Capital Budgeting Techniques: How to Compare and Contrast the Different Capital Budgeting Techniques

1. Introduction to Capital Budgeting Techniques

capital budgeting techniques are methods of evaluating and comparing the profitability of different investment projects. They help managers and investors decide which projects to undertake and which ones to reject. Capital budgeting techniques can be classified into two broad categories: discounted cash flow (DCF) methods and non-discounted cash flow methods.

- DCF methods use the concept of time value of money to calculate the present value of future cash flows generated by an investment project. They compare the present value of cash inflows with the present value of cash outflows to determine the net present value (NPV) of the project. The NPV is the difference between the present value of cash inflows and the present value of cash outflows. A positive NPV indicates that the project is profitable and should be accepted, while a negative NPV indicates that the project is unprofitable and should be rejected. The higher the NPV, the more desirable the project is. Some of the common DCF methods are:

1. Net present value (NPV): This is the most widely used and preferred DCF method. It calculates the NPV of a project by discounting the cash flows at a required rate of return or hurdle rate. The hurdle rate is the minimum acceptable rate of return that an investor or a firm expects from an investment project. It reflects the risk and opportunity cost of investing in the project. The NPV formula is:

$$\text{NPV} = \sum_{t=0}^n \frac{C_t}{(1 + r)^t} - C_0$$

Where $C_t$ is the net cash flow in period $t$, $r$ is the hurdle rate, and $C_0$ is the initial investment or cost of the project. For example, suppose a project requires an initial investment of \$10,000 and generates cash flows of \$3,000, \$4,000, \$5,000, and \$6,000 in the next four years. The hurdle rate is 10%. The NPV of the project is:

$$\text{NPV} = \frac{3,000}{(1 + 0.1)^1} + \frac{4,000}{(1 + 0.1)^2} + \frac{5,000}{(1 + 0.1)^3} + \frac{6,000}{(1 + 0.1)^4} - 10,000$$

$$\text{NPV} = 2,727.27 + 3,305.79 + 3,756.14 + 4,058.64 - 10,000$$

$$\text{NPV} = \$3,847.84$$

Since the NPV is positive, the project is profitable and should be accepted.

2. internal rate of return (IRR): This is another popular DCF method. It calculates the break-even rate of return of a project. The IRR is the discount rate that makes the NPV of a project equal to zero. It represents the actual or expected rate of return of the project. A project is acceptable if its irr is greater than or equal to the hurdle rate, and unacceptable if its irr is less than the hurdle rate. The higher the IRR, the more desirable the project is. The IRR formula is:

$$\text{NPV} = \sum_{t=0}^n \frac{C_t}{(1 + \text{IRR})^t} - C_0 = 0$$

Where $C_t$ is the net cash flow in period $t$, $\text{IRR}$ is the internal rate of return, and $C_0$ is the initial investment or cost of the project. The IRR cannot be solved algebraically and has to be found by trial and error or using a calculator or spreadsheet. For example, using the same project as above, the IRR can be found by plugging in different values of $\text{IRR}$ until the NPV is zero. One possible value of $\text{IRR}$ is 36.02%. The NPV of the project at this rate is:

$$\text{NPV} = \frac{3,000}{(1 + 0.3602)^1} + \frac{4,000}{(1 + 0.3602)^2} + \frac{5,000}{(1 + 0.3602)^3} + \frac{6,000}{(1 + 0.3602)^4} - 10,000$$

$$\text{NPV} = 2,205.47 + 2,163.93 + 1,912.15 + 1,718.45 - 10,000$$

$$\text{NPV} = \text{-0.01}$$

Since the IRR is greater than the hurdle rate of 10%, the project is profitable and should be accepted.

3. Profitability index (PI): This is a variation of the NPV method. It calculates the ratio of the present value of cash inflows to the present value of cash outflows of a project. It measures the profit per unit of investment of a project. A project is acceptable if its PI is greater than or equal to one, and unacceptable if its PI is less than one. The higher the PI, the more desirable the project is. The PI formula is:

$$\text{PI} = \frac{\sum_{t=1}^n \frac{C_t}{(1 + r)^t}}{C_0}$$

Where $C_t$ is the net cash flow in period $t$, $r$ is the hurdle rate, and $C_0$ is the initial investment or cost of the project. For example, using the same project as above, the PI of the project is:

$$\text{PI} = \frac{\frac{3,000}{(1 + 0.1)^1} + \frac{4,000}{(1 + 0.1)^2} + \frac{5,000}{(1 + 0.1)^3} + \frac{6,000}{(1 + 0.1)^4}}{10,000}$$

$$\text{PI} = \frac{2,727.27 + 3,305.79 + 3,756.14 + 4,058.64}{10,000}$$

$$\text{PI} = 1.3848$$

Since the PI is greater than one, the project is profitable and should be accepted.

