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1
Copyright 1996 by The McGraw-Hill Companies, Inc
WHAT DISCOUNT RATE SHOULD THE FIRM USE IN CAPITAL BUDGETING?
WHAT DISCOUNT RATE SHOULD THE FIRM USE IN CAPITAL BUDGETING?
MANY FIRMS USE OVERALL FIRM COST OF CAPITAL TO DISCOUNT CASH FLOWS FOR ALL NEW PROJECTS
WRONG IF NEW PROJECT MORE OR LESS RISKY THAN ITS EXISTING BUSINESS
EACH PROJECT SHOULD IN PRINCIPLE BE DISCOUNTED USING ITS OWN OPPORTUNITY COST OF CAPITAL
2
Copyright 1996 by The McGraw-Hill Companies, Inc
COMPANY COST OF CAPITAL AND
REQUIRED RETURN ON PROJECT
COMPANY COST OF CAPITAL AND
REQUIRED RETURN ON PROJECT
REQUIRED RETURN
PROJECT BETA
Company cost of capital
required return on projectSecurity market line showing
Average betaof firm's assets
3
Copyright 1996 by The McGraw-Hill Companies, Inc
COMPANY COST OF CAPITAL RULECOMPANY COST OF CAPITAL RULE
DUKE POWER HAS LOW RISK AND LOW COMPANY COST OF CAPITAL
MICROSOFT HAS HIGH RISK AND HIGH COMPANY COST OF CAPITAL
IF BOTH FIRMS USED THE COMPANY COST OF CAPITAL RULE TO EVALUATE THE SAME PROJECT, POSSIBLE THAT
– DUKE POWER WOULD ACCEPT THE PROJECT
– MICROSOFT WOULD REJECT THE PROJECT
WRONG!!
4
Copyright 1996 by The McGraw-Hill Companies, Inc
COMPANY COST OF CAPITAL RULECOMPANY COST OF CAPITAL RULE
WIDESPREAD USE OF A UNIFORM COST OF CAPITAL BY MANY COMPANIES IN EVALUATING PROJECTS
BUT MANY FIRMS DO REQUIRE DIFFERENT RETURNS FOR DIFFERENT CATEGORIES OF INVESTMENT– EXAMPLE ON NEXT SLIDE
5
Copyright 1996 by The McGraw-Hill Companies, Inc
CATEGORY DISCOUNT RATE
SPECULATIVE VENTURES 30%
NEW PRODUCTS 20%
EXPANSION OF 15% (company cost of capital)
EXISTING BUSINESS
COST IMPROVEMENT 10%KNOWN TECHNOLOGY
6
Copyright 1996 by The McGraw-Hill Companies, Inc
USING CAPM AND PROJECT USING CAPM AND PROJECT
MANY LARGE CORPORATIONS USE CAPM AND AN
ESTIMATE OF THE PROJECT TO ESTIMATE
PROJECT DISCOUNT RATE
EXPECTED PROJECT RETURN = rf + project (rm-
rf)
7
Copyright 1996 by The McGraw-Hill Companies, Inc
BEGIN WITH PROBLEMS IN MEASURING COMPANY
BEGIN WITH PROBLEMS IN MEASURING COMPANY
IS DIFFICULT TO MEASURE FOR INDIVIDUAL FIRM
BETTER ACCURACY BY LOOKING AT AVERAGE OF SIMILAR COMPANIES
– BUT FIRM’S BORROWING POLICIES AFFECTS ITS STOCK
– IBM AND DEC ARE NOT SIMILAR COMPANIES FOR PURPOSE OF ESTIMATING BECAUSE THEY USE DIFFERENT DEGREES OF LEVERAGE
8
Copyright 1996 by The McGraw-Hill Companies, Inc
MEASURING COMPANY MEASURING COMPANY
APPROPRIATE FOR ACROSS-THE-BOARD EXPANSION
COMPARE RETURN ON STOCK WITH MARKET RETURN
OVER 60-MONTH TIME PERIOD
– AT&T
– HEWLETT-PACKARD
SLOPE IS
VARIES BY PERIOD
ESTIMATES OF ARE PUBLISHED BY BROKERAGE
HOUSES AND ADVISORY SERVICES
9
Copyright 1996 by The McGraw-Hill Companies, Inc
ESTIMATING BETA
ESTIMATING BETA
RETURN ON SHARE
RETURN ON MARKET
+
Beta = .4
++
++ +
++++
++
+
+
++
+
++
+
++ +
++
+++
RETURN ON SHARE
RETURN ON MARKET
+
Beta = 1.6
++
+
+ +
++++
++
+
+
++
+
++
+
++ +
++
+
+
+
10
Copyright 1996 by The McGraw-Hill Companies, Inc
PFIZERPFIZER
WHICH IS THE BETTER ESTIMATE OF FOR PFIZER?
