Chapter 12 other topics in capital budgeting
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CHAPTER 12 Other Topics in Capital Budgeting. Evaluating projects with unequal lives Identifying embedded options Valuing real options in projects. Evaluating projects with unequal lives. Projects S and L are mutually exclusive, and will be repeated. If k = 10%, which is better?

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CHAPTER 12 Other Topics in Capital Budgeting

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CHAPTER 12Other Topics in Capital Budgeting

Evaluating projects with unequal lives

Identifying embedded options

Valuing real options in projects


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

YearProject SProject L

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

1 59,000 33,500

2 59,000 33,500

3 - 33,500

4 - 33,500


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 analysis.


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

3

4

10%

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

-100,000

-41,000

NPVS = $4,377 (on extended basis)


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.


What are some examples of real options?

  • Investment timing options

  • Abandonment/shutdown options

  • Growth/expansion options

  • Flexibility options


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 $100,000 and 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.


Investment timing decision tree

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

  • 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.

50% prob.

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

50% prob.

0 1 2 3 4 5

Years


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% discount rate).

  • Therefore, it makes sense to wait.


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 $53,500 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 > $18,944.57


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.


0 12 3

k = 10%

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

NPV = -$1,051.84

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?


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.


Abandonment decision tree

150,000 150,000 150,000

  • 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

60% prob.

-$200,000

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

40% prob.

0

1 2 3

Years


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.


NPV with abandonment option

150,000 150,000 150,000

  • 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

60% prob.

-$200,000

-25,000

40% prob.

0

1 2 3

Years


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.


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.


NPV with the growth option

$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

100,000 100,000 100,000100,000 100,000

10% prob.

-$1,000,000

-$500,000

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

90% prob.

0

1 2 3 4 5

Years


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 -$500,000 initial outlay and the $100,000 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.


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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