1. Capital Budgeting Investment Rules
Finance - Pedro Barroso

2. 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

3. 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

4. Finance - Pedro Barroso
Example: Project
Using previous example and discount rate of 10%:
NPV > 0: go-on with project
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5. 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:
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6. 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
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7. 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

8. 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

9. 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

10. Finance - Pedro Barroso
IRR: Example
Consider the project: 1 2 3 50
100
150
-200
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11. 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

12. Finance - Pedro Barroso
Problems with IRR
Investing or financing?
Multiple IRRs
Problems with mutually exclusive investments (alternative)
Scale Problem
Timing Problem
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13. 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

14. 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

15. 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
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16. 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

17. 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

18. 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

19. 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

20. 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

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

22. 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

23. Finance - Pedro Barroso
PI: Limited Funds
Consider three independent projects (r = 12%):
A (-20, 70, 10) NPV = PI = 3.53
B (-10, 15, 40) NPV = PI = 4.53
C (-10, -5, 60) NPV = 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 = = 68.7 > 50.5
Finance - Pedro Barroso

24. 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

25. 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

26. 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

27. 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

28. 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)
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29. 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
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30. Replacement Chain Approach
Machine A time line of cash flows:
-4, –
Machine B cash flows over ten years:
-1,000 – ,
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31. Replacement Chain Approach
Machine A:
Machine B:
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32. 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
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33. Finance - Pedro Barroso
EAC: Example
Machine A:
Machine B:
Pick machine A because has lower EAC
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34. 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

35. 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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36. 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

37. 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