Corporate finance chapter 8
The IRR on an investment is the required return that results in
A zero NPV when it is used as the discount rate
Discuss accounting rates of return and some of the problems with them.
Accounting rates of return (ARR) is one of the investment criteria used in capital budgeting. It measures the profitability of an investment by comparing the average annual accounting profit to the initial investment cost. ARR is calculated by dividing the average annual accounting profit by the initial investment cost and multiplying by 100 to express it as a percentage. However, there are several problems associated with using ARR as an investment criterion. Firstly, ARR does not consider the time value of money, as it focuses solely on average accounting profits without discounting them to reflect the present value. This can lead to inaccurate investment decisions, especially when comparing projects with different cash flow patterns over time. Secondly, ARR relies on accounting profit, which is based on historical cost and depreciation methods. This can be problematic because accounting profit may not accurately reflect the economic profitability of an investment. Different depreciation methods can result in different profit figures, leading to inconsistent ARR calculations. Additionally, ARR does not consider the entire cash flow stream generated by an investment. It only looks at average accounting profit, ignoring the timing and magnitude of cash flows. This can result in misleading investment decisions, as projects with higher initial costs but better long-term cash flows may be overlooked. Furthermore, ARR does not account for the risk associated with an investment. It does not consider the variability of cash flows or incorporate a risk-adjusted discount rate. This can lead to the selection of projects with higher risk but lower ARR over projects with lower risk but higher ARR. In summary, while accounting rates of return can provide a quick and simple measure of profitability, they have limitations and should be used with caution in capital budgeting decisions. It is important to consider other investment criteria, such as net present value (NPV) and internal rate of return (IRR), which address the shortcomings of ARR and provide a more comprehensive analysis of investment profitability
What are the most commonly used capital budgeting procedures?
IRR or NPV... The most commonly used capital budgeting procedures are: 1. Net Present Value (NPV) approach: This approach calculates the present value of expected cash flows from an investment and subtracts the initial investment cost. If the NPV is positive, the investment is considered worthwhile. 2. Internal Rate of Return (IRR): This procedure calculates the discount rate at which the NPV of an investment becomes zero. If the IRR exceeds the required rate of return, the investment is accepted. 3. Payback Period: This method calculates the time it takes for an investment to recover its initial cost through cash flows. If the payback period is within a specified time frame, the investment is considered acceptable. 4. Profitability Index: This ratio compares the present value of expected cash inflows to the initial investment cost. If the profitability index is greater than 1, the investment is considered profitable. These procedures help financial managers analyze potential projects and make informed decisions about which investments are worth pursuing.
How would you state the profitability index rule?
If the profitability index or ratio is greater than 1, the project is profitable and may receive the green signal to proceed. Conversely, if the profitability ratio or index is below, the optimum course of action may be to reject or abandon the project.
If we say an investment has an NPV of $1,000, what exactly do we mean?
If we say an investment has an NPV of $1,000, it means that the present value of the cash inflows from the investment exceeds the initial cost of the investment by $1,000. This indicates that the investment is financially favorable and is expected to increase the total value of the investment or project
In capital budgeting what does Mutually Exclusive mean?
In capital budgeting, the term "mutually exclusive" refers to a situation where the acceptance of one investment project means the rejection of another. In other words, mutually exclusive projects are alternative investment options that cannot be undertaken simultaneously. When evaluating mutually exclusive projects, the financial manager must choose the most profitable or beneficial option among the available alternatives
If NPV is conceptually the best tool for capital budgeting, why do you think multiple measures are used in practice?
In practice, multiple measures are used in capital budgeting because NPV alone may not capture all the relevant factors and considerations involved in investment decision-making. While NPV is a widely accepted and conceptually sound tool for evaluating the profitability of an investment, it has its limitations. Firstly, NPV relies heavily on accurate and reliable estimates of cash flows, discount rates, and project timelines. However, these inputs are often subject to uncertainty and can be difficult to predict with complete accuracy. Therefore, using multiple measures allows for a more comprehensive analysis that considers different scenarios and potential risks. Secondly, different measures provide different perspectives on the investment's performance and profitability. For example, the payback period provides information on how quickly the initial investment can be recovered, which is important for businesses with limited liquidity or short-term financial goals. Similarly, measures like the internal rate of return (IRR) and profitability index (PI) offer additional insights into the project's financial attractiveness and potential returns. Additionally, using multiple measures can help mitigate potential biases or flaws in individual measures. Each measure has its own strengths and weaknesses, and by considering a range of measures, financial managers can gain a more well-rounded understanding of the investment's viability and make more informed decisions. Overall, while NPV is a fundamental tool in capital budgeting, using multiple measures allows for a more comprehensive evaluation of investment opportunities and helps to address the limitations and uncertainties associated with individual measures
What are the weaknesses of the AAR rule?
