what discount rate should the firm use in capital budgeting?

1Copyright 1996 by The McGraw-Hill Companies, Inc

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

2Copyright 1996 by The McGraw-Hill Companies, Inc

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

3Copyright 1996 by The McGraw-Hill Companies, Inc

COMPANY 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!!

4Copyright 1996 by The McGraw-Hill Companies, Inc

COMPANY 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

5Copyright 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

6Copyright 1996 by The McGraw-Hill Companies, Inc

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)

7Copyright 1996 by The McGraw-Hill Companies, Inc

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

8Copyright 1996 by The McGraw-Hill Companies, Inc

MEASURING COMPANY

APPROPRIATE FOR ACROSS-THE-BOARD EXPANSIONCOMPARE RETURN ON STOCK WITH MARKET RETURN OVER

60-MONTH TIME PERIOD– AT&T– HEWLETT-PACKARD

SLOPE IS VARIES BY PERIODESTIMATES OF ARE PUBLISHED BY BROKERAGE HOUSES

AND ADVISORY SERVICES

9Copyright 1996 by The McGraw-Hill Companies, Inc

ESTIMATING BETA

RETURN ON SHARE

RETURN ON MARKET

+

Beta = .4

++

++ +

++++

++

+

+

++

+

+++

++ +

++

+++

RETURN ON SHARE

RETURN ON MARKET

+

Beta = 1.6

++

+

+ +

++++

++

+

+

++

+

++

+

++ +

++

+

++

10Copyright 1996 by The McGraw-Hill Companies, Inc

PFIZERWHICH 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

11Copyright 1996 by The McGraw-Hill Companies, Inc

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

12Copyright 1996 by The McGraw-Hill Companies, Inc

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

13Copyright 1996 by The McGraw-Hill Companies, Inc

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

14Copyright 1996 by The McGraw-Hill Companies, Inc

UNLEVERING 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

15Copyright 1996 by The McGraw-Hill Companies, Inc

UNLEVERING 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

16Copyright 1996 by The McGraw-Hill Companies, Inc

REVIEWCOST 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

17Copyright 1996 by The McGraw-Hill Companies, Inc

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

18Copyright 1996 by The McGraw-Hill Companies, Inc

OPERATING LEVERAGEWE KNOW FINANCIAL LEVERAGE INCREASES BETAFOR 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)

19Copyright 1996 by The McGraw-Hill Companies, Inc

OPERATING LEVERAGEFIXED COST = 0 ALSO REVENUES VARIABLE COST

– AS THEY ARE BOTH PROPORTIONAL TO OUTPUT

REVENUEASSET

[1 PV(FIXED COST)PV(ASSET) ]REVENUE

PV(REVENUE) -PV(FIXED COST)PV(ASSET)

20Copyright 1996 by The McGraw-Hill Companies, Inc

NET 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

21Copyright 1996 by The McGraw-Hill Companies, Inc

INTERNAL RATE OF RETURN, IRR

C C C C0

1 22

TT(1 IRR) (1 IRR)

....(1 IRR)

0

NPV =

IRR IS THE DISCOUNT RATE FOR WHICH NPV=0

22Copyright 1996 by The McGraw-Hill Companies, Inc

CALCULATING 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

23Copyright 1996 by The McGraw-Hill Companies, Inc

IRR = 28%

+2

0

-1

50DISCOUNTRATE (%)

NPV

NET PRESENT VALUE PROFILE

C0 = - 4C1 = +2C3 = +4

24Copyright 1996 by The McGraw-Hill Companies, Inc

INTERNAL RATE OF RETURN RULE

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

25Copyright 1996 by The McGraw-Hill Companies, Inc

CONVENTIONAL PROJECT

CASH OUTFLOWS FOLLOWED BY CASH INFLOWSNPV DECLINES WITH INCREASING DISCOUNT

RATES

26Copyright 1996 by The McGraw-Hill Companies, Inc

WARNING

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

27Copyright 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 BOTH PROJECTS HAVE IRR OF 50%NPV PROFILE FOR PROJECT B INCREASES

WITH INCREASING DISCOUNT RATESACCEPT PROJECT B WHEN IRR IS LESS THAN

THE OPPORTUNITY COST OF CAPITAL

LENDING OR BORROWING?

28Copyright 1996 by The McGraw-Hill Companies, Inc

MULTIPLE 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

29Copyright 1996 by The McGraw-Hill Companies, Inc

MULTIPLE 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

30Copyright 1996 by The McGraw-Hill Companies, Inc

MULTIPLE 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 > 0ACCEPT PROJECT

31Copyright 1996 by The McGraw-Hill Companies, Inc

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

GH

32Copyright 1996 by The McGraw-Hill Companies, Inc

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% 6,000PROJECT H HAS HIGHER NPV THAN PROJECT G

– BUT LOWER IRR

GH

I

33Copyright 1996 by The McGraw-Hill Companies, Inc

H

G

33.315.6

20

NPV($)

DISCOUNT RATE

6,000

34Copyright 1996 by The McGraw-Hill Companies, Inc

MUTUALLY 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

35Copyright 1996 by The McGraw-Hill Companies, Inc

Real Options

36Copyright 1996 by The McGraw-Hill Companies, Inc

Topics Covered Sensitivity Analysis Break Even Analysis Monte Carlo Simulation Decision Trees

37Copyright 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.

38Copyright 1996 by The McGraw-Hill Companies, Inc

Monte Carlo Simulation

Step 1: Modeling the Project Step 2: Specifying Probabilities Step 3: Simulate the Cash Flows

Modeling Process

39Copyright 1996 by The McGraw-Hill Companies, Inc

Decision Trees960 (.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

0or

Turboprop

Piston

40Copyright 1996 by The McGraw-Hill Companies, Inc

Decision Trees960 (.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

0or

812

456

660

364

148

Turboprop

Piston

41Copyright 1996 by The McGraw-Hill Companies, Inc

Decision Trees960 (.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

0or

812

456

660

364

148 81220.22080.960

Turboprop

Piston

42Copyright 1996 by The McGraw-Hill Companies, Inc

Decision Trees960 (.8)

220(.2)

930(.4)

140(.6)

800(.8)

100(.2)

410(.8)

180(.2)

220(.4)

100(.6)

-550

NPV= ?

-250

NPV= ?

-150

0or

812

456

660

364

148

+150(.6)

+30(.4)

+100(.6)

+50(.4)

*450

331

45015010.1

660Turboprop

Piston

43Copyright 1996 by The McGraw-Hill Companies, Inc

Decision Trees960 (.8)

220(.2)

930(.4)

140(.6)

800(.8)

100(.2)

410(.8)

180(.2)

220(.4)

100(.6)

-550

NPV= ?

-250

NPV= ?

-150

0or

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

Turboprop

Piston

44Copyright 1996 by The McGraw-Hill Companies, Inc

Decision Trees960 (.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

Turboprop

Piston

45Copyright 1996 by The McGraw-Hill Companies, Inc

Decision Trees960 (.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

Turboprop

Piston

46Copyright 1996 by The McGraw-Hill Companies, Inc

Decision Trees960 (.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