Discount Rate: Unlocking the Secrets of Discount Rate in the Profitability Index Formula

1. Introduction to Discount Rate and Its Importance in Investment Decisions

understanding the discount rate is crucial in the realm of finance, particularly when it comes to making informed investment decisions. It serves as a critical tool for investors and analysts alike, allowing them to determine the present value of future cash flows. The discount rate can be seen as a reflection of the opportunity cost of capital, the risk associated with the investment, and the time value of money. It is the rate at which future cash flows are discounted back to their present value, essentially balancing the risk and time factors against the potential rewards of an investment.

From the perspective of a corporate finance manager, the discount rate is a benchmark for making strategic decisions about capital budgeting. It helps in assessing whether a project will yield a return greater than the cost of capital. For an individual investor, it represents the rate of return they require to make an investment worthwhile, considering alternative options available in the market.

Here's an in-depth look at the importance of the discount rate in investment decisions:

1. Time Value of Money: The concept that money available today is worth more than the same amount in the future due to its potential earning capacity. This core principle of finance holds that, provided money can earn interest, any amount of money is worth more the sooner it is received.

- Example: A sum of $100 received today could be invested to earn interest, making it worth more than $100 received a year from now.

2. Risk Assessment: The discount rate incorporates the risk associated with an investment. Higher risk typically demands a higher discount rate as compensation for the increased uncertainty.

- Example: A startup company might have a higher discount rate compared to a well-established corporation due to the higher perceived risk of the investment.

3. Opportunity Cost: It reflects the return an investor could earn from the next-best alternative investment with a similar risk profile.

- Example: If an investor can receive a 5% return from a risk-free government bond, any riskier investment should offer a higher potential return to justify the additional risk.

4. Inflation: The discount rate accounts for the erosion of purchasing power due to inflation. Future cash flows need to be discounted to reflect their decreased value in today's terms.

- Example: If inflation is expected to be 2% per year, the value of $100 a year from now is effectively less due to the reduced purchasing power.

5. Investment Appraisal: It is used in various investment appraisal techniques such as Net Present Value (NPV) and internal Rate of return (IRR), which are fundamental in determining the viability of projects.

- Example: In NPV calculations, if the present value of cash inflows, discounted at the project's discount rate, exceeds the initial investment, the project is considered profitable.

6. Capital Allocation: Helps companies allocate their capital efficiently by investing in projects that offer the highest returns above the discount rate, thus maximizing shareholder value.

- Example: A company may decide to invest in a new product line only if the projected returns exceed its weighted average cost of capital (WACC), which serves as the discount rate.

The discount rate is a pivotal element in the financial toolkit, guiding investors and businesses in their quest to maximize returns while managing risks. Its multifaceted role in evaluating the time value of money, adjusting for risk, considering inflation, and aiding in strategic capital allocation underscores its significance in shaping investment strategies and decisions. Understanding and applying the correct discount rate is a testament to the savvy investor's or financial manager's acumen in navigating the complex landscape of investment opportunities.

2. A Primer

The Profitability Index (PI), also known as the Profit Investment Ratio (PIR) or Value Investment Ratio (VIR), is a financial metric used to evaluate the attractiveness of an investment or project. It represents the relationship between the benefits and costs of a proposed investment, essentially measuring the bang-for-the-buck provided by the project. The index is calculated by dividing the present value of future cash flows by the initial investment cost. A PI greater than 1 indicates that the net present value (NPV) of future cash flows exceeds the initial investment, suggesting that the investment would add value to the firm and should be considered.

From an investor's perspective, the PI is a handy tool for comparing projects of different scales and complexities. It's particularly useful when available investment funds are limited and choices must be made about which projects to fund.

1. calculation of Profitability index:

The formula for calculating the PI is:

$$ PI = \frac{Present\ Value\ of\ Future\ Cash\ Flows}{Initial\ Investment\ Cost} $$

2. Interpretation of Results:

A PI of:

- > 1 suggests that the investment would generate value and should be considered.

- = 1 indicates a breakeven point where the project generates no additional value.

- < 1 implies that the investment would destroy value and should typically be avoided.

3. Incorporating the Discount Rate:

The discount rate plays a crucial role in the calculation of the PI. It's used to discount future cash flows back to their present value. The choice of discount rate can significantly affect the PI, as it reflects the risk and time value of money.