It is not a true rate of return because the time value of money is ignored. It uses an arbitrary benchmark cutoff rate. Lastly, it is based on accounting net income and book values, not cash flows and market values.
NPV and IRR generally give the same results except in cases of Non-conventional cash-flows and Mutually Exclusive projects. Explain why?
NPV (Net Present Value) and IRR (Internal Rate of Return) are both methods used to evaluate the profitability of investment projects. While they often give similar results, there are cases where they may differ, particularly in non-conventional cash flows and mutually exclusive projects. Non-conventional cash flows refer to situations where the cash flows change direction more than once during the life of the project. This means that there are both positive and negative cash flows occurring at different periods. In such cases, the IRR may give multiple rates of return or may not even exist. On the other hand, NPV takes into account the timing and magnitude of all cash flows, which allows it to accurately evaluate non-conventional projects. Mutually exclusive projects are those where selecting one project means rejecting another. In such cases, the IRR can lead to incorrect decisions. This is because the IRR assumes that the cash flows from the project will be reinvested at the same rate of return, which may not be realistic. On the other hand, NPV takes into consideration the opportunity cost of capital and provides a more reliable measure of the project's profitability. In summary, while NPV and IRR are both valuable tools for investment analysis, they may differ in cases of non-conventional cash flows and mutually exclusive projects. NPV is generally considered to be more reliable and widely used in practice as it considers the timing and magnitude of cash flows and the opportunity cost of capital
Is it generally true that an advantage of the IRR rule over the NPV rule is that we don't need to know the required return to use the IRR rule?
No, it is not generally true that an advantage of the IRR (Internal Rate of Return) rule over the NPV (Net Present Value) rule is that we don't need to know the required return to use the IRR rule. In fact, the IRR rule requires the use of the required return to calculate the internal rate of return, which is the discount rate that makes the NPV of an investment equal to zero. The IRR rule is used to determine the rate of return that an investment is expected to generate, whereas the NPV rule compares the present value of cash inflows to the present value of cash outflows to determine the profitability of an investment.
Explain the NPV Rule.
The NPV Rule is a financial decision-making tool that helps determine whether or not a project or investment is financially viable. It stands for Net Present Value and is calculated by discounting the future cash flows of a project back to their present value and subtracting the initial cost of the project. If the NPV is positive, it indicates that the project is expected to generate more value than its cost, and therefore, it is considered a good investment. Conversely, if the NPV is negative, it suggests that the project is expected to generate less value than its cost and should be avoided. The NPV Rule is based on the principle that money today is worth more than the same amount of money in the future due to the time value of money. By considering the discounted cash flows, the NPV Rule takes into account the timing and risk associated with the project, making it a more comprehensive and accurate decision-making tool compared to other methods such as the payback period rule
Explain PI ratio
The PI ratio, or profitability index, is a financial metric used in capital budgeting to evaluate the profitability of an investment. It is calculated by dividing the present value of future cash flows by the initial investment cost. The formula for calculating the PI ratio is: PI = Present Value of Future Cash Flows / Initial Investment Cost A PI ratio greater than 1 indicates that the investment is expected to generate positive returns and is considered favorable. A PI ratio less than 1 suggests that the investment may not be profitable. Therefore, the higher the PI ratio, the more attractive the investment opportunity is considered.
What is an average accounting rate of return, or AAR?
The average accounting rate of return (AAR) is a method used in capital budgeting to evaluate investments. It is calculated by dividing the average net income of an investment by its average book value. The AAR is considered a flawed approach to making capital budgeting decisions as it relies solely on accounting measures and does not take into account the time value of money or the cash flows generated by the investment.
