Under simple one-period capital rationing, the profitability index can rank projects by present value created per unit of scarce investment. The ranking is useful, but managers must test whether project sizes and relationships make another combination more valuable.
What is capital rationing?
Capital rationing exists when a business cannot fund every positive-NPV project. The objective is not merely to choose individually profitable projects; it is to select the feasible portfolio that creates the highest total NPV within the available budget.
Profitability index formula
Equivalent form: PI = 1 + (NPV ÷ Initial investment)
A PI above 1 indicates a positive NPV when the same cash-flow definition and discount rate are used.
Ranking procedure
- Estimate incremental project cash flows.
- Discount them at risk-appropriate rates.
- Calculate NPV and PI.
- Rank projects from highest to lowest PI.
- Add projects while respecting the budget.
- Test feasible combinations before final approval.
Worked capital-rationing example
| Project | Initial investment | PV of inflows | NPV | PI |
|---|---|---|---|---|
| A | 50,000 | 65,000 | 15,000 | 1.30 |
| B | 40,000 | 50,000 | 10,000 | 1.25 |
| C | 60,000 | 72,000 | 12,000 | 1.20 |
| D | 30,000 | 35,400 | 5,400 | 1.18 |
Assume the budget is 100,000. A simple PI ranking selects A and B, using 90,000 and creating total NPV of 25,000. The remaining 10,000 cannot fund another project.
Managers should compare other feasible combinations. A + D costs 80,000 and creates 20,400; B + C uses the full 100,000 and creates 22,000; C + D costs 90,000 and creates 17,400. A + B remains best among these indivisible choices.
The unused-budget problem
A high-ranked project may leave money that cannot be invested. A lower-PI combination can sometimes use the budget more effectively and create greater total NPV. This is why the final decision must compare feasible portfolios, not stop at a mechanical ranking.
When PI works best
- There is one binding budget period.
- Projects are independent or relationships are explicitly handled.
- Cash flows and discount rates are comparable.
- Projects can be combined without hidden operational constraints.
When another method is needed
Multi-period constraints, project indivisibility, mutually exclusive alternatives and dependencies can make a simple PI ranking unreliable. Integer programming or another optimisation approach may be required for a large project set.
Manager checklist
- Confirm all projects have positive NPV before ranking.
- Use consistent cash-flow definitions.
- Test the budget fit of combinations.
- Consider future-period funding constraints.
- Document rejected positive-NPV projects for later review.
Frequently asked questions
Why use PI under capital rationing?
PI measures present value relative to scarce initial investment and can provide a useful first ranking.
Should the highest-PI projects always be selected?
No. Indivisible project sizes and unused budget can make another combination produce more total NPV.
Can a project with PI below 1 be selected?
Normally no, because it has a negative NPV under the stated assumptions.
What is the final objective?
Choose the feasible project portfolio with the highest total NPV, not simply the highest average PI.
Continue learning
- Investment decisions under capital rationing
- Limitations of profitability index
- Profitability index fundamentals
- Investment appraisal methods compared
Use the formulas and examples as learning tools. Real decisions should use reliable data, appropriate assumptions and professional judgment where necessary.
Let us consider a simple situation where a firm has the following investment opportunities and has a 10% cost of capital.
If the firm has no capital rationing constraint, if should undertake all three projects because they all have possible net present values (NPVs). Suppose there is a capital constraint and the firm can spend only 50000$ in year zero, what should the firm do? If the firm strictly follows the net present value (NPV) rule and starts with the highest individual net present value (NPV), it will accept the highest net present value (NPV) project L, which will exhaust the entire budget. We can, however, see that projects M and N together have higher net present value (15870 $) than project L (12940 $) and their outlays are within the budget ceiling. The firm should, therefore, undertake M and N rather than L to obtain highest possible net present value (NPV). It should be noted that the firm couldn't select projects solely on the basis of individual net present values (NPVs) when funds are limited. The firm should intend to get the largest benefit for the available funds. That is, those projects should be selected that give the highest ratio of present value to initial outlay. This ratio is the profitability index (PI). In the example, M has the highest PI followed by N and L. If the budget limit is 50000 $, we should choose M and N following the PI rule.
The capital budgeting procedure under the simple situation of capital rationing may be summarized as follows:
- The net present value (NPV) rule should be modified while choosing among projects under capital constraint. The objective should be to maximize NPV per rupee of capital rather than to maximize NPV. Projects should be ranked by their profitability index, and top-ranked projects should be undertaken until funds are exhausted.
No comments:
Post a Comment