other topics in capital budgeting

8/14/2019 Other Topics in Capital Budgeting

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CHAPTER 12Other Topics in CapitalBudgeting

Evaluating projects with unequal

lives Identifying embedded options

Valuing real options in projects


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Evaluating projects with

unequal livesProjects S and L are mutually exclusive, andwill be repeated. If k = 10%, which is better?

Expected Net CFs

Year Project S Project L

0 ($100,000) ($100,000)

1 59,000 33,500

2 59,000 33,500

3 - 33,500

4 - 33,500


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of

real options? Investment timing options

Abandonment/shutdownoptions

Growth/expansion options

Flexibility options


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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 outputprices and the cash flows from Project L.

If we wait, the up-front cost will remain at$100,000 and there is a 50% chance thesubsequent CFs will be $43,500 a year, and a

50% chance the subsequent CFs will be $23,500a year.


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Investment timing decision

tree

At k = 10%, the NPV at t = 1 is: $37,889, if CFs are $43,500 per year, or

-$25,508, if CFs are $23,500 per year, inwhich case the firm would not proceed withthe project.

50% prob.

50% prob.0 1 2 3 4 5

Years

-$100,000 43,500 43,500 43,500 43,500

-$100,000 23,500 23,500 23,500 23,500


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Should we wait or

proceed? If we proceed today, NPV = $6,190.

If we wait one year, Expected NPV

at t = 1 is 0.5($37,889) + 0.5(0) =$18,944.57, which is worth$18,944.57 / (1.10) = $17,222.34 intodays dollars (assuming a 10%

discount rate).Therefore, it makes sense to wait.


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Issues to consider with

investment timing options Whats 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 $53,500 a year,and a 50% chance the subsequent CFs

will be $13,500 a year, expected NPVnext year (if we delay) would be:

0.5($69,588) + 0.5(0) = $34,794 >$18,944.57


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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 todayif there are important advantages tobeing the first competitor to enter amarket.

Waiting may allow you to takeadvantage of changing conditions.


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Abandonment/shutdown

option Project Y has an initial, up-front cost

of $200,000, at t = 0. The project isexpected to produce after-tax netcash flows of $80,000 for the nextthree years.

At a 10% discount rate, what is

Project Ys NPV?0 1 2 3

-$200,000 80,000 80,000 80,000

k = 10%

NPV = -$1,051.84


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Abandonment option Project Ys A-T net cash flows

depend critically upon customer

acceptance of the product.There is a 60% probability that

the product will be wildlysuccessful and produce A-T netCFs of $150,000, and a 40%chance it will produce annual A-Tnet CFs of -$25,000.


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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)

= -1,051.84

-$200,000

60% prob.

40% prob.

1 2 3Years

0

150,000 150,000 150,000

-25,000 -25,000 -25,000


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Issues with abandonment

optionsThe company does not have the

option to delay the project.

The company may abandon theproject after a year, if the customerhas not adopted the product.

If the project is abandoned, there will

be no operating costs incurred norcash inflows received after the firstyear.


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Is it reasonable to assume thatthe abandonment option does not

affect the cost of capital? No, it is not reasonable to

assume that the abandonment

option has no effect on thecost of capital.

The abandonment option

reduces risk, and thereforereduces the cost of capital.


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Growth option

Project Z has an initial up-front cost of$500,000.

The project is expected to produce A-T cash

inflows of $100,000 at the end of each of thenext 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 tosubsequent opportunities that have an NPV of$3,000,000 at t = 5, and a 90% chance of anNPV of -$1,000,000 at t = 5.


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NPV with the growthoption

100,000 100,000 100,000 100,000 100,000

-$500,000

10% prob.

90% prob.

1 2 3 4 5Years

0

100,000 100,000 100,000 100,000 100,000-$1,000,000

$3,000,000

At k = 12%, NPV of top branch (10% prob) =

$1,562,758.19

NPV of lower branch (90% prob) = -

$139,522.38


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NPV with the growthoption

If it turns out that the project has futureopportunities with a negative NPV, thecompany would choose not to pursue them.

Therefore, the NPV of the bottom branchshould include only the -$500,000 initialoutlay and the $100,000 annual cash flows,which lead to an NPV of -$139,522.38.

Thus, the expected value of this projectshould be:

NPV = 0.1($1,562,758) + 0.9(-$139,522)

= $30,706.


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Flexibility options

Flexibility options exist when itsworth spending money today,

which enables you to maintainflexibility down the road.

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