FIN 331 in a Nutshell
Financial Management I Review
331NS-1
FIN 331 in a Nutshell - Index








Financial Statements, Ratios, & AFN
Time Value of Money
Bond Valuation
Risk & Return (SML/CAPM)
Stock Valuation
WACC
NPV, IRR, MIRR
Cash Flow Estimation
Click on the selected topic to go directly to that section
Index
331NS-2
Financial Statements, Cash
Flow, and Taxes
 Key Financial Statements
 Balance sheet
 Income statements
 Statement of cash flows
Index
331NS-3
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
Index
331NS-4
Sample Balance Sheet
Allied Food Products
Balance Sheets
Assets =
Liabilities +
Owner’s Equity
Index
ASSETS
Cash & Equivalents
2005
$
10
2004
$
80
Accounts receivable
$
375
$
315
Inventories
Total current assets
$
615
$ 1,000
$
$
415
810
Net plant & equipment
TOTAL ASSETS
$ 1,000
$ 2,000
$
870
$ 1,680
LIABILITIES & EQUITY
Accounts payable
Notes payable
Accruals
Total current liabilities
Long-term bonds
Total liabilities
Common stock (50,000,000 shares)
Retained earnings
Total common equity
Total Liabilities & Equity
2008
$
60
$
110
$
140
$
310
$
750
$ 1,060
$
130
$
810
$
940
$ 2,000
2007
$
30
$
60
$
130
$
220
$
580
$
800
$
130
$
750
$
880
$ 1,680
331NS-5
Sample Income Statement
Allied Food Products
INCOME STATEMENTS
2005
Net sales
$
3,000.0
Operating costs
$
2,616.2
Gross profit (EBITDA)
$
383.8
Depreciation
$
100.0
Operating Income (EBIT)
$
283.8
Interest expense
$
88.0
Pretax income (EBT)
$
195.8
Taxes (40%)
$
78.3
NET INCOME
$
117.5
Common dividends
Addtion to retained earnings
Index
$
$
57.5
60.0
$
$
$
$
$
$
$
$
$
2004
2,850.0
2,497.0
353.0
90.0
263.0
60.0
203.0
81.2
121.8
$
$
53.0
56.0
Net income=Dividends + Retained earnings
331NS-6
Allied Food Products
Allied Food Products
Per Share Data
Common stock price
Earnings per share
Dividends per share
Book value per share
Cash Flow per share
Index
$23.00
$2.35
$1.15
$18.80
$4.35
$26.00
$2.44
$1.06
$17.60
$4.24
331NS-7
Allied 2005 Per-Share Ratios
Ratio
Earnings per
Share (EPS)
Dividends per
Share (DPS)
Book Value per
Share (BVPS)
Cash flow per
Share (CFPS)
Index
Formula & Calculation
Net Incom e
$117.5

 $2.35
SharesOutstanding
50
Com m ondividends $57.5

 $1.15
SharesOutstanding
50
Shareholder Equity $940.00

 $18.80
SharesOutstanding
50
OperatingCashFlow $217.5

 $4.35
SharesOutstanding
50
331NS-8
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
Index
331NS-9
Statement of Cash Flows
Allied Food Products
Balance Sheets
ASSETS
2005
Cash & Equivalents
$
10
Accounts receivable
$
375
Inventories
$
615
Total current assets
$ 1,000
Net plant & equipment
$ 1,000
TOTAL ASSETS
$ 2,000
2004
$
80
$
315
$
415
$
810
$
870
$ 1,680
Reconciles the change in Cash & Equivalents
Index
331NS-10
Allied Food Products: Statement of Cash Flows
2005
I
Operating Activities
Net Income before dividends
Adjustments
Additions
Increase in accounts payable
Increase in accruals
Depreciation
Subtractions
Increase in accounts receivable
Increase in inventories
Net cash provided by operating activities
II Long-term Investing activities
Cash used to acquire fixed assets
III Financing Activities
Increase in notes payable
Increase in bonds
Payment of dividends
Net cash provided by financing activities
Net change in cash & equivalents
Cash & equivalents at beginning of year
IV Cash & equivalents at end of year
Index
$117.5
$30.0
$10.0
$100.0
($60.0)
($200.0)
($2.5)
($230.0)
$50.0
$170.0
($57.5)
$162.5
($70.0)
$80.0
$10.0
331NS-11
Statement of Cash Flows
Why is it important???
 Reconciles the Income Statement
and Balance Sheet to the flow of
cash
 The Matching Principle requires
estimates and accruals to prepare
Financial statements
 Financial Analysis is concerned with
Cash Flow
Index
331NS-12
Statement of Cash Flows
“A positive net income on the income
statement is ultimately insignificant
unless a company can translate its
earnings into cash, and the only source
in financial statement data for learning
about the generation of cash from
operations is the statement of cash
flows”
Index
331NS-13
Allied Food Products: Statement of Cash Flows
2005
I
Operating Activities
Net Income before dividends
Adjustments
Additions
Increase in accounts payable
Increase in accruals
Depreciation
Subtractions
Increase in accounts receivable
Increase in inventories
Net cash provided by operating activities
II Long-term Investing activities
Cash used to acquire fixed assets
III Financing Activities
Increase in notes payable
Increase in bonds
Payment of dividends
Net cash provided by financing activities
Net change in cash & equivalents
Cash & equivalents at beginning of year
IV Cash & equivalents at end of year
Index
$117.5
$30.0
$10.0
$100.0
($60.0)
($200.0)
($2.5)
Deficits
($230.0)
$50.0
$170.0
($57.5)
$162.5
($70.0)
$80.0
Covered
by new
debt and
cash
$10.0
331NS-14
Net Operating Working Capital
ASSETS
Cash & Equivalents
Accounts receivable
Inventories
Total current assets
Current Operating Assets
2005
$
10
$
375
$
615
$ 1,000
$ 1,000
Allied Food Products
Balance Sheets
2004
LIABILITIES & EQUITY
$
80
Accounts payable
$
315
Notes payable
$
415
Accruals
$
810
Total current liabilities
$
810
Current Operating Liabilities
$
$
$
$
$
2008
60
110
140
310
200
$
$
$
$
$
2007
30
60
130
220
160
Net Operating Working Capital = Current Operating Assets - Current Operating Liabilities
Net Operating Working Capital (2005)
$ 800
Net Operating Working Capital (2004)
$ 650
rNet Operating Working Capital
$ 150
If the Asset side had included “Short-term investments” they
would have been excluded as well.
Index
331NS-15
Operating Capital
(also called Total Net Operating Capital)
 Operating Capital
= NOWC + Net fixed assets
 Operating Capital
 (2005) = $800 + $1,000 = $1,800 million
 (2004) = $650 + $870 = $1,520 million
 Net Investment in Operating Capital
= Op Cap (2005) – Op Cap (2004)
= $1,800 - $1,520 = $280 million
Index
331NS-16
Net Operating Profit after Taxes
(NOPAT) & Operating Cash Flow
NOPAT
= EBIT(1 - Tax rate)
NOPAT05 = $283.8(1 - 0.4) = $170.3 m
OCF05
= NOPAT + Deprec + Amort
= $170.3 + $100
= $270.3
Index
331NS-17
Free Cash Flow (FCF) for 2005
FCF  EBIT(1  T)  Deprec& Am ort
 CapitalExpenditures  ΔNOWC 
 OCF - Investm entin OperatingCapital
EBIT = $283.8 m
T = 40% Depreciation = $100 m
Capital Expenditures = rFA + Deprec = $130+$100 = $230
rNOWC
= $800 - $650 = $150 m
FCF
Index
= [$283.8(1-.4)+$100] –[$230-$150]
= -$109.7 m
331NS-18
Analysis of Financial
Statements
 Ratio Analysis
 Limitations of ratio analysis
 Qualitative factors
Index
331NS-19
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)
Index
331NS-20
Five Major Categories of Ratios
 Profitability




