Capital Budgeting Investment Rules Finance - Pedro Barroso

Net Present Value (NPV) Rule Total PV of future CFs - Initial Investment Estimating NPV: 1. Estimate future cash flows: how much? and when? 2. Estimate discount rate: time value of money; risk 3. Estimate initial costs Minimum Acceptance Criteria: Accept if NPV > 0 Ranking Criteria: Choose the highest NPV Note that although we add the initial investment, this value is a negative number. Finance - Pedro Barroso

Why Use Net Present Value? Accepting positive NPV projects benefits shareholders NPV uses cash flows NPV discounts the cash flows properly Maximizes shareholder value (stock price) Reinvestment assumption: NPV rule assumes that all cash flows can be reinvested at the discount rate Finance - Pedro Barroso

Finance - Pedro Barroso Example: Project Using previous example and discount rate of 10%: NPV > 0: go-on with project Finance - Pedro Barroso

Finance - Pedro Barroso Payback Period Rule How long does it take the project to “pay back” its initial investment? Payback Period = number of years to recover initial costs Minimum Acceptance Criteria: Set by management Ranking Criteria: Finance - Pedro Barroso

Problems with Payback Period Ignores the time value of money Ignores cash flows after the payback period (biased against long-term projects) Requires an arbitrary acceptance criteria Finance - Pedro Barroso

Discounted Payback Period How long does it take the project to “pay back” its initial investment, taking the time value of money into account? Decision rule: Accept the project if it pays back on a discounted basis within the specified time Finance - Pedro Barroso

Payback Period: Example Project A (-100, 100, 25, 25) Project B (-100, 25, 75, 150) Discount rate = 0% Project A: Payback = 1, NPV = 50 Project B: Payback = 2, NPV = 150 Finance - Pedro Barroso

Internal Rate of Return (IRR) IRR: discount rate that sets NPV to zero Minimum Acceptance Criteria: Accept if the IRR exceeds the discount rate Ranking Criteria: Select alternative with the highest IRR Reinvestment assumption: All future cash flows assumed reinvested at the IRR Finance - Pedro Barroso

Finance - Pedro Barroso IRR: Example Consider the project: 1 2 3 50 100 150 -200 Finance - Pedro Barroso

Finance - Pedro Barroso NPV Payoff Profile If we graph NPV versus the discount rate, we can see the IRR as the x-axis intercept Discount rate NPV 0% 100.00 2% 86.48 4% 73.88 6% 62.11 8% 51.11 10% 40.80 12% 31.13 14% 22.05 16% 13.52 18% 5.49 20% -2.08 22% -9.22 24% -15.97 Finance - Pedro Barroso

Finance - Pedro Barroso Problems with IRR Investing or financing? Multiple IRRs Problems with mutually exclusive investments (alternative) Scale Problem Timing Problem Finance - Pedro Barroso

IRR: Investing or Financing? Project (financing) (100,-130) Project (investing) (-100, 130) also has IRR = 30% Do financing project if IRR < discount rate! Finance - Pedro Barroso

Finance - Pedro Barroso Multiple IRRs Consider the project: (-100, 230, -132) Project has two IRRs: 10% and 20%. Which one to use? We can have multiple IRR (or none) when cash flows change signs two or more times Finance - Pedro Barroso

Mutually Exclusive vs. Independent Mutually Exclusive Projects: only ONE of several potential projects can be chosen, e.g., acquiring an accounting system RANK all alternatives, and select the best one Independent Projects: accepting or rejecting one project does not affect the decision of the other projects. Must exceed a MINIMUM acceptance criteria Finance - Pedro Barroso

Finance - Pedro Barroso IRR: Scale Problem Consider two mutual exclusive projects (r = 10%): Small (-1000, 2000) IRR = 100% NPV = 818 Large (-2000, 3500) IRR = 75% NPV = 1182 IRR and NPV give different answers: IRR favors small scale project, which has lower NPV; but we should pick large scale project Look at incremental cash flows Large-Small (-1000, 1500) IRR = 50% > 10% Finance - Pedro Barroso

Finance - Pedro Barroso IRR: Timing Problem Consider two mutual exclusive projects (r = 10%): Slow (-100, 10, 35, 100) IRR = 15.4% NPV = 13 Fast (-100, 60, 60, 10) IRR = 18% NPV = 12 IRR and NPV give different answers: IRR favors fast project, which has lower NPV; but we should pick slow project Look at incremental cash flows Slow-Fast (0, -50, -25, 90) IRR = 11.5% > 10% Finance - Pedro Barroso

Finance - Pedro Barroso IRR: Timing Problem Cross-over rate = 11.5% Slow project is better at lower discount rates < 11.5% Fast project is better at higher discount rates > 11.5% Finance - Pedro Barroso

