# Net Present Value

Oil and Offshore

Nov 8, 2013 (4 years and 6 months ago)

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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

\$1,000

Expenses

500

Cash flow

\$500

Revenues

\$2,000

Expenses

1,000

Cash flow

\$1,000

\$1,100.00

+454.55

+826.45

+\$
181.00

1

\$500
x

1.10

1

\$1,000
x

1.10

2

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
%

Year Cash flow

0

\$275

1

100

2

100

3

100

4

100

C13 Net Present Value Profile

Discount rate

2%

6%

10%

14%

18%

120

100

80

60

40

20

Net present value

0

20

40

22%

IRR

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

C14 Multiple Rates of Return

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)

\$0.06

\$0.04

\$0.02

\$0.00

(\$0.02)

NPV

(\$0.04)

(\$0.06)

(\$0.08)

0.2

0.28

0.36

0.44

0.52

0.6

0.68

IRR = 1/4

IRR = 1/3

IRR = 3/7

IRR = 2/3

Discount rate

C18 IRR, NPV, and Mutually Exclusive Projects

Discount rate

2%

6%

10%

14%

18%

60

40

20

0

20

40

Net present value

60

80

100

22%

IRR

A

IRR

B

0

140

120

100

80

160

Year

0

1 2

3

4

Project A:

\$350

50

100

150

200

Project B:

\$250

125

100

75

50

26%

Crossover Point

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

14,000

7,000

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 + \$12,280/1.20
1
+ \$12,280/1.20

2
+ \$22,280/1.20

3

=

\$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

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

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

200

0

=

\$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

Class

Examples

3
-
year

Equipment used in research

5
-
year

Autos, computers

7
-
year

Most industrial equipment

T48 Modified ACRS Depreciation Allowances

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

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

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

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)

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

Working Capital

Initial requirement = \$3,000

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

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

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

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

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)

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

Let:

OCF

=

operating cash flow

S

=

sales

C

=

operating costs

D

=

depreciation

T

=

corporate tax rate

T61 Alternative Definitions of OCF (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

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

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)

Project cash flows are thus:

0

1

2

3

OCF

\$39.8

\$39.8

\$39.8

Chg. in NWC

-
40

40

Cap. Sp.

-
60

-
\$100

\$39.8

\$39.8

\$79.8

Payback period

=
___________

NPV =
____________

T65 Quick Quiz
--

Part 1 of 3 (concluded)

Project cash flows are thus:

0

1

2

3

OCF

\$39.8

\$39.8

\$39.8

Chg. in NWC

40

40

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