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CHAPTER 13Real Options and Other Topics in Capital Budgeting

Identifying embedded options Valuing real options in projects Evaluating projects with unequal

lives

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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.

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What are some examples of real options?

Investment timing options Abandonment/shutdown

options Growth/expansion options Flexibility options

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Investment timing option Project X has an up-front cost of

$100,000. The project is expected to produce after-tax cash flows of $33,500 at the end of each of the next four years (t=1, 2, 3, and 4). The project has a WACC=10%.

The project’s NPV is $6,190. Therefore, it appears that the company should go ahead with the project.

However, if the company waits a year they will find out more about the project’s expected cash flows.

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Investment timing option If they wait a year:

There is a 50% chance the market will be strong and the expected cash flows will be $43,500 a year for four years.

There is a 50% chance the market will be weak and the expected cash flows will be $23,500 a year for four years.

The project’s initial cost will remain $100,000, but it will be incurred at t=1 only if it makes sense at that time to proceed with the project.

Should the company go ahead with the project today or wait for more information?

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Investment timing decision tree

At WACC = 10%, the NPV at t = 1 is: $37,889, if CF’s are $43,500 per year, or -$25,508, if CF’s are $23,500 per year, in

which case the firm would not proceed with the project.

50% prob.

50% prob.0 1 2 3 4 5

Years

-$100,000 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 in today’s dollars (assuming a 10% WACC).

Therefore, it makes sense to wait.

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Issues to consider with investment timing options

What is 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 NPV next year (if we delay) would be:

0.5($69,588) + 0.5(0) = $34,794 > $18,945

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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 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.

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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 $80,000 for the next three years.

At a 10% WACC, what is Project Y’s NPV?0 1 2 3

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

10%

NPV = -$1,051.84

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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.

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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

-$200,00060% 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 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.

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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) = $14,725.77

-$200,00060% prob.

40% prob.

1 2 3Years

0

150,000 150,000 150,000

-25,000

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Should an abandonment option affect a project’s WACC? Yes, an abandonment option

should have an effect on the WACC.

The abandonment option reduces risk, and therefore reduces the WACC.

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Growth option

Project Z has an initial cost of $500,000. The project is expected to produce A-T

cash inflows of $100,000 at the end of each of the next five years, and has a WACC of 12%. It clearly has a negative NPV.

There is a 10% chance the project will lead to subsequent opportunities that have an NPV of $3,000,000 at t = 5, and a 90% chance of an NPV of -$1,000,000 at t = 5.

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NPV with the growth option

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

-$500,000

10% prob.

90% prob.1 2 3 4 5

Years0

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

$3,000,000

At WACC = 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 growth option

If the project’s future opportunities have a negative NPV, the company would choose not to pursue them.

The bottom branch only has the -$500,000 initial outlay and the $100,000 annual cash flows, which lead to an NPV of -$139,522.

The expected value of this project should be:NPV= 0.1($1,562,758) + 0.9(-

$139,522)= $30,706.

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Flexibility options

Flexibility options exist when it’s worth spending money today, which enables you to maintain flexibility down the road.

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Evaluating projects with unequal lives

Projects S and L are mutually exclusive, and will be repeated. If WACC = 10%, which is better?

Expected Net CFsYear 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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Solving for NPV, with no repetition

Enter CFs into calculator CFLO register for both projects, and enter I/YR = 10%. NPVS = $2,397 NPVL = $6,190

Is Project L better? Need replacement chain and/or

equivalent annual annuity analysis.

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-100,000 59,000 59,000 59,000 59,000 -100,000

-41,000

Replacement chain Use the replacement chain to calculate an

extended NPVS to a common life. Since Project S has a 2-year life and L has a

4-year life, the common life is 4 years.

0 1 2 310%

4

NPVS = $4,377 (on extended basis)

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Equivalent Annual Annuity Using the previously solved for project

NPVs, the EAA is the annual payment that the project would provide if it were an annuity.

Project S Enter N = 2, I/YR = 10, PV = -2397, FV = 0;

solve for PMT = EAA = $1,381. Project L

Enter N = 4, I/YR = 10, PV = -6190, FV = 0; solve for PMT = EAA = $1,953.

Project L is better!