– PFIZER HAS A OF 1.02 WITH A STANDARD ERROR OF 0.14
– A MARKET VALUE-WEIGHTED INDUSTRY PORTFOLIO OF LARGE PHARMACEUTICAL COMPANIES HAS A OF 0.98 WITH A STANDARD ERROR OF 0.07
DIFFERENCE BETWEEN ESTIMATE OF COMPANY BETA AND INDUSTRY BETA IS PROBABLY NOISE
– UNLESS YOU HAVE REASON TO BELIEVE THAT PFIZER IS RISKIER THAN INDUSTRY AVERAGE
11
Copyright 1996 by The McGraw-Hill Companies, Inc
HOW CAPITAL STRUCTURE AFFECTS EXPECTED RETURNS
HOW CAPITAL STRUCTURE AFFECTS EXPECTED RETURNS
IF YOU OWN ALL OF THE EQUITY AND ALL OF THE
DEBT OF A COMPANY, YOU WOULD ALSO
RECEIVE ALL CASH FLOWS FROM THE COMPANY
COMPANY’S COST OF CAPITAL IS EXPECTED
RETURN ON THIS PORTFOLIO
12
Copyright 1996 by The McGraw-Hill Companies, Inc
HOW CHANGING CAPITAL STRUCTURE AFFECTS
HOW CHANGING CAPITAL STRUCTURE AFFECTS
AFTER REFINANCING, RISK OF TOTAL PORTFOLIO OF DEBT AND EQUITY IS UNCHANGED – BUT BOTH DEBT AND EQUITY ARE
INDIVIDUALLY LESS RISKYFIRM’S ASSET BETA IS WEIGHTED AVERAGE OF
PORTFOLIO OF DEBT AND EQUITY BETAS assets portfolio
DV
EV
debt equity
13
Copyright 1996 by The McGraw-Hill Companies, Inc
HOW CHANGING CAPITAL STRUCTURE AFFECTS
HOW CHANGING CAPITAL STRUCTURE AFFECTS
AFTER REFINANCING, RISK OF TOTAL PORTFOLIO OF DEBT AND EQUITY IS UNCHANGED – BUT BOTH DEBT AND EQUITY ARE INDIVIDUALLY
LESS RISKYFIRM’S ASSET BETA IS WEIGHTED AVERAGE OF
PORTFOLIO OF DEBT AND EQUITY BETAS
SUPPOSE debt FALLS TO .1
.8 = (.3 X .1) + (.7 X equity )
equity = 1.1
assets portfolio
DV
EV
debt equity
14
Copyright 1996 by The McGraw-Hill Companies, Inc
UNLEVERING BETASUNLEVERING BETAS
GOING FROM AN OBSERVED equity TO assets
WE KNOW equity
debt
MARKET WEIGHTS OF DEBT AND EQUITY, (D/V )AND (E/V)
assets portfolio
DV
EV
debt equity
15
Copyright 1996 by The McGraw-Hill Companies, Inc
UNLEVERING BETASUNLEVERING BETAS
GOING FROM AN OBSERVED equity TO assets
WE KNOW equity
debt
MARKET WEIGHTS OF DEBT AND EQUITY, (D/V )AND (E/V)
WE WILL ADD TAX EFFECTS LATER
assets portfolio
DV
EV
debt equity
16
Copyright 1996 by The McGraw-Hill Companies, Inc
REVIEWREVIEW
COST OF CAPITAL IS RELEVANT IN CAPITAL BUDGETING DECISIONS– NOT EXPECTED RETURN ON COMMON STOCK
COMPANY COST OF CAPITAL IS WEIGHTED AVERAGE RETURN THAT INVESTORS EXPECT ON FIRM’S DEBT AND EQUITY– RELATED TO FIRM’S ASSET BETA, NOT TO EQUITY BETA
ASSET BETA CALCULATED AS WEIGHTED AVERAGE OF BETAS OF DEBT AND EQUITY
WHEN FIRM CHANGES ITS CAPITAL STRUCTURE– RISK AND EXPECTED RETURNS OF DEBT AND EQUITY
CHANGE– ASSET BETA AND COMPANY COST OF CAPITAL DO
NOT CHANGE
17
Copyright 1996 by The McGraw-Hill Companies, Inc
WHAT DETERMINES ASSET BETAS?WHAT DETERMINES ASSET BETAS?
