Capital Rationing: How to Allocate Limited Resources Among Multiple Projects Using Capital Evaluation

1. What is capital rationing and why is it important?

capital rationing is a process of selecting the most profitable projects from a pool of available investment opportunities, subject to a limited budget or a constraint on the amount of capital that can be invested. Capital rationing is important because it helps managers to allocate scarce resources efficiently and effectively, and to maximize the value of the firm. capital rationing can be done using various methods of capital evaluation, such as net present value (NPV), internal rate of return (IRR), profitability index (PI), or payback period (PP). However, each method has its own advantages and disadvantages, and may not always yield consistent or optimal results. Therefore, it is essential to understand the underlying assumptions and limitations of each method, and to apply them appropriately in different scenarios. In this section, we will discuss the following aspects of capital rationing and capital evaluation:

1. The difference between soft and hard capital rationing. Soft capital rationing occurs when the firm imposes an internal limit on the amount of capital that can be invested, based on its own policies, preferences, or goals. For example, the firm may want to maintain a certain debt-to-equity ratio, or to avoid diluting its ownership by issuing new shares. Hard capital rationing occurs when the firm faces an external constraint on the availability of capital, due to market conditions, regulations, or other factors. For example, the firm may not be able to borrow enough funds from lenders, or to raise enough equity from investors, at a reasonable cost. Soft capital rationing can be relaxed or removed by the firm itself, while hard capital rationing is beyond the firm's control.

2. The criteria for ranking and selecting projects under capital rationing. The most common criterion for ranking and selecting projects under capital rationing is the npv, which measures the present value of the future cash flows generated by the project, minus the initial investment. The NPV reflects the incremental value that the project adds to the firm, and the opportunity cost of capital. The higher the NPV, the more profitable the project. Therefore, the firm should rank the projects in descending order of their NPVs, and select the projects with the highest NPVs, until the budget is exhausted. However, the NPV criterion may not always be feasible or optimal, especially when the projects have different sizes, durations, or risk levels. In such cases, the firm may need to use other criteria, such as the PI, which measures the ratio of the NPV to the initial investment, or the IRR, which measures the annualized return on the investment. The PI and the IRR reflect the profitability and efficiency of the project, respectively. The higher the PI or the IRR, the more desirable the project. Therefore, the firm should rank the projects in descending order of their PIs or IRRs, and select the projects with the highest PIs or IRRs, until the budget is exhausted. However, the PI and the IRR criteria may also have some drawbacks, such as the possibility of multiple or negative IRRs, or the inconsistency with the NPV criterion, known as the ranking problem or the scale problem.

3. The techniques for solving the capital rationing problem. The capital rationing problem can be formulated as a mathematical optimization problem, where the objective is to maximize the total NPV of the selected projects, subject to the budget constraint and other possible constraints, such as the minimum or maximum number of projects, or the interdependence or exclusivity of projects. The capital rationing problem can be solved using various techniques, such as linear programming, integer programming, or dynamic programming. However, these techniques may require complex calculations, or may not be applicable to all types of projects or constraints. Therefore, the firm may need to use some heuristic or approximate methods, such as the profitability index method, the internal rate of return method, the incremental internal rate of return method, or the integer approximation method. These methods are simpler and easier to implement, but they may not guarantee the optimal or unique solution. Therefore, the firm should compare the results of different methods, and use some sensitivity analysis or simulation to test the robustness and reliability of the solution.

2. How to measure the profitability and risk of different projects?

In this section, we will delve into the various methods used to evaluate the profitability and risk of different projects. It is crucial to assess these factors accurately to make informed decisions regarding the allocation of limited resources among multiple projects.

1. Net Present Value (NPV): NPV is a widely used method that calculates the present value of cash flows generated by a project, taking into account the time value of money. By discounting future cash flows to their present value, NPV helps determine whether a project is financially viable. A positive NPV indicates that the project is expected to generate more value than the initial investment.