PM - Profit margin on sales
BEP – Basic earning power
ROA – Return on total assets
ROE – Return on common equity
 Market value
 P/E – Price-Earnings ratio
 P/CF – Price – cash flow ratio
 M/B – Market to book
Index
331NS-21
Liquidity Ratios
 CR
= Current Ratio
= CA/CL
 QR = Quick Ratio or “Acid-Test”
= (CA-INV)/CL
Index
331NS-22
Asset Management Ratios
 Inventory Turnover = Sales/Inventories
 DSO
= Days sales outstanding
= Receivables /(Annual sales/365)
 FAT
= Fixed Assets Turnover
= Sales/Net Fixed Assets
 TAT
= Total Assets Turnover
= Sales/Total Assets
Index
331NS-23
Debt Management Ratios
 Debt Ratio = Total Liabilities/Total Assets
 TIE = Times interest earned
= EBIT/Interest
 EBITDA coverage = EC
(EBITDA + lease pmts)
.
(Interest + principal pmts + lease pmts)
Index
331NS-24
Profitability Ratios
 PM
=
=
 BEP =
=
 ROA =
=
 ROE =
=
Index
Profit margin on sales
NI/Sales
Basic earning power
EBIT/Total Assets
Return on total assets
NI/Total Assets
Return on common equity
NI/Common Equity
331NS-25
Market Value Metrics
 P/E = Price-Earnings ratio
= Price per share/Earnings per
share
 P/CF = Price–cash flow ratio
= Price per share/Cash flow per share
 M/B = Market to book
= Market price per share
Book value per share
Index
331NS-26
The 5 Major Categories of Ratios and
What Questions They Answer
Ratio Category
Liquidity
Questions Answered
Can we make required payments?
Asset Management Right amount of assets vs. sales?
Debt Management Right mix of debt and equity?
Profitability
Market Value
Index
Do sales prices exceed unit costs
Are sales high enough as reflected in
PM, ROE, and ROA?
Do investors like what they see as
reflected in P/E and M/B ratios
331NS-27
Potential Problems and
Limitations of Ratio Analysis
 Comparison with industry averages is
difficult if the firm operates many
different divisions
 “Average” performance ≠ necessarily
good
 Seasonal factors can distort ratios
 Window dressing techniques
Index
331NS-28
Problems and Limitations
(Continued)
 Different accounting and operating
practices can distort comparisons
 Sometimes difficult to tell if a ratio
value is “good” or “bad”
 Different ratios give different signals
 Difficult to tell, on balance, whether a
company is in a strong or weak financial
condition
Index
331NS-29
Qualitative Factors
Revenues tied to a single customer?
Revenues tied to a single product?
Reliance on a single supplier?
Percentage of business generated
overseas?
 Competitive situation?
 Legal and regulatory environment?




Index
331NS-30
Financial Planning and
Forecasting
 Forecasting sales
 Projecting the assets and internally
generated funds
 Projecting outside funds needed
 Deciding how to raise funds
Index
331NS-31
The AFN Formula
If ratios are expected to remain constant:
AFN = (A*/S0)∆S - (L*/S0)∆S - M(S1)(RR)
Required  Assets
Spontaneously 
Liabilities
Index
 Retained
Earnings
331NS-32
Variables in the AFN Formula





A* = Assets tied directly to sales
S0 = Last year’s sales
S1 = Next year’s projected sales
∆S = Increase in sales; (S1-S0)
L* = Liabilities that spontaneously
increase with sales
Index
331NS-33
Variables in the AFN Formula
 A*/S0: assets required to support
sales;
“Capital Intensity Ratio”
 L*/S0: spontaneous liabilities ratio
 M: profit margin (Net income/sales)
 RR: retention ratio; percent of net
income not paid as dividend
Index
331NS-34
Key Factors in AFN