FIRMS WITH HIGH ACCOUNTING OR CASH
FLOW BETAS ALSO TEND TO HAVE HIGH STOCK
BETAS
– CYCLICAL FIRMS WHOSE EARNINGS ARE
STRONGLY RELATED TO THE BUSINESS
CYCLE TEND TO BE HIGH BETA FIRMS
DEMAND A HIGHER RATE OF RETURN FROM
SECURITIES WHOSE PERFORMANCE MOVES
WITH THE ECONOMY
18
Copyright 1996 by The McGraw-Hill Companies, Inc
OPERATING LEVERAGEOPERATING LEVERAGE
WE KNOW FINANCIAL LEVERAGE INCREASES BETA
FOR SIMILAR REASONS, OPERATING LEVERAGE
ALSO INCREASES BETA
– PRESENCE OF FIXED COSTS OF PRODUCTION CASH FLOWS FROM THE ASSET
= REVENUES - FIXED COST - VARIABLE COST
PV(CASH FLOWS FROM THE ASSET) = PV(ASSET)
=PV(REVENUE) - PV(FIXED COST) - PV(VARIABLE
COST)
PV(REVENUE)
=PV(FIXED COST) + PV(VARIABLE COST) + PV(ASSET)
19
Copyright 1996 by The McGraw-Hill Companies, Inc
OPERATING LEVERAGEOPERATING LEVERAGEFIXED COST = 0
ALSO REVENUES VARIABLE COST
– AS THEY ARE BOTH PROPORTIONAL TO OUTPUT
REVENUEASSET
[1PV(FIXED COST)
PV(ASSET)]REVENUE
PV(REVENUE) -PV(FIXED COST)PV(ASSET)
20
Copyright 1996 by The McGraw-Hill Companies, Inc
NET PRESENT VALUE RULENET PRESENT VALUE RULE
WHY DOES THE NPV OF A PROJECT SHOW UP AS INCREASE IN MARKET VALUE?
IMAGINE THE CASH FLOWS OF THE PROJECT ARE PAID OUT AS DIVIDENDS
THE SHARE PRICE WOULD INCREASE BY THE PRESENT VALUE OF THE DIVIDENDS LESS THE COST OF THE PROJECT (DIVIDENDS FOREGONE) THIS IS THE NPV OF THE PROJECT
21
Copyright 1996 by The McGraw-Hill Companies, Inc
INTERNAL RATE OF RETURN, IRR
INTERNAL RATE OF RETURN, IRR
CC C C
01 2
2T
T(1 IRR) (1 IRR)....
(1 IRR)0
NPV
=
IRR IS THE DISCOUNT RATE FOR WHICH NPV=0
22
Copyright 1996 by The McGraw-Hill Companies, Inc
CALCULATING IRRCALCULATING IRR
FINANCIAL CALCULATOR .
