Capital Budgeting: Decision Criteria Chapter 12 Capital Budgeting: Decision Criteria

Topics Overview Methods Unequal lives Economic life NPV IRR, MIRR Profitability Index Payback, discounted payback Unequal lives Economic life

Capital Budgeting: Analysis of potential projects Long-term decisions Large expenditures Difficult/impossible to reverse Determines firm’s strategic direction

Steps in Capital Budgeting Estimate cash flows (Ch 13) Assess risk of cash flows (Ch 13) Determine r = WACC for project (Ch10) Evaluate cash flows – Chapter 12

Independent versus Mutually Exclusive Projects The cash flows of one are unaffected by the acceptance of the other Mutually Exclusive: The acceptance of one project precludes accepting the other

Cash Flows for Projects L and S

NPV: Sum of the PVs of all cash flows. ∑ n t = 0 CFt (1 + r)t . NOTE: t=0 Cost often is CF0 and is negative NPV = ∑ n t = 1 CFt (1 + r)t - CF0

Project S’s NPV

Project L’s NPV

TI BAII+: Project L NPV Cash Flows: CF0 = -1000 CF1 = 100 CF2 = 300 Display You Enter ' C00 1000 S !# C01 100 !# F01 1 !# C02 300 !# F02 1 !# C03 400 !# F03 1 !# C04 600 !# F04 1 !# ( I 10 !# NPV % 49.18 Cash Flows: CF0 = -1000 CF1 = 100 CF2 = 300 CF3 = 400 CF4 = 600

Rationale for the NPV Method NPV = PV inflows – Cost NPV=0 → Project’s inflows are “exactly sufficient to repay the invested capital and provide the required rate of return.” NPV = net gain in shareholder wealth Choose between mutually exclusive projects on basis of higher NPV Rule: Accept project if NPV > 0

NPV Method Meets all desirable criteria Considers all CFs Considers TVM Can rank mutually exclusive projects Value-additive Directly related to increase in VF Dominant method; always prevails

Using NPV method, which franchise(s) should be accepted? Project S NPV = $78.82 Project L NPV = $49.18 If Franchise S and L are mutually exclusive, accept S because NPVs > NPVL If S & L are independent, accept both; NPV > 0

Internal Rate of Return: IRR IRR = the discount rate that forces PV inflows = cost  Forcing NPV = 0 ≈ YTM on a bond Preferred by executives 3:1

∑ ∑ NPV vs IRR NPV: Enter r, solve for NPV CFt = NPV (1 + r)t IRR: Enter NPV = 0, solve for IRR = 0 ∑ n t = 0 CFt (1 + IRR)t

Franchise L’s IRR

TI BAII+: Project L IRR Cash Flows: CF0 = -1000 CF1 = 100 CF2 = 300 Display You Enter ' C00 1000 S !# C01 100 !# F01 1 !# C02 300 !# F02 1 !# C03 400 !# F03 1 !# C04 600 !# F04 1 !# ( I 10 !# IRR % 11.79 Cash Flows: CF0 = -1000 CF1 = 100 CF2 = 300 CF3 = 400 CF4 = 600

Decisions on Projects S and L per IRR Project S IRR = 14.5% Project L IRR = 11.8% Cost of capital = 10.0% If S and L are independent, accept both: IRRS > r and IRRL > r If S and L are mutually exclusive, accept S because IRRS > IRRL

Construct NPV Profiles Enter CFs in CFLO and find NPVL and NPVS at different discount rates:

NPV Profile

To Find the Crossover Rate Find cash flow differences between the projects. Enter these differences in CFLO register, then press IRR. Crossover rate = 7.17%, rounded to 7.2%. Can subtract S from L or vice versa If profiles don’t cross, one project dominates the other

Finding the Crossover Rate

NPV and IRR: No conflict for independent projects r > IRR and NPV < 0. Reject NPV ($) r (%) IRR IRR > r and NPV > 0 Accept

