1. Lecture 6 Capital Budgeting Complications
Managerial Finance
FINA 6335
Ronald F. Singer

2. We have stated that we want the firm to take all projects that generate positive NPV and reject all projects that have a negative NPV. Capital budgeting complications arise when you cannot, either physically or financial undertake all positive NPV projects. Then we have to devise methods of choosing between alternative positive NPV projects.

3. Mutually Exclusive Projects
If,among a number of projects, the firm can only choose one, then the projects are said to be mutually exclusive.
Example: Suppose you have the choice of modifying an existing machine, or replacing it with a brand new one. You could not do both and produce the desired amount of output. Thus, these projects are mutually exclusive. Given the cash flows below, which of these projects do you choose?

4. Time Modify Replace Difference
, , ,000
, , ,000
, , ,500
IRR
10%) 36, , ,700
Notice the conflict that can exist between NPV and IRR.

5. Examples of Capital Budgeting Complications
Optimal Timing 
Long versus Short Life
Replacement Problem 
Excess Capacity 
Peak Load Problem (Fluctuating Load) 
Capital Constraints 

6. Capital Budgeting Complications
These Capital Budgeting Complications will stop the Firm from taking all possible positive NPV PROJECTS. Thus, the firm is faced with the choice of two possibilities.
Remember: Goal is still Max NPV of all possibilities

7. Capital Budgeting Complications
We can divide these problems into three separate classes, each with their own method of solutions.
1- Once and for all deal.
Choose the one alternative having the highest NPV.
2- Repetitive Deal.
Choose the one alternative having the highest equivalent annual cash flow.
3- Capital Budgeting Constraint
Choose the combination of projects having the highest NET PRESENT VALUE.

8. Once and for All Deal Investment Timing:
When is the optimal time to take on an investment project? Consider T possible times, where,
t = 1, ...T.
Then each "starting time" can be considered a different project in a set of T mutually exclusive projects. Then find that t which Max:
NPV(t)
(1+r)t

9. Example
You are in the highly competitive area of producing laundry soap and detergents. You have a new product which you feel does a superior job in washing clothes, but you anticipate that the product will have difficulty being accepted by the consumer. Thus you expect that if you introduce the product now, you will have to suffer a few years of losses until the product is accepted by the consumer. A competitor is about to come out with a similar product. You feel that if you allow your competitor to come out with the product first, you can benefit from the time he spends acclimating your potential customers. However, you will then be giving up your competitive edge.

10. Example(continued)
The initial investment in the product has already been spent, is a sunk cost and can be ignored for this problem. The anticipated life of the productive process is ten years from the time the product is first produced. Thereafter, there will be so much competition that any new investment in this product will have a zero NPV. The discount rate is 15%.

11. Example(continued) Cash Flow ($ Millions) 1 2 3 4-10 -4 -3 -2 20 -1
Year from start of project 1 2 3
4-10
Immediately -4 -3 -2 20
If introduced after One year -1
3.5
19.5
If introduced after Two years 4 19
What should you do?

12. Example(continued) NPV(0) (Introduced Immediately) is: 47.649 million
NPV(1) (Introduced in one year's time) is: million
NPV(2) (Introduced in two year's time) is: million
Which one of these three options should be taken?

13. Example(continued)
Calculate NPV from time 0.  
Shortcut: Calculate the annualized rate of change of NPV. if delaying causes the NPV to increase by more than the discount rate, the project should be delayed. If not, the project should not be delayed.
Caution: This method assumes that the project cannot be reproduced at a positive NPV after the initial life of the project. Otherwise, you have to also account for the fact that the project that is started earlier can also be reproduced earlier. In that case, the alternatives look like:

14. Example(continued) Start immediately └─────────┴─────────┴─────────┘   
One year delay
└─┴─────────┴─────────┴─────────┘
 This leads to the second class of problems:

15. Alternatives with Different Lives
Repetitive Deals
Mutually exclusive projects with different Starting Times
Mutually exclusive projects with different Economic Lives
Replacement Decision
Management of Excess of Peak Capacity
 Alternatives with Different Lives
3 Little Pigs
Brick vs. Wood vs. Straw.

