML: ri = 5.5% + (5.0%) i

ri (%)

SML

.

HT

.

.

rM = 10.5

rRF = 5.5

.

USR

T-bills

.

Risk, i

-1 0 1 2

Coll.

portfolio beta
Portfolio Beta

Where:

wi =weight (% dollars invested in asset i)

βi = Beta of asset i

βp=Portfolio Beta

stocks and their valuation

Stocks and Their Valuation

Constant growth stock valuation

Non-constant growth stock valuation

Corporate value model

Index

constant growth stock
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:
constant growth model
Constant Growth Model

Needed data:

D0 = Dividend just paid

D1 = Next expected dividend

g = constant growth rate

rs = required return on the stock

expected value at time t
Expected Value at time t

Value at t=0

Value at t

supernormal growth
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
valuing common stock with nonconstant growth

0

1

2

3

4

rs = 13%

...

g = 30%

g = 30%

g = 30%

g = 6%

D0 = 2.00 2.600 3.380 4.394

4.658

2.301

2.647

3.045

4.658

=

=

$66.54

46.114

-

0.13

0.06

54.107 = P0

Valuing common stock with nonconstant growth

$

P

corporate value model
Corporate Value Model
  • = Free Cash Flow method
    • Value of the firm = present value of the firm’s expected future free cash flows
    • Free cash flow =after-tax operating income less net capital investment
    • FCF = NOPAT – Net capital investment
applying the corporate value model
Applying the corporate value model

Market value of firm:

  • (MVF) = PV(future FCFs)

MV of common stock:

  • = MVF – MV of debt

Intrinsic stock value:

  • = MVCS /# shares
issues regarding the corporate value model
Issues regarding the corporate value model
  • Oftenpreferred to the dividend growth model
    • Firms that don’t pay dividends
    • Dividends hard to forecast
  • Assumes at some point free cash flow growth rate will be constant
  • Terminal value (TVN) = value of firm at the point that growth becomes constant
firm s intrinsic value

0

1

2

3

4

r = 10%

...

g = 6%

-5 10 20

21.20

-4.545

8.264

15.026

21.20

398.197

530= = TV3

0.10

-

0.06

416.942

Firm’s Intrinsic Value

Long-run gFCF = 6% WACC = 10%

slide123
If the firm has $40 million in debt and has 10 million shares of stock, what is the firm’s intrinsic value per share?
  • MV of equity = MV of firm – MV of debt

= $416.94 - $40

= $376.94 million

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

= $376.94 / 10

= $37.69

firm multiples method
Firm multiples method
  • Often used by analysts to value stocks
    • P / E Price-earning
    • P / CF Price-cash flow
    • P / Sales Price-sales
  • Method:
    • Estimate appropriate ratio based on comparable firms
    • Multiply estimate by expected metric to estimate stock price
the cost of capital

The Cost of Capital

Cost of equity

WACC

Adjusting for risk

Index

wacc weighted average cost of capital
WACCWeighted Average Cost of Capital

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

Where:

wD = % of debt in capital structure

wP= % of preferred stock in capital structure

wC= % of common equity in capital structure

rD = firm’s cost of debt

rP= firm’s cost of preferred stock

rC= firm’s cost of equity

T = firm’s corporate tax rate

Weights

Component costs

three ways to determine the cost of equity r s
Three ways to determine the cost of equity, rs:

1. DCF: rs = D1/P0 + g

2. CAPM: rs = rRF + (rM - rRF)βi

= rRF + (RPM)βi

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

rs = rd + Bond RP

dcf approach inputs
DCF Approach: Inputs
  • Current stock price (P0)
  • Current dividend (D0)
  • Growth rate (g)
four mistakes to avoid
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
should the company use the composite wacc as the hurdle rate for each of its projects
Should the company use the composite WACC as the hurdle rate for each of its projects?
  • NO!
  • A firm’s composite WACC reflects the risk of an average project
    • WACC = “hurdle rate” for an average risk project
  • Different divisions/projects may have different risks
    • Division or project WACC should be adjusted to reflect appropriate risk
divisional and project costs of capital
Divisional and Project Costs of Capital
  • Using the WACC as the discount rate is only appropriate for projects that are the same risk as the firm’s current operations
  • If considering a project that is NOT of the same risk as the firm, then an appropriate discount rate for that project is needed
  • Divisions also often require separatediscount rates
using wacc for all projects example
Using WACC for All Projects - Example
  • What would happen if we use the WACC for all projects regardless of risk?
  • Assume the WACC = 15%
divisional risk and the cost of capital
Divisional Risk and the Cost of Capital

