Human wants are unlimited but resources are limited. A business with many viable projects as investment opportunities at a particular time will always have a problem of limited funds.
So, what should a business with a fixed amount of funds for investment within an accounting period do, when it has many acceptable projects begging for immediate investment? This situation makes capital rationing a very useful investment decision making tool.
There are some methods of capital rationing and decision criteria. These methods are:
- The aggregation method under the Net Present Value (NPV) and Discounted Cash Flow (DCF),
2. The incremental method under the Internal Rate of Return (IRR),
3. The Benefit Cost (BC) criterion.
4. The postponement analysis.
- Aggregation method:
The aggregation method uses the NPV or DCF criterion to select best projects in the light of limited funds. This is how the method works:
The NPV of all projects which fit into the available funds are added to determine projects combination that maximizes the total NPV as far as the cost of capital is stable.
In reality, there is always a substantial number of projects for any possible list of projects. It’s often suggested that the maximum number in the combination be narrowed down by ranking projects in ascending order of cost and accepting them until the available capital is exhausted. The minimum number is the combination is obtained by ranking projects in descending order of their NPVs and accepting this order until the budget is exhausted.
An example: A company with a capital limitation of $2,000 can make a feasible combination from the following projects:
Table 1. Aggregation Method.
| Feasible combinations | Aggregate NPV ($) |
| 1.0 | 420 |
| 1.1 | 200 |
| 1.2 | 100 |
| 1.3 | 700 |
| 1.4 | 1,000 |
| 1.7 | 1,300 |
Table 1. shows that the maximum combination is four and the minimum combination is two.
2. Incremental analysis:
Internal Rate of Return (IRR) can be incorporated into capital rationing using the incremental method. Here, projects are ranked in descending order of their IRR. After ranking, all projects from the highest IRR down to the point where funds are exhausted, are accepted.
There is a problem of indivisibility of projects with the use of this method. This problem arises when there left over funds which are not enough to fund any project left on the list. The left over funds may be placed in temporary security investment yielding less than the business’s cost of funds, falling short of the maximization objective.
What the incremental analysis does is, to help decide whether giving up a relatively small but high yield project frees up sufficient funds for larger but lower yield project which will increase the total return.
An example:
Table 2. Capital Rationing Using IRR Ranking
| Project | Cost ($) | IRR (%) | Funds available ($) |
| 1 | 30,000 | 25 | 300,000 |
| 3 | 50,000 | 21 | 270,000 |
| 6 | 100,000 | 19 | 220,000 |
| 2 | 70,000 | 16 | 120,000 |
| 4 | 70,000 | 13 | 50,000 |
| 5 | 65,000 | 11 | 50,000 |
| 7 | 45,000 | 9 | 5,000 |
| 8 | 25,000 | 8 | 5,000 |
3. Benefit/Cost Ratio and Capital Rationing:
Ranking of projects in descending order of their benefit cost (BC) ratios may deviate from ranking under NPV criterion. This will certainly lead to contradictory results. The BC criterion ranks projects in different order than the NPV criterion does. Let us look at the table below:
Table 3. Ranking by BC Ratio
| Project | Present Discounted Value/PV ($) | Cost ($) | NPV($) | BC |
| 1 | 10,000 | 6,000 | 4,000 | 1.67 |
| 3 | 3,000 | 2,000 | 1,000 | 1.5 |
| 4 | 6,000 | 4,500 | 1,500 | 1.33 |
| 2 | 6,000 | 6,000 | 0 | 1.0 |
| 5 | 7,000 | 8,000 | -1,000 | 0.875 |
Table 3. shows that project 3 is ranked higher than project 4 despite having lower NPV. This is because it gives the benefits (present discount value) per cost, while the NPV gives the absolute amount of benefits in excess of cost.
The confusion which to recommend between projects 3 and 4 arises because of the scaling problem associated with the benefit cost ratio and the indivisibility of leftover projects after funds have been exhausted. The BC is a ratio that compares all projects in a way that hides the differences in size.
The confusion is resolved by investing all available funds at a higher total NPV than investing part in relatively small projects with higher BC ratios and the balance in low BC projects.
Where there are sufficient funds, accept all projects with either a positive NPV or a BC ratio greater than one.
4. Postponement Analysis:
Postponement analysis is a method for determining which of the projects are the most postponable in the sense that the business incurs the least cost by their postponement.
If BC ratio were used, the postponable projects would be those which suffered the least decline in that ratio by waiting one period.
The postponability of a project is determined by;
1. Ranking acceptable projects in descending order of their BC ratio.
2. computing the net present value of each project assuming that the starting point (i) is zero,
3. recomputed NPV of each project as if the project was started a year earlier, taking into consideration any changes in cost and expected cashflow and,
4. the difference between the two NPVs is the cost of the postponement.
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