16. Example
You have the option of undertaking one of two different ways of achieving some goal. Which one should you take?
 (A) A Bridge costing 5M lasts 15 years 
(B) A Bridge costing 4M lasts 10 years 
Both generate 1 Million in net revenues per year.
Let the Discount rate = 12% for each alternative.
NPV (A) = $1.81 Million
NPV (B) = $1.65 Million 
Conceptually The naive NPV rule would say, take the project with the highest Net Present Value. This would be wrong.

17. Example(continued)
Consider what happens after ten years. In particular by year 30.  A   B
PV(A) over infinite horizon: 
PV(A) = = = 2,214, (1.12)
PV(B) over infinite horizon: PV(B) = = 2,435,

18. Alternative Equivalent Annual Cash Flow
(EACF) or (NUS in Hewlett Packard) 
Consider the annuity having the same NPV and life of the project. 
EACF (A) = That annuity having a Present Value of 1.81, lasting 15 years at a discount rate of 12%. 
(A): PVA = Annuity x PVFA(r%, T) 
Annuity(A) = PVA
PVFA(12%,15) 
= Million = 265,700 = EACF(A)
6.811 
(B): Annuity(B) = Million = 292,000 = EACF(B)
This "Equivalent Annual Cash Flow" (or Cost) is a convenient way of examining the host of complicated, mutually exclusive capital budgeting problems listed above: These all involve

19. A Timing Problem (1) When to start project
(2) When to "cash in"  Forestry Wine 
(3) Replacement 
(4) Short vs. Long lived Project 
(5) When and how to increase capacity
Can all be dealt with in a similar way 
Mutually exclusive projects with different Starting Times
Instead of assuming that this is a once and for all deal,
assume that the alternatives can be reproduced indefinitely.
Note that this case differs from the Laundry Detergent Example treated above:
1. How? 
2. What impact will this have on the timing decision?

20. Example
Consider an example: The mutually exclusive decision, when to cut down a forest:
In ten years with NCF of ,000
In eleven years with NCF of ,000
In twelve years with NCF of ,000
 If this were a one-time-only deal, you would simply calculate the NPV of each alternative:
  NPV of cutting in ten years: ,132.74
NPV of cutting in eleven years: 15,236.23
NPV of cutting in twelve years: 14,887.16
 But, more realistically, you will be able to continue cutting down these trees every ten, eleven, or twelve years. Which is the best alternative as a repetitive procedure?

21. Example(continued) The question is, what is better,
receiving an annuity of 47,000 every ten years 
(2) receiving an annuity of 53,000 every eleven years 
(3) receiving an annuity of 58,000 every twelve years 
 For any set of reproducible mutually exclusive projects with different lives, you can: Find the NPV of each project through one repetition, and then find its Equivalent Annual Cash Flow, (EACF)and choose the one with the highest EACF.   

22. Example(continued) Where EACF is calculated as:
 EACF(t) = NET PRESENT VALUE
PVFA(r%,t)
So: EACF(10) = 15,132 = 2, (5.650) 
EACF(11) = 15,236 = 2,566.98
(5.938)
EACF(12) You know this isn't the right one since it has a lower present value but takes longer to produce 
Thus you want to take the shorter lived project now.

23. Replacement Decision
Return to the first example, you choose project (2), and now you are in the fifth year of that project. The project, as expected, is returning $19.5 million this year. But production difficulties have resulted in a machine which is wearing out faster than anticipated. So that your expected cash flow for the next five years will be: 
Cash Flow
NPV of Operating
Cash Flows 1 2 3 4 5
19.5 18 17 16 15
62.54
50.54
38.61
26.24
13.39

24. Example
A new production technology has been devised which will cost $100 million and generate $39 million for the next 7 years, with an anticipated scrap value of 3 million at the end of the seventh year. Should you replace the machine now, never, or plan to replace it some time in the future?
It is assumed that the scrap value of the old machine will be 0 if not replaced during the next 5 years (the life of the old project), but can be sold for 3 million at any time during the next five years. The discount rate is assumed to be 12%.
Find the equivalent annual cash flow for the new machine, net of the current scrap value.