TRIAL AND ERROR
– EXAMPLE: C0 = - 4,000
C1 = +2,000
C3 = +4,000
TRY IRR = 0, NPV = +2,000, IRR > 0
TRY IRR = 50%, NPV = - 889, IRR < 50
TRY IRR = 25%, NPV = +160, IRR >25
TRY IRR = 28%, NPV = 0
23
Copyright 1996 by The McGraw-Hill Companies, Inc
IRR = 28%
+2
0
-1
50DISCOUNTRATE (%)
NPV
NET PRESENT VALUE PROFILE
C0 = - 4
C1 = +2
C3 = +4
24
Copyright 1996 by The McGraw-Hill Companies, Inc
INTERNAL RATE OF RETURN RULEINTERNAL RATE OF RETURN RULE
ACCEPT PROJECT
IF IRR IS GREATER THAN
THE OPPORTUNITY COST OF
CAPITAL
ACCEPT PROJECT
IF IRR IS GREATER THAN
THE OPPORTUNITY COST OF
CAPITAL
LOOKING AT THE NET PRESENT VALUE PROFILE
FOR A CONVENTIONAL PROJECT,
WE WILL BE ACCEPTING PROJECTS
WITH POSITIVE NPV
25
Copyright 1996 by The McGraw-Hill Companies, Inc
CONVENTIONAL PROJECTCONVENTIONAL PROJECT
CASH OUTFLOWS FOLLOWED BY CASH INFLOWS
NPV DECLINES WITH INCREASING DISCOUNT RATES
26
Copyright 1996 by The McGraw-Hill Companies, Inc
WARNINGWARNING
DISTINGUISH BETWEEN IRR AND OPPORTUNITY COST OF CAPITAL
– BOTH APPEAR AS DISCOUNT RATES IN NPV FORMULA.
IRR IS A MEASURE OF PROFITABILITY, DEPENDS ON AMOUNT AND TIMING OF CASH FLOWS
OPPORTUNITY COST OF CAPITAL MEASURES WHAT WE COULD EARN BY INVESTING IN FINANCIAL ASSETS OF SIMILAR RISK
– SET BY CAPITAL MARKETS
– IT IS A COST OF FINANCING THE PROJECT
– IT PROVIDES US WITH A MINIMUM ACCEPTABLE LEVEL OF PROFITABILITY
27
Copyright 1996 by The McGraw-Hill Companies, Inc
NPV Year: 0 1 IRR(%) At 10% ($)
A -1,000 +1,500 +50 +364 B +1,000 -1,500 +50 +364
NPV Year: 0 1 IRR(%) At 10% ($)
A -1,000 +1,500 +50 +364 B +1,000 -1,500 +50 +364
BOTH PROJECTS HAVE IRR OF 50%
NPV PROFILE FOR PROJECT B INCREASES
WITH INCREASING DISCOUNT RATES
ACCEPT PROJECT B WHEN IRR IS LESS THAN
THE OPPORTUNITY COST OF CAPITAL
LENDING OR BORROWING?
28
Copyright 1996 by The McGraw-Hill Companies, Inc
MULTIPLE RATES OF RETURNMULTIPLE RATES OF RETURN
DESCARTES’ RULE OF SIGNS SAYS THERE ARE AS THERE ARE CHANGES IN SIGN
– BUT SOME OF THE ROOTS MAY BE THE SAME!