Explain the conflict between NPV and IRR and which one we choose?
The conflict between NPV (Net Present Value) and IRR (Internal Rate of Return) arises when evaluating investment projects. NPV is a measure that calculates the present value of expected cash flows and compares it to the initial investment. It takes into account the time value of money by discounting future cash flows. On the other hand, IRR is the discount rate at which the NPV of an investment becomes zero. It represents the rate of return that an investment is expected to generate. The conflict between NPV and IRR arises when there are multiple investment projects to choose from. NPV and IRR may provide conflicting results in terms of project selection. This is because the two methods use different criteria for evaluating investments. In general, if the NPV of an investment is positive (greater than zero), it indicates that the project is expected to generate more cash inflows than the initial investment, and therefore, it is considered favorable. On the other hand, if the IRR of an investment is higher than the required rate of return, it indicates that the project is expected to generate a return higher than the cost of capital. When evaluating investment projects, it is generally recommended to prioritize NPV over IRR. This is because NPV takes into account the time value of money and provides a clearer measure of profitability. It considers all cash flows throughout the project's life and provides a more accurate measure of the project's value. IRR, on the other hand, has limitations. It assumes that cash flows generated by the project will be reinvested at the IRR, which may not always be feasible or realistic. Additionally, IRR may provide multiple values or no value at all in cases where cash flows change direction multiple times. Therefore, while IRR can be a useful measure for comparing projects with similar cash flow patterns, NPV is generally considered a more reliable and comprehensive measure for project evaluation and selection.
Explain the internal rate of return criterion and its associated strengths and weaknesses.
The internal rate of return (IRR) criterion is a capital budgeting technique used to evaluate the profitability of an investment project. It is defined as the discount rate that makes the net present value (NPV) of the project equal to zero. In other words, it is the rate at which the present value of cash inflows equals the present value of cash outflows. Strengths of the internal rate of return criterion include: 1. Easy to understand: The concept of IRR is relatively simple to grasp, making it accessible for decision-makers without advanced financial knowledge. 2. Intuitive measure of profitability: The IRR provides a percentage return on investment, which can be easily compared to other potential projects or investment opportunities. 3. Considers the time value of money: Like the NPV criterion, the IRR takes into account the concept of the time value of money by discounting future cash flows. Weaknesses of the internal rate of return criterion include: 1. Multiple IRR problem: In some cases, a project may have multiple IRRs or no real IRR. This can make it difficult to interpret the results and make accurate investment decisions. 2. Assumptions about reinvestment: The IRR assumes that cash inflows are reinvested at the same rate as the IRR itself. However, this assumption may not always hold true in practice. 3. Ignores project size differences: The IRR does not consider the absolute size of the project or the scale of the cash flows. As a result, it may favor smaller projects with higher IRRs over larger projects with lower IRRs, even if the latter would generate more overall value. In conclusion, while the internal rate of return criterion is a useful tool for evaluating investment projects, it is important to consider its limitations and use it in conjunction with other investment criteria, such as the net present value
Summerize investment criteria
The investment criteria can be summarized as follows: 1. Payback Rule: This rule measures the time it takes to recover the initial investment. However, it does not consider the time value of money and may lead to incorrect decisions. 2. Accounting Rates of Return: This criterion calculates the average accounting profit as a percentage of the initial investment. It has its own limitations and may not provide an accurate measure of profitability. 3. Internal Rate of Return: This criterion calculates the discount rate at which the present value of cash inflows equals the initial investment. It provides a measure of profitability and considers the time value of money. However, it may have multiple solutions and can be difficult to interpret. 4. Net Present Value: This criterion calculates the present value of future cash flows, taking into account the discount rate. It provides a measure of profitability and considers the time value of money. A positive NPV indicates a good investment. 5. Modified Internal Rate of Return: This criterion adjusts for the reinvestment rate assumption of the internal rate of return. It provides a more accurate measure of profitability when cash flows are reinvested at different rates. 6. Profitability Index: This criterion calculates the ratio of the present value of cash inflows to the initial investment. It provides a measure of profitability relative to the investment cost. A value greater than 1 indicates a good investment.
Explain how you apply the modified internal rate of return?