Rate of Return

(%)

Acceptance Region

WACC

WACC

H

Acceptance Region

Rejection Region

WACC

F

Rejection Region

WACC

L

Risk

0

Risk

Risk

L

H

subjective approach
Subjective Approach
  • Consider the project’s risk relative to the firm overall
    • If project risk > firm risk  project discount rate > WACC
    • If project risk < firm risk  project discount rate < WACC
the basics of capital budgeting

The Basics of Capital Budgeting

Independent vs. mutually exclusive CFs

Normal vs. non-normal CFs

NPV

IRR

MIRR

PB

DPB

Index

steps to capital budgeting
Steps to capital budgeting
  • Estimate CFs (inflows & outflows)
  • Assess riskiness of CFs
  • Determine appropriate cost of capital
  • Find NPV and/or IRR
  • Accept if NPV>0 and/or IRR>WACC
independent vs mutually exclusive projects
Independent vs. Mutually Exclusive Projects
  • Independent:
    • The cash flows of one are unaffected by the acceptance of the other
  • Mutually Exclusive:
    • The acceptance of one project precludes acceptance of the other
npv sum of the pvs of all cash flows

n

CFt

.

NPV =

(1 + r)t

t = 0

n

CFt

- CF0

NPV =

(1 + r)t

t = 1

NPV: Sum of the PVs of all cash flows.

NOTE: t=0

Cost often is CF0 and is negative

ti baii uneven cash flows1
TI BAII+: Uneven Cash Flows

CF

C00100 +/-ENTER

C0110 ENTER

F011 ENTER

C0260 ENTER 

F021 ENTER 

C0380 ENTER

F031 ENTER NPV

I10 ENTER 

NPV CPT

$18.78

Cash Flows:

CF0 = -100

CF1 = 10

CF2 = 60

CF3 = 80

internal rate of return irr
Internal Rate of Return (IRR)

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

Solving for IRR with a financial calculator:

  • Enter CFs in CFLO register
  • Press IRR
npv vs irr

n

CFt

= NPV

(1 + r)t

t = 0

n

CFt

= 0

(1 + IRR)t

t = 0

NPV vs IRR

NPV: Enter r, solve for NPV

IRR: Enter NPV = 0, solve for IRR

modified internal rate of return mirr
Modified Internal Rate of Return (MIRR)
  • MIRR = discount rate which causes the PV of a project’s terminal value (TV) to equal the PV of costs
    • TV = inflows compounded at WACC
  • MIRR assumes cash inflows reinvested at WACC
normal vs non normal cash flows
Normal vs. Non-normal Cash Flows

Normal Cash Flow Project:

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

Non-normal Cash Flow Project:

  • Two or more changes of signs
  • Most common: Cost (negative CF), then string of positive CFs, then cost to close project
  • For example, strip mine
multiple irrs
Multiple IRRs
  • Descartes Rule of Signs
  • Polynomial of degree n→n roots
    • 1 real root per sign change
    • Rest = imaginary (i2 = -1)
slide146

The Pavillion Project:Non-normal CFs and MIRR

1

2

0

-800,000

5,000,000

-5,000,000

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

TV inflows @ 10% = 5,500,000.00

MIRR = 5.6%

mirr versus irr
MIRR versus IRR
  • MIRR correctly assumes reinvestment at opportunity cost = WACC
  • MIRR avoids the multiple IRR problem
  • Managers like rate of return comparisons, and MIRR is better for this than IRR
when to use the mirr instead of the irr accept project p
When to use the MIRR instead of the IRR? Accept Project P?
  • 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%.
cash flow estimation and risk analysis