Example:

Consider a project requiring an initial investment of $100,000 and expected to generate cash flows of $30,000 per year for 5 years. If the discount rate is 10%, the present value of future cash flows would be calculated using the formula for the present value of an annuity:

$$ PV = C \times \left[\frac{1 - (1 + r)^{-n}}{r}\right] $$

Where \( C \) is the annual cash flow, \( r \) is the discount rate, and \( n \) is the number of periods.

4. Advantages of Using Profitability Index:

- It considers the time value of money.

- It's useful for ranking and comparing projects.

- It takes into account the scale of the investment.

5. Limitations of Profitability Index:

- It assumes the reinvestment of cash flows at the discount rate.

- It may not be suitable for mutually exclusive projects if they have different scales.

6. Practical Considerations:

In practice, the PI should be used in conjunction with other financial metrics like NPV, Internal Rate of Return (IRR), and payback period for a comprehensive analysis.

7. Diverse Perspectives on Profitability Index:

- Financial Analysts often favor the PI for its simplicity and direct economic interpretation.

- Project Managers might prefer it for its ability to compare projects of different sizes.

- Investors could use it to gauge the efficiency of their capital allocation.

The Profitability Index is a versatile and valuable tool in the arsenal of financial analysis, providing clear signals about the potential profitability of investments. It allows for a quick comparison across different projects, helping decision-makers to prioritize investments that are likely to yield the best returns relative to their costs. However, it's important to remember that no single financial metric should be used in isolation, and the PI is most effective when used as part of a broader financial analysis strategy.

3. Understanding the Role of Discount Rate in the Profitability Index

The discount rate plays a pivotal role in the calculation of the Profitability Index (PI), serving as a critical factor in determining the present value of future cash flows. It is essentially the rate of return that could be earned on an investment in the financial markets with similar risk or the cost of capital. The PI itself is a ratio, and its formula is given by:

$$ PI = \frac{PV \text{ of Future Cash Flows}}{Initial Investment} $$

Where:

- PV stands for Present Value

- The numerator represents the present value of expected cash flows, discounted at the project's cost of capital or the hurdle rate.

From an investor's perspective, the discount rate is a measure of risk. A higher discount rate implies greater uncertainty and a higher risk associated with the investment's cash flows. This is why riskier projects often require a higher rate of return to justify the investment.

From a managerial standpoint, the discount rate is used to ensure that capital is allocated efficiently, favoring projects that are expected to generate returns above the threshold set by the company's cost of capital.

1. impact of Discount rate on PI:

- A higher discount rate will reduce the present value of future cash flows, potentially lowering the PI.

- Conversely, a lower discount rate increases the present value, which could make an investment appear more attractive.

2. Decision-Making:

- A PI greater than 1 indicates that the NPV (Net Present Value) is positive, and the project should theoretically be accepted.

- A PI less than 1 suggests that the project's NPV is negative, and it should be rejected.

3. Sensitivity Analysis:

- By adjusting the discount rate, managers can perform sensitivity analysis to understand how changes in the rate affect the PI.

- This helps in assessing the robustness of the project's financial viability against interest rate fluctuations.

Example:

Consider a project requiring an initial investment of $100,000, with expected cash flows of $30,000 per year for 5 years. If the discount rate is 10%, the PV of future cash flows can be calculated using the formula for the present value of an annuity:

$$ PV = \frac{C \times (1 - (1 + r)^{-n})}{r} $$

Where:

- C is the annual cash flow ($30,000)

- r is the discount rate (10% or 0.1)

- n is the number of periods (5 years)

The calculated PV of future cash flows would then be compared to the initial investment to determine the PI. If the discount rate were to increase to 15%, the PV would decrease, thus affecting the PI and potentially the decision on whether to proceed with the investment.

understanding the interplay between the discount rate and the Profitability index is crucial for making informed investment decisions. It allows investors and managers to gauge the attractiveness of a project and align their strategies with their financial goals and risk appetite. By carefully selecting the appropriate discount rate, they can ensure that only projects with the potential to add value are pursued.

