1. CHAPTER 13 Other Topics in Capital Budgeting
Evaluating projects with unequal lives
Evaluating projects with embedded options
Valuing real options in projects

2. S and L are mutually exclusive and will be repeated. k = 10%
S and L are mutually exclusive and will be repeated. k = 10%. Which is better?
Expected Net CFs
Year
Project S
Project L
($100,000)
($100,000) 1
59,000
33,500 2
59,000
33,500 3 --
33,500 4 --
33,500

3. 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.

4. 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.

5. L: 1 2 3 4
10%
-100,000
33,500
33,500
33,500
33,500
NPVL = $6,190 (already to Year 4) S: 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)

6. 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.

7. What are some examples of real options?
Investment timing options
Abandonment/shutdown options
Growth/expansion options
Flexibility options

8. 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.

9. 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.

10. Investment Timing Decision Tree
-$100, , , , ,500
50% prob.
-$100, , , , ,500
50% prob.
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.

11. 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, in today’s dollars (assuming a 10% discount rate).
Therefore, it makes sense to wait.

12. What’s the appropriate discount rate?
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,

13. 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.

14. 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?
k = 10%
-$200, , , ,000
NPV = -$1,051.84
(More…)

15. 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.

16. Abandonment/Shutdown Decision Tree
150, , ,000
k = 10%
60% prob.
-$200,000
-25, , ,000
40% prob.
Years
If the customer uses the product,
NPV is $173,
If the customer does not use the product,
NPV is -$262,
E(NPV) = 0.6(173,027) + 0.4(-262,171) = -1,

17. 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.

18. NPV with the Abandonment Option
150, , ,000
k = 10%
60% prob.
-$200,000
-25,000
40% prob.
Years
If the customer uses the product,
NPV is $173,
If the customer does not use the product,
NPV is -$222,
E(NPV) = 0.6(173,027) + 0.4(-222,727) = 14,

19. 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.

20. 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.

21. NPV with the Growth Option
$3,000,000
100, , , , ,000
10% prob.
-$1,000,000
-$500,000
100, , , , ,000
90% prob.
Years
At k = 12%,
NPV of top branch
(w / 10% prob.) = $1,562,
NPV of bottom branch
(w / 90% prob.) = -$ 139,

22. 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,

23. 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.

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