1. CHAPTER 12 Other Topics in Capital Budgeting
Evaluating projects with unequal lives
Identifying embedded options
Valuing real options in projects

2. 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)
, ,500
, ,500
,500
,500

3. 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.

4. 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. 1 2 3 4
10%
-100, , , , ,000
-100,000
-41,000
NPVS = $4,377 (on extended basis)

5. 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.

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

7. 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.

8. 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.

9. 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, / (1.10) = $17, in today’s dollars (assuming a 10% discount rate).
Therefore, it makes sense to wait.

10. 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

11. 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.

12. 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?
-$200, , , ,000
k = 10%
NPV = -$1,051.84

13. 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.

14. Abandonment decision tree
150, , ,000
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(173,027.8) + 0.4(-262,171.3)
= -1,051.84

15. 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.

16. NPV with abandonment option
150, , ,000
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(173,027.8) + 0.4(-222,727.27)
= 14,725.77

17. 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.

18. 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.

19. 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 (10% prob) = $1,562,758.19
NPV of lower branch (90% prob) = -$139,522.38

20. 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,
Thus, the expected value of this project should be:
NPV = 0.1($1,562,758) + 0.9(-$139,522)
= $30,706.

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