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C1 Outline

Capital Budgeting - Decision Criteria

- Net Present Value
- The Payback Rule
- The Discounted Payback
- The Average Accounting Return
- The Internal Rate of Return
- The Profitability Index
- The Practice of Capital Budgeting

C2 Outline (continued)

- Project Cash Flows: A First Look
- Incremental Cash Flows
- Pro Forma Financial Statements and Project Cash Flows
- More on Project Cash Flows
- Alternative Definitions of Operating Cash Flow
- Some Special Cases of Discounted Cash Flow Analysis
- Summary and Conclusions

C3 NPV Illustrated

- Assume you have the following information on Project X:
Initial outlay -$1,100 Required return = 10%

Annual cash revenues and expenses are as follows:

Year Revenues Expenses

1 $1,000 $500

2 2,000 1,000

- Draw a time line and compute the NPV of project X.

C4 NPV Illustrated (concluded)

0

1

2

Initial outlay

($1,100)

Revenues $2,000

Expenses 1,000

Cash flow $1,000

Revenues $1,000

Expenses 500

Cash flow $500

– $1,100.00

+454.55

+826.45

+$181.00

1

$500 x

1.10

1

$1,000 x

1.102

NPV

C5 Underpinnings of the NPV Rule

- Why does the NPV rule work? And what does “work” mean? Look at it this way:
A “firm” is created when securityholders supply the funds to acquire assets that will be used to produce and sell a good or a service;

The market value of the firm is based on the present value of the cash flows it is expected to generate;

Additional investments are “good” if the present value of the incremental expected cash flows exceeds their cost;

Thus, “good” projects are those which increase firm value - or, put another way, good projects are those projects that have positive NPVs!

Moral of the story: Invest only in projects with positive NPVs.

C6 Payback Rule Illustrated

Initial outlay -$1,000

Year Cash flow

1 $200

2 400

3 600

Accumulated

Year Cash flow

1 $200

2 600

3 1,200

Payback period = 2 2/3 years

C7 Discounted Payback Illustrated

Initial outlay -$1,000

R = 10%

PV of

Year Cash flow Cash flow

1 $ 200 $ 182

2 400 331

3 700 526

4 300 205

Accumulated

Year discounted cash flow

1 $ 182

2 513

3 1,039

4 1,244

Discounted payback period is just under 3 years

C8 Ordinary and Discounted Payback

Cash Flow Accumulated Cash Flow

Year Undiscounted Discounted Undiscounted Discounted

1 $100 $89 $100 $89

2 100 79 200 168

3 100 70 300 238

4 100 62 400 300

5 100 55 500 355

C9 Average Accounting Return Illustrated

- Average net income:
Year

1 2 3

Sales $440 $240 $160

Costs 220 120 80

Gross profit 220 120 80

Depreciation 80 80 80

Earnings before taxes 140 40 0

Taxes (25%) 35 10 0

Net income $105 $30 $0

Average net income = ($105 + 30 + 0)/3 = $45

C10 Average Accounting Return Illustrated (concluded)

- Average book value:
Initial investment = $240

Average investment = ($240 + 0)/2 = $120

- Average accounting return (AAR):
Average net income $45

AAR = = = 37.5%

Average book value $120

C11 Internal Rate of Return Illustrated

Initial outlay = -$200

Year Cash flow

1 $ 50

2 100

3 150

- Find the IRR such that NPV = 0
50 100 150

0 = -200 + + +

(1+IRR)1 (1+IRR)2 (1+IRR)3

50 100 150

200 = + +

(1+IRR)1 (1+IRR)2 (1+IRR)3

C12 Internal Rate of Return Illustrated (concluded)

- Trial and Error
Discount rates NPV

0% $100

5% 68

10% 41

15% 18

20% -2

IRR is just under 20% -- about 19.44%

C13 Net Present Value Profile

Net present value

120

Year Cash flow

0 – $275

1 100

2 100

3 100

4 100

100

80

60

40

20

0

– 20

Discount rate

– 40

2%

6%

10%

14%

18%

22%

IRR

C14 Multiple Rates of Return

- Assume you are considering a project for which the cash flows are as follows:
Year Cash flows