Cash Flow Estimation and Risk Analysis

Relevant cash flows

Net salvage value

Inflation

Sensitivity analysis

Scenario analysis

Real options

Index

relevant cash flows incremental cash flow for a project
Relevant Cash Flows:Incremental Cash Flow for a Project

Project’s incremental cash flow is:

Corporate cash flow with the project

Minus

Corporate cash flow without the project

relevant cash flows
Relevant Cash Flows

Changes in Net Working Capital…… Y

Interest/Dividends …………..………….. N

“Sunk” Costs ………………………………….. N

Opportunity Costs ………………………….Y

Externalities/Cannibalism …………….. Y

Tax Effects ………………………..………….. Y

tax effect on salvage
Tax Effect on Salvage

Net Salvage Cash Flow

= SP - (SP-BV)(T)

Where:

SP = Selling Price

BV = Book Value

T = Corporate tax rate

including inflation when estimating cash flows
Including inflation when estimating cash flows

Nominal r > real r

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

Nominal CF > real CF

Nominal cash flows incorporate inflation

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

slide155

INFLATION

Real vs. Nominal Cash flows

Real

Nominal

slide156
2 Ways to adjust

Adjust WACC

Cash Flows = Real

Adjust WACC to remove inflation

Adjust Cash Flows for Inflation

Use Nominal WACC

INFLATION

Real vs. Nominal Cash flows

sensitivity analysis
Sensitivity Analysis

Shows how changes in an input variable affect NPV or IRR

Each variable is fixed except one

Change one variable to see the effect on NPV or IRR

Answers “what if” questions

sensitivity graph
Sensitivity Graph

Variable Cost

Unit Sales

Fixed Cost

sensitivity ratio
Sensitivity Ratio

%NPV = (New NPV - Base NPV)/Base NPV

%VAR = (New VAR - Base VAR)/Base VAR

14-162

  • If SR>0  Direct relationship
  • If SR<0  Inverse relationship
sensitivity ratio1
Sensitivity Ratio

-30% $ -62 $54 $266

0 20 20 20

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

%VAR -30% -30% -30%

SR 13.74 -5.72 -41.22

14-163

Change from Resulting NPV (000s)

Base Level Unit Sales FCVC

sensitivity graph1
Sensitivity Graph

Variable Cost

-41.22

Unit Sales

13.74

Fixed Cost

-5.72

results of sensitivity analysis
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.

sensitivity analysis weaknesses
Sensitivity Analysis:Weaknesses

Does not reflect diversification

Says nothing about the likelihood of change in a variable

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

Ignores relationships among variables

sensitivity analysis strengths
Sensitivity Analysis:Strengths

Provides indication of stand-alone risk

Identifies dangerous variables

Gives some breakeven information

scenario analysis
Scenario Analysis

Examines several possible situations, usually:

Worst case

Base case or most likely case, and

Best case

Provides a range of possible outcomes

problems with scenario analysis
Problems with Scenario Analysis

Only considers a few possible out-comes

Assumes that inputs are perfectly correlated

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

Focuses on stand-alone risk

monte carlo simulation analysis
Monte Carlo Simulation Analysis

Computerized version of scenario analysis using continuous probability distributions

Computer selects values for each variable based on given probability distributions

monte carlo simulation analysis1
Monte Carlo Simulation Analysis

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

advantages of simulation analysis
Advantages of Simulation Analysis

Reflects the probability distributions of each input

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

Gives an intuitive graph of the risk situation

disadvantages of simulation analysis
Disadvantages of Simulation Analysis

Difficult to specify probability distributions and correlations

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

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

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

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

Sensitivity, scenario, and simulation analyses all ignore diversification

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

real options
Real Options

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

Alert managers always look for real options in projects

Smarter managers try to create real options

types of real options
Types of Real Options

Investment timing options

Growth options

Expansion of existing product line

New products

New geographic markets

Abandonment options

Contraction

Temporary suspension

Flexibility options

fin 331 in a nutshell1

FIN 331 in a Nutshell

Financial Management I Review

Index