4. How to Calculate the Discount Rate for Your Investment Project?

calculating the discount rate is a critical step in evaluating the attractiveness of an investment project. It represents the rate of return that could be earned on an investment in the financial markets with similar risk or the cost of capital. The discount rate is used to convert future cash flows from the investment into present value terms, which is essential in determining the viability and profitability of a project. Different stakeholders may view the discount rate differently: investors might consider it as their required rate of return, while for project managers, it could reflect the opportunity cost of capital.

From an investor's perspective, the discount rate is the minimum acceptable return on investment. This rate is often derived from the Weighted average Cost of capital (WACC), which takes into account the cost of equity and debt financing. The WACC is calculated using the formula:

$$ WACC = E/V \times Re + D/V \times Rd \times (1 - Tc) $$

Where:

- \( E \) is the market value of the equity,

- \( V \) is the total market value of equity and debt,

- \( Re \) is the cost of equity,

- \( D \) is the market value of the debt,

- \( Rd \) is the cost of debt,

- \( Tc \) is the corporate tax rate.

For project managers, the discount rate can be seen as the company's hurdle rate, which is the minimum rate that the company expects to earn when investing in new projects. It is often set higher than the WACC to include a margin of safety.

Here are the steps to calculate the discount rate for your investment project:

1. determine the Cost of equity (Re):

- Use the capital Asset Pricing model (CAPM) to estimate the cost of equity:

$$ Re = Rf + \beta \times (Rm - Rf) $$

Where:

- \( Rf \) is the risk-free rate,

- \( \beta \) is the beta of the investment,

- \( Rm \) is the expected market return.

2. calculate the Cost of debt (Rd):

- This can be the current yield on the company's existing debt or the interest rate on new debt.

3. Compute the Proportions of Debt and Equity (D/V and E/V):

- These are based on the market values of debt and equity.

4. Adjust for Taxes (Tc):

- Since interest expenses are tax-deductible, the cost of debt is adjusted by the corporate tax rate.

5. Calculate the WACC:

- Use the WACC formula provided above.

6. Consider Adjustments for Project-Specific Risks:

- Adjust the WACC upwards if the project has higher risk than the company's average project.

7. Use the Discount rate to Discount Future cash Flows:

- Apply the discount rate to the project's expected cash flows to determine the present value.

Example:

Imagine a company with a market value of equity of $500,000 and debt of $300,000. The cost of equity is 8%, the cost of debt is 5%, and the corporate tax rate is 30%. The WACC would be:

$$ WACC = \frac{500,000}{800,000} \times 0.08 + \frac{300,000}{800,000} \times 0.05 \times (1 - 0.30) $$

This would yield a WACC of approximately 6.65%, which would be used as the discount rate for the company's projects.

By understanding and accurately calculating the discount rate, investors and managers can make more informed decisions about which projects to pursue, ensuring that they meet their financial goals and contribute to the company's growth. Remember, the discount rate is not just a number; it's a reflection of the risk, time value of money, and opportunity cost associated with your investment project.

5. The Impact of Varying Discount Rates on Project Valuation

The discount rate is a critical factor in project valuation, acting as the bridge between the future and the present value of cash flows. It reflects the opportunity cost of capital, the risk of the project, and the time value of money. When evaluating a project, varying the discount rate can significantly alter the perceived profitability and viability of an investment. This is because the discount rate directly affects the present value of future cash flows, which are the cornerstone of any valuation method, such as Net Present Value (NPV) or Internal Rate of Return (IRR).

From the perspective of a conservative investor, a higher discount rate is used to reflect the increased risk or uncertainty associated with the project's cash flows. This results in a lower present value, making it less likely for the project to meet the required threshold for investment. Conversely, a more optimistic investor might use a lower discount rate, indicative of a lower perceived risk, thus increasing the present value and potentially making the project appear more attractive.

1. Influence on NPV and IRR:

The Net Present Value (NPV) of a project is calculated by discounting the expected cash flows to their present value and subtracting the initial investment. As the discount rate increases, the NPV decreases, and vice versa. Similarly, the Internal Rate of Return (IRR) is the discount rate at which the NPV equals zero. A project with cash flows that can withstand higher discount rates before the NPV turns negative is generally considered more robust.

Example: Consider a project with an initial investment of $100,000 and expected annual cash flows of $30,000 for five years. At a discount rate of 5%, the NPV is positive, suggesting the project is viable. However, if the discount rate is increased to 10%, the NPV may turn negative, indicating the project is not financially feasible.

