Evaluating Projects with Unequal Lives, Real Options, and Abandonment in Capital Budgeting, Slides of Management Fundamentals

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12-112-

CHAPTER

Other

Topics

in

Capital

Budgeting



Evaluating

projects

with

unequal

lives



Identifying

embedded

options



Valuing

real

options

in

projects

12-

Evaluating

projects

with

unequal

lives

Projects

S

and

L

are mutually exclusive, and will be repeated. If k

=

10%,

which is better? Expected Net CFs Year Project

S

Project

L

0

($100,000)

($100,000)

59,

33,

59,

33,

‐

33,

‐

33,

12-

Solving

for

NPV,

with

no

repetition

•

Enter CFs into calculator

CFLO

register for both projects, and enter

I/YR

=

10%.

–

NPV

S

=

$2,

–

NPV

L

=

$6,

•

Is Project

L

better?

Need replacement chain analysis.

12- -100, 59, 59, 59, 59, -100, -41,

Replacement

chain

•

Use the replacement chain to calculate an extended NPV S to a common life.

Since Project

S

has a

‐

year life and

L

has a 4

‐

year life, the common life is

years. 0 1 2 3 10% 4 NPV S = $4,377 (on extended basis)

12-

What

is

real

option

analysis?

•

Real

options

exist

when

managers

can

influence

the

size

and

riskiness

of

a

project’s

cash

flows

by

taking

different

actions

during

the

project’s

life.

•

Real

option

analysis

incorporates

typical

NPV

budgeting

analysis

with

an

analysis

for

opportunities

resulting

from

managers’

decisions.

12-

What

are

some

examples

of

real

options?

•

Investment

timing

options

•

Abandonment/shutdown

options

•

Growth/expansion

options

•

Flexibility

options

12-

Illustrating

an

investment

timing

option

•

If we proceed with Project

L,

its annual cash flows are

$33,500,

and its

NPV

is

$6,190.

•

However, if we wait one year, we will find out some additional information regarding output prices and the cash flows from Project

L.

•

If we wait, the up

‐

front cost will remain at $100, and there is a

50%

chance the subsequent CFs will be

$43,

a year, and a 50% chance the subsequent CFs will be

$23,

a year.

12-

Investment

timing

decision

tree

•

At

k

=

10%,

the

NPV

at

t

=

is:

–

$37,889,

if CF’s are

$43,

per year, or

‐

$25,508,

if CF’s are

$23,

per year, in which case the firm would not proceed with the project. 50% prob.50% prob. 0 1 2 3 4 5 Years -$100, 43, 43, 43, 43, -$100, 23, 23, 23, 23,

12-

Should

we

wait

or

proceed?

•

If

we

proceed

today,

NPV

=

$6,190.

•

If

we

wait

one

year,

Expected

NPV

at

t

=

is

0.5($37,889)

+

0.5(0)

=

$18,944.57,

which

is

worth

$18,944.

/

(1.10)

=

$17,222.

in

today’s

dollars

(assuming

a

10%

discount

rate).

•

Therefore,

it

makes

sense

to

wait.

12-

Issues

to

consider

with

investment

timing

options

•

What’s the appropriate discount rate?

Note that increased volatility makes the option to delay more attractive. - If instead, there was a

50%

chance the subsequent CFs will be

$53,

a year, and a

50%

chance the subsequent CFs will be

$13,

a year, expected NPV next year (if we delay) would be: 0.5($69,588)

+

0.5(0)

=

$34,

>

$18,944.

12-

Factors

to

consider

when

deciding

when

to

invest

•

Delaying

the

project

means

that

cash

flows

come

later

rather

than

sooner.

•

It

might

make

sense

to

proceed

today

if

there

are

important

advantages

to

being

the

first

competitor

to

enter

a

market.

•

Waiting

may

allow

you

to

take

advantage

of

changing

conditions.

12-

Abandonment/shutdown

option

Project Y has an initial, up ‐ front cost of $200,000, at t = 0. The project is expected to produce after ‐ tax net cash flows of $80, for the next three years. - At a 10% discount rate, what is Project Y’s NPV? 0 1 2 3 -$200, 80, 80, 80, k = 10% NPV = -$1,051.

12-

Abandonment

option

•

Project

Y’s

A

‐

T

net

cash

flows

depend

critically

upon

customer

acceptance

of

the

product.

•

There

is

a

60%

probability

that

the

product

will

be

wildly

successful

and

produce

A

‐

T

net

CFs

of

$150,000,

and

a

40%

chance

it

will

produce

annual

A

‐

T

net

CFs

of

‐

$25,000.

12-

Abandonment

decision

tree

If the customer uses the product, NPV is $173,027.80. - If the customer does not use the product, NPV is ‐ $262,171.30. - E(NPV) = 0.6(173,027.8) + 0.4( ‐ 262,171.3) = ‐ 1,051. -$200, 60% prob.40% prob. 1 2 3 Years 0 150, 150, 150, -25, -25, -25,

12-

Issues

with

abandonment

options

•

The

company

does

not

have

the

option

to

delay

the

project.

•

The

company

may

abandon

the

project

after

a

year,

if

the

customer

has

not

adopted

the

product.

•

If

the

project

is

abandoned,

there

will

be

no

operating

costs

incurred

nor

cash

inflows

received

after

the

first

year.

12-

NPV

with

abandonment

option

If the customer uses the product, NPV is $173,027.80. - If the customer does not use the product, NPV is ‐ $222,727.27. - E(NPV) = 0.6(173,027.8) + 0.4( ‐ 222,727.27) = 14,725. -$200, 60% prob.40% prob. 1 2 3 Years 0 150, 150, 150, -25,

12- Is it reasonable to assume that the abandonment option does not affect the cost of capital?

•

No,

it

is

not

reasonable

to

assume

that

the

abandonment

option

has

no

effect

on

the

cost

of

capital.

•

The

abandonment

option

reduces

risk,

and

therefore

reduces

the

cost

of

capital.

12-

Growth

option

•

Project

Z

has an initial up

‐

front cost of

$500,000.

•

The project is expected to produce

A

‐

T

cash inflows of

$100,

at the end of each of the next five years. Since the project carries a

12%

cost of capital, it clearly has a negative

NPV.

•

There is a

10%

chance the project will lead to subsequent opportunities that have an

NPV

of $3,000, at t

=

5,

and a

90%

chance of an

NPV

of

‐

$1,000,

at t

=

Docsity.com

12-

NPV

with

the

growth

option

•

At

k

=

12%,

NPV of top branch (10% prob) = $1,562,758. - NPV of lower branch (90% prob) = ‐ $139,522. 100, 100, 100, 100, 100, -$500, 10% prob.90% prob. 1 2 3 4 5 Years 0 100, 100, 100, 100, 100, -$1,000, $3,000,

12-

NPV

with

the

growth

option

•

If it turns out that the project has future opportunities with a negative

NPV,

the company would choose not to pursue them.

Therefore, the

NPV

of the bottom branch should include only the

‐

$500,

initial outlay and the

$100,

annual cash flows, which lead to an

NPV

of

‐

$139,522.38.

•

Thus, the expected value of this project should be: NPV

=

0.1($1,562,758)

+

0.9(

‐

$139,522)

=

$30,706.

12-21

Flexibility

options

•

Flexibility

options

exist

when

it’s

worth

spending

money

today,

which

enables

you

to

maintain

flexibility

down

the

road.