- Non-DCF methods do not use the concept of time value of money to evaluate investment projects. They use simple accounting or financial ratios to measure the profitability or performance of a project. They ignore the timing and risk of cash flows and may lead to erroneous decisions. Some of the common non-DCF methods are:

1. Payback period (PP): This is the simplest and most widely used non-DCF method. It calculates the number of years it takes for a project to recover its initial investment or cost. It measures the liquidity or speed of recovery of a project. A project is acceptable if its PP is less than or equal to a pre-determined cutoff period, and unacceptable if its PP is greater than the cutoff period. The lower the PP, the more desirable the project is. The PP formula is:

$$\text{PP} = \frac{C_0}{\text{Average annual cash flow}}$$

Where $C_0$ is the initial investment or cost of the project, and $\text{Average annual cash flow}$ is the average of the net cash flows over the life of the project. For example, using the same project as above, the PP of the project is:

$$\text{PP} = \frac{10,000}{\frac{3,000 + 4,000 + 5,000 + 6,000}{4}}$$

$$\text{PP} = \frac{10,000}{4,500}$$

$$\text{PP} = 2.22 \text{ years}$$

If the cutoff period is 3 years, the project is acceptable and should be accepted. If the cutoff period is 2 years, the project is unacceptable and should be rejected.

2. accounting rate of return (ARR): This is another common non-DCF method. It calculates the ratio of the average accounting profit to the average book value of the investment. It measures the return on investment or profitability of a project. A project is acceptable if its ARR is greater than or equal to a pre-determined minimum rate, and unacceptable if its ARR is less than the minimum rate. The higher the ARR, the more desirable the project is. The ARR formula is:

$$\text{ARR} = \frac{\text{Average annual accounting profit}}{\text{Average book value of investment}}$$

Where $\text{Average annual accounting profit}$ is the average of the accounting profits (net income) over the life of the project, and $\text{Average book value of investment}$ is the average of the book values (net assets) of the project at the beginning and end of each year.

2. Payback Period Method

The payback period method is one of the simplest and most widely used capital budgeting techniques. It measures how long it takes for a project to recover its initial investment by generating positive cash flows. The payback period method is often used as a screening tool to eliminate projects that take too long to pay back or have uncertain cash flows. However, the payback period method also has some limitations and drawbacks that need to be considered. In this section, we will discuss the following aspects of the payback period method:

1. How to calculate the payback period. The payback period is calculated by dividing the initial investment by the annual cash flow of the project. For example, if a project costs $100,000 and generates $20,000 of cash flow per year, the payback period is 5 years ($100,000 / $20,000). If the cash flows are not constant, the payback period is calculated by adding up the cash flows until the cumulative sum equals the initial investment. For example, if a project costs $100,000 and generates $10,000, $15,000, $25,000, $30,000, and $35,000 of cash flow in the first five years, the payback period is 3.8 years ($10,000 + $15,000 + $25,000 + $30,000 = $80,000 in 3 years, and $20,000 / $35,000 = 0.8 year in the fourth year).

2. How to interpret the payback period. The payback period indicates the risk and liquidity of a project. A shorter payback period means that the project recovers its initial investment faster, which reduces the risk of losing money and increases the liquidity of the funds. A longer payback period means that the project takes longer to break even, which increases the risk of failure and decreases the liquidity of the funds. Generally, a project is accepted if its payback period is less than or equal to a predetermined cutoff period, which reflects the management's preference and tolerance for risk and liquidity. For example, if the cutoff period is 4 years, a project with a payback period of 3 years is accepted, while a project with a payback period of 5 years is rejected.

3. How to compare the payback period with other capital budgeting techniques. The payback period method has some advantages and disadvantages compared to other capital budgeting techniques, such as the net present value (NPV), the internal rate of return (IRR), and the profitability index (PI). Some of the advantages are:

- The payback period method is easy to understand and apply, as it does not require complex calculations or assumptions.

- The payback period method is useful for evaluating projects with high uncertainty or volatility, as it focuses on the early cash flows that are more predictable and reliable.

- The payback period method is consistent with the goal of maximizing the shareholders' wealth, as it favors projects that generate cash flows sooner rather than later.

Some of the disadvantages are:

- The payback period method ignores the time value of money, as it does not discount the future cash flows to reflect their present value.

- The payback period method ignores the cash flows that occur after the payback period, as it does not consider the total profitability or return of the project.