Summary: NPV versus IRR NPV and IRR will generally give the same decision Exceptions: Non-conventional cash flows – cash flow signs change more than once Mutually exclusive projects (reinvestment rate = IRR) Initial investments are substantially different Timing of cash flows is substantially different Finance - Pedro Barroso

Profitability Index (PI) PI = PV of cash flows subsequent to initial investment / Initial investment Minimum Acceptance Criteria: Accept if PI > 1 Ranking Criteria: Select alternative with highest PI Finance - Pedro Barroso

Finance - Pedro Barroso PI: Example Consider the project (discount rate = 10%): 1 2 3 50 100 150 -200 Finance - Pedro Barroso

Finance - Pedro Barroso Problem with PI Problem: Problem with mutually exclusive investments (scale problem) Advantages: May be useful when available investment funds are limited Finance - Pedro Barroso

Finance - Pedro Barroso PI: Limited Funds Consider three independent projects (r = 12%): A (-20, 70, 10) NPV = 50.5 PI = 3.53 B (-10, 15, 40) NPV = 35.3 PI = 4.53 C (-10, -5, 60) NPV = 33.4 PI = 4.34 We have 20 to invest; which projects to pick? Project A does not maximize NPV Rank projects by PI (B, C, A); pick B and C as NPV = 35.3 + 33.4 = 68.7 > 50.5 Finance - Pedro Barroso

Inflation and Capital Budgeting Inflation is an important fact of economic life and must be considered in capital budgeting Consider the relationship between interest rates and inflation, often referred to as the Fisher equation: (1 + Nominal Rate) = (1 + Real Rate) × (1 + Inflation Rate) Finance - Pedro Barroso

Inflation and Capital Budgeting In capital budgeting: discount real cash flows with real rates discount nominal cash flows with nominal rates When using real cash flows do not forget that depreciation (tax shield) is a nominal quantity Finance - Pedro Barroso

Inflation and Capital Budgeting: Example Real cash flows Year 0 Year 1 Year 2 Nominal discount rate 15.5% Investment -1,210 Inflation 10.0% EBITDA 950 1,000 Real discount rate 5.0% Depreciation (nominal) 605 Depreciation (real) 550 500 Tax rate 40% Operational cash flow 790 800 Total cash flow NPV 268 Nominal cash flows 1,045 1,210 Depreciation 869 968 Finance - Pedro Barroso

Investments of Unequal Lives NPV rule can lead to the wrong decision when we have to decide between alternative projects with unequal lives Consider a two machines that do the same job, but: Machine A costs $4,000, has annual operating costs of $100, and lasts 10 years Machine B costs $1,000, has annual operating costs of $500, and lasts 5 years Assuming a 10% discount rate, which one should we choose? Finance - Pedro Barroso

Investments of Unequal Lives Machine A: Machine B: Using NPV rule we pick machine B, but Overlooks that the machine A lasts twice as long When we incorporate difference in lives, machine A is actually cheaper (i.e., has a higher NPV) Finance - Pedro Barroso

Investments of Unequal Lives Replacement Chain Repeat projects until they end at the same time Compute NPV for the “repeated projects” Equivalent Annual Cost Method Finance - Pedro Barroso

Replacement Chain Approach Machine A time line of cash flows: -4,000 –100 -100 -100 -100 -100 -100 -100 -100 -100 -100 0 1 2 3 4 5 6 7 8 9 10 Machine B cash flows over ten years: -1,000 –500 -500 -500 -500 -1,500 -500 -500 -500 -500 -500 0 1 2 3 4 5 6 7 8 9 10 Finance - Pedro Barroso

Replacement Chain Approach Machine A: Machine B: Finance - Pedro Barroso

Equivalent Annual Cost (EAC) Simple approach to compare two machines with different lives Puts costs on a per-year basis EAC is the value of constant annuity that has the same NPV as our original set of cash flows (with no initial investment) Assumes machines can be replaced by similar machines at end of its life Finance - Pedro Barroso

Finance - Pedro Barroso EAC: Example Machine A: Machine B: Pick machine A because has lower EAC Finance - Pedro Barroso

Finance - Pedro Barroso Decision to Replace A common decision is when to replace an existing machine by a new one When annual cost of new machine is less than annual cost of old machine We can use EAC to decide Finance - Pedro Barroso

Decision to Replace: Example New machine: costs $9,000, annual maintenance cost of $1,000, lasts for 8 years and salvage value of $2,000 after taxes (discount rate = 15%) Finance - Pedro Barroso

Decision to Replace: Example Old machine: can last one more year with maintenance cost of $1,000; salvage value after taxes is now $4,000 and $2,500 in one-year Replace machine immediately because has lower (absolute) EAC than keeping the old machine one more year Finance - Pedro Barroso

Investments of Unequal Lives If projects differ in revenues as well as costs We can use the same methods applied to NPV: NPV of replacement chain Equivalent annual NPV Finance - Pedro Barroso