OFTEN HAVE CASH OUTCASH OUTFLOWS FROM INITIAL INVESTMENT,
FOLLOWED BY POSITIVE CASH FLOWS DURING PROJECT LIFE, FOLLOWED BY CASH OUTFLOWS AT END OF PROJECT
LIFE– DECOMMISSIONING COSTS OF NUCLEAR POWER PLANT
– RECLAMATION COSTS AFTER STRIPMINING COAL
– DELAY BETWEEN EARNING INCOME AND PAYING TAX
29
Copyright 1996 by The McGraw-Hill Companies, Inc
MULTIPLE RATES OF RETURNMULTIPLE RATES OF RETURN
Year: 0 1 2 IRR NPV @ 10 C -4 +25 -25 25% & 400% -1.9
TWO CHANGES IN SIGN OF CASH FLOWS
TWO INTERNAL RATES OF RETURN
r < 25%, NPV < 0
30
Copyright 1996 by The McGraw-Hill Companies, Inc
MULTIPLE RATES OF RETURNMULTIPLE RATES OF RETURN
Year: 0 1 2 IRR NPV @ 10 C -4 +25 -25 25% & 400% -1.9
TWO CHANGES IN SIGN OF CASH FLOWS
TWO INTERNAL RATES OF RETURN
r < 25%, NPV < 0
25% < r < 400%, NPV > 0
ACCEPT PROJECT
31
Copyright 1996 by The McGraw-Hill Companies, Inc
IRR MAY GIVE THE WRONG DECISION WITH MUTUALLY
EXCLUSIVE PROJECTS WHICH DIFFER IN:
IRR MAY GIVE THE WRONG DECISION WITH MUTUALLY
EXCLUSIVE PROJECTS WHICH DIFFER IN:
SCALEPATTERN OF CASH FLOWS OVER TIME
– COMPARE PROJECTS G AND H
0 1 2 3 4 5
IRR NPV @ 10% -9 +6 +5 +4
0 0 ........ 33% 3,592 -9 +1.8
+1.8 +1.8 +1.8 +1.8...... 20% 9,000
G
H
32
Copyright 1996 by The McGraw-Hill Companies, Inc
IRR MAY GIVE THE WRONG DECISION WITH MUTUALLY
EXCLUSIVE PROJECTS WHICH DIFFER IN:
IRR MAY GIVE THE WRONG DECISION WITH MUTUALLY
EXCLUSIVE PROJECTS WHICH DIFFER IN:
SCALEPATTERN OF CASH FLOWS OVER TIME
– COMPARE PROJECTS G AND H 0
1 2 3 4 5 IRR NPV @ 10% -9
+6 +5 +4 0 0 ........ 33% 3,592 -9
+1.8 +1.8 +1.8 +1.8 +1.8...... 20% 9,000
-6 +1.2 +1.2 +1.2 +1.2...... 20% 6,000
PROJECT H HAS HIGHER NPV THAN PROJECT G – BUT LOWER IRR
G
H
I
34
Copyright 1996 by The McGraw-Hill Companies, Inc
MUTUALLY EXCLUSIVE PROJECTSMUTUALLY EXCLUSIVE PROJECTS
PROJECT G HAS IRR OF 33%PROJECT H HAS IRR OF 20%NPVG = NPVH AT CROSSOVER POINT OF 15.6%CASH FLOWS OF PROJECT H ARE LARGER BUT
OCCUR LATER – FOR DISCOUNT RATES < 15.6%, PROJECT H
HAS HIGHER NPV– FOR DISCOUNT RATES > 15.6%, PROJECT G
HAS HIGHER NPV
36
Copyright 1996 by The McGraw-Hill Companies, Inc
Topics CoveredTopics Covered
Sensitivity Analysis Break Even Analysis Monte Carlo Simulation Decision Trees
37
Copyright 1996 by The McGraw-Hill Companies, Inc
How To Handle Uncertainty
Sensitivity Analysis - Analysis of the effects of changes in sales, costs, etc. on a project.
Scenario Analysis - Project analysis given a particular combination of assumptions.
Simulation Analysis - Estimation of the probabilities of different possible outcomes.
Break Even Analysis - Analysis of the level of sales (or other variable) at which the company breaks even.
38
Copyright 1996 by The McGraw-Hill Companies, Inc
Monte Carlo SimulationMonte Carlo Simulation
Step 1: Modeling the Project Step 2: Specifying Probabilities Step 3: Simulate the Cash Flows
Modeling Process
39
Copyright 1996 by The McGraw-Hill Companies, Inc
Decision TreesDecision Trees
960 (.8)
220(.2)
930(.4)
140(.6)
800(.8)
100(.2)
410(.8)
180(.2)
220(.4)
100(.6)
+150(.6)
+30(.4)
+100(.6)
+50(.4)
-550
NPV= ?
