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

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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)
• 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 CFj register for both
  projects, and enter I/YR 10.
• NPVS 2,397
• NPVL 6,190
• Is Project L always better - NO?
• Need replacement chain analysis.
• Reason Unfair to compare to projects with
  unequal lives.

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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) L still better?
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Replacement Chain Approach

• See example in book, p. 455.
• Project F (3-year) has a lower NPV over 3 years,
  but higher NPV over 6 years.
• Furthermore, Project F has another advantage over
  Project C?

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What is real option analysis?

• Real options exist when managers can influence
  the size and riskiness of a projects cash flows
  by taking different actions during the projects
  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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1. Investment timing option

• Project L costs 100,000, its annual CFs are
  33,500 for 4 yrs, k 10, and 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 (vs. 33,500), and a
  50 chance the subsequent CFs will be 23,500 a
  year (vs. 33,500).

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Investment timing decision tree
-100,000 43,500 43,500 43,500
43,500
50 prob.
-100,000 23,500 23,500 23,500
23,500
50 prob.
0 1 2 3 4
5
Years

• At k 10, the NPV at t 1 is
• 37,889, if CFs are 43,500 per year (vs. NPV of
  6,190 before), or
• -25,508, if CFs 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) Accept
• 0.5(0) Reject 18,944, which is worth 18,944
  / (1.10) 17,222 in todays 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
  NPV next year (if we delay) would be
• 0.5(69,588) 0.5(0) 34,794 gt 18,944.57
• Accept Reject

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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 (first mover
  advantage).
• Waiting may allow you to take advantage of
  changing market and economic conditions.

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Investment Timing Options

• See Example in text on p. 461.

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2. Abandonment 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 Ys NPV?

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Abandonment option

• Project Ys net CFATs depend critically upon
  customer acceptance of the product.
• There is a 60 probability that the product will
  be wildly successful and produce CFATs of
  150,000, and a 40 chance it will produce annual
  CFATs of -25,000.
• .60 (150,000) .40 (-25,000) 80,000

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Abandonment decision tree
150,000 150,000 150,000
60 prob.
-200,000
-25,000 -25,000 -25,000
40 prob.
0
1 2 3
Years

• If the customer uses the product, CF 150,000
• NPV is 173,027.80 at 10 (blue).
• If the customer does not use the product,
• NPV is -262,171.30 (red).
• E(NPV) 0.6(173,027.8) 0.4(-262,171.3)
• -1,051.84

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Issues with abandonment options

• The company does not have the option to delay the
  project now or never.
• However, the company can 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
  (outflows) after the first year.

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NPV with abandonment option
150,000 150,000 150,000
60 prob.
-200,000
-25,000
40 prob.
0
1 2 3
Years

• If the customer uses the product, NPV is
  173,027.80 (same as before).
• If the customer does not use the product,
• NPV is -222,727.27 (vs. -262,171 before)
• E(NPV) 0.6(173,027.8) 0.4(-222,727.27)
• 14,725.77 (vs. -1051 from before)

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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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3. Shutdown Options

• See example in text on p. 458.

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4. 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 a NPV of
  3,000,000 at t 5, and a 90 chance of a NPV of
  -1,000,000 at t 5.

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NPV with the growth option
3,000,000
100,000 100,000 100,000 100,000
100,000
10 prob.
-1,000,000
-500,000
100,000 100,000 100,000 100,000
100,000
90 prob.
1 2 3 4 5
0
Years

• At k 12,
• NPV of top branch (10 prob) 1,562,758
• NPV of lower branch (90 prob) -139,522

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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.

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5. Flexibility options

• Flexibility options exist when its worth
  spending more money today, which enables you to
  maintain flexibility (and lower costs and/or
  higher revenues) down the road.
• See BMW and Power Companies examples on p. 464.

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Optimal Capital Budget

• Optimal Capital Budget
• Capital Rationing
• See p. 465-466
• Problem 12-2 on p. 469