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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

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WHAT DISCOUNT RATE SHOULD THE FIRM USE IN CAPITAL BUDGETING?

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  1. 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. COMPANY COST OF CAPITAL ANDREQUIRED RETURN ON PROJECT REQUIRED RETURN Security market line showing required return on project Company cost of capital Average beta PROJECT BETA of firm's assets

  3. 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!!

  4. 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

  5. CATEGORYDISCOUNT RATE SPECULATIVE VENTURES 30% NEW PRODUCTS 20% EXPANSION OF 15% (company cost of capital) EXISTING BUSINESS COST IMPROVEMENT 10% KNOWN TECHNOLOGY

  6. USING CAPM AND PROJECT b MANY LARGE CORPORATIONS USE CAPM AND AN ESTIMATE OF THE PROJECT b TO ESTIMATE PROJECT DISCOUNT RATE EXPECTED PROJECT RETURN = rf + bproject (rm- rf)

  7. BEGIN WITH PROBLEMS IN MEASURING COMPANY b • b IS DIFFICULT TO MEASURE FOR INDIVIDUAL FIRM • BETTER ACCURACY BY LOOKING AT AVERAGE OF SIMILAR COMPANIES • BUT FIRM’S BORROWING POLICIES AFFECTS ITS STOCK b • IBM AND DEC ARE NOT SIMILAR COMPANIES FOR PURPOSE OF ESTIMATING b BECAUSE THEY USE DIFFERENT DEGREES OF LEVERAGE

  8. MEASURING COMPANY b • APPROPRIATE FOR ACROSS-THE-BOARD EXPANSION • COMPARE RETURN ON STOCK WITH MARKET RETURN OVER 60-MONTH TIME PERIOD • AT&T • HEWLETT-PACKARD • SLOPE IS b • VARIES BY PERIOD • ESTIMATES OF b ARE PUBLISHED BY BROKERAGE HOUSES AND ADVISORY SERVICES

  9. ESTIMATING BETA RETURN ON SHARE RETURN ON SHARE Beta = 1.6 + + + + + + + + + + + + + + + + + + + + Beta = .4 + + + + + + + + + + + + + + + + + + + + RETURN ON MARKET + RETURN ON MARKET + + + + + + + + + + + + + + +

  10. PFIZER • WHICH IS THE BETTER ESTIMATE OF b FOR PFIZER? • PFIZER HAS A b OF 1.02 WITH A STANDARD ERROR OF 0.14 • A MARKET VALUE-WEIGHTED INDUSTRY PORTFOLIO OF LARGE PHARMACEUTICAL COMPANIES HAS A b 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. 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. HOW CHANGING CAPITAL STRUCTURE AFFECTS b • AFTER REFINANCING, RISK OF TOTAL PORTFOLIO OF DEBT AND EQUITY IS UNCHANGED • BUT BOTH DEBT AND EQUITY ARE INDIVIDUALLY LESS RISKY • FIRM’S ASSET BETA IS WEIGHTED AVERAGE OF PORTFOLIO OF DEBT AND EQUITY BETAS

  13. HOW CHANGING CAPITAL STRUCTURE AFFECTS b • AFTER REFINANCING, RISK OF TOTAL PORTFOLIO OF DEBT AND EQUITY IS UNCHANGED • BUT BOTH DEBT AND EQUITY ARE INDIVIDUALLY LESS RISKY • FIRM’S ASSET BETA IS WEIGHTED AVERAGE OF PORTFOLIO OF DEBT AND EQUITY BETAS • SUPPOSE bdebt FALLS TO .1 .8 = (.3 X .1) + (.7 X bequity ) bequity = 1.1

  14. UNLEVERING BETAS • GOING FROM AN OBSERVED bequity TObassets • WE KNOW bequity bdebt MARKET WEIGHTS OF DEBT AND EQUITY, (D/V )AND (E/V)

  15. UNLEVERING BETAS • GOING FROM AN OBSERVED bequity TObassets • WE KNOW bequity bdebt MARKET WEIGHTS OF DEBT AND EQUITY, (D/V )AND (E/V) • WE WILL ADD TAX EFFECTS LATER