Mutually Exclusive Projects NPVS> NPVL IRRS > IRRL NO CONFLICT r < 7.2% NPVL> NPVS IRRS > IRRL CONFLICT NPV L S IRRS % 7.2 IRRL

Mutually Exclusive Projects CONFLICT r < 7.2% NPVL> NPVS IRRS > IRRL r > 7.2% NPVS > NPVL IRRS > IRRL NO CONFLICT

Two Reasons NPV Profiles Cross Size (scale) differences Smaller project frees up funds sooner for investment The higher the opportunity cost, the more valuable these funds, so high r favors small projects Timing differences Project with faster payback provides more CF in early years for reinvestment If r is high, early CF especially good, NPVS > NPVL

Issues with IRR Reinvestment rate assumption Non-normal cash flows

Reinvestment Rate Assumption NPV assumes reinvest at r (opportunity cost of capital) IRR assumes reinvest at IRR Reinvest at opportunity cost, r, is more realistic, so NPV method is best NPV should be used to choose between mutually exclusive projects

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

MIRR for Project S: First, find PV and TV (r = 10%)

Second: Find discount rate that equates PV and TV MIRR = 12.1%

Second: Find discount rate that equates PV and TV PV = PV(Outflows) = -1000 FV = TV(Inflows) = 1579.5 N = 4 PMT = 0 CPY I/Y = 12.1063 = 12.1% EXCEL: =MIRR(Value Range, FR, RR)

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

Normal vs. Nonnormal Cash Flows Normal Cash Flow Project: Cost (negative CF) followed by a series of positive cash inflows One change of signs Nonnormal 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, nuclear power plant or strip mine

Pavilion Project: NPV and IRR? 5,000 -5,000 1 2 r = 10% -800 Enter CFs, enter I = 10 NPV = -386.78 IRR = ERROR

Nonnormal CFs: Two sign changes, two IRRs NPV Profile 450 -800 400 100 IRR2 = 400% IRR1 = 25% r NPV

Multiple IRRs Descartes Rule of Signs 1 real root per sign change Polynomial of degree n→n roots 1 real root per sign change Rest = imaginary (i2 = -1)

Logic of Multiple IRRs At very low discount rates: The PV of CF2 is large & negative NPV < 0 At very high discount rates: The PV of both CF1 and CF2 are low CF0 dominates Again NPV < 0

Logic of Multiple IRRs In between: Result: 2 IRRs The discount rate hits CF2 harder than CF1 NPV > 0 Result: 2 IRRs

The Pavillion Project: Non-normal CFs and MIRR: 1 2 -800,000 5,000,000 -5,000,000 RR FR PV outflows @ 10% = -4,932,231.40 TV inflows @ 10% = 5,500,000.00 MIRR = 5.6%

Profitability Index PI =present value of future cash flows divided by the initial cost Measures the “bang for the buck”

Project S’s PV of Cash Inflows

Profitability Indexs PV future CF $1078.82 PIS = = Initial Cost $1000 PIL = 1.0492

Profitability Index Rule: If PI>1.0  Accept Useful in capital rationing Closely related to NPV Can conflict with NPV if projects are mutually exclusive

Profitability Index Strengths: Weaknesses: Considers all CFs Considers TVM Useful in capital rationing Weaknesses: Cannot rank mutually exclusive Not Value-additive

Payback Period The number of years required to recover a project’s cost How long does it take to get the business’s money back? A breakeven-type measure Rule: Accept if PB<Target

Payback for Projects S and L

Payback for Projects S and L

Strengths and Weaknesses of Payback Provides indication of project risk and liquidity Easy to calculate and understand Weaknesses: Ignores the TVM Ignores CFs occurring after the payback period Biased against long-term projects ASKS THE WRONG QUESTION!

