chapter 13 other topics in capital budgeting

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CHAPTER 13Other Topics in Capital Budgeting

Evaluating projects with unequal lives

Evaluating projects with embedded options

Valuing real options in projects

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S and L are mutually exclusive and will be repeated. k = 10%. Which is better?

Expected Net CFs

Year Project S Project L0 ($100,000) ($100,000)1 59,000 33,5002 59,000 33,5003 -- 33,5004 -- 33,500

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S LCF0 -100,000 -100,000CF1 59,000 33,500Nj 2 4I 10 10NPV 2,397 6,190

Q. NPVL > NPVS. Is L better?

A. Can’t say. Need replacement chain analysis.

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Note that Project S could be repeated after 2 years to generate additional profits.

Use replacement chain to calculate extended NPVS to a common life.

Since S has a 2-year life and L has a 4-year life, the common life is 4 years.

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L:

S:

0 1 2 310%

33,500

4

0 1 2 310%

59,000

4

33,50033,50033,500-100,000

59,00059,00059,000-100,000

NPVL = $6,190 (already to Year 4)

NPVS = $4,377 (on extended basis)

-100,000-41,000

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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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An Illustration of Investment Timing Options

If we proceed with Project L, its NPV is $6,190. (Recall the up-front cost was $100,000 and the subsequent CFs were $33,500 a year for four years).

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

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Investment Timing (Continued)

If we wait, there is a 50% chance the subsequent CFs will be $43,500 a year, and a 50% chance the subsequent CFs will be $23,500 a year.

If we wait, the up-front cost will remain at $100,000.

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Investment Timing Decision Tree

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

At k = 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.

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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) = $18,944.58, which is worth $18,944.58/(1.10) = $17,222.34 in today’s dollars (assuming a 10% discount rate).

Therefore, it makes sense to wait.

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Issues to Consider

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 $53,500 a year, and a 50% chance the subse-quent 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 > $18,944.57.

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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 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% discount rate, what is Project Y’s NPV?

(More…)

0 1 2 3

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

k = 10%

NPV = -$1,051.84

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Abandonment/Shutdown (continued)

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 cash flows of $150,000, and a 40% chance it will produce annual A-T cash flow of -$25,000.

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-$200,000

Abandonment/Shutdown Decision Tree

60% prob.

40% prob.

1 2 3Years

0

150,000 150,000 150,000

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

k = 10%

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) + 0.4(-262,171) = -1,051.84.

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Abandonment/Shutdown (continued)

Company does not have the option to delay the project.

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 the 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) + 0.4(-222,727) = 14,725.77.

-$200,000

60% prob.

40% prob.

1 2 3Years

150,000 150,000 150,000

-25,000

k = 10%

0

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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.

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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 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 $3,000,000 at t = 5, and a 90% chance of an NPV of -$1,000,000 at t = 5.

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

NPV with the Growth Option

-$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 k = 12%,NPV of top branch (w / 10% prob.) = $1,562,758.19.NPV of bottom branch (w / 90% prob.) = -$ 139,522.38.

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NPV with the Growth Option (cont’d)

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 -$500,000 initial outlay and the $100,000 annual cash flows, which lead to an NPV of -$139,522.38.

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NPV with the Growth Option (cont’d)

Thus, 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.