2. Internal Rate of Return (IRR): IRR is another important metric used in capital evaluation. It represents the discount rate at which the present value of cash inflows equals the present value of cash outflows. The IRR helps assess the project's profitability by comparing it to the required rate of return. If the IRR exceeds the required rate of return, the project is considered financially attractive.

3. payback period: The payback period measures the time required for a project to recover its initial investment. It is a simple method that focuses on cash flow timing. Projects with shorter payback periods are generally preferred as they offer quicker returns on investment. However, this method does not consider the time value of money and may overlook long-term profitability.

4. profitability index (PI): The profitability index is calculated by dividing the present value of cash inflows by the initial investment. It helps assess the value created per unit of investment. A PI greater than 1 indicates that the project is expected to generate positive value.

5. Sensitivity Analysis: Sensitivity analysis involves assessing the impact of changes in key variables on the project's financial outcomes. By varying factors such as sales volume, costs, or interest rates, analysts can understand the project's sensitivity to different scenarios. This analysis provides insights into the project's risk and helps identify critical factors that may affect its profitability.

6. scenario analysis: Scenario analysis involves evaluating the project's performance under different hypothetical scenarios. By considering various combinations of factors such as market conditions, regulatory changes, or technological advancements, analysts can assess the project's resilience and adaptability. This analysis helps in understanding the potential risks and rewards associated with different scenarios.

It is important to note that these evaluation methods provide valuable insights, but they should be used in conjunction with other qualitative and quantitative factors. Each method has its strengths and limitations, and a comprehensive evaluation approach considers multiple perspectives to make well-informed decisions.

3. What are the types and sources of capital rationing?

One of the main challenges that managers face when making capital budgeting decisions is how to deal with capital rationing constraints. capital rationing is the situation where a firm has more profitable investment opportunities than it can finance with its available funds. In other words, the firm has a limited budget or a ceiling on the total amount of capital it can invest in any given period. Capital rationing can be either internal or external, depending on the source of the constraint. In this section, we will explore the types and sources of capital rationing, and how they affect the capital evaluation process.

Some of the types and sources of capital rationing are:

1. Internal capital rationing: This occurs when a firm imposes its own restrictions on the amount of capital it can invest, regardless of the availability of funds in the capital market. This can be due to various reasons, such as:

- Dividend policy: A firm may want to maintain a stable dividend payout ratio, which limits the amount of retained earnings it can use for investment.

- Earnings stability: A firm may want to avoid large fluctuations in its earnings per share (EPS), which can affect its stock price and investor confidence. Therefore, it may limit the number of projects it undertakes in any given period.

- Managerial conservatism: A firm may have a conservative approach to risk and uncertainty, and prefer to invest in safe and familiar projects rather than new and innovative ones. This can result in underinvestment and missed opportunities.

- Agency problems: A firm may have conflicts of interest between its managers and shareholders, which can lead to suboptimal investment decisions. For example, managers may have incentives to invest in projects that increase their own power and prestige, rather than those that maximize shareholder value.

2. External capital rationing: This occurs when a firm faces constraints on the amount of capital it can raise from external sources, such as debt and equity. This can be due to various factors, such as:

- Market imperfections: A firm may face market frictions, such as transaction costs, asymmetric information, taxes, and regulations, that increase the cost of external financing and reduce its availability. For example, a firm may have to pay higher interest rates or issue more shares to raise funds from external sources, which can dilute its earnings and ownership.

- Capital market conditions: A firm may face fluctuations in the supply and demand of funds in the capital market, which can affect its access and cost of external financing. For example, during a recession or a financial crisis, the capital market may become tight and risk-averse, and lenders and investors may be reluctant to provide funds to firms, especially those with low credit ratings or high leverage.