2. risk Assessment and management:

Varying discount rates can be used as a tool for risk assessment. By applying different rates, analysts can simulate various scenarios and gauge the project's sensitivity to changes in the cost of capital, market conditions, and other uncertainties.

Example: A real estate development project may have a base-case discount rate of 8%. However, due to market volatility, a sensitivity analysis is performed using rates of 6% and 10%. The analysis shows that the project is highly sensitive to interest rate fluctuations, signaling higher risk.

3. strategic Decision making:

The choice of discount rate can influence strategic decisions such as project selection, capital allocation, and mergers and acquisitions. It can prioritize projects that align with the company's risk profile and long-term objectives.

Example: A company with a low-risk tolerance might favor projects with stable cash flows that remain profitable even at higher discount rates, such as utility or infrastructure projects, over more speculative ventures like tech startups.

4. impact on Profitability index (PI):

The Profitability Index (PI) is the ratio of the present value of future cash flows to the initial investment. A PI greater than 1 indicates a desirable project. The discount rate's impact on PI is direct; as the rate increases, the PI typically decreases.

Example: A project with expected cash flows that have a present value of $120,000 and an initial investment of $100,000 has a PI of 1.2 at a discount rate of 5%. If the discount rate rises to 7%, the present value might drop to $110,000, reducing the PI to 1.1.

The discount rate is not just a number; it embodies the investor's attitude towards risk, time, and value. It is a powerful variable that can shape the fate of projects, and understanding its impact is essential for making informed investment decisions. By considering different viewpoints and conducting thorough analyses, investors and analysts can better navigate the complexities of project valuation.

6. Discount Rate Analysis in Real-World Scenarios

In the realm of finance, the discount rate is a pivotal factor in determining the present value of future cash flows. It reflects the time value of money, indicating how much future cash flows are worth today. This concept is particularly crucial when assessing investment opportunities, where the profitability index formula comes into play, guiding investors to make informed decisions. The formula, which is the ratio of the present value of future cash flows to the initial investment, hinges on the discount rate to evaluate an investment's efficiency. A profitability index greater than 1 suggests a good investment, as it indicates that the present value of returns exceeds the cost.

Case studies in various real-world scenarios provide a rich source of insights into how the discount rate is applied and its impact on investment decisions. Here are some in-depth analyses:

1. public Infrastructure projects: Governments often use a lower discount rate for public projects to reflect the long-term benefits and societal value. For instance, the construction of a new highway may have a discount rate of 3-4%, considering the extended time horizon and the project's contribution to economic growth.

2. Technology Startups: high-growth potential startups might be evaluated with a higher discount rate, say 12-15%, due to the higher risk and uncertainty associated with their future cash flows. An example is a tech startup in the renewable energy sector, where the initial years may not generate profit, but the long-term prospects are promising.

3. real estate Development: In real estate, the discount rate can vary significantly based on location, market trends, and project specifics. A luxury residential development in a prime urban area might use a 7% discount rate, reflecting the stable demand and premium pricing potential.

4. Pharmaceuticals: The pharmaceutical industry often faces long development cycles and regulatory hurdles. A new drug development project might use a discount rate of 10-11%, balancing the high costs of research and development against the potential for substantial future earnings upon successful market entry.

5. Energy Sector: Traditional energy projects like oil and gas exploration might use a discount rate of 8-10%, considering the volatility in commodity prices and regulatory environment. In contrast, renewable energy projects might opt for a slightly lower rate, aligning with global shifts towards sustainable energy sources.

These case studies illustrate the nuanced application of the discount rate across different industries and projects. The choice of rate is influenced by factors such as risk, time horizon, and the nature of the cash flows. By examining these examples, investors and analysts can gain a deeper understanding of how the discount rate shapes the assessment of an investment's present value and its subsequent classification as a potentially profitable venture. The interplay between the discount rate and the profitability index formula is a testament to the intricate dance of numbers that underpins financial decision-making.

7. Adjusting Discount Rates for Risk and Inflation

When evaluating investment opportunities, the discount rate is a critical factor in the profitability index formula, serving as a tool to account for the time value of money. However, the basic discount rate often needs adjustment to accurately reflect the additional risks and the impact of inflation. These adjustments are not just about altering a percentage point here or there; they require a nuanced understanding of the investment environment and the specific risks associated with the project. From the perspective of a conservative investor, the risk might be paramount, leading to a higher adjustment, while an aggressive investor might prioritize growth potential over risk, resulting in a lower adjustment. Similarly, an economist might adjust the discount rate based on expected inflation rates, which can erode the value of future cash flows.