- The payback period method is arbitrary and subjective, as it depends on the choice of the cutoff period, which may vary from project to project or from firm to firm.

3. Net Present Value (NPV) Method

Net Present Value (NPV) Method is a crucial capital budgeting technique used to evaluate the profitability of an investment project. In this section, we will delve into the concept of NPV and its significance in decision-making.

1. NPV Overview:

The NPV method takes into account the time value of money by discounting future cash flows to their present value. It compares the present value of cash inflows with the present value of cash outflows associated with an investment project. The goal is to determine whether the project will generate positive or negative net cash flows.

2. Calculation of NPV:

To calculate NPV, we subtract the initial investment cost from the present value of expected cash inflows. The present value is determined by discounting future cash flows using an appropriate discount rate, such as the cost of capital or the required rate of return. If the NPV is positive, it indicates that the project is expected to generate more cash inflows than the initial investment, making it financially viable.

3. Decision Rule:

The decision rule for NPV is straightforward. If the NPV is positive, the project is considered financially attractive and should be pursued. Conversely, if the NPV is negative, it suggests that the project may not generate sufficient returns to cover the initial investment and should be rejected. The higher the positive NPV, the more financially lucrative the project is deemed to be.

4. Advantages of NPV:

- Incorporates the time value of money: NPV recognizes that a dollar received in the future is worth less than a dollar received today due to factors like inflation and opportunity cost.

- Considers all cash flows: NPV accounts for both positive and negative cash flows throughout the project's life, providing a comprehensive evaluation.

- Considers the required rate of return: By discounting cash flows at the appropriate rate, NPV reflects the project's risk and return profile.

5. Limitations of NPV:

- Subjectivity in discount rate selection: The choice of discount rate can vary, leading to different NPV outcomes. It requires careful consideration and analysis.

- Ignores non-monetary factors: NPV focuses solely on financial aspects and may overlook qualitative factors like environmental impact or social benefits.

Example:

Let's consider a hypothetical investment project with an initial cost of $100,000. The expected cash inflows over a five-year period are $30,000, $35,000, $40,000, $45,000, and $50,000, respectively. Using a discount rate of 10%, we can calculate the present value of each cash inflow and subtract the initial cost to determine the NPV.

1. Calculate the present value of each cash inflow:

Year 1: $30,000 / (1 + 0.10)^1 = $27,273

Year 2: $35,000 / (1 + 0.10)^2 = $28,512

Year 3: $40,000 / (1 + 0.10)^3 = $30,579

Year 4: $45,000 / (1 + 0.10)^4 = $32,344

Year 5: $50,000 / (1 + 0.10)^5 = $33,057

2. Calculate the NPV:

NPV = present value of cash inflows - initial cost

NPV = ($27,273 + $28,512 + $30,579 + $32,344 + $33,057) - $100,000

NPV = $151,765 - $100,000

NPV = $51,765

Based on the positive NPV of $51,765, we can conclude that the investment project is financially viable and should be considered.

4. Internal Rate of Return (IRR) Method

The internal rate of return (IRR) method is one of the most popular and widely used capital budgeting techniques. It is based on the concept of discounting cash flows to find the rate of return that makes the net present value (NPV) of a project equal to zero. The IRR is the interest rate that equates the present value of the expected cash inflows with the present value of the expected cash outflows of a project. In other words, it is the rate of return that the project earns over its life. The IRR method has some advantages and disadvantages that need to be considered before applying it to a capital budgeting decision. Here are some of the main points to keep in mind:

1. The IRR method is easy to understand and communicate. It expresses the profitability of a project as a single percentage figure that can be compared with other projects or the cost of capital. It also appeals to the intuition of managers and investors who prefer to see the rate of return rather than the absolute value of a project.

2. The IRR method assumes that the cash flows of the project are reinvested at the same rate as the IRR. This may not be realistic, especially if the IRR is very high or very low. A more realistic assumption is that the cash flows are reinvested at the cost of capital or the opportunity cost of capital. This is why some analysts prefer to use the modified internal rate of return (MIRR) method, which adjusts the irr for the reinvestment rate.

3. The IRR method may not always give a unique or clear answer. Sometimes, a project may have more than one IRR, which is called multiple IRRs. This happens when the project has non-conventional cash flows, such as negative cash flows followed by positive cash flows or vice versa. In this case, the IRR method may not be able to rank the project correctly. Another problem is that the IRR method may not agree with the NPV method, which is considered the most reliable capital budgeting technique. This is called the ranking problem or the IRR-NPV conflict. It occurs when the projects have different sizes, lives, or timing of cash flows. In this case, the IRR method may favor a project with a higher IRR but a lower NPV, or vice versa.