- Market timing: A firm may want to take advantage of favorable market conditions, such as low interest rates or high stock prices, to raise funds from external sources. However, these conditions may not last for long, and the firm may miss the opportunity to invest in profitable projects if it delays its financing decision.

capital rationing constraints can have significant implications for the capital evaluation process. A firm that faces capital rationing cannot simply accept all positive net present value (NPV) projects, as it may not have enough funds to finance them. Instead, it has to rank the projects according to some criteria, such as profitability index (PI), internal rate of return (IRR), or payback period, and select the best combination of projects that maximizes the NPV of the firm within the budget constraint. This is known as the capital rationing problem, which can be solved using various methods, such as integer programming, linear programming, or heuristic approaches. However, these methods can be complex and time-consuming, and may not always yield the optimal solution. Therefore, managers should also consider other factors, such as strategic fit, risk, and flexibility, when making capital budgeting decisions under capital rationing.

4. How to select the optimal combination of projects under capital rationing?

In this section, we will discuss some of the techniques that can help us select the optimal combination of projects under capital rationing. Capital rationing is a situation where a firm has a limited amount of funds to invest in various projects, and the demand for funds exceeds the supply. In such a case, the firm has to choose the best projects that maximize its value or profitability, subject to the budget constraint. There are different methods that can be used to rank and select projects under capital rationing, such as:

1. The profitability index (PI) method: This method calculates the ratio of the present value of cash inflows to the initial investment for each project, and ranks them in descending order of PI. The firm then selects the projects with the highest PI until the budget is exhausted. This method is consistent with the net present value (NPV) rule, and ensures that the firm invests in projects that have a positive NPV and a high return per dollar invested. For example, suppose a firm has a budget of $100,000 and three projects to choose from, with the following cash flows:

| Project | Initial Investment | Year 1 | Year 2 | Year 3 | PI |

| A | $50,000 | $20,000 | $25,000 | $30,000 | 1.50 |

| B | $40,000 | $15,000 | $20,000 | $25,000 | 1.38 |

| C | $60,000 | $25,000 | $30,000 | $35,000 | 1.33 |

Using the PI method, the firm would rank the projects as A, B, and C, and select projects A and B, which have a total initial investment of $90,000 and a total PI of 2.88. Project C would be rejected, as it would exceed the budget.

2. The internal rate of return (IRR) method: This method calculates the discount rate that makes the npv of each project equal to zero, and ranks them in descending order of IRR. The firm then selects the projects with the highest IRR until the budget is exhausted. This method is based on the assumption that the firm can reinvest the cash flows from the projects at their respective IRRs, and thus maximizes the growth rate of the firm's capital. However, this method may not always be reliable, as some projects may have multiple IRRs, or no IRR at all. Moreover, this method may not be consistent with the NPV rule, and may lead to suboptimal decisions. For example, suppose the same firm has another project D, with the following cash flows:

| Project | Initial Investment | Year 1 | Year 2 | Year 3 | IRR |

| D | $30,000 | -$10,000 | $40,000 | $10,000 | 25.98% |

Using the IRR method, the firm would rank the projects as D, A, B, and C, and select projects D and A, which have a total initial investment of $80,000 and a total IRR of 41.48%. Project B would be rejected, even though it has a higher NPV and PI than project D. Project C would also be rejected, as it would exceed the budget.

3. The linear programming (LP) method: This method uses mathematical optimization techniques to find the optimal combination of projects that maximizes the firm's NPV, subject to the budget constraint and other possible constraints. This method is more flexible and accurate than the previous methods, as it can handle multiple constraints, such as minimum or maximum investment limits, mutually exclusive or dependent projects, and different risk levels. However, this method may also be more complex and time-consuming, as it requires the formulation of an objective function and a set of constraints, and the use of specialized software or algorithms to solve the problem. For example, suppose the same firm has the following additional information about the projects:

| Project | Risk Level | Minimum Investment | Maximum Investment |

| A | High | $40,000 | $60,000 |

| B | Low | $30,000 | $50,000 |

| C | Medium | $50,000 | $70,000 |

| D | High | $20,000 | $40,000 |

Using the LP method, the firm would formulate the following problem:

Maximize NPV = 50,000 - 50,000 x + 20,000 x (1.1)^-1 + 25,000 x (1.1)^-2 + 30,000 x (1.1)^-3 + 40,000 - 40,000 y + 15,000 y (1.1)^-1 + 20,000 y (1.1)^-2 + 25,000 y (1.1)^-3 + 60,000 - 60,000 z + 25,000 z (1.1)^-1 + 30,000 z (1.1)^-2 + 35,000 z (1.1)^-3 + 30,000 - 30,000 w - 10,000 w (1.1)^-1 + 40,000 w (1.1)^-2 + 10,000 w (1.1)^-3

Subject to:

50,000 x + 40,000 y + 60,000 z + 30,000 w <= 100,000 (budget constraint)

0.4 <= x <= 0.6 (minimum and maximum investment limits for project A)

0.3 <= y <= 0.5 (minimum and maximum investment limits for project B)

0.5 <= z <= 0.7 (minimum and maximum investment limits for project C)

0.2 <= w <= 0.4 (minimum and maximum investment limits for project D)

X, y, z, w are binary variables (mutually exclusive projects)

Where x, y, z, and w are the decision variables that indicate whether to accept or reject projects A, B, C, and D, respectively. The objective function represents the total NPV of the selected projects, and the constraints represent the budget and other limitations. The firm would then use a software or an algorithm to solve this problem and find the optimal values of x, y, z, and w that maximize the NPV. One possible solution is:

X = 0.6, y = 0.3, z = 0, w = 0.4

This means that the firm would invest 60% of project A, 30% of project B, and 40% of project D, and reject project C. The total initial investment would be $96,000, and the total NPV would be $51,614. This solution may be different from the ones obtained by the PI or IRR methods, but it would be the most efficient one, given the constraints.

5. How to apply capital rationing techniques to real-world scenarios?

Capital rationing is a crucial aspect of allocating limited resources among multiple projects using capital evaluation. In this section, we will delve into various examples of capital rationing techniques applied to real-world scenarios. By exploring different perspectives, we can gain valuable insights into how organizations make strategic decisions when faced with resource constraints.

1. Scenario Analysis: One approach to capital rationing is conducting scenario analysis. This involves evaluating different scenarios based on varying resource availability and project requirements. For instance, a company may assess the impact of allocating resources to high-priority projects versus low-priority ones, considering factors such as potential returns, market demand, and strategic alignment.

2. Payback Period: Another technique is to consider the payback period, which measures the time required to recover the initial investment. In the context of capital rationing, organizations may prioritize projects with shorter payback periods to ensure a quicker return on investment. This approach allows them to allocate resources efficiently and minimize the risk of prolonged capital tie-up.

3. Net Present Value (NPV): npv analysis is widely used in capital rationing decisions. It involves calculating the present value of expected cash flows generated by each project and comparing them to the initial investment. Projects with higher NPVs are typically given priority as they offer greater value creation potential. By considering NPV, organizations can make informed decisions about resource allocation and maximize their overall profitability.

4. Internal Rate of Return (IRR): The IRR is another important metric used in capital rationing. It represents the discount rate at which the present value of cash inflows equals the present value of cash outflows. Projects with higher IRRs are generally preferred as they offer higher returns relative to the cost of capital. By incorporating IRR analysis, organizations can prioritize projects that generate the most significant returns within the given resource constraints.

5. Sensitivity Analysis: Sensitivity analysis helps organizations assess the impact of uncertain factors on project outcomes. By conducting "what-if" scenarios, they can identify projects that are more resilient to changes in key variables such as market conditions, costs, or demand. This approach enables organizations to make informed decisions considering potential risks and uncertainties associated with resource allocation.

To illustrate these concepts, let's consider a manufacturing company that is evaluating multiple projects for expansion. The company conducts scenario analysis to assess the impact of allocating resources to projects with different market potentials, production capacities, and expected returns. Based on the analysis, they prioritize projects that align with their long-term growth strategy and offer the highest potential for profitability.