The modified internal rate of return (MIRR) is a modified version of the traditional internal rate of return (IRR) method that addresses some of its limitations. The MIRR takes into account the reinvestment rate for cash flows received during the investment period and the finance rate for cash flows invested at the end of the investment period. To apply the MIRR, follow these steps: 1. Identify the initial investment and the cash flows received during the investment period. 2. Determine the reinvestment rate, which represents the rate at which cash flows received during the investment period are reinvested. 3. Calculate the future value (FV) of the cash inflows received during the investment period using the reinvestment rate. 4. Determine the finance rate, which represents the rate at which cash flows invested at the end of the investment period grow. 5. Calculate the present value (PV) of the cash outflows invested at the end of the investment period using the finance rate. 6. Calculate the MIRR using the formula: MIRR = (FV of cash inflows / PV of cash outflows)^(1/n) - 1, where n is the number of periods. The MIRR provides a more accurate measure of profitability by considering both the reinvestment rate and the finance rate. It addresses the limitations of the traditional IRR method, such as assuming reinvestment at the IRR and not considering the cost of capital.
What is the net present value rule?
The net present value rule states that an investment should be accepted if the net present value is positive and rejected if it is negative. If the net present value is exactly zero, then the decision to take or reject the investment is indifferent
what is the payback period? The payback period rule?
The payback period is a measure used in capital budgeting to determine the length of time it takes for an investment to recover its initial cost. It is calculated by adding up the cash inflows from the investment until the total cumulative cash inflows equal or exceed the initial cost. The payback period rule is a guideline that states that an investment is acceptable if its payback period is shorter than a predetermined cutoff period, which is determined by the company's management or investors.
Why do we say that the payback period is, in a sense, an accounting break-even measure?
The payback period is considered an accounting break-even measure because it focuses on the length of time it takes to recover the initial investment. It does not take into account the time value of money or the impact of the investment on the overall value of the stock. It only looks at when the investment will break even in terms of accounting profits
Summarize the payback rule and some of its shortcomings.
The payback rule is a simple investment criterion that calculates the time it takes to recover the initial investment. It is often used as a screening tool for minor investment decisions. However, it has several shortcomings. First, it ignores the time value of money, meaning it does not consider the value of cash flows in the future. Second, it requires an arbitrary cutoff point to determine the payback period, lacking an objective basis for choosing a specific number. Third, it ignores cash flows beyond the cutoff date, disregarding the potential profitability of investments in the long term. Additionally, the payback rule fails to consider risk differences, treating both risky and safe projects the same way. These limitations make the payback rule less reliable compared to other investment criteria like net present value.
Explain how you calculate the profitability index and its relation to net present value.
To calculate the profitability index (PI), you divide the present value of future cash flows by the initial investment. The formula for calculating PI is: PI = Present Value of Future Cash Flows / Initial Investment The profitability index is a measure of the value created per unit of investment. It represents the ratio between the present value of expected future cash flows and the initial investment. A profitability index greater than 1 indicates a positive net present value (NPV) and is considered a good investment. Conversely, a profitability index less than 1 indicates a negative NPV and is considered a poor investment. The relationship between the profitability index and net present value is that a positive profitability index corresponds to a positive net present value, while a negative profitability index corresponds to a negative net present value. The profitability index provides a relative measure of the value created by an investment, while the net present value provides an absolute measure of the value created by considering the time value of money. In summary, the profitability index is calculated by dividing the present value of future cash flows by the initial investment. It is used to assess the value created by an investment and is closely related to the net present value.
How do you compute payback for a project?
To compute the payback for a project, you need to determine the amount of time required for the project to generate cash flows sufficient to recover its initial cost. The formula for calculating the payback period is as follows: Payback Period = Initial Cost / Annual Cash Flows 1. Determine the initial cost of the project. 2. Calculate the annual cash flows generated by the project. 3. Divide the initial cost by the annual cash flows to get the payback period. For example, if the initial cost of a project is $500 and the annual cash flows are $100, the payback period would be 5 years ($500 / $100 = 5)
Suppose an investment will cost $90,000 initially and will generate the following cash flows: Year 1: 132,000 Year 2: 100,000 Year 3: −150,000 The required return is 15%. Should we accept or reject the project?