∆S
A*/S0
L*/S0
M
RR
Index
=
=
=
=
=
Sales Growth
Capital Intensity Ratio
Spontaneous Liability Ratio
Profit Margin
Retention Ratio
331NS-35
Time Value of Money
•
•
•
•
Timelines
Future Value
Present Value
Present Value of Uneven Cash Flows
Index
331NS-36
Time Lines: Timing of Cash Flows
0
1
2
3
CF1
CF2
CF3
I%
CF0
• Tick marks occur at the end of periods
•
•
Time 0 = today
Time 1 = the end of the first period or the
beginning of the second period
+CF = Cash INFLOW -CF = Cash OUTFLOW
Index
PMT = Constant CF
331NS-37
Basic Definitions
Present Value
(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
Index
331NS-38
Future Value: General Formula
FV = PV(1 + I)N
•
•
•
•
•
•
Index
FV = future value
PV = present value
I = period interest rate, expressed
as a decimal
N = number of periods
Future value interest factor = (1 + I)N
• Note: “yx” key on your calculator
331NS-39
Texas Instruments BA-II Plus
One of these MUST
FV = future value
be negative
PV = present value
PMT = periodic payment
I/Y = period interest rate
N = number of periods
N
Index
I/Y
PV
PMT
FV
331NS-40
Excel Spreadsheet Functions
=FV(rate,nper,pmt,pv)
=PV(rate,nper,pmt,fv)
=RATE(nper,pmt,pv,fv)
=NPER(rate,pmt,pv,fv)
 Use the formula icon (ƒx) when you
can’t remember the exact formula
Index
331NS-41
Future Values – Example
Suppose you invest $100 for 5 years at
10%
How much would you have?
Formula Solution:
FV
=PV(1+I)N
=100(1.10)5
=100(1.6105)
=161.05
Index
331NS-42
Future Value – Example
Suppose you invest $100 for 5 years
at 10%. How much would you
have?
Calculator Solution
 5
N
 10
I/Y
 -100 PV
 0
PMT
 CPT FV
= 161.05
Index
331NS-43
Future Value:
Important Relationship 1
For a given interest rate:
The longer the time period,
The higher the future value
FV = PV(1 + I)N
For a given I, as N increases, FV increases
Index
331NS-44
Future Value
Important Relationship 2
For a given time period:
 The higher the interest rate,
 The larger the future value
FV = PV(1 + I)N
For a given N, as I increases, FV increases
Index
331NS-45
Present Values
•
The current value of future cash flows
discounted at the appropriate discount rate
•
Value at t=0 on a time line
•
Answers the questions:
Index
•
How much do I have to invest today to have
some amount in the future?
•
What is the current value of an amount to
be received in the future?
331NS-46
Present Values
FV = PV(1 + I)N
•
Rearrange to solve for PV
PV = FV / (1+I)N
PV = FV(1+I)-N
•
“Discounting” = finding the present
value of one or more future amounts
Index
331NS-47
Present Value: One Period
Example
You need
$10,000 for the
down payment
on a new car
• You can earn 7%
annually.
• How much do
you need to
invest today?
•
Index
1 N;
7 I/Y;
0 PMT;
10000 FV;
CPT PV = -9345.79
PV = 10,000(1.07)-1 = 9,345.79
=PV(0.07,1,0,10000)
331NS-48
Present Value:
Important Relationship 1
For a given interest rate:
The longer the time period,
The lower the present value
FV
PV 
N
( 1 I )
For a given I, as N increases, PV decreases
Index
331NS-49
Present Value
Important Relationship 2
For a given time period:
 The higher the interest rate,
 The smaller the present value
FV
PV 
N
( 1 I )
For a given N, as I increases, PV decreases
Index
331NS-50
The Basic PV Equation Refresher
PV = FV / (1 + I)N
There are four parts to this equation
PV, FV, I and N
• Know any three, solve for the fourth
•
• If you are using a financial calculator,
be sure and remember the sign
convention
+CF = Cash INFLOW -CF = Cash OUTFLOW
Index
331NS-51
Multiple Cash Flows
Present Value
 The Basic Formula
 The TI BA II+
 Using the PV/FV keys
 Using the Cash Flow Worksheet
 Excel
Index
331NS-52
Multiple Uneven Cash Flows
Present Value
• You are offered an investment that
will pay
•
•
•
•
•
•
Index
$200 in year 1,
$400 the next year,
$600 the following year, and
$800 at the end of the 4th year.
You can earn 12% on similar investments.
What is the most you should pay for this
investment?
331NS-53
What is the PV of this
uneven cash flow stream?
0
1
2
3
4
200
400
600
800
12%
-178.57
-318.88
-427.07
-508.41
-1,432.93 = PV
Index
331NS-54
Present Value of an Uneven
Cash Flow Stream: Formula
 1 
PV   CFt 

 1 I 
t 1
N
N
t
PV   CFt 1  I 
t
t 1
Index
331NS-55
Multiple Uneven Cash Flows – PV
Year
Year
Year
Year
Index
1
2
3
4
CF:
CF:
CF:
CF:
1
2
3
4
N;
N;
N;
N;
12
12
12
12
I/Y;
I/Y;
I/Y;
I/Y;
200
400
600
800
FV; CPT
FV; CPT
FV; CPT
FV; CPT
Total PV
PV
PV
PV
PV
=
-178.57
=
-318.88
=
-427.07
=
-508.41
= -$1,432.93
331NS-56
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
Index
331NS-57
TI BAII+: Uneven CFs
 Press the down arrow () to move to the
next cash flow register.
 Enter the cash flow amount, press ENTER
and then down arrow to move to the cash
flow counter (Fn).
 The default counter value is “1”.
 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.
Index
331NS-58
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”
Index
331NS-59
TI BAII+: Uneven Cash Flows
Cash Flows:
Index
CF0
=
0
CF1
=
200
CF2
=
400
CF3
=
600
CF4
=
800
C00
C01
F01
C02
F02
C03
F03
C04
F04
I
NPV
CF
0 ENTER 
200 ENTER 
1 ENTER 
400 ENTER 
1 ENTER 
600 ENTER 
1 ENTER 
800 ENTER 
1 ENTER  NPV
12 ENTER 
CPT
1432.93
331NS-60
Excel – PV of multiple uneven CFs
12%
Rate
Period
1
2
3
4
Cash Flow
$
$
$
$
200.00
400.00
600.00
800.00
Total PV =
Present
Value
($178.57)
($318.88)
($427.07)
($508.41)
=PV($B$3,A6,0,B6)
=PV($B$3,A7,0,B7)
=PV($B$3,A8,0,B8)
=PV($B$3,A9,0,B9)
($1,432.93)
($1,432.93)
=SUM(C6:C9)
=-NPV(B3,B6:B9)
Formula
The functions require a PMT = 0.
Index
331NS-61
Bonds and Their Valuation
 Interest rates
 Bond valuation
 Measuring yield
Index
331NS-62
“Nominal” vs. “Real” rates
r
= Any nominal rate
r* = The “real” risk-free rate
≈ T-bill rate with no inflation
Typically ranges from 1% to 4% per
year
rRF = Rate on Treasury securities
Proxied by T-bill or T-bond rate
Index
331NS-63
r = r* + IP + DRP + LP + MRP
Here:
r = Required rate of return on a
debt security
r* = Real risk-free rate
rRF =
IP = Inflation premium
DRP = Default risk premium
LP = Liquidity premium
MRP = Maturity risk premium
Index
331NS-64
Premiums Added to r* for
Different Types of Debt
Debt Instrument
IP
DRP
ST Treasury
ST IP
LT Treasury
LT IP
ST Corporate
ST IP
DRP
LT Corporate
LT IP
DRP
Index
MRP LP
MRP
LP
MRP
LP
331NS-65
Discount Rate = YTM
The discount rate (YTM) is:
 The opportunity cost of capital
 The rate that could be earned on
alternative investments of equal risk
 Required return
For debt securities:
YTM = r* + IP + LP + MRP + DRP
Index
331NS-66
Bond Value
 Bond Value = PV(coupons) + PV(par)
 Bond Value = PV(annuity) + PV(lump sum)
 Remember:
 As interest rates increase present values
decrease – as YTM ↑ → PV ↓
 As interest rates increase, bond prices
decrease and vice versa
Index
331NS-67
The Bond-Pricing Equation
1