25. Example(continued) Net Cash Flow of Replacement Machine
NET PRESENT VALUE: Million
EQUIVALENT ANNUAL CASH FLOW: Million
IRR: 35.56%

26. Example(continued)
Replace in the beginning of year 2. Note, simply comparing NPV will not give the right answer, neither will looking at incremental cash flow. This is because the replacement has a different life than the current process and they are obviously mutually exclusive. Furthermore, and more important, the alternatives of replacing now versus not replacing now is not the appropriate alternatives. You can also replace next year, the year after, etc. The alternative which gives the greatest incremental value relative to all the other possible alternatives could be calculated by looking at the incremental cash flows from each alternative. But it is easier to simply calculate the EACF and compare that to the current cash flow to see what to do.
In general, Equivalent Annual Cash Flow or Cost is used to consider a problem where the investment is considered ongoing and you have to examine what happens at the end of the project's life. All that EACF does is help you discover the decision which gives the highest NPV as a whole.

27. Capital Rationing
In this situation, the decision maker is faced with a limited capital budget. As a result, it may not be possible to take all positive net present value projects. Under this scenario, the problem is to find that combination of projects (within the capital budgeting constraint) that leads to the highest Net Present Value.
The problem here is that the number of possibilities become very large with a relatively small number of projects. Thus, in order to make the problem "manageable", we can systematize the search.

28. Capital Rationing
Since we have a constraint, what we want to do is invest in those projects which gives us the highest BENEFIT per dollar invested. (The highest bang per buck). What is the benefit?, it is the Present Value of the Cash Flows. So that we would want to choose that set of projects within the capital budgeting constraint that gives the highest:  PV
INVESTMENT 
This ratio is called the Profitability Index.

29. Example
Suppose we have a $13 million capital budgeting constraint, with 7 alternative capital budgeting projects with the following projections.   
Project NPV Investment
A  
B  
C  
D  
E  
F   G

30. Example(continued) Rank by Profitability Index {(NPV+INV)/INV}
 Project Profitability Index Investment Total E C
G F D B A
Combination with highest profitability index within the capital budget 
(E,C,G,F) has a NPV of $20.5 million, and a cost of $13 million.

31. Example(continued)
However, if the budget were 15 million rather than 13 million we would have a problem. Adding D would go over the budget and be infeasible, but the combination CDEF has a higher NPV ($22 million) than the chosen combination of ECGF. This is because the amount spent was only 13 million leaving 2 million in unspent funds. In this case, we are better off choosing a combination which spends all the funds.
The only way to do this right is to do a full blown linear programming problem with constraints.

32. Problem of the Day
You are given the following statistics about three projects being considered by your firm. All project cash flows should be discounted at the rate of 8% per year. Answer the question, showing all work and explain fully (Assume these projects cannot be reproduced at the end of their life at a positive NPV unless stated otherwise).

33. Problem of the Day Project Initial Investment NPV Life
(1) What project(s) would you choose if funds were unlimited and the projects were not mutually exclusive?
(2) What project(s) would you adopt if the projects were not mutually exclusive but funds were limited to $2,000,000?
(3) What project(s) would you choose if the projects were mutually exclusive, funds were unlimited, and the projects could be reproduced indefinitely, at the end of their lives, at the same NPV as given in the table?
(4) What project(s) would you choose if the projects were not mutually exclusive, funds were unlimited, and the projects could be reproduced indefinitely, at the end of their lives, at the same NPV as given in the table?