Capital rationing techniques play a vital role in allocating limited resources among multiple projects. By considering scenario analysis, payback period, NPV, IRR, and sensitivity analysis, organizations can make informed decisions that maximize value creation and align with their strategic objectives. These techniques provide a framework for effectively managing resource constraints and optimizing project selection in real-world scenarios.

6. What are the limitations and drawbacks of capital rationing?

Capital rationing is a process of selecting the most profitable projects from a pool of available investment opportunities, subject to a budget constraint. It is often used by firms that have limited financial resources or face borrowing constraints. However, capital rationing also has some limitations and drawbacks that may affect the optimal allocation of resources and the value of the firm. In this section, we will discuss some of the major challenges of capital rationing from different perspectives, such as the shareholders, the managers, and the project evaluators.

Some of the challenges of capital rationing are:

1. Shareholder value maximization: Capital rationing may prevent the firm from undertaking all the positive net present value (NPV) projects, which are the projects that increase the shareholder value. For example, if the firm has a budget of $10 million and three projects with NPVs of $8 million, $6 million, and $4 million, respectively, the firm can only choose two projects under capital rationing. However, the optimal decision is to invest in all three projects, as they have a total NPV of $18 million, which is greater than the budget. By rejecting the third project, the firm is leaving $4 million of value on the table, which reduces the shareholder wealth.

2. Managerial incentives: Capital rationing may create agency problems between the managers and the shareholders, as the managers may have different objectives and preferences than the shareholders. For example, the managers may prefer to invest in safer, lower-return projects that protect their reputation and job security, rather than riskier, higher-return projects that maximize the shareholder value. Alternatively, the managers may favor the projects that benefit their personal interests, such as perks, power, or prestige, rather than the projects that enhance the firm's performance. Capital rationing may exacerbate these conflicts, as the managers have more discretion and influence over the project selection process, and may manipulate the information or the criteria to justify their choices.

3. Project evaluation methods: Capital rationing may require the use of different project evaluation methods than the standard NPV rule, which is the most reliable and consistent method for ranking and selecting projects. For example, the firm may use the profitability index (PI), which is the ratio of the NPV to the initial investment, to rank the projects by their efficiency. However, the PI may not always yield the same ranking as the NPV, especially when the projects have different sizes or timing of cash flows. Moreover, the PI may not be applicable when the projects are mutually exclusive or have multiple investment opportunities. Another method that may be used under capital rationing is the internal rate of return (IRR), which is the discount rate that makes the npv equal to zero. However, the IRR may also have some problems, such as multiple or nonexistent solutions, scale dependency, or reinvestment rate assumption. Therefore, capital rationing may introduce some errors or biases in the project evaluation process, which may lead to suboptimal decisions.

7. What are the other ways to deal with capital constraints?

Capital rationing is a common problem faced by many firms that have limited funds to invest in various projects. Capital rationing means that the firm has to choose the best combination of projects that maximizes its value, subject to the budget constraint. However, capital rationing is not the only way to deal with capital constraints. There are other alternatives that can help the firm to overcome the limitations of capital rationing and achieve its optimal investment decisions. In this section, we will discuss some of these alternatives and their advantages and disadvantages.

Some of the alternatives to capital rationing are:

1. Raising external funds: One way to avoid capital rationing is to raise more funds from external sources, such as debt, equity, or hybrid securities. This can increase the available capital for the firm and allow it to undertake more positive NPV projects. However, raising external funds also has some drawbacks, such as:

- Cost of capital: External funds are not free. The firm has to pay interest on debt, dividends on equity, or both on hybrid securities. This increases the cost of capital for the firm and reduces the NPV of the projects.

- Agency problems: External funds can create agency problems between the managers and the investors. Managers may have different incentives and preferences than the investors, and may not act in the best interest of the firm. For example, managers may take on more risky projects, overinvest in negative NPV projects, or underinvest in positive NPV projects. This can reduce the value of the firm and create conflicts between the parties.