Here are some advanced techniques for adjusting discount rates:

1. risk-Adjusted Discount rate (RADR): This method involves increasing the discount rate to compensate for the risk associated with the investment. For example, if the base discount rate is 5% and the investment carries a significant risk, the RADR might be set at 7%. The formula for RADR is typically expressed as:

$$ RADR = R_f + \beta \times (R_m - R_f) $$

Where \( R_f \) is the risk-free rate, \( \beta \) is the beta coefficient reflecting the investment's volatility compared to the market, and \( R_m \) is the expected market return.

2. Country Risk Premiums: For investments in foreign countries, especially those with unstable political or economic environments, a country risk premium is added to the discount rate. This premium compensates for the risk of investing in a different country, which might include factors like currency risk, political instability, and differing legal systems.

3. Inflation Premium: Inflation can significantly affect the purchasing power of future cash flows. To account for this, an inflation premium is added to the discount rate. If the expected inflation rate is 2%, and the base discount rate is 5%, the adjusted rate would be 7%.

4. Size Premium: Smaller companies often carry more risk than larger, more established companies. To account for this, a size premium may be added to the discount rate for investments in small-cap stocks or small private companies.

5. Liquidity Premium: Investments that are not easily converted into cash without a significant loss in value may require a liquidity premium. This premium compensates investors for the added risk of not being able to quickly liquidate the investment.

Example:

Consider a company evaluating a potential project in a country with high inflation and political risk. The base discount rate is 5%, the expected inflation rate is 4%, and the country risk premium is estimated at 3%. The adjusted discount rate would be calculated as follows:

$$ Adjusted\ Discount\ rate = Base\ rate + Inflation\ Premium + Country\ Risk\ Premium $$

$$ Adjusted\ Discount\ Rate = 5\% + 4\% + 3\% = 12\% $$

This adjusted discount rate would then be used in the profitability index formula to determine the present value of the project's cash flows, ensuring that the investment is evaluated with a comprehensive view of all potential risks and the impact of inflation. By incorporating these advanced techniques, investors and analysts can make more informed decisions that better reflect the true cost of capital.

8. Common Pitfalls in Selecting the Appropriate Discount Rate

Selecting the appropriate discount rate is a critical step in evaluating investment opportunities and financial models. It is the rate of return used in a discounted cash flow (DCF) analysis to determine the present value of future cash flows. While it may seem straightforward, the process is fraught with complexities and potential missteps that can significantly impact the outcome of a financial analysis. Different stakeholders may view the discount rate from various perspectives, leading to a range of acceptable rates rather than a single definitive figure. For instance, investors might prefer a higher rate to ensure a buffer for their risk, while project managers might advocate for a lower rate to make their projects appear more attractive.

Here are some common pitfalls to avoid when selecting the discount rate:

1. Overlooking Project-Specific Risks: Each project has unique risks that should be reflected in the discount rate. For example, a startup in a volatile industry should have a higher discount rate than a stable, established company.

2. Ignoring Market Conditions: Economic indicators such as inflation rates, interest rates, and market volatility should influence the discount rate. During periods of high inflation, a higher rate should be used to account for the decreased purchasing power of future cash flows.

3. Misjudging Opportunity Cost: The discount rate should also represent the opportunity cost of capital, which is the return that investors could earn from an alternative investment with a similar risk profile. If an investor can earn 5% from a risk-free government bond, then a riskier investment should offer a higher potential return to be considered worthwhile.

4. Failing to Reassess Over Time: The discount rate is not static and should be reassessed periodically to reflect changes in the business environment and risk profile. A company that has significantly reduced its debt, for example, might warrant a lower discount rate than it did in the past.

5. Using a Single Rate for Diverse Projects: Different projects may have different risk profiles and cash flow patterns, which should be reflected in varying discount rates. Using a single rate across the board can lead to incorrect valuations.

6. Neglecting to Benchmark: It's important to compare the chosen discount rate with industry standards and the rates used by competitors. This helps ensure that the rate is not out of line with what is considered reasonable by others in the market.