Discounted Payback: Use discounted CFs

Summary Calculate ALL -- each has value Method What it measures Metric NPV  $ increase in VF $$ Payback  Liquidity Years IRR  E(R), risk % MIRR  Corrects IRR % PI  If rationed Ratio

Business Practices

Special Applications Projects with Unequal Lives Economic vs. Physical life The Optimal Capital Budget Capital Rationing

SS and LL are mutually exclusive. r = 10%. 1 2 3 4 Project SS: (100) Project LL: 60 33.5

NPVLL > NPVSS But is LL better? CF0 -100,000 CF1 60,000 33,500 F 2 4 I 10 NPV 4,132 6,190

Solving for EAA PMT = EAA Project SS Project LL 2 , 10 - 4132 S. 0 0 %/ = 2.38 4 , 10 - 6190 S. 0 0 %/ = 1.95 =PMT(0.10,2,-4132,0) =PMT(0.10,4,-6190,0) 56

Unequal Lives Project SS could be repeated after 2 years to generate additional profits Use Replacement Chain to put projects on a common life basis Note: equivalent annual annuity analysis is alternative method.

Replacement Chain Approach (000s) Project SS with Replication: NPVSS = $7,547 Compare: NPVLL = $6,190 . 1 2 3 4 Project SS: (100) 60 (40)

Or, use NPVss: Compare to Project LL NPV = $6,190 1 2 3 4 4,132 3,415 1 2 3 4 4,132 3,415 7,547 10%

Suppose cost to repeat SS in two years rises to $105,000 NPVSS = $3,415 < NPVLL = $6,190 1 2 3 4 Project SS: (100) 60 (105) (45)

Economic Life vs. Physical Life Consider a project with a 3-year life If terminated prior to Year 3, the machinery will have positive salvage value Should you always operate for the full physical life?

Economic Life vs. Physical Life

Economic vs. Physical Life

Conclusions NPV(3) = -$14.12 NPV(2) = $34.71 NPV(1) = -$254.55 The project is acceptable only if operated for 2 years. A project’s engineering life does not always equal its economic life.

The Optimal Capital Budget Finance theory says: Accept all positive NPV projects Two problems can occur when there is not enough internally generated cash to fund all positive NPV projects: An increasing marginal cost of capital Capital rationing

Increasing Marginal Cost of Capital Externally raised capital  large flotation costs Increases the cost of capital Investors often perceive large capital budgets as being risky Drives up the cost of capital If external funds will be raised, then the NPV of all projects should be estimated using this higher marginal cost of capital

Increasing Marginal Cost of Capital % 16 15 14 WACC2 = 12.5% 13 12 WACC1 = 11.0% External debt & equity 10 No external funds 9 8 500 700 Capital Required 61 48

Capital Rationing Firm chooses not to fund all positive NPV projects Company typically sets an upper limit on the total amount of capital expenditures that it will make in the upcoming year

Capital Rationing – Reason 1 Companies want to avoid the direct costs (i.e., flotation costs) and the indirect costs of issuing new capital Solution: Increase the cost of capital by enough to reflect all of these costs Then accept all projects that still have a positive NPV with the higher cost of capital

Capital Rationing – Reason 2 Companies don’t have enough managerial, marketing, or engineering staff to implement all positive NPV projects Solution: Use linear programming to maximize NPV subject to not exceeding the constraints on staffing

Capital Rationing – Reason 3 Companies believe that the project’s managers forecast unreasonably high cash flow estimates “Filter” out the worst projects by limiting the total amount of projects that can be accepted Solution: Implement a post-audit process and tie the managers’ compensation to the subsequent performance of the project

Excel 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; no entry needed) Annuity Due = 1 (must be entered)

Excel Spreadsheet Functions NPV(Rate, Value Range**) IRR(Value Range) MIRR(Value Range, FR, RR) ** NPV value range includes CF1 through CFn CF0 must be handled independently, outside the function =NPV(Rate, CF1-CFn) + CF0