4. The IRR method can be applied to different types of projects, such as independent, mutually exclusive, or contingent projects. However, the IRR method has some limitations and challenges in each case. For independent projects, the IRR method can accept or reject a project based on whether the IRR is higher or lower than the cost of capital. However, the IRR method may not be able to rank the projects correctly if they have different IRRs and NPVs. For mutually exclusive projects, the IRR method can rank the projects based on their IRRs, but it may not agree with the NPV method if the projects have different sizes, lives, or timing of cash flows. For contingent projects, the IRR method may not be able to capture the interdependencies and uncertainties of the projects, and it may ignore the option value of the projects.

5. The IRR method can be illustrated with some examples. Suppose a project requires an initial investment of $10,000 and generates cash inflows of $4,000, $5,000, and $6,000 in the next three years. The cost of capital is 10%. To find the IRR of the project, we need to solve the following equation:

$$0 = -10,000 + \frac{4,000}{(1+IRR)} + \frac{5,000}{(1+IRR)^2} + \frac{6,000}{(1+IRR)^3}$$

Using a financial calculator or a spreadsheet, we can find that the IRR of the project is 18.42%. Since the IRR is higher than the cost of capital, the project is acceptable. The NPV of the project is $1,840.40, which confirms that the project is profitable.

Now suppose another project requires an initial investment of $20,000 and generates cash inflows of $10,000, $12,000, and $15,000 in the next three years. The cost of capital is still 10%. The IRR of the project is 20.49%, which is higher than the IRR of the first project. However, the NPV of the project is $3,604.88, which is lower than the NPV of the first project. This is an example of the ranking problem or the IRR-NPV conflict. The IRR method favors the second project, while the NPV method favors the first project. The reason for the conflict is that the projects have different sizes and timing of cash flows. The second project has a larger initial investment and a later payback period than the first project. To resolve the conflict, we can use the incremental IRR method, which compares the IRR of the difference between the two projects. The incremental IRR of the second project over the first project is 12.49%, which is higher than the cost of capital. Therefore, the second project is preferred over the first project. The NPV of the difference between the two projects is $1,764.48, which confirms that the second project is more valuable than the first project.

5. Profitability Index (PI) Method

The Profitability Index (PI) Method is a capital budgeting technique used to evaluate investment projects based on their profitability. It is a ratio that measures the present value of future cash flows generated by a project relative to the initial investment. The higher the PI, the more profitable the project is considered.

From a financial perspective, the PI method provides valuable insights into the potential return on investment. It takes into account the time value of money by discounting future cash flows back to their present value. This allows decision-makers to assess the profitability of a project in today's dollars.

Here are some key points to consider when using the PI method:

1. Calculation: The PI is calculated by dividing the present value of future cash flows by the initial investment. The formula is as follows:

PI = present Value of Cash Flows / initial Investment

2. Interpretation: A PI greater than 1 indicates that the project is expected to generate positive net present value (NPV) and is considered financially viable. On the other hand, a PI less than 1 suggests that the project may not generate sufficient returns to cover the initial investment.

3. Decision Rule: The decision rule for the PI method is to accept projects with a PI greater than 1 and reject projects with a PI less than 1. This rule ensures that the investment generates a positive return and adds value to the organization.

4. Advantages: The PI method has several advantages. Firstly, it considers the time value of money, providing a more accurate assessment of profitability. Secondly, it allows for easy comparison of different investment projects by using a standardized ratio. Lastly, it considers all cash flows throughout the project's life, providing a comprehensive evaluation.

5. Limitations: Like any capital budgeting technique, the PI method has its limitations. It assumes that cash flows can be accurately estimated, which may not always be the case. Additionally, it does not consider the project's size or the timing of cash flows, which can impact the overall profitability.

To illustrate the concept, let's consider an example. Suppose a company is evaluating two investment projects: Project A and Project B. Project A requires an initial investment of $100,000 and is expected to generate a present value of cash flows of $150,000. Project B, on the other hand, requires an initial investment of $200,000 and is expected to generate a present value of cash flows of $250,000.

Calculating the PI for Project A:

PI = $150,000 / $100,000 = 1.5

Calculating the PI for Project B:

PI = $250,000 / $200,000 = 1.25

Based on the PI values, both projects have a PI greater than 1, indicating that they are financially viable. However, Project A has a higher PI, suggesting that it may be more profitable compared to Project B.