0 -$252

1 1,431

2 -3,035

3 2,850

4 -1,000

C15 Multiple Rates of Return (continued)

- What’s the IRR? Find the rate at which the computed NPV = 0:
at 25.00%: NPV = _______

at 33.33%: NPV = _______

at 42.86%: NPV = _______

at 66.67%: NPV = _______

C16 Multiple Rates of Return (continued)

- What’s the IRR? Find the rate at which the computed NPV = 0:
at 25.00%: NPV = 0

at 33.33%: NPV = 0

at 42.86%: NPV = 0

at 66.67%: NPV = 0

- Two questions:
- 1. What’s going on here?
- 2. How many IRRs can there be?

C17 Multiple Rates of Return (concluded)

NPV

$0.06

$0.04

IRR = 1/4

$0.02

$0.00

($0.02)

IRR = 2/3

IRR = 1/3

IRR = 3/7

($0.04)

($0.06)

($0.08)

0.2

0.28

0.36

0.44

0.52

0.6

0.68

Discount rate

C18 IRR, NPV, and Mutually Exclusive Projects

Net present value

Year

0 1 2 3 4

Project A: – $350 50 100 150 200

Project B: – $250 125 100 75 50

160

140

120

100

80

60

40

Crossover Point

20

0

– 20

– 40

– 60

– 80

Discount rate

– 100

0

2%

14%

18%

22%

10%

6%

26%

IRRA IRRB

C19 Profitability Index Illustrated

- Now let’s go back to the initial example - we assumed the following information on Project X:
Initial outlay -$1,100 Required return = 10%

Annual cash benefits:

Year Cash flows

1 $ 500

2 1,000

- What’s the Profitability Index (PI)?

C20 Profitability Index Illustrated (concluded)

- Previously we found that the NPV of Project X is equal to:
($454.55 + 826.45) - 1,100 = $1,281.00 - 1,100 = $181.00.

- The PI = PV inflows/PV outlay = $1,281.00/1,100 = 1.1645.
- This is a good project according to the PI rule. Can you explain why?
It’s a good project because the present value of the inflows exceeds the outlay.

C21 Summary of Investment Criteria

- I. Discounted cash flow criteria
A. Net present value (NPV). The NPV of an investment is the difference between its market value and its cost. The NPV rule is to take a project if its NPV is positive. NPV has no serious flaws; it is the preferred decision criterion.

B.Internal rate of return (IRR).The IRR is the discount rate that makes the estimated NPV of an investment equal to zero. The IRR rule is to take a project when its IRR exceeds the required return. When project cash flows are not conventional, there may be no IRR or there may be more than one.

C. Profitability index (PI). The PI, also called the benefit-cost ratio, is the ratio of present value to cost. The profitability index rule is to take an investment if the index exceeds 1.0. The PI measures the present value per dollar invested.

C22 Summary of Investment Criteria (concluded)

- II. Payback criteria
A. Payback period. The payback period is the length of time until the sum of an investment’s cash flows equals its cost. The payback period rule is to take a project if its payback period is less than some prespecified cutoff.

B. Discounted payback period. The discounted payback period is the length of time until the sum of an investment’s discounted cash flows equals its cost. The discounted payback period rule is to take an investment if the discounted payback is less than some prespecified cutoff.

- III. Accounting criterion
A. Average accounting return (AAR). The AAR is a measure of accounting profit relative to book value. The AAR rule is to take an investment if its AAR exceeds a benchmark.

C23 A Quick Quiz

1. Which of the capital budgeting techniques do account for both the time value of money and risk?

2. The change in firm value associated with investment in a project is measured by the project’s _____________ .

a. Payback period

b. Discounted payback period

c. Net present value

d. Internal rate of return

3. Why might one use several evaluation techniques to assess a given project?

C24 A Quick Quiz

1. Which of the capital budgeting techniques do account for both the time value of money and risk?

Discounted payback period, NPV, IRR, and PI

2. The change in firm value associated with investment in a project is measured by the project’s Net present value.

3. Why might one use several evaluation techniques to assess a given project?

To measure different aspects of the project; e.g., the payback period measures liquidity, the NPV measures the change in firm value, and the IRR measures the rate of return on the initial outlay.

