capital budgeting investment rules 1finance - pedro barroso
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Capital BudgetingInvestment Rules
1Finance - Pedro Barroso
Net Present Value (NPV) Rule
• Net Present Value (NPV) = 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; risk3. Estimate initial costs
• Minimum Acceptance Criteria: Accept if NPV > 0• Ranking Criteria: Choose the highest NPV
2Finance - Pedro Barroso
Why Use Net Present Value?
• Accepting positive NPV projects benefits shareholdersNPV uses cash flowsNPV discounts the cash flows properlyMaximizes shareholder value (stock price)
• Reinvestment assumption: NPV rule assumes that all cash flows can be reinvested at the discount rate
3Finance - Pedro Barroso
Example: Project
924,58)1.1(
421,219)1.1(
634,69)1.1(
893,82)1.1(
990,49)1.1(
680,34000,260 5432
NPV
NPV
Microsoft Office Excel 97-2003 Worksheet
• Using previous example and discount rate of 10%:
• NPV > 0: go-on with project
4Finance - 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: – Set by management
5Finance - 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
6Finance - 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
7Finance - 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
8Finance - 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
9Finance - Pedro Barroso
IRR: ExampleConsider the project:
0 1 2 3
50 100 150-200
%44.19
0)1(
150)1(
100)1(
50200 32
IRRIRRIRRIRR
Microsoft Office Excel 97-2003 Worksheet
10Finance - Pedro Barroso
NPV Payoff ProfileIf we graph NPV versus the discount rate, we can see the IRR as the x-axis intercept
Microsoft Office Excel 97-2003 Worksheet
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
11Finance - Pedro Barroso
Problems with IRR• Investing or financing?
• Multiple IRRs
• Problems with mutually exclusive investments (alternative)– Scale Problem
– Timing Problem
12Finance - Pedro Barroso
IRR: Investing or Financing?Project (financing) (100,-130)
Project (investing) (-100, 130) also has IRR = 30%
%3001
130100
IRR
IRRMicrosoft Office
Excel 97-2003 Worksheet
Do financing project if IRR < discount rate!13Finance - Pedro Barroso
Multiple IRRsConsider the project: (-100, 230, -132)
14Finance - Pedro Barroso
Microsoft Office Excel 97-2003 Worksheet
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
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
15Finance - 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%16Finance - 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%17Finance - Pedro Barroso
IRR: Timing Problem
18Finance - Pedro Barroso
Microsoft Office Excel 97-2003 WorksheetCross-over rate = 11.5%
• Slow project is better at lower discount rates < 11.5%
• Fast project is better at higher discount rates > 11.5%
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
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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
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PI: ExampleConsider the project (discount rate = 10%):
0 1 2 3
50 100 150-200
204.1200
8.240
8.240)1.1(
150)1.1(
100)1.1(
5032
PI
21Finance - Pedro Barroso
Problem with PI
• Problem:– Problem with mutually exclusive investments
(scale problem)
• Advantages:– May be useful when available investment funds
are limited
22Finance - 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
23Finance - 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)
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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
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Inflation and Capital Budgeting: Example
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Microsoft Office Excel 97-2003 Worksheet
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) 605 605
Depreciation (real) 550 500 Tax rate 40%
Operational cash flow 790 800
Total cash flow -1,210 790 800
NPV 268
Nominal cash flows
Year 0 Year 1 Year 2
Investment -1,210
EBITDA 1,045 1,210
Depreciation 605 605
Operational cash flow 869 968
Total cash flow -1,210 869 968
NPV 268
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?
27Finance - 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)
28Finance - Pedro Barroso
5.614,4100000,4 10%10cos APV ts
4.895,2500000,1 5%10cos APV ts
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
29Finance - Pedro Barroso
Replacement Chain ApproachMachine 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
-1,000 –500 -500 -500 -500 -1,500 -500 -500 -500 -500 -500
0 1 2 3 4 5 6 7 8 9 10
Machine B cash flows over ten years:
30Finance - Pedro Barroso
Replacement Chain Approach• Machine A:
• Machine B:
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5.614,4100000,4 10%10cos APV ts
2.693,41.1
4.895,24.895,2
1.1500000,1
500000,1
5
5
5%105
%10cos
AAPV ts
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
32Finance - Pedro Barroso
EAC: Example
• Machine A:
• Machine B:
• Pick machine A because has lower EAC
33Finance - Pedro Barroso
0.7515.614,4 10%10 EACAEAC
8.7635.895,2 5%10 EACAEAC
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
34Finance - 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%)
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860,2833,12
833,1215.1000,2
000,1000,9
8%15
88
%15cos
EACAEAC
APV ts
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
36Finance - Pedro Barroso
100,315.1696,2696,2
696,215.1
500,215.1
000,1000,4
1%15
cos
EACAEAC
PV ts
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
37Finance - Pedro Barroso
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