The Profitability Index (PI) Method is a valuable tool in capital budgeting that helps assess the profitability of investment projects. By considering the present value of cash flows and the initial investment, decision-makers can make informed choices about which projects to pursue.

6. Accounting Rate of Return (ARR) Method

The accounting rate of return (ARR) method is one of the simplest and most widely used techniques for evaluating the profitability of a capital investment project. It measures the average annual income generated by the project as a percentage of the initial or average investment. The ARR method is also known as the return on investment (ROI) or return on capital employed (ROCE) method. The ARR method has some advantages and disadvantages that need to be considered before applying it to a capital budgeting decision. In this section, we will discuss the following aspects of the ARR method:

1. How to calculate the ARR for a project

2. The advantages and disadvantages of the ARR method

3. The criteria for accepting or rejecting a project based on the ARR method

4. The limitations and challenges of the ARR method

5. How to compare the ARR method with other capital budgeting techniques

### 1. How to calculate the ARR for a project

The basic formula for calculating the ARR for a project is:

$$\text{ARR} = \frac{\text{Average annual income}}{\text{Initial or average investment}} \times 100\%$$

The average annual income is the net income or cash flow generated by the project after deducting depreciation and taxes. The initial or average investment is the amount of money invested in the project at the beginning or over the life of the project. There are two ways to calculate the average investment:

- Initial investment method: This method uses the initial cost of the project as the denominator in the ARR formula. This method is simpler and more conservative, but it ignores the fact that the investment value decreases over time due to depreciation.

- Average investment method: This method uses the average book value of the project as the denominator in the ARR formula. The average book value is calculated by adding the initial and final book values of the project and dividing by two. This method is more realistic and accurate, but it requires more information and calculation.

For example, suppose a company is considering investing in a project that costs $100,000 and has a useful life of five years. The project is expected to generate the following net income and book values over its life:

| Year | Net Income | Book Value |

| 1 | $30,000 | $80,000 | | 2 | $25,000 | $60,000 | | 3 | $20,000 | $40,000 | | 4 | $15,000 | $20,000 | | 5 | $10,000 | $0 |

Using the initial investment method, the ARR for the project is:

$$\text{ARR} = \frac{\text{Average annual income}}{\text{Initial investment}} \times 100\%$$

$$\text{ARR} = \frac{($30,000 + $25,000 + $20,000 + $15,000 + $10,000) / 5}{\$100,000} \times 100\%$$

$$\text{ARR} = \frac{\$20,000}{\$100,000} \times 100\%$$

$$\text{ARR} = 20\%$$

Using the average investment method, the ARR for the project is:

$$\text{ARR} = \frac{\text{Average annual income}}{\text{Average investment}} \times 100\%$$

$$\text{ARR} = \frac{($30,000 + $25,000 + $20,000 + $15,000 + $10,000) / 5}{(\$100,000 + \$0) / 2} \times 100\%$$

$$\text{ARR} = \frac{\$20,000}{\$50,000} \times 100\%$$

$$\text{ARR} = 40\%$$

As we can see, the ARR method gives different results depending on the choice of the investment base. The average investment method gives a higher ARR than the initial investment method, because it considers the declining value of the investment over time.

### 2. The advantages and disadvantages of the ARR method

The ARR method has some advantages and disadvantages that need to be weighed before applying it to a capital budgeting decision. Some of the advantages are:

- Simplicity: The ARR method is easy to understand and calculate, as it uses the familiar concepts of income and investment. It does not require any complex mathematical or financial techniques, such as discounting or compounding.

- Consistency: The ARR method is consistent with the accounting principles and standards, as it uses the net income and book value data from the financial statements. It also reflects the impact of depreciation and taxes on the project's profitability.

- Comprehensiveness: The ARR method considers the entire life of the project, not just a single period or a specific cash flow. It captures the average performance of the project over its useful life.

Some of the disadvantages are:

- Time value of money: The ARR method ignores the time value of money, which is the idea that money received or paid in the future is worth less than money received or paid today. The ARR method does not discount the future income or cash flows to their present value, nor does it account for the opportunity cost of the investment. This can lead to inaccurate and misleading results, especially for long-term projects or projects with uneven cash flows.

- Arbitrary cutoff rate: The ARR method requires a cutoff rate or a minimum acceptable rate of return to evaluate the project. This cutoff rate is usually determined by the management based on their expectations, preferences, or industry benchmarks. However, there is no objective or rational way to set the cutoff rate, and different managers may have different opinions or criteria. This can lead to inconsistency and subjectivity in the decision-making process.