1 (1 YTM )t
Bond Value  C
YTM




F

t
(1

YTM
)


PV(lump sum)
PV(Annuity)
C = Coupon payment; F = Face value
Index
331NS-68
Texas Instruments BA-II Plus





FV
PV
I/Y
N
PMT
= future value/face value/par value
= present value=bond value/price
= period interest rate = YTM
= number of periods to maturity
= coupon payment
N
Index
I/Y
PV
PMT
FV
331NS-69
Spreadsheet Functions
FV(Rate,Nper,Pmt,PV,0/1)
PV(Rate,Nper,Pmt,FV,0/1)
RATE(Nper,Pmt,PV,FV,0/1)
NPER(Rate,Pmt,PV,FV,0/1)
PMT(Rate,Nper,PV,FV,0/1)
• Inside
parens: (RATE,NPER,PMT,PV,FV,0/1)
• “0/1” Ordinary annuity = 0 (default)
Annuity Due = 1 (must be entered)
Index
331NS-70
Pricing Specific Bonds
 TI BA II+
 Bond Worksheet [2nd] BOND
 SDT CPN RDT RV ACT 2/Y YLD PRI
 Excel:
 PRICE(Settlement,Maturity,Rate,Yld,Redemption,
Frequency,Basis)
 YIELD(Settlement,Maturity,Rate,Pr,Redemption,
Frequency,Basis)
 Settlement and maturity need to be actual dates
 Redemption and Pr need to given as % of par value
Index
331NS-71
Yield to Maturity (YTM)
 The market required rate of return for





bonds of similar risk and maturity
The discount rate used to value a bond
Return earned if bond held to maturity
Usually = coupon rate at issue
Quoted as an APR
The IRR of a bond
Index
331NS-72
What is the YTM on a 10-year, 9% annual
coupon, $1,000 par value bond, selling for $887?
 Must find the rd that solves this model:
INT
INT
M
VB 
 ...

1
N
N
(1  rd )
(1  rd )
(1  rd )
90
90
1,000
$887 
 ...

1
10
10
(1  rd )
(1  rd )
(1  rd )
Index
331NS-73
Using a financial calculator to
solve for the YTM
 YTM =10.91%
 Bond sells at a discount because YTM >
coupon rate
INPUTS
10
N
OUTPUT
Index
I/YR
- 887
90
1000
PV
PMT
FV
10.91
331NS-74
Solving for YTM
YTM on a 10-year, 9% annual coupon,
$1,000 par value bond selling for $887





Coupon rate = 9%
Annual coupons
Par = $1,000
Maturity = 10 years
Price = $887
Using the calculator:
N = 10
PV = -887
PMT = 90
FV = 1000
CPT I/Y = 10.91
=RATE(10,90,-887,1000)
Index
331NS-75
Find YTM,
if the bond price is $1,134.20
 YTM = 7.08%
 Bond sells at a premium because YTM <
coupon rate
INPUTS
10
N
OUTPUT
Index
I/YR
-1134.2
90
1000
PV
PMT
FV
7.08
331NS-76
Solving for YTM
YTM on a 10-year, 9% annual coupon,
$1,000 par value bond selling for $1,134.20





Coupon rate = 9%
Annual coupons
Par = $1,000
Maturity = 10 years
Price = $1,134.20
Using the calculator:
N = 10
PV = -1134.20
PMT = 90
FV = 1000
CPT I/Y = 7.08
=RATE(10,90,-1134.20,1000)
Index
331NS-77
Semiannual bonds
1.
2.
3.
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.
INPUTS
2N
rd / 2
OK
cpn / 2
OK
N
I/YR
PV
PMT
FV
OUTPUT
Index
331NS-78
What is the value of a 10-year, 10%
semiannual coupon bond, if rd = 13%?
1.
2.
3.
Multiply years by 2 : N = 2 * 10 = 20
Divide nominal rate by 2 : I/YR = 13 / 2 = 6.5
Divide annual coupon by 2 : PMT = 100 / 2 = 50
INPUTS
OUTPUT
Index
20
6.5
N
I/YR
PV
50
1000
PMT
FV
- 834.72
331NS-79
Valuing a Semiannual Bond





Coupon rate = 10%
Annual coupons
Par = $1,000
Maturity = 10 years
YTM = 13%
Using the formula:
1

1


(1.065)20
B  50 
0.065


Using the calculator:
N = 20
I/Y = 6.5
PMT = 50
FV = 1000
CPT PV = -834.72


1000

20
 (1.065)

=PV(0.065, 10, 50, 1000)
Index
331NS-80
YTM with Semiannual Coupons
 Suppose a bond with a 10% coupon
rate and semiannual coupons, has a
face value of $1000, 20 years to
maturity and is selling for $1197.93.
 Is the YTM more or less than 10%?
 What is the semiannual coupon payment?
 How many periods are there?
Index
331NS-81
YTM with Semiannual Coupons
 Suppose a bond with a 10% coupon rate and
semiannual coupons, has a face value of
$1000, 20 years to maturity and is selling for
$1197.93.
N = 40
PV = -1197.93
NOTE: Solving a semiPMT = 50
annual payer for YTM
FV = 1000
will result in a 6-month
CPT I/Y = 4%
YTM answer
YTM = 4%*2 = 8%
 Result = ½ YTM
Index
Calculator solves what you enter.
331NS-82
Risk and Rates of Return
 Stand-alone Risk
 Portfolio Risk
 Risk & Return: CAPM / SML
Index
331NS-83
The Expected Rate of Return
n
rˆ   ri Pi
i 1
r “hat” = expected return
ri = expected return in “ith” state of the economy
Pi = Probability of “ith” state occurring
Index
331NS-84
Calculating the Expected Return
^
r  e xpe cte d rate of re turn
^
N
r   ri Pi
i1
Economy
Recession
Below Avg
Average
Above Avg
Boom
Prob
0.1
0.2
0.4
0.2
0.1
HT
-27%
-7%
15%
30%
45%
E(R )
Prob x HT
-2.7%
-1.4%
6.0%
6.0%
4.5%
12.4%
^
r HT  (-27%) (0.1)  (-7%) (0.2)
 (15%) (0.4)  (30%) (0.2)
 (45%) (0.1)  12.4%
Index
331NS-85
The Standard Deviation of Returns
σ = Standard deviation
σ = √ Variance = √ σ2

n
 (r
i 1
Index
i
 rˆ ) Pi
2
331NS-86
Standard deviation for each investment

N

i1
^
(ri  r )2 Pi
(5.5 - 5.5) (0.1)  (5.5 - 5.5) (0.2) 