C25 Problem

- Offshore Drilling Products, Inc. imposes a payback cutoff of 3 years for its international investment projects. If the company has the following two projects available, should they accept either of them?
Year Cash Flows A Cash Flows B

0 -$30,000 -$45,000

1 15,000 5,000

2 10,000 10,000

3 10,000 20,000

4 5,000 250,000

C26 Solution to Problem (concluded)

- Project A:
Payback period = 1 + 1 + ($30,000 - 25,000)/10,000

= 2.50 years

- Project B:
Payback period = 1 + 1 + 1 + ($45,000 - 35,000)/$250,000

= 3.04 years

- Project A’s payback period is 2.50 years and project B’s payback period is 3.04 years. Since the maximum acceptable payback period is 3 years, the firm should accept project A and reject project B.

C27 Another Problem

- A firm evaluates all of its projects by applying the IRR rule. If the required return is 18 percent, should the firm accept the following project?
Year Cash Flow

0 -$30,000

1 25,000

2 0

3 15,000

C28 Another Problem (continued)

- To find the IRR, set the NPV equal to 0 and solve for the discount rate:
NPV = 0 = -$30,000 + $25,000/(1 + IRR)1 + $0/(1 + IRR)2 +$15,000/(1 + IRR)3

- At 18 percent, the computed NPV is ____.
- So the IRR must be (greater/less) than 18 percent. How did you know?

C29 Another Problem (concluded)

- To find the IRR, set the NPV equal to 0 and solve for the discount rate:
NPV = 0 = -$30,000 + $25,000/(1 + IRR)1 + $0/(1 + IRR)2 +$15,000/(1 + IRR)3

- At 18 percent, the computed NPV is $316.
- So the IRR must be greater than 18 percent. We know this because the computed NPV is positive.
- By trial-and-error, we find that the IRR is 18.78 percent.

T30 Fundamental Principles of Project Evaluation

- Fundamental Principles of Project Evaluation:
Project evaluation - the application of one or more capital budgeting decision rules to estimated relevant project cash flows in order to make the investment decision.

Relevant cash flows - the incremental cash flows associated with the decision to invest in a project.

The incremental cash flows for project evaluation consist of any and all changes in the firm’s future cash flows that are a direct consequence of taking the project.

Stand-alone principle - evaluation of a project based on the project’s incremental cash flows.

T31 Incremental Cash Flows

Incremental Cash Flows

- Key issues:
- When is a cash flow incremental?
- Terminology
A. Sunk costs

B. Opportunity costs

C. Side effects

D. Net working capital

E. Financing costs

F. Other issues

T32 Example: Preparing Pro Forma Statements

- Suppose we want to prepare a set of pro forma financial statements for a project for Norma Desmond Enterprises. In order to do so, we must have some background information. In this case, assume:
1. Sales of 10,000 units/year @ $5/unit.

2. Variable cost per unit is $3. Fixed costs are $5,000 per year. The project has no salvage value. Project life is 3 years.

3. Project cost is $21,000. Depreciation is $7,000/year.

4. Additional net working capital is $10,000.

5. The firm’s required return is 20%. The tax rate is 34%.

T33 Example: Preparing Pro Forma Statements (continued)

Pro Forma Financial Statements

Projected Income Statements

Sales $______

Var. costs ______

$20,000

Fixed costs 5,000

Depreciation 7,000

EBIT $______

Taxes (34%) 2,720

Net income $______

T34 Example: Preparing Pro Forma Statements (continued)

Pro Forma Financial Statements

Projected Income Statements

Sales $50,000

Var. costs 30,000

$20,000

Fixed costs 5,000

Depreciation 7,000

EBIT $ 8,000

Taxes (34%) 2,720

Net income $ 5,280

T35 Example: Preparing Pro Forma Statements (concluded)