To determine whether the project should be accepted or rejected, we need to calculate the net present value (NPV) of the investment. The NPV accounts for the time value of money by discounting the future cash flows back to the present value using the required return rate of 15%. To calculate the NPV, we can use the following formula: NPV = CF1 / (1+r)^1 + CF2 / (1+r)^2 + CF3 / (1+r)^3 - Initial Investment Where CF1, CF2, and CF3 are the cash flows in each year, r is the required return rate, and the Initial Investment is the initial cost of $90,000. Using the given cash flows and the required return rate, the NPV can be calculated as follows: NPV = 132,000 / (1+0.15)^1 + 100,000 / (1+0.15)^2 + (-150,000) / (1+0.15)^3 - 90,000 Simplifying the calculation: NPV = 132,000 / 1.15 + 100,000 / 1.3225 + (-150,000) / 1.52087 - 90,000 NPV = 114,782.61 + 75,647.67 - 98,671.57 - 90,000 NPV = 1,758.71 Since the NPV is positive ($1,758.71), the project should be accepted. A positive NPV indicates that the project is expected to generate more value than its initial cost, taking into account the required return rate
Based on the payback rule an investment is acceptable if
its calculated payback period is less than some prespecified number of years
How do you evaluate proposed investments by using the net present value criterion?
To evaluate proposed investments using the net present value (NPV) criterion, you need to follow these steps: 1. Estimate the cash flows: Determine the expected cash inflows and outflows associated with the investment over its lifespan. These cash flows should be projected for each period. 2. Determine the discount rate: Identify an appropriate discount rate that reflects the time value of money and the riskiness of the investment. This rate is often the cost of capital for the company. 3. Calculate the present value of cash flows: Apply the discount rate to each projected cash flow and calculate its present value. The present value is the value of a future cash flow in today's dollars. 4. Sum up the present values: Add up all the present values of the cash flows to obtain the net present value. If the sum is positive, the investment is expected to generate more value than its cost. A negative NPV indicates that the investment may not be financially viable. 5. Interpret the NPV: A positive NPV suggests that the investment is potentially profitable and should be considered. However, other factors such as risk and strategic alignment should also be taken into account. It is important to note that the NPV criterion assumes that cash flows can be accurately estimated and discounted at an appropriate rate. Additionally, the NPV approach considers the time value of money, which means that cash received earlier is more valuable than cash received later
Under what circumstances will the IRR and NPV rules lead to the same accept-reject decisions? When might they conflict?
Under what circumstances will the IRR and NPV rules lead to the same accept-reject decisions? When might they conflict? The IRR (Internal Rate of Return) and NPV (Net Present Value) rules will lead to the same accept-reject decisions when the NPV is positive and the IRR is greater than the required rate of return. This means that the project is expected to generate a return greater than the cost of capital, making it a favorable investment. However, the IRR and NPV rules might conflict under certain circumstances. One such circumstance is when there are multiple cash flow sign changes during the life of the project. In this case, the IRR rule may give multiple solutions or no real solution, making it difficult to determine the acceptability of the project based solely on the IRR. Another circumstance where the IRR and NPV rules might conflict is when comparing mutually exclusive projects with different scales of investment. The IRR rule favors projects with higher rates of return, regardless of the scale of investment. On the other hand, the NPV rule takes into account the total cash flows and the scale of investment, providing a more accurate measure of profitability. In such cases, the NPV rule should be given more weight in making investment decisions. In summary, the IRR and NPV rules generally lead to the same accept-reject decisions, but conflicts may arise in cases of multiple cash flow sign changes or when comparing mutually exclusive projects with different scales of investment.
Based on the average accounting return rule, a project is acceptable if
its average accounting return exceeds a target average accounting return
Based on the IRR rule, an investment is acceptable if
the IRR exceeds the required return. It should be rejected otherwise.
What does the profitability index measure?
the value created per dollar invested. The profitability index measures the ratio between the present value of cash inflows and the present value of cash outflows for an investment project. It is calculated by dividing the present value of cash inflows by the initial investment. The profitability index helps determine the profitability and value of an investment project, with values greater than 1 indicating a positive net present value and potential profitability