2
2
 T bills    (5.5 - 5.5) (0.4)  (5.5 - 5.5) (0.2) 
  (5.5 - 5.5)2 (0.1)



2
 T bills  0.0%
 HT  20.0%
Index
2
1
2
 Coll  13.2%
 USR  18.8%
 M  15.2%
331NS-87
Standard Deviation of HT’s Returns
Economy
Recession
Below Avg
Average
Above Avg
Boom
Index
Prob
0.1
0.2
0.4
0.2
0.1
E(R )
Deviation
HT
Deviation Squared
-27%
-39.4%
15.5%
-7%
-19.4%
3.8%
15%
2.6%
0.1%
30%
17.6%
3.1%
45%
32.6%
10.6%
12.4%
Variance
Std Dev
x Prob
1.6%
0.8%
0.0%
0.6%
1.1%
4.0%
20.0%
331NS-88
Risk versus Return:
Do we know enough now?
Security
Expected
return, ^r
5.5%
Risk, σ
HT
12.4%
20.0%
Coll
1.0%
13.2%
USR
9.8%
18.8%
10.5%
15.2%
T-bills
Market
Index
0.0%
331NS-89
Coefficient of Variation (CV)
CV = Standard deviation/expected return
= Risk per unit of return
=  / rˆ
Standard deviation 
CV 

Expectedreturn
rˆ
Index
331NS-90
Portfolio Expected Return
^
rp = weighted average
wi = % of portfolio in stock i
ri = return on stock i
n
rˆp   w i rˆi
i 1
Index
331NS-91
Portfolio Expected Return
Assume a two-stock portfolio is created with
$50,000 invested in both HT and Collections
n
rˆp   w i rˆi
i 1
^rp = 0.5(12.4%) + 0.5(1.0%) = 6.7%
Index
331NS-92
Portfolio Return
Portfolio Return
Portfolio %
Economy
Prob
Recession
0.1
Below Avg
0.2
Average
0.4
Above Avg
0.2
Boom
0.1
E(R )
50%
HT
-27%
-7%
15%
30%
45%
12.4%
50%
Coll
27%
13%
0%
-11%
-21%
1.0%
Portfolio
Portfolio Return
0.0%
0.0%
3.0%
0.6%
7.5%
3.0%
9.5%
1.9%
12.0%
1.2%
6.7%
“Portfolio” = (50% x HT) + (50% x Coll)
“Portfolio Return” = Prob x “Portfolio”
Index
331NS-93
Portfolio Risk
Portfolio Standard deviation is
NOT a weighted average of the
standard deviations of the
component assets
Index
331NS-94
Calculating portfolio standard
deviation and CV
 0.10 (0.0 - 6.7) 

2 
  0.20 (3.0 - 6.7) 
 p    0.40 (7.5 - 6.7)2 
  0.20 (9.5 - 6.7)2 


2
  0.10 (12.0 - 6.7) 
2
1
2
 3.4%
3.4%
CVp 
 0.51
6.7%
Index
331NS-95
Portfolio Standard Deviation
Portfolio Standard Deviation
Economy
Recession
Below Avg
Average
Above Avg
Boom
Index
Prob
0.1
0.2
0.4
0.2
0.1
E(R )
Squared
Portfolio Deviation
0.0%
0.00045
3.0%
0.00027
7.5%
0.00003
9.5%
0.00016
12.0%
0.00028
6.7%
0.00119 Variance
σ=
3.4%
331NS-96
Portfolio Risk & Return
E(R )
Std Dev
CV




HT
12.40%
20.00%
1.6
COLL
1.00%
13.20%
13.2
Portfolio
6.7%
3.4% 
0.51
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
Index
331NS-97
Covariance of Returns
Measures how much the returns on
two risky assets move together
Cov(a , b)   ab
 ab   ra  rˆa rb  rˆb Pi
i
i
i
Index
331NS-98
Covariance vs. Variance of Returns
Cov(a , b)   ab
 ab   ra  rˆa rb  rˆb Pi
i
i
i
Var(a )   aa  
2
a
   ra  rˆa ra  rˆa Pi
2
a
i
i
i
Index
331NS-99
Covariance
Cov (a , b)   ab
 ab   ra  rˆa rb  rˆb Pi
i
i
i
Economy
Recession
Below Avg
Average
Above Avg
Boom
Prob
0.1
0.2
0.4
0.2
0.1
E(R )
HT
-27%
-7%
15%
30%
45%
12.4%
Coll
27%
13%
0%
-11%
-21%
1.0%
HT Dev
-39.4%
-19.4%
2.6%
17.6%
32.6%
Coll Dev HT x Coll
26.0%
-10.244%
12.0%
-2.328%
-1.0%
-0.026%
-12.0%
-2.112%
-22.0%
-7.172%
COV(HT,Coll) =
x Prob
-0.0102
-0.0047
-0.0001
-0.0042
-0.0072
-0.0264
Covariance (HT:Coll) = -0.0264
Index
331NS-100
Correlation Coefficient
 Correlation Coefficient = ρ (rho)
 Scales covariance to [-1,+1]
 -1 = Perfectly negatively correlated
 0 = Uncorrelated; not related
 +1 = Perfectly positively correlated
 ab
 ab 
 a b
Index
331NS-101
Two-Stock Portfolios
If  = -1.0
•
Two stocks can be combined to form a
riskless portfolio
If  = +1.0
•
No risk reduction at all
In general, stocks have  ≈ 0.35
•
Risk is lowered but not eliminated
Investors typically hold many stocks
Index
331NS-102
 of n-Stock Portfolio
n
n
    w i w j i j  ij
2
p
i 1 j 1
n
 ab
 ab 
 a b
n
    w i w j ij
2
p




Index
i 1 j 1
Subscripts denote stocks i and j
i,j = Correlation between stocks i and j
σi and σj =Standard deviations of stocks i and j
σij = Covariance of stocks i and j
331NS-103
Portfolio Risk-n Risky Assets
n
n
   wi w j ij
2
p
i 1 j 1
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
Index
331NS-104
Portfolio Risk-2 Risky Assets
 