Projected Balance Sheets

0 1 2 3

NWC $______ $10,000 $10,000 $10,000

NFA 21,000 ______ ______ 0

Total $31,000 $24,000 $17,000 $10,000

T36 Example: Preparing Pro Forma Statements (concluded)

Projected Balance Sheets

0 1 2 3

NWC $10,000 $10,000 $10,000 $10,000

NFA 21,000 14,0007,000 0

Total $31,000 $24,000 $17,000 $10,000

T37 Example: Using Pro Formas for Project Evaluation

- Now let’s use the information from the previous example to do a capital budgeting analysis.
Project operating cash flow (OCF):

EBIT $8,000

Depreciation +7,000

Taxes -2,720

OCF $12,280

T38 Example: Using Pro Formas for Project Evaluation (continued)

- Project Cash Flows
0 1 2 3

OCF $12,280 $12,280 $12,280

Chg. NWC ______ ______

Cap. Sp. -21,000

Total ______ $12,280 $12,280 $______

T39 Example: Using Pro Formas for Project Evaluation (continued)

- Project Cash Flows
0 1 2 3

OCF $12,280 $12,280 $12,280

Chg. NWC -10,000 10,000

Cap. Sp. -21,000

Total -31,000 $12,280 $12,280 $22,280

T40 Example: Using Pro Formas for Project Evaluation (concluded)

- Capital Budgeting Evaluation:
NPV = -$31,000 + $12,280/1.201 + $12,280/1.202 + $22,280/1.203= $655

IRR = 21%

PBP = 2.3 years

AAR = $5280/{(31,000 + 24,000 + 17,000 + 10,000)/4} = 25.76%

- Should the firm invest in this project? Why or why not?
Yes -- the NPV > 0, and the IRR > required return

T41 Example: Estimating Changes in Net Working Capital (concluded)

- In estimating cash flows we must account for the fact that some of the incremental sales associated with a project will be on credit, and that some costs won’t be paid at the time of investment. How?
Answer: Estimate changes in NWC. Assume:

1. Fixed asset spending is zero.

2. The change in net working capital spending is $200:

0 1 Change S/U

A/R $100 $200 +100 ___

INV 100 150 +50 ___

-A/P 100 50 (50) ___

NWC $100 $300 Chg. NWC = $_____

T42 Example: Estimating Changes in Net Working Capital (concluded)

- In estimating cash flows we must account for the fact that some of the incremental sales associated with a project will be on credit, and that some costs won’t be paid at the time of investment. How?
Answer: Estimate changes in NWC. Assume:

1. Fixed asset spending is zero.

2. The change in net working capital spending is $200:

0 1 Change S/U

A/R $100 $200 +100 U

INV 100 150 +50 U

-A/P 100 50 (50)U

NWC $100 $300 Chg. NWC = $200

T43 Example: Estimating Changes in Net Working Capital (continued)

- Now, estimate operating and total cash flow:
Sales $300

Costs 200

Depreciation 0

EBIT $100

Tax 0

Net Income $100

OCF = EBIT + Dep. Taxes = $100

Total Cash flow = OCF Change in NWC Capital Spending

= $100 ______ ______ = ______

T44 Example: Estimating Changes in Net Working Capital (continued)

- Now, estimate operating and total cash flow:
Sales $300

Costs 200

Depreciation 0

EBIT $100

Tax 0

Net Income $100

OCF = EBIT + Dep. Taxes = $100

Total Cash flow = OCF Change in NWC Capital Spending

= $100 2000 = $100

T45 Example: Estimating Changes in Net Working Capital (concluded)

- Where did the - $100 in total cash flow come from?
- What really happened:
Cash sales = $300 - ____ = $200 (collections)

Cash costs = $200 + ____ + ____ = $300 (disbursements)

T46 Example: Estimating Changes in Net Working Capital (concluded)

- Where did the - $100 in total cash flow come from?
- What really happened:
Cash sales = $300 -100 = $200 (collections)

Cash costs = $200 + 50 + 50 = $300 (disbursements)