-250
NPV= ?
-150
0
or
Turboprop
Piston
40
Copyright 1996 by The McGraw-Hill Companies, Inc
Decision TreesDecision Trees
960 (.8)
220(.2)
930(.4)
140(.6)
800(.8)
100(.2)
410(.8)
180(.2)
220(.4)
100(.6)
+150(.6)
+30(.4)
+100(.6)
+50(.4)
-550
NPV= ?
-250
NPV= ?
-150
0
or
812
456
660
364
148
Turboprop
Piston
41
Copyright 1996 by The McGraw-Hill Companies, Inc
Decision TreesDecision Trees
960 (.8)
220(.2)
930(.4)
140(.6)
800(.8)
100(.2)
410(.8)
180(.2)
220(.4)
100(.6)
+150(.6)
+30(.4)
+100(.6)
+50(.4)
-550
NPV= ?
-250
NPV= ?
-150
0
or
812
456
660
364
148 81220.22080.960
Turboprop
Piston
42
Copyright 1996 by The McGraw-Hill Companies, Inc
Decision TreesDecision Trees
960 (.8)
220(.2)
930(.4)
140(.6)
800(.8)
100(.2)
410(.8)
180(.2)
220(.4)
100(.6)
-550
NPV= ?
-250
NPV= ?
-150
0
or
812
456
660
364
148
+150(.6)
+30(.4)
+100(.6)
+50(.4)
*450
331
45015010.1
660 450150
10.1
660Turboprop
Piston
43
Copyright 1996 by The McGraw-Hill Companies, Inc
Decision TreesDecision Trees
960 (.8)
220(.2)
930(.4)
140(.6)
800(.8)
100(.2)
410(.8)
180(.2)
220(.4)
100(.6)
-550
NPV= ?
-250
NPV= ?
-150
0
or
812
456
660
364
148
+150(.6)
+30(.4)
+100(.6)
+50(.4)
NPV=444.55
NPV=888.18
NPV=550.00
NPV=184.55
*450
331
18.88815010.1
812 18.888150
10.1
812
Turboprop
Piston
44
Copyright 1996 by The McGraw-Hill Companies, Inc
Decision TreesDecision Trees
960 (.8)
220(.2)
930(.4)
140(.6)
800(.8)
100(.2)
410(.8)
180(.2)
220(.4)
100(.6)
812
456
660
364
148
+150(.6)
710.73
+30(.4)
+100(.6)
403.82
+50(.4)
-150
0
*450
331
or
NPV=444.55
NPV=888.18
NPV=550.00
NPV=184.55
-550
NPV= ?
-250
NPV= ?
40.55.44460.18.888 40.55.44460.18.888
Turboprop
Piston
45
Copyright 1996 by The McGraw-Hill Companies, Inc
Decision TreesDecision Trees
960 (.8)
220(.2)
930(.4)
140(.6)
800(.8)
100(.2)
410(.8)
180(.2)
220(.4)
100(.6)
812
456
660
364
148
+150(.6)
710.73
+30(.4)
+100(.6)
403.82
+50(.4)
-550
NPV=96.12
-250
NPV=117.00
-150
0
*450
331
or
NPV=444.55
NPV=888.18
NPV=550.00
NPV=184.55
12.9655010.1
73.710 12.96550
10.1
73.710
Turboprop
Piston
46
Copyright 1996 by The McGraw-Hill Companies, Inc
Decision TreesDecision Trees
960 (.8)
220(.2)
930(.4)
140(.6)
800(.8)
100(.2)
410(.8)
180(.2)
220(.4)
100(.6)
812
456
660
364
148
+150(.6)
710.73
+30(.4)
+100(.6)
403.82
+50(.4)
-550
NPV=96.12
-250
NPV=117.00
-150
0
*450
331
or
NPV=444.55
NPV=888.18
NPV=550.00
NPV=184.55
Turboprop
Piston