- Financial distress: External funds can also increase the risk of financial distress for the firm. Financial distress occurs when the firm is unable to meet its obligations to the creditors or shareholders. This can result in bankruptcy, liquidation, or restructuring of the firm. Financial distress can have negative consequences for the firm, such as loss of reputation, customers, suppliers, employees, and assets. It can also increase the cost of capital and reduce the NPV of the projects.

2. Dividend policy: Another way to avoid capital rationing is to adjust the dividend policy of the firm. Dividend policy refers to the decision of how much of the earnings to distribute to the shareholders and how much to retain in the firm. By reducing the dividend payout ratio, the firm can increase the retained earnings and use them to finance more projects. However, dividend policy also has some implications, such as:

- Signaling effect: Dividend policy can have a signaling effect on the market. A change in the dividend policy can convey information about the future prospects of the firm. For example, a reduction in the dividend payout ratio can signal that the firm has more profitable investment opportunities, or that the firm is facing financial difficulties. This can affect the market perception and the share price of the firm.

- Clientele effect: dividend policy can also have a clientele effect on the investors. Different investors may have different preferences for dividends, depending on their income, tax, and liquidity needs. For example, some investors may prefer high dividends, while others may prefer low dividends or capital gains. A change in the dividend policy can attract or repel different types of investors, and affect the demand and supply of the shares.

3. Project sequencing: A third way to avoid capital rationing is to sequence the projects over time. Project sequencing means that the firm does not have to invest in all the projects at once, but can spread them over different periods. This can help the firm to match the cash inflows and outflows of the projects, and reduce the need for external funds. However, project sequencing also has some challenges, such as:

- timing risk: Project sequencing can expose the firm to timing risk. Timing risk is the risk that the optimal timing of the projects may change due to unforeseen factors, such as changes in the market conditions, competition, technology, or regulation. This can affect the NPV and the feasibility of the projects. For example, if the firm delays a project, it may lose the first-mover advantage, face higher costs, or face lower demand. On the other hand, if the firm accelerates a project, it may incur higher risks, face lower returns, or face higher competition.

- Flexibility: Project sequencing can also affect the flexibility of the firm. Flexibility is the ability of the firm to adapt to the changing environment and to take advantage of new opportunities. By sequencing the projects, the firm may commit to a certain path of investment, and lose the option to alter or abandon the projects. This can reduce the value of the firm and the projects. For example, if the firm invests in a project that turns out to be unprofitable, it may not be able to exit the project or switch to a better project. On the other hand, if the firm does not invest in a project that turns out to be profitable, it may not be able to enter the project or catch up with the competitors.

8. How to improve the capital rationing process and outcomes?

Capital rationing is the process of selecting the most profitable projects from a pool of investment opportunities, given a limited amount of capital. Capital rationing can be done using various methods, such as net present value (NPV), internal rate of return (IRR), profitability index (PI), or payback period (PP). However, these methods have some limitations and challenges, such as ranking conflicts, scale differences, timing differences, or risk differences. Therefore, it is important to follow some best practices to improve the capital rationing process and outcomes. Here are some of them:

1. Use multiple criteria to evaluate projects. Instead of relying on a single criterion, such as NPV or IRR, it is better to use a combination of criteria that capture different aspects of the projects, such as profitability, liquidity, risk, and strategic fit. This can help to avoid ranking conflicts and select the projects that best align with the company's goals and objectives. For example, a project with a high NPV but a long payback period may not be suitable for a company that needs quick cash flows. Similarly, a project with a high IRR but a low NPV may not be worth investing in if the initial outlay is too large.