- Mutually exclusive projects: The ARR method may not be suitable for comparing or ranking mutually exclusive projects, which are projects that compete for the same resources and only one can be accepted. The ARR method may give different rankings depending on the choice of the investment base or the cutoff rate. Moreover, the ARR method does not consider the scale or size of the project, which can affect the profitability and risk of the project.

### 3. The criteria for accepting or rejecting a project based on the ARR method

The criteria for accepting or rejecting a project based on the ARR method are simple and straightforward. A project is accepted if its ARR is greater than or equal to the cutoff rate, and rejected if its ARR is less than the cutoff rate. The cutoff rate is the minimum acceptable rate of return that the management expects or requires from the project. The cutoff rate can be based on the cost of capital, the desired return on equity, the average return on assets, or the industry average.

For example, suppose a company has a cutoff rate of 15% for its capital budgeting decisions. If a project has an ARR of 20%, it is accepted, because it exceeds the cutoff rate. If a project has an ARR of 10%, it is rejected, because it falls below the cutoff rate.

### 4. The limitations and challenges of the ARR method

The ARR method has some limitations and challenges that need to be addressed or overcome before applying it to a capital budgeting decision. Some of the limitations and challenges are:

- Dependence on accounting data: The ARR method relies on the accounting data and assumptions, such as the net income and book value, which may not reflect the true economic value or cash flow of the project. The accounting data may be affected by the choice of the depreciation method, the tax rate, the accounting policies, or the accounting standards. These factors can vary across different projects, companies, or countries, and may distort the ARR results.

- Sensitivity to changes: The ARR method is sensitive to changes in the income or investment of the project, which may occur due to external or internal factors, such as market conditions, competition, inflation, technology, or management decisions. A small change in the income or investment can have a significant impact on the ARR, and may alter the acceptability or ranking of the project.

- Multiple solutions: The ARR method may give multiple solutions or ARR values for the same project, depending on the choice of the investment base or the calculation method. For example, using the initial investment or the average investment can give different ARR values, as we saw in the previous example. Similarly, using the net income or the cash flow can give different ARR values, as the cash flow includes the depreciation expense, which is a non-cash item. This can create confusion and ambiguity in the decision-making process.

### 5. How to compare the ARR method with other capital budgeting techniques

The ARR method is one of the many capital budgeting techniques that can be used to evaluate the profitability of a capital investment project. Some of the other common techniques are:

- Net present value (NPV) method: This method calculates the present value of the future cash flows of the project, minus the initial investment. The NPV method considers the time value of money and uses a discount rate that reflects the cost of capital or the opportunity cost of the investment. A project is accepted if its NPV is positive, and rejected if its NPV is negative. The NPV method is considered the most reliable and accurate technique, as it maximizes the shareholder value and wealth.

- Internal rate of return (IRR) method: This method calculates the discount rate that makes the npv of the project equal to zero. The IRR method also considers the time value of money and uses the project's own cash flows to determine the profitability. A project is accepted if its IRR is greater than or equal to the discount rate, and rejected if its IRR is less than the discount rate.

Raising capital is challenging. We can help!

FasterCapital's team works on matching you with the right funding sources and presents your startup to them through warm introductions

Join us!

7. Modified Internal Rate of Return (MIRR) Method

The modified internal rate of return (MIRR) method is a variation of the internal rate of return (IRR) method that addresses some of the limitations of the latter. The IRR method is a popular technique for evaluating the profitability of a project based on the cash flows it generates. However, the IRR method has some drawbacks, such as:

- It assumes that the cash flows are reinvested at the same rate as the IRR, which may not be realistic.

- It may give multiple or no solutions for the IRR, which makes it difficult to compare and rank projects.

- It may favor projects with shorter duration or lower initial investment, which may not be optimal in the long run.

The MIRR method overcomes these problems by modifying the cash flows of the project in two ways:

- It discounts the negative cash flows (outflows) to the present value using the cost of capital, which is the minimum required rate of return for the project.

- It compounds the positive cash flows (inflows) to the future value using the reinvestment rate, which is the actual or expected rate of return for the cash flows.

The MIRR is then calculated as the discount rate that equates the present value of the modified outflows with the future value of the modified inflows. The MIRR method has some advantages over the IRR method, such as:

- It gives a unique and realistic solution for the MIRR, which makes it easier to compare and rank projects.

- It considers the time value of money and the opportunity cost of capital, which reflects the true profitability of the project.

- It may favor projects with higher net present value (NPV) or longer duration, which may be more beneficial in the long run.

The MIRR method can be applied using the following steps:

1. Identify the cash flows of the project, including the initial investment and the subsequent inflows and outflows.

2. Choose the cost of capital and the reinvestment rate for the project. These rates may be given or estimated based on the market conditions and the risk profile of the project.