7. Overreliance on historical data: While historical data can provide a starting point, relying solely on it without considering current and future expectations can lead to an inappropriate discount rate.

8. Underestimating the Impact of Taxation: Taxes can significantly affect the net cash flows and should be considered when determining the discount rate. For instance, if a project generates taxable income, the discount rate should be adjusted to reflect the after-tax return required by investors.

9. Confusing the discount rate with the Interest Rate: Although related, the discount rate and the interest rate are not the same. The discount rate includes the interest rate plus additional premiums for risk and other factors.

10. Lack of Transparency: When presenting financial models to stakeholders, it's crucial to clearly explain how the discount rate was determined and the assumptions behind it. This transparency builds trust and aids in the decision-making process.

Example: Consider a company evaluating two projects: one involves expanding into a new market, and the other is upgrading existing equipment. The expansion project is high-risk and should have a higher discount rate to reflect potential challenges such as unfamiliar regulatory environments and market acceptance. In contrast, the equipment upgrade is a lower-risk project that primarily involves efficiency improvements and cost savings, justifying a lower discount rate.

The selection of the discount rate is not merely a technical exercise but a strategic decision that requires careful consideration of numerous factors. By avoiding these common pitfalls, financial analysts can ensure a more accurate and reliable valuation, leading to better-informed investment decisions. Remember, the goal is not to find a 'correct' discount rate but to choose a rate that best reflects the project's risk and aligns with the company's financial strategy.

9. Strategic Implications of Discount Rate on Long-Term Profitability

The strategic implications of the discount rate on long-term profitability cannot be overstated. As the rate at which future cash flows are discounted back to the present value, the discount rate serves as a critical factor in the assessment of investment projects and business ventures. It is the investor's yardstick for measuring the time value of money, risk, and the opportunity cost of capital. From a financial perspective, a higher discount rate reflects greater risk and/or a higher opportunity cost of capital, leading to a more stringent evaluation of potential projects. Conversely, a lower discount rate suggests a less risky environment or a lower opportunity cost, potentially making more projects appear attractive.

From the standpoint of a CFO, the discount rate is a tool for balancing risk and growth. A conservative approach might favor a higher rate, safeguarding against over-optimism in cash flow projections. On the other hand, an aggressive growth strategy might justify a lower rate, reflecting confidence in the company's ability to generate future revenue.

Investors view the discount rate through a different lens. For them, it represents the minimum acceptable return on an investment. It's a benchmark that investments must exceed to be considered viable. A venture capitalist, for example, might require a high discount rate to compensate for the high risk associated with early-stage companies.

Economists might analyze the discount rate's impact on an industry-wide scale, considering how changes in the rate influence overall investment trends. A lower discount rate could stimulate investment by making more projects meet the profitability threshold.

Let's delve deeper with a numbered list:

1. Risk Assessment: The discount rate is intrinsically linked to risk. Higher rates are often applied to projects with uncertain cash flows to account for the risk of not achieving projected returns.

2. Opportunity Cost: It reflects the returns that could be earned from the next best alternative investment. This is particularly relevant for companies with limited capital; choosing where to invest becomes a strategic decision influenced by the discount rate.

3. Time Value of Money: This principle states that a dollar today is worth more than a dollar tomorrow. The discount rate quantifies this concept, affecting long-term profitability calculations.

4. Project Viability: The Net Present Value (NPV) of a project, calculated using the discount rate, determines whether a project is worth pursuing. A positive NPV indicates a profitable venture, while a negative NPV suggests otherwise.

5. Inflation: The discount rate often includes an inflation premium to ensure that future cash flows are not overvalued in today's terms.

To illustrate these points, consider a renewable energy company evaluating the installation of new solar panels. The project requires significant upfront investment, and the cash flows are spread over many years. If the company uses a discount rate that's too low, it may underestimate the risk and overestimate the project's profitability. Conversely, a rate that's too high could lead the company to pass on a project that could have been beneficial in the long run.

The strategic use of the discount rate is a powerful lever in steering a company towards long-term profitability. It requires a delicate balance between risk, opportunity cost, and the time value of money, all of which must be carefully considered to make sound investment decisions. The discount rate is not just a number; it's a reflection of a company's strategic direction and its tolerance for risk.

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