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CHAPTER 13 Other Topics in Capital Budgeting

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- Evaluating projects with unequal lives
- Evaluating projects with embedded options
- Valuing real options in projects

Expected Net CFs

Year

Project S

Project L

($100,000)

0

($100,000)

59,000

1

33,500

59,000

2

33,500

--

3

33,500

--

4

33,500

S

L

CF0

-100,000

-100,000

CF1

59,000

33,500

Nj

2

4

I

10

10

NPV

2,397

6,190

Q. NPVL > NPVS. Is L better?

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

- 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.

L:

0

1

2

3

4

10%

-100,000

33,500

33,500

33,500

33,500

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

S:

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)

- 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.

- Investment timing options
- Abandonment/shutdown options
- Growth/expansion options
- Flexibility 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.

- 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.

-$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 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.

- 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.

- 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.

- 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.

- 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?

0 1 2 3

k = 10%

-$200,000 80,00080,000 80,000

NPV = -$1,051.84

(More…)

- 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.

150,000 150,000 150,000

k = 10%

60% prob.

-$200,000

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

40% prob.

0

1 2 3

Years

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.

- 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.

150,000 150,000 150,000

k = 10%

60% prob.

-$200,000

-25,000

40% prob.

0

1 2 3

Years

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.

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.

- 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.

$3,000,000

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

At k = 12%,

NPV of top branch

(w / 10% prob.)= $1,562,758.19.

NPV of bottom branch

(w / 90% prob.)= -$ 139,522.38.

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