3. Discount the negative cash flows to the present value using the cost of capital. This gives the total present value of the outflows (PVout).

4. Compound the positive cash flows to the future value using the reinvestment rate. This gives the total future value of the inflows (FVin).

5. Calculate the MIRR using the formula: $$\text{MIRR} = \left(\frac{\text{FVin}}{\text{PVout}}\right)^{\frac{1}{n}} - 1$$ where n is the number of periods of the project.

6. Compare the MIRR with the cost of capital and the irr. A higher MIRR indicates a more profitable project. A project is acceptable if the MIRR is greater than or equal to the cost of capital.

For example, suppose a project requires an initial investment of $10,000 and generates cash inflows of $3,000, $4,000, and $5,000 in the next three years. The cost of capital is 10% and the reinvestment rate is 12%. The MIRR of the project can be calculated as follows:

- The negative cash flow is the initial investment of $10,000, which is already in present value. Therefore, PVout = $10,000.

- The positive cash flows are the inflows of $3,000, $4,000, and $5,000, which are compounded to the future value using the reinvestment rate of 12%. Therefore, FVin = $3,000 x 1.12^2 + $4,000 x 1.12 + $5,000 = $14,784.

- The MIRR is calculated using the formula: $$\text{MIRR} = \left(\frac{\text{FVin}}{\text{PVout}}\right)^{\frac{1}{n}} - 1 = \left(\frac{14,784}{10,000}\right)^{\frac{1}{3}} - 1 = 0.1399 = 13.99\%$$

- The MIRR of the project is 13.99%, which is higher than the cost of capital of 10%. Therefore, the project is acceptable. The MIRR is also higher than the IRR of the project, which is 11.49%. Therefore, the MIRR method gives a more favorable evaluation of the project than the IRR method.

As I've evolved, I'm capable of doing a lot of things at once, but really, as an entrepreneur and business person, it's more about adding the right structure to be able to handle scaling all those things as opposed to being at the forefront of doing a lot of them.

Rob Dyrdek

8. Sensitivity Analysis in Capital Budgeting

sensitivity analysis is a technique that helps to evaluate how the outcome of a capital budgeting decision changes when one or more of the input variables are altered. It is useful for assessing the risk and uncertainty involved in a project, as well as identifying the critical factors that affect the project's profitability. Sensitivity analysis can be performed in different ways, such as:

1. Changing one variable at a time. This method involves keeping all other variables constant and changing only one variable to see how it affects the net present value (NPV) or internal rate of return (IRR) of the project. For example, if the initial investment is increased by 10%, how much will the NPV decrease? This method is simple and easy to understand, but it does not capture the interactions among the variables or the possibility of simultaneous changes in multiple variables.

2. Changing multiple variables at a time. This method involves changing more than one variable at the same time and observing the impact on the NPV or irr of the project. For example, if both the initial investment and the discount rate are increased by 10%, how much will the NPV change? This method is more realistic and comprehensive, but it also requires more data and calculations, and it may be difficult to isolate the effect of each variable.

3. Using scenarios. This method involves creating different scenarios that reflect different assumptions or expectations about the future, and calculating the NPV or IRR of the project under each scenario. For example, a pessimistic scenario may assume lower sales, higher costs, and higher discount rate, while an optimistic scenario may assume higher sales, lower costs, and lower discount rate. This method is helpful for comparing the best-case and worst-case outcomes, as well as the expected outcome, of the project. However, it also requires making subjective judgments about the probability and plausibility of each scenario, and it may not cover all possible outcomes.

Sensitivity analysis can provide valuable insights for capital budgeting decisions, but it also has some limitations. Some of the limitations are:

- It does not account for the interdependence or correlation among the variables. For example, if the sales volume increases, the variable costs may also increase, or if the discount rate increases, the inflation rate may also increase. These relationships may affect the NPV or IRR of the project in a non-linear way, which may not be captured by sensitivity analysis.

- It does not account for the dynamic nature of the variables. For example, the initial investment may not be a fixed amount, but may depend on the timing and availability of funds, or the discount rate may not be constant, but may vary over time depending on the market conditions. These changes may affect the NPV or IRR of the project in a different way than sensitivity analysis assumes.