2
p
HT
Coll
i
1
1
2
2
Index
j
1
2
1
2
W
50%
50%
n
n
 w w  
i 1 j 1
i
j
Std Dev Variance
20.00%
0.0400
13.20%
0.0174
i
j
 ij
Cov
ρ
-0.0264
-1.00
for n=2
0.0100
(0.0066)
(0.0066)
0.0044
0.00116 Variance
3.40%
Std Dev
331NS-105
Capital Asset Pricing Model (CAPM)
 Links risk and required returns
 Security Market Line (SML):
 A stock’s required return equals the riskfree 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 welldiversified portfolio.
Index
331NS-106
The SML and Required Return
 The Security Market Line (SML) is part of
the Capital Asset Pricing Model (CAPM)
ri  rRF  rM  rRF  i
ri  rRF  RPM  i
 rRF = Risk-free rate
 RPM = Market risk premium = rM – rRF
Index
331NS-107
The Market Risk Premium
(rM – rRF = RPM)
 Additional return over the risk-free
rate to compensate investors for
assuming an average amount of risk
 Size depends on:
 Perceived risk of the stock market
 Investors’ degree of risk aversion
 Varies from year to year
 Estimates suggest a range between 4%
and 8% per year
Index
331NS-108
Required Rates of Return
Assume:
 rHT
 rM
 rUSR
 rT-bill
 rColl
Index
=
=
=
=
=
=
rRF = 5.5%
5.5%
5.5%
5.5%
5.5%
5.5%
5.5%
+
+
+
+
+
+
RPM = 5%
(5.0%)(1.32)
6.6%
=
(5.0%)(1.00) =
(5.0%)(0.88) =
(5.0%)(0.00) =
(5.0%)(-0.87) =
12.10%
10.50%
9.90%
5.50%
1.15%
331NS-109
Expected vs Required Returns
“Expected”
by YOU
“Required” by
the market
Expected
Required
Return
Return
HT
12.40
12.10
Undervalued
Market
10.50
10.50
Fairly valued
USR
9.80
9.90
Overvalued
T-bills
5.50
5.50
Fairly valued
Coll
1.00
1.15
Overvalued
Index
331NS-110
Illustrating the
Security Market Line
SML: ri = 5.5% + (5.0%) i
ri (%)
SML
.
..
HT
rM = 10.5
rRF = 5.5
-1
Index
.
Coll.
. T-bills
0
USR
1
2
Risk, i
331NS-111
Portfolio Beta
n
 p   wi  i
i 1
Where:
wi = weight (% dollars invested in asset i)
βi = Beta of asset i
βp = Portfolio Beta
Index
331NS-112
Stocks and Their Valuation
 Constant growth stock valuation
 Non-constant growth stock valuation
 Corporate value model
Index
331NS-113
Constant growth stock
•
Dividends expected to grow forever at a
constant rate, g:
D1 = D0 (1+g)1
D2 = D0 (1+g)2
Dt = D0 (1+g)t
•
Dividend growth formula converges to:
D0 (1  g)
D1
P0 

rs - g
rs - g
^
Index
331NS-114
Constant Growth Model
D0 (1  g)
D1
P0 

rs - g
rs - g
^
Needed data:
D0 = Dividend just paid
D1 = Next expected dividend
g = constant growth rate
rs = required return on the stock
Index
331NS-115
Expected Value at time t
D1
ˆ
P0 
rs  g
D
t 1
ˆ
Pt 
rs  g
Index
Value at t=0
Value at t
331NS-116
Supernormal Growth
 What if g = 30% for 3 years before
achieving long-run growth of 6%?
 Constant growth model no longer
applicable
 But - growth constant after 3 years
Index
331NS-117
Valuing common stock with
nonconstant growth
0 r = 13% 1
s
g = 30%
D0 = 2.00
2
g = 30%
2.600
3
g = 30%
3.380
4
...
g = 6%
4.394
4.658
2.301
2.647
3.045
4.658
46.114
54.107
Index
= P0
P$  0.13  0.06  $66.54
331NS-118
Corporate Value Model
 = Free Cash Flow method
 Value of the firm = present value of the
firm’s expected future free cash flows
 Free cash flow =after-tax operating
income less net capital investment
 FCF = NOPAT – Net capital investment
Index
331NS-119
Applying the corporate value model
Market value of firm:
 (MVF) = PV(future FCFs)
MV of common stock:
= MVF – MV of debt
Intrinsic stock value:
= MVCS /# shares
Index
331NS-120
Issues regarding the corporate
value model
 Often preferred to the dividend
growth model
 Firms that don’t pay dividends
 Dividends hard to forecast
 Assumes at some point free cash
flow growth rate will be constant
 Terminal value (TVN) = value of firm
at the point that growth becomes
constant
Index
331NS-121
Firm’s Intrinsic Value
Long-run gFCF = 6%
0 r = 10%
1
-5
-4.545
8.264
15.026
398.197
416.942
Index
2
10
WACC = 10%
3
4
20
...
g = 6%
21.20
21.20
530 =
0.10 - 0.06
= TV3
331NS-122
If the firm has $40 million in debt and has 10
million shares of stock, what is the 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
Index
331NS-123
Firm multiples method
 Often used by analysts to value stocks
 P/E
Price-earning
 P / CF
Price-cash flow
 P / Sales Price-sales
 Method:
 Estimate appropriate ratio based on
comparable firms
 Multiply estimate by expected metric
to estimate stock price
Index
331NS-124
The Cost of Capital
 Cost of equity
 WACC
 Adjusting for risk
Index
331NS-125
WACC
Weighted Average Cost of Capital
WACC = wdrd(1-T) + wprp + wcrs
Where:
Weights
Component
costs
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
Index
331NS-126
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
Index
331NS-127
DCF Approach: Inputs
1. Current stock price (P0)
2. Current dividend (D0)
3. Growth rate (g)
Index
331NS-128
Four Mistakes to Avoid
 Current (YTM) vs. historical (Coupon rate)
cost of debt
 Mixing current and historical measures to
estimate the market risk premium
 Book weights vs. Market Weights
 Use Target weights
 Use market value of equity
 Book value of debt = reasonable proxy
for market value.
 Incorrect cost of capital components
 Only investor provided funding
Index
331NS-129
Should the company use the composite WACC
as the hurdle rate for each of its projects?
 NO!
 A 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
Index
331NS-130
Divisional and Project Costs of
Capital
 Using the WACC as the discount rate is
only appropriate for projects that are the
same risk as the firm’s current operations
 If considering a project that is NOT of the
same risk as the firm, then an appropriate
discount rate for that project is needed
 Divisions also often require separate
discount rates
Index
331NS-131
Using WACC for All Projects - Example
 What would happen if we use the WACC for all
projects regardless of risk?
 Assume the WACC = 15%
Project
A
B
C
Index
Required Expected
Return
Return
20%
17%
15%
18%
10%
12%
Decision
If 15%
Risk Adj
Accept
Reject
Accept
Accept
Reject
Accept
331NS-132
Divisional Risk and the Cost of
Capital
Rate of Return
(%)
Acceptance Region
WACC
WACC H
Acceptance Region
Rejection Region
WACC F
Rejection Region
WACC L
0
Index
Risk L
Risk H
Risk
331NS-133
Subjective Approach
 Consider the 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
Index
331NS-134
Subjective Approach - Example
Risk Level
Discount Rate
Very Low Risk
WACC – 8%
7%
Low Risk
WACC – 3%
12%
Same Risk as Firm
WACC
15%
High Risk
WACC + 5%
20%
Very High Risk
WACC + 10%
25%
Index
331NS-135
The Basics of Capital
Budgeting