Cash flow = $200 - 300 = -$100 (= cash in cash out)

T47 Modified ACRS Property Classes (concluded)

Class Examples

3-year Equipment used in research

5-year Autos, computers

7-year Most industrial equipment

T48 Modified ACRS Depreciation Allowances (concluded)

Property Class

Year 3-Year 5-Year 7-Year

1 33.33% 20.00% 14.29%

2 44.44 32.00 24.49

3 14.82 19.20 17.49

4 7.41 11.52 12.49

5 11.52 8.93

6 5.76 8.93

7 8.93

8 4.45

T49 MACRS Depreciation: An Example (concluded)

- Calculate the depreciation deductions on an asset which costs $30,000 and is in the 5-year property class:
Year MACRS % Depreciation

1 20% $_____

2 32% _____

3 19.20% 5,760

4 11.52% 3,456

5 11.52% 3,456

6 5.76%1,728

100% $ _____

T50 MACRS Depreciation: An Example (concluded)

- Calculate the depreciation deductions on an asset which costs $30,000 and is in the 5-year property class:
Year MACRS % Depreciation

1 20% $6,000

2 32% 9,600

3 19.20% 5,760

4 11.52% 3,456

5 11.52% 3,456

6 5.76%1,728

100% $30,000

T51 Example: Fairways Equipment and Operating Costs (concluded)

- Two golfing buddies are considering opening a new driving range, the “Fairways Driving Range” (motto: “We always treat you fairly at Fairways”). Because of the growing popularity of golf, they estimate the range will generate rentals of 20,000 buckets of balls at $3 a bucket the first year, and that rentals will grow by 750 buckets a year thereafter. The price will remain $3 per bucket.
- Capital spending requirements include:
- Ball dispensing machine $ 2,000
- Ball pick-up vehicle 8,000
- Tractor and accessories 8,000
- $18,000
- All the equipment is 5-year ACRS property, and is expected to have a salvage value of 10% of cost after 6 years.
- Anticipated operating expenses are as follows:

T52 Example: Fairways Equipment and Operating Costs (concluded)

Working Capital

Initial requirement = $3,000

Working capital requirements are expected to grow at 5% per year for the life of the project

Operating Costs (annual)

Land lease $ 12,000

Water 1,500

Electricity 3,000

Labor 30,000

Seed & fertilizer 2,000

Gasoline 1,500

Maintenance 1,000

Insurance 1,000

Misc. Expenses 1,000

$53,000

T53 Example: Fairways Revenues, Depreciation, and Other Costs

Projected Revenues

Year Buckets Revenues

1 20,000 $60,000

2 20,750 62,250

3 21,500 64,500

4 22,250 66,750

5 23,000 69,000

6 23,750 71,250

T54 Example: Fairways Revenues, Depreciation, and Other Costs (continued)

Cost of balls and buckets

Year Cost

1 $3,000

2 3,150

3 3,308

4 3,473

5 3,647

6 3,829

T55 Example: Fairways Revenues, Depreciation, and Other Costs (concluded)

Depreciation on $18,000 of 5-year equipment

Year ACRS % Depreciation Book value

1 20.00 $3,600 $14,400

2 32.00 5,760 8,640

3 19.20 3,456 5,184

4 11.52 2,074 3,110

5 11.52 2,074 1,036

6 5.76 1,036 0

T56 Example: Fairways Pro Forma Income Statement Costs (concluded)

Year

1 2 3 4 5 6

Revenues $60,000 $62,250 $64,500 $66,750 $69,000 $71,250

Variable costs 3,000 3,150 3,308 3,473 3,647 3,829

Fixed costs 53,000 53,000 53,000 53,000 53,000 53,000

Depreciation 3,600 5,760 3,456 2,074 2,074 1,036

EBIT $ 400 $ 340 $ 4,736 $ 8,203 $10,279 $13,385

Taxes 60 51 710 1,230 1,542 2,008

Net income $ 340 $ 289 $ 4,026 $ 6,973 $ 8,737 $11,377

T57 Example: Fairways Projected Changes in NWC Costs (concluded)