- It does not account for the strategic or qualitative aspects of the project. For example, the project may have some intangible benefits or costs, such as enhancing the reputation or image of the company, or creating or eliminating some competitive advantages or disadvantages. These factors may not be easily quantified or incorporated into sensitivity analysis, but they may have a significant impact on the overall value of the project.

sensitivity analysis is a useful tool for capital budgeting, but it should not be the only tool. It should be complemented by other techniques, such as break-even analysis, simulation, decision trees, and real options, to provide a more complete and robust evaluation of the project. sensitivity analysis can help to identify the key drivers and risks of the project, but it cannot provide a definitive answer or recommendation. The final decision should be based on a careful consideration of all the relevant factors, both quantitative and qualitative, as well as the judgment and experience of the decision makers.

9. Conclusion and Recommendations

In this blog, we have discussed the different capital budgeting techniques that can be used to evaluate and compare investment projects. We have seen that each technique has its own advantages and disadvantages, and that no single technique can capture all the relevant aspects of a project. Therefore, it is important to use a combination of techniques and consider the context and objectives of the decision maker. In this section, we will provide some general recommendations and suggestions for applying the capital budgeting techniques in practice.

Some of the recommendations are:

1. Use the net present value (NPV) technique as the primary criterion for accepting or rejecting a project. NPV measures the increase in the value of the firm as a result of the project, and it takes into account the time value of money and the risk of the cash flows. NPV is consistent with the goal of maximizing shareholder wealth, and it can be easily adjusted for different scenarios and assumptions. However, NPV also has some limitations, such as requiring an accurate estimate of the cost of capital and ignoring the potential interactions among projects.

2. Use the internal rate of return (IRR) technique as a secondary criterion for ranking and selecting projects. IRR measures the return on investment of the project, and it is easy to understand and communicate. irr can also be used to compare projects with different sizes and lifespans, as long as they have the same risk and are mutually exclusive. However, IRR also has some drawbacks, such as being sensitive to the timing and pattern of the cash flows, and possibly giving multiple or no solutions for some projects.

3. Use the payback period (PP) and the discounted payback period (DPP) techniques as supplementary criteria for screening and eliminating projects. PP and DPP measure the time required to recover the initial investment of the project, and they reflect the liquidity and risk of the project. PP and DPP can also be used to incorporate the managerial preferences and constraints, such as the maximum acceptable payback period. However, PP and DPP also have some flaws, such as ignoring the cash flows beyond the payback period, and not taking into account the time value of money (in the case of PP).

4. Use the profitability index (PI) technique as an alternative criterion for ranking and selecting projects. PI measures the benefit-cost ratio of the project, and it is similar to NPV in terms of considering the time value of money and the risk of the cash flows. PI can also be used to evaluate projects with different sizes and lifespans, as long as they have the same risk and are independent. However, PI also has some limitations, such as being inconsistent with NPV for mutually exclusive projects, and requiring an accurate estimate of the cost of capital.

To illustrate the application of these techniques, let us consider the following example. Suppose a firm has two investment projects, A and B, with the following cash flows (in millions of dollars):

| Year | Project A | Project B |

| 0 | -100 | -150 | | 1 | 40 | 60 | | 2 | 40 | 60 | | 3 | 40 | 60 | | 4 | 40 | 60 | | 5 | 40 | 60 |

Assume that the cost of capital for both projects is 10%, and that the maximum acceptable payback period is 3 years. Using the different capital budgeting techniques, we can calculate the following values for each project:

| Technique | Project A | Project B |

| NPV | 36.71 | 4.21 |

| IRR | 15.49% | 12.61% |

| PP | 2.5 years | 2.5 years |

| DPP | 3.02 years| 3.17 years|

| PI | 1.37 | 1.03 |

Based on these values, we can make the following conclusions:

- Both projects have positive NPV, which means that they are acceptable and add value to the firm. However, project A has a higher NPV than project B, which means that it is more desirable and preferable.

- Both projects have IRR higher than the cost of capital, which means that they are profitable and have a positive return. However, project A has a higher IRR than project B, which means that it is more efficient and attractive.

- Both projects have PP and DPP lower than the maximum acceptable payback period, which means that they are liquid and have a low risk. However, project A has a lower PP and DPP than project B, which means that it recovers its initial investment faster and has a lower exposure to uncertainty.

- Both projects have PI greater than 1, which means that they have a benefit-cost ratio higher than 1. However, project A has a higher PI than project B, which means that it has a higher net benefit per unit of cost.

Therefore, based on the combination of the capital budgeting techniques, we can recommend project A over project B, as it has a higher NPV, IRR, PI, and a lower PP and DPP. Project A is the best choice among the two projects, as it maximizes the value, return, liquidity, and profitability of the firm.

At a certain point in your career - I mean, part of the answer is a personal answer, which is that at a certain point in your career, it becomes more satisfying to help entrepreneurs than to be one.

Marc Andreessen