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

19Finance - 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

20Finance - Pedro Barroso

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)

24Finance - 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

25Finance - Pedro Barroso

Inflation and Capital Budgeting: Example

26Finance - Pedro Barroso

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:

31Finance - Pedro Barroso

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%)

35Finance - Pedro Barroso

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