- Projected increases in net working capital
Year Net working capital Change in NWC

0 $ 3,000 $ 3,000

1 3,150 150

2 3,308 158

3 3,473 165

4 3,647 174

5 3,829 182

6 4,020 -3,829

T58 Example: Fairways Cash Flows Costs (concluded)

- Operating cash flows:
Operating Year EBIT + Depreciation – Taxes = cash flow

0 $ 0 $ 0 $ 0 $ 0

1 400 3,600 60 3,940

2 340 5,760 51 6,049

3 4,736 3,456 710 7,482

4 8,203 2,074 1,230 9,047

5 10,279 2,074 1,542 10,811

6 13,385 1,036 2,008 12,413

T59 Example: Fairways Cash Flows (concluded) Costs (concluded)

- Total cash flow from assets:
Year OCF – Chg. in NWC – Cap. Sp. = Cash flow

0 $ 0 $ 3,000 $18,000 –$21,000

1 3,940 150 0 3,790

2 6,049 158 0 5,891

3 7,482 165 0 7,317

4 9,047 174 0 8,873

5 10,811 182 0 10,629

6 12,413 –3,829 –1,530 17,772

T60 Alternative Definitions of OCF Costs (concluded)

Let:

OCF = operating cash flow

S = sales

C = operating costs

D = depreciation

T = corporate tax rate

T61 Alternative Definitions of OCF (concluded) Costs (concluded)

- The Tax-Shield Approach
OCF = (S - C - D) + D - (S - C - D) T

= (S - C) (1 - T) + (D T)

= (S - C) (1 - T) + Depreciation x T

- The Bottom-Up Approach
OCF = (S - C - D) + D - (S - C - D) T

= (S - C - D) (1 - T) + D

= Net income + Depreciation

- The Top-Down Approach
OCF = (S - C - D) + D - (S - C - D) T

= (S - C) - (S - C - D) T

= Sales - Costs - Taxes

T62 Quick Quiz -- Part 1 of 3 Costs (concluded)

- Now let’s put our new-found knowledge to work. Assume we have the following background information for a project being considered by Gillis, Inc.
- See if we can calculate the project’s NPV and payback period. Assume:
Required NWC investment = $40; project cost = $60; 3 year life

Annual sales = $100; annual costs = $50; straight line depreciation to $0

Tax rate = 34%, required return = 12%

- Step 1: Calculate the project’s OCF
- OCF = (S - C)(1 - T) + Dep T
- OCF = (___ - __)(1 - .34) + (____)(.34) = $_____

T63 Quick Quiz -- Part 1 of 3 Costs (concluded)

- Now let’s put our new-found knowledge to work. Assume we have the following background information for a project being considered by Gillis, Inc.
- See if we can calculate the project’s NPV and payback period. Assume:
Required NWC investment = $40; project cost = $60; 3 year life

Annual sales = $100; annual costs = $50; straight line depreciation to $0

Tax rate = 34%, required return = 12%

- Step 1: Calculate the project’s OCF
- OCF = (S - C)(1 - T) + Dep T
- OCF = (100 - 50)(1 - .34) + (60/3)(.34) = $39.80

T64 Quick Quiz -- Part 1 of 3 (concluded) Costs (concluded)

- Project cash flows are thus:
0 1 2 3

OCF $39.8 $39.8 $39.8

Chg. in NWC -4040

Cap. Sp. -60

-$100 $39.8 $39.8 $79.8

Payback period= ___________

NPV = ____________

T65 Quick Quiz -- Part 1 of 3 (concluded) Costs (concluded)

- Project cash flows are thus:
0 1 2 3

OCF $39.8 $39.8 $39.8

Chg. in NWC – 4040

Cap. Sp. – 60

– 100 $39.8 $39.8 $79.8

Payback period= 1 + 1 + (100 – 79.6)/79.8 = 2.26 years

NPV = $39.8/(1.12) + $39.8/(1.12)2 + 79.8 /(1.12)3 - 100 = $24.06

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