2. adjust the discount rate for risk. Different projects have different levels of risk, and this should be reflected in the discount rate used to calculate the NPV or IRR. A higher discount rate means a higher required return and a lower present value. A lower discount rate means a lower required return and a higher present value. Therefore, riskier projects should have a higher discount rate and safer projects should have a lower discount rate. This can help to account for the risk differences among the projects and select the ones that offer the best risk-return trade-off. For example, a project with a high NPV but a high discount rate may not be preferable to a project with a lower NPV but a lower discount rate, if the latter has a lower risk and a more stable cash flow.

3. Consider the interdependencies among the projects. Some projects may have synergies or conflicts with each other, meaning that their cash flows or outcomes may depend on the acceptance or rejection of other projects. For example, two projects may be mutually exclusive, meaning that only one of them can be undertaken. Or, two projects may be complementary, meaning that both of them need to be undertaken to achieve the maximum benefit. Or, two projects may be independent, meaning that their cash flows or outcomes do not affect each other. Therefore, it is important to consider the interdependencies among the projects and select the optimal combination of projects that maximizes the overall value of the portfolio. For example, a project with a low NPV but a high synergy with another project may be worth investing in if the combined NPV of the two projects is higher than the NPV of any other project.

9. What are the key takeaways and recommendations from the blog?

In this blog, we have discussed the concept of capital rationing, which is the process of allocating limited resources among multiple projects using capital evaluation methods. We have also explained the advantages and disadvantages of different methods, such as net present value (NPV), internal rate of return (IRR), profitability index (PI), and payback period (PP). In this section, we will summarize the key takeaways and recommendations from the blog and provide some practical tips for applying capital rationing in real-world scenarios.

Some of the main points to remember are:

- Capital rationing is a common problem faced by many organizations that have more profitable projects than they can fund with their available capital.

- capital rationing can be either hard or soft. Hard capital rationing occurs when the external sources of funding are limited or costly, while soft capital rationing occurs when the internal sources of funding are restricted by the management for various reasons.

- capital evaluation methods are tools that help managers compare and rank different projects based on their expected cash flows and required investments. The most widely used methods are NPV, IRR, PI, and PP.

- NPV is the difference between the present value of the cash inflows and the present value of the cash outflows of a project. It measures the net value added by the project to the firm's wealth. NPV is the most reliable and consistent method of capital evaluation, as it considers the time value of money, the risk of the cash flows, and the opportunity cost of capital.

- irr is the discount rate that makes the NPV of a project equal to zero. It measures the annualized return of the project. IRR is a popular and intuitive method of capital evaluation, as it shows the percentage return of the project. However, IRR has some limitations, such as the possibility of multiple or no IRRs, the scale problem, and the reinvestment rate assumption.

- PI is the ratio of the present value of the cash inflows to the present value of the cash outflows of a project. It measures the profitability of the project per unit of investment. PI is a useful method of capital evaluation, as it shows the relative efficiency of the project. However, PI has some drawbacks, such as the dependence on the discount rate and the ranking problem.

- PP is the time required for the cumulative cash inflows of a project to equal the initial investment. It measures the liquidity of the project. PP is a simple and easy method of capital evaluation, as it shows the break-even point of the project. However, PP has some flaws, such as the ignorance of the time value of money, the cash flows beyond the payback period, and the profitability of the project.

Some of the recommendations for applying capital rationing in practice are:

- Use NPV as the primary criterion for selecting projects, as it maximizes the firm's value and reflects the objective of financial management.

- Use IRR, PI, and PP as supplementary criteria for screening projects, as they provide additional information and insights about the projects.

- Use the incremental IRR approach for choosing between mutually exclusive projects with different scales and lives, as it compares the marginal benefits and costs of the projects.

- Use the profitability index approach for choosing among independent projects with a fixed budget constraint, as it maximizes the NPV per unit of investment.

- Use the payback period approach for choosing projects with high uncertainty and risk, as it reduces the exposure to future losses and enhances the flexibility of the firm.

- Use sensitivity analysis, scenario analysis, and simulation techniques for incorporating the uncertainty and variability of the cash flows and the discount rate into the capital evaluation process, as they provide a range of possible outcomes and probabilities for the projects.