Independent vs. mutually exclusive CFs
Normal vs. non-normal CFs
NPV
IRR
MIRR
PB
DPB
Index
331NS-136
Steps to capital budgeting
Estimate CFs (inflows & outflows)
2. Assess riskiness of CFs
3. Determine appropriate cost of capital
4. Find NPV and/or IRR
5. Accept if NPV>0 and/or IRR>WACC
1.
Index
331NS-137
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
Index
331NS-138
NPV: Sum of the PVs of all cash
flows.
n
NPV = ∑
t=0
CFt .
(1 + r)t
NOTE: t=0
Cost often is CF0 and is negative
n
NPV = ∑
t=1
Index
CFt
(1 + r)t
- CF0
331NS-139
TI BAII+: Uneven Cash Flows
Cash Flows:
Index
CF0
=
-100
CF1
=
10
CF2
=
60
CF3
=
80
C00
C01
F01
C02
F02
C03
F03
I
NPV
CF
100 +/- ENTER 
10 ENTER 
1 ENTER 
60 ENTER 
1 ENTER 
80 ENTER 
1 ENTER NPV
10 ENTER 
CPT
$18.78
331NS-140
Internal Rate of Return (IRR)
IRR = discount rate that forces PV of
inflows equal to cost, and NPV = 0:
N
0
t 0
CFt
t
( 1  IRR )
Solving for IRR with a financial
calculator:
 Enter CFs in CFLO register
 Press IRR
Index
331NS-141
NPV vs IRR
NPV: Enter r, solve for NPV
n CF
t
=
NPV
∑ (1 + r)t
t=0
IRR: Enter NPV = 0, solve for IRR
n
∑
t=0
Index
CFt
=0
(1 + IRR)t
331NS-142
Modified Internal Rate of Return
(MIRR)
 MIRR = discount rate which causes
the PV of a project’s terminal value
(TV) to equal the PV of costs
 TV = inflows compounded at WACC
 MIRR assumes cash inflows
reinvested at WACC
Index
331NS-143
Normal vs. Non-normal Cash Flows
Normal Cash Flow Project:
 Cost (negative CF) followed by a series of
positive cash inflows
 One change of signs
Non-normal Cash Flow Project:
 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
Index
331NS-144
Multiple IRRs
 Descartes Rule of Signs
n
CFt