  16. REVIEW • 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. 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. OPERATING 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. OPERATING LEVERAGE • bFIXED COST = 0 • ALSObREVENUES @ bVARIABLE COST • AS THEY ARE BOTH PROPORTIONAL TO OUTPUT

  20. 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

  21. INTERNAL RATE OF RETURN, IRR NPV = IRR IS THE DISCOUNT RATE FOR WHICH NPV=0

  22. 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

  23. NET PRESENT VALUE PROFILE • C0 = - 4 • C1 = +2 • C3 = +4 NPV +2 IRR = 28% DISCOUNT 0 RATE (%) 50 -1

  24. 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

  25. CONVENTIONAL PROJECT • CASH OUTFLOWS FOLLOWED BY CASH INFLOWS • NPV DECLINES WITH INCREASING DISCOUNT RATES

  26. 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

  27. NPV Year: 01IRR(%)At 10% ($) A -1,000 +1,500 +50 +364 B +1,000 -1,500 +50 +364 LENDING OR BORROWING? • 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

  28. 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

  29. 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

  30. 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 > 0 ACCEPT PROJECT

  31. IRR MAY GIVE THE WRONG DECISION WITH MUTUALLY EXCLUSIVE PROJECTS WHICH DIFFER IN: • SCALE • PATTERN 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. IRR MAY GIVE THE WRONG DECISION WITH MUTUALLY EXCLUSIVE PROJECTS WHICH DIFFER IN: • SCALE • PATTERN 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

  33. NPV($) 6,000 15.6 33.3 DISCOUNT RATE G 20 H

  34. 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

  35. Real Options

  36. Topics Covered • Sensitivity Analysis • Break Even Analysis • Monte Carlo Simulation • Decision Trees

  37. 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. Monte Carlo Simulation • Step 1: Modeling the Project • Step 2: Specifying Probabilities • Step 3: Simulate the Cash Flows Modeling Process

  39. Decision 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) Turboprop -550 NPV= ? -150 +100(.6) +50(.4) or Piston 0 -250 NPV= ?

  40. Decision 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) +30(.4) Turboprop -550 NPV= ? -150 +100(.6) +50(.4) or Piston 0 -250 NPV= ?

  41. Decision 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) +30(.4) Turboprop -550 NPV= ? -150 +100(.6) +50(.4) or Piston 0 -250 NPV= ?

  42. Decision 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) +30(.4) Turboprop -550 NPV= ? *450 -150 +100(.6) +50(.4) or Piston 0 331 -250 NPV= ?

  43. Decision Trees 960 (.8) 220(.2) 930(.4) 140(.6) 800(.8) 100(.2) 410(.8) 180(.2) 220(.4) 100(.6) NPV=888.18 812 456 660 364 148 +150(.6) +30(.4) Turboprop -550 NPV= ? NPV=444.55 *450 -150 NPV=550.00 +100(.6) +50(.4) or Piston 0 331 -250 NPV= ? NPV=184.55

  44. Decision Trees 960 (.8) 220(.2) 930(.4) 140(.6) 800(.8) 100(.2) 410(.8) 180(.2) 220(.4) 100(.6) NPV=888.18 812 456 660 364 148 +150(.6) 710.73 +30(.4) Turboprop -550 NPV= ? NPV=444.55 *450 -150 NPV=550.00 +100(.6) 403.82 +50(.4) or Piston 0 331 -250 NPV= ? NPV=184.55

  45. Decision Trees 960 (.8) 220(.2) 930(.4) 140(.6) 800(.8) 100(.2) 410(.8) 180(.2) 220(.4) 100(.6) NPV=888.18 812 456 660 364 148 +150(.6) 710.73 +30(.4) Turboprop -550 NPV=96.12 NPV=444.55 *450 -150 NPV=550.00 +100(.6) 403.82 +50(.4) or Piston 0 331 -250 NPV=117.00 NPV=184.55

  46. Decision Trees 960 (.8) 220(.2) 930(.4) 140(.6) 800(.8) 100(.2) 410(.8) 180(.2) 220(.4) 100(.6) NPV=888.18 812 456 660 364 148 +150(.6) 710.73 +30(.4) Turboprop -550 NPV=96.12 NPV=444.55 *450 -150 NPV=550.00 +100(.6) 403.82 +50(.4) or Piston 0 331 -250 NPV=117.00 NPV=184.55

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