1. Issues in Capital Budgeting II
FINA 4463
(Chapter 12 in text)

2. Capital Rationing

3. Capital Rationing
Usual assumption is that firm should accept all NPV>0- projects
What if firm has a number of NPV>0 projects, but doe not have resources to take on all of them?
This is situation of capital rationing
Limited amount of capital to invest
Must decide how to best invest the limited resources

4. Sources of Rationing Two types of capital rationing:
Soft rationing: capital constraint imposed internally by the firm
Head office may assign a budget to each division
If soft rationing is leading to a division foregoing many NPV>0 projects, then the budget should be changed

5. Hard rationing: capital constraint imposed on firm by the capital markets
Firm has limited internal cash, cannot borrow and cannot (or will not) issue new equity
In a perfect world, there would never be externally imposed capital constraints
In perfect world, firm could simply announce it had a good project to invest in, show investors the risk and return projections, and then investors would be willing to invest equity in/lend to the project

6. However, the world is not perfect.
There are several reasons that firms may be unable or unwilling to bring in external financing for a good projects:
Firm and investors may disagree on value of project
Management may lack creditability
Especially true for smaller, newer firms, or firms with poor records
Flotation Costs
It costs money to issue new shares/bonds
The additional cost may make raising money to finance a project not worthwhile
Flotation costs are higher for smaller issues, so small firms are affected the most (also higher for equity issues compared to debt).

7. 3. Underpriced shares
Firms shares may be trading below their true value
Management knows that the shares are undervalued (management has better info about firm than market = asymmetric information)
Selling shares to raise funds to finance a project means that shareholders get a good project, but are selling part of the firm at a discount
In some cases the project will not be worthwhile and firm will skip project
Biggest effect on firms with high degree of asymmetric information (complicated firms, new firms, firms with few analysts following them)

8. Note: firms can benefit from having cash on hand available.
Can fund NPV>0 projects that without accessing markets
Do not have to skip a good projects because of reasons above
Assuming a firm is subject to capital rationing, how should it solve for the optimal investment strategy, given the constraint?

9. Firm has $10 million available for investment, 3 potential projects
Example:
Firm has $10 million available for investment, 3 potential projects
Simply choosing highest NPV means choose A
Uses up total budget
NPV = 21.4
Cashflows (millions)
Project
Year 0
Year 1
Year 2
10% A
-10 30 5
21.4 B -5 20
16.1 C 15
11.9

10. However you could take B and C instead
Uses up entire budget
Total NPV = 28
B and C is the better choice
Best combination of projects is fairly obvious in this case, but may not be in more complicated situations

11. Solving for Optimal Decision in Capital Rationing Problems
Common way to approach capital rationing problem is to use the profitability index
PI shows which projects give “most value for your money”
PI = value of project per dollar invested
Choose project with highest PI, and keep choosing projects until your budget runs out

12. From previous example:
Solution by PI: choose B and C
Project PI A
3.1 B
4.2 C
3.4

13. Problems with Profitability Index
If projects chosen via PI do not exhaust the budget, you may not get the optimal solution
Example
Required return = 10%, budget constraint = $100
Cashflows
Year 0
Year 1
P.I.
NPV -5 8
1.454
2.27 7
1.272
1.36
-100
120
1.091
9.09

14. Problems with Profitability Index
PI says take first two projects for total NPV = = 3.63
This leaves $90 of budget unspent
Better to take third project by itself, for total NPV = 9.09
Reason: PI has difficulty in comparing projects of different sizes
Note: As long as your answer using PI uses up entire budget the NPV should be the maximum possible

15. Problems with Profitability Index
PI also runs into problems if there is more than one constraint faced by firm
Projects are mutually exclusive (if you take one you cannot take the other)
Projects are dependant (you can only take on one project, if you have already taken another)
Budget constraints in more than one period
Etc.
The usual approach to capital rationing situations is to solve for the optimal investment using optimization software on a computer
Maximize an objective function subject to certain constraints
Can use “Solver” on Excel

16. Investments of Unequal Lives

17. Investments of Unequal Lives
When comparing mutually exclusive alternatives, NPV does not always give correct choice as to the best alternative if they are of different lengths
e.g. comparing Machine A to Machine B where B costs more but lasts longer
NPV does not take into account the different lifespans of the projects

18. Investments of Unequal Lives
Example
Machine A costs $10,000 and increase profits by $5000/year. It lasts 6 years.
Machine B costs $5,500 and increases profits by $5000/year. It lasts 3 years
Discount rate = 10%

19. A has highest NPV
A is best choice if this is a “one time deal”
If you will only buy a machine once and never replace it
More commonly, machines have to be replaced as they wear out
If replacement of machines as they wear out is relevant, there are two methods to correctly compare the alternatives
Project Replication
Equivalent Annuities

20. Project Replication
Find a common multiple of the two life lengths
Use this as total project length for both alternatives, where each alternative is repeated the appropriate number of times
Calculate NPV over this common time frame and compare
Equivalent Annuities
Equate the NPV of each alternative to an annuity
The length of the annuity equals the life of the project
Solve for annuity payment that would give the same NPV
The annuity payment represents the value per year created by the project
Since projects are now on a common time frame (per year), can simply compare

21. Optimal Replacement Time
It may sometimes pay to replace a machine before the end of its “natural” life
May happen if:
Better machine becomes available
Salvage value is decreasing as machine ages
Machine becomes more expensive to operate or less efficient overtime
Optimal time to replace a machine is just a special case of comparing projects of unequal lives

22. Example:
A machine you always need for your production process
Lasts a maximum of three years before replacement needed
It becomes less efficient over time
When replaced, you will replace with an identical (but new) machine
How often should you replace?
Discount rate=10%

23. Salvage value if sold this year
(example continued)
To solve, compare 3 projects of unequal lives: replace in year 1
vs. replace in year 2
vs. replace in year 3
Year 1 2 3
Cashflow
-60000
40000
35000
25000
Salvage value if sold this year
30000
15000