0

t
t  0 ( 1  IRR )
 Polynomial of degree n→n roots
 1 real root per sign change
 Rest = imaginary (i2 = -1)
Index
331NS-145
The Pavillion Project:
Non-normal CFs and MIRR
0
-800,000
1
5,000,000
2
-5,000,000
PV outflows @ 10% = -4,932,231.40
TV inflows @ 10% = 5,500,000.00
MIRR = 5.6%
Index
331NS-146
MIRR versus IRR
 MIRR correctly assumes reinvestment
at opportunity cost = WACC
 MIRR avoids the multiple IRR problem
 Managers like rate of return
comparisons, and MIRR is better for
this than IRR
Index
331NS-147
When to use the MIRR instead of the
IRR? Accept Project P?
 When there are nonnormal CFs and
more than one IRR, use MIRR.
 PV of outflows @ 10% = -$4,932.2314.
 TV of inflows @ 10% = $5,500.
 MIRR = 5.6%.
 Do not accept Project P.
 NPV = -$386.78 < 0.
 MIRR = 5.6% < WACC = 10%.
Index
331NS-148
Excel Functions
A1
B
2
3
4
5
6
7
8
9
10
11
Year
0
1
2
3
NPV
IRR
MIRR
C
D
Project Expected
Net Cash Flows
L
S
($100)
($100)
10
70
60
50
80
20
$18.78
$19.98
18.13%
23.56%
16.50%
16.89%
12
13
14
Index
15
=NPV(0.1,C6:C8)+C5
=IRR(C5:C8)
=MIRR(C5:C8,0.1,0.1)
331NS-149
Cash Flow Estimation and
Risk Analysis
 Relevant cash flows
 Net salvage value
 Inflation
 Sensitivity analysis
 Scenario analysis
 Real options
Index
331NS-150
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
Index
331NS-151
Relevant Cash Flows
• Changes in Net Working Capital…… Y
• Interest/Dividends …………..………….. N
• “Sunk” Costs ………………………………….. N
• Opportunity Costs ………………………….Y
• Externalities/Cannibalism ……………..Y
• Tax Effects ………………………..………….. Y
Index
331NS-152
Tax Effect on Salvage
Net Salvage Cash Flow
= SP - (SP-BV)(T)
Where:
SP = Selling Price
BV = Book Value
T = Corporate tax rate
Index
331NS-153
Including inflation when estimating cash
flows
 Nominal r > real r
 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
Index
331NS-154
INFLATION
Real vs. Nominal Cash flows
n
CFt
NPV  
t
t  0 1  WACC 
Real
Nominal
Index
331NS-155
INFLATION
Real vs. Nominal Cash flows
 2 Ways to adjust
 Adjust WACC
 Cash Flows = Real
 Adjust WACC to remove inflation
 Adjust Cash Flows for Inflation
 Use Nominal WACC
Index
331NS-156
Sensitivity Analysis
 Shows how changes in an input
variable affect NPV or IRR
 Each variable is fixed except one
 Change one variable to see the effect on
NPV or IRR
 Answers “what if” questions
Index
331NS-157
Sensitivity Analysis
Sensitivity Analysis
Units
Price/unit
Variable cost/unit
Fixed cost/year
Base
6,000
$
80
$
60
$
50,000
Units
Fixed Cost
6,600
6,000
80
80
60
60
50,000
55,000
Var Cost
6,000
80
54
50,000
Initial investment
$ 200,000
Depreciated to salvage value of 0 over 5 years
Deprec/yr
$
40,000
Tax rate
40%
Required Return
10%
Index
331NS-158
Units
Price/unit
Variable cost/unit
Fixed cost
Sales
Variable Cost
Fixed Cost
Depreciation
EBIT
Taxes
Net Income
+ Deprec
BASE
6,000
$
80
$
60
$
50,000
UNITS
6,600
$
80
$
60
$
50,000
$
$
$
$
$
$
TOTAL CF
NPV
% Change in NPV
% Change in Variable
SENSITIVITY RATIO
Index
480,000
360,000
50,000
40,000
30,000
12,000
18,000
40,000
58,000
$
19,866
528,000
396,000
50,000
40,000
42,000
16,800
25,200
40,000
65,200
$
47,159
137.4%
10.0%
13.74
DIRECT
FC
6,000
80
60
55,000
480,000
360,000
55,000
40,000
25,000
10,000
15,000
40,000
$
$
$
$
55,000
$
8,493
-57.2%
10.0%
-5.72
INVERSE
VC
6,000
80
54
50,000
480,000
324,000
50,000
40,000
66,000
26,400
39,600
40,000
79,600
$
101,747
412.2%
-10.0%
-41.22
INVERSE
331NS-159
Sensitivity Analysis
UNITS
FC
VC
-30%
$
(62,015) $
53,983
$
265,509
-20%
$
(34,722) $
42,610
$
183,628
-10%
$
(7,428) $
31,238
$
101,747
BASE
$
19,866
$
19,866
$
19,866
10%
$
47,159
$
8,493
$
(62,015)
20%
$
74,453
$
(2,879) $
(143,896)
30%
$
101,747
$
(14,251) $
(225,777)
Index
331NS-160
Sensitivity Graph
$300,000
Variable Cost
$200,000
$100,000
Unit Sales
Fixed Cost
$-30%
-20%
-10%
BASE
10%
20%
30%
$(100,000)
$(200,000)
$(300,000)
Units
Index
FC
VC
331NS-161
14-162
Sensitivity Ratio
 %NPV = (New NPV - Base NPV)/Base NPV
 %VAR = (New VAR - Base VAR)/Base VAR
%NPV
SR 
%VAR
• If SR>0  Direct relationship
• If SR<0  Inverse relationship
Index
331NS-162
14-163
Sensitivity Ratio
Change from
Base Level
-30%
0
%NPV
%VAR
SR
Index
Resulting NPV (000s)
Unit Sales
FC
$ -62
20
(-62-20)/20
-4.1%
$54
20
(54-20)/20
1.7%
-30%
-30%
13.74
-5.72
VC
$266
20
(266-20)/20
12.3%
-30%
-41.22
331NS-163
Sensitivity Graph
$300,000
Variable Cost
$200,000
Fixed Cost
$100,000
Unit Sales
-41.22
13.74
-5.72
$-30%
-20%
-10%
BASE
10%
20%
30%
$(100,000)
$(200,000)
$(300,000)
Units
Index
FC
VC
331NS-164
Results of Sensitivity Analysis
 Steeper sensitivity lines = greater
risk
 Small changes → large declines in NPV
 The Variable Cost line is steeper than
unit sales or fixed cost so, for this
project, the firm should focus on the
accuracy of variable cost forecasts.
Index
331NS-165
Sensitivity Analysis:
Weaknesses
 Does not reflect diversification
 Says nothing about the likelihood of
change in a variable
 i.e. a steep sales line is not a problem if
sales won’t fall
 Ignores relationships among variables
Index
331NS-166
Sensitivity Analysis:
Strengths
 Provides indication of stand-alone risk
 Identifies dangerous variables
 Gives some breakeven information
Index
331NS-167
Scenario Analysis
 Examines several possible situations,
usually:
 Worst case
 Base case or most likely case, and
 Best case
 Provides a range of possible
outcomes
Index
331NS-168
Scenario Example
Scenario Analysis
Units
Price/unit
Variable cost/unit
Fixed cost/year
$
$
$
Base
6,000
80.00 $
60.00 $
50,000 $
BASE
Lower
5,500
75.00 $
58.00 $
45,000 $
BEST
Upper
6,500
85.00
62.00
55,000
WORST
Initial investment
$ 200,000
Depreciated to salvage value of 0 over 5 years
Deprec/yr
$
40,000
Project Life
5 years
Tax rate
34%
Required return
12%
Index
331NS-169
Scenario Analysis
Units
Price/unit
Variable cost/unit
Fixed cost/year
$
$
$
Base
6,000
80.00 $
60.00 $
50,000 $
BASE
Lower
5,500
75.00 $
58.00 $
45,000 $
BEST
Upper
6,500
85.00
62.00
55,000
WORST
Initial investment
$ 200,000
Depreciated to salvage value of 0 over 5 years
Deprec/yr $ 40,000
Project Life
5 years
Tax rate
34%
Required return
12%
Index
BASE
6,000
80.00 $
60.00 $
50,000 $
Units
Price/unit
Variable cost/unit
Fixed Cost
$
$
$
Sales
Variable Cost
Fixed Cost
Depreciation
EBIT
Taxes
Net Income
+ Deprec
$ 480,000
360,000
50,000
40,000
30,000
10,200
19,800
40,000
WORST
5,500
75.00 $
62.00 $
55,000 $
BEST
6,500
85.00
58.00
45,000
$ 412,500 $ 552,500
341,000
377,000
55,000
45,000
40,000
40,000
(23,500)
90,500
(7,990)
30,770
(15,510)
59,730
40,000
40,000
TOTAL CF
59,800
24,490
99,730
NPV
15,566
(111,719)
159,504
15.1%
-14.4%
40.9%
IRR
331NS-170
Problems with Scenario Analysis
 Only considers a few possible outcomes
 Assumes that inputs are perfectly
correlated
 All “bad” values occur together and all
“good” values occur together
 Focuses on stand-alone risk
Index
331NS-171
Monte Carlo Simulation Analysis
 Computerized version of scenario
analysis using continuous probability
distributions
 Computer selects values for each
variable based on given probability
distributions
Index
331NS-172
Monte Carlo Simulation Analysis
 Calculates NPV and IRR
 Process is repeated many times
(1,000 or more)
 End result: Probability distribution of
NPV and IRR based on sample of
simulated values
 Generally shown graphically
Index
331NS-173
Index
00
30 0)
,0
00
)
60
,
$3 $0
0,
0
$6 00
0,
0
$9 00
0,
$1 000
20
,
$1 000
50
,
$1 000
80
,
$2 000
10
,
$2 000
40
,
$2 000
70
,
$3 000
00
,
$3 000
30
,
$3 000
60
,0
00
($
($
Probability of NPV
Histogram of Results
12%
10%
8%
6%
4%
2%
0%
NPV
331NS-174
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
Index
331NS-175
Disadvantages of Simulation Analysis
 Difficult to specify probability
distributions and correlations
 If inputs are bad, output will be bad:
“Garbage in, garbage out”
Index
331NS-176
Disadvantages of Sensitivity, Scenario
and Simulation Analysis
 Sensitivity, scenario, and simulation
analyses do not provide a decision rule
 Do not indicate whether a 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
Index
331NS-177
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
Index
331NS-178
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
Index
331NS-179
FIN 331 in a Nutshell
Financial Management I Review
Index
331NS-180