Both IRR and MIRR are methods used for valuation.
Proper firm valuation is essential for efficient planning and allocation. The decisions made by managers, in both the short and long term, greatly affect a firm’s value. Accurate valuation methods are crucial in assessing the impact of projects and business activities on this value. The internal rate of return, including its modified form, is one such method that offers firms a dependable framework for managing assets and capital to achieve their objectives (Mendel University, 2004).
Investopedia states that firm valuation entails calculating the current value of an asset or company using objective or subjective approaches. The valuation of a firm is often connected to effective management and decision-making, as it influences its worth. To maintain the value of the firm, it is crucial to undertake projects or investments that enhance its overall value.
A key characteristic of a high-value company is having a strong cash flow position. This enables the company to fulfill its financial obligations without needing to borrow funds and accrue interest expenses. Consequently, the company can reinvest capital back into its operations for generating additional profits.
Valuation is essential for a firm as it involves determining the monetary price of itself. Additionally, project valuation is crucial in evaluating the contribution it can make to the firm’s profit generation and overall value. Consequently, the firm will prioritize investing in projects that offer higher returns.
Nevertheless, the issue persists: how can a company evaluate the worth of a project that will enhance its overall value?
When assessing a company’s value, it is crucial to take into account the future cash flows it generates. These cash flows must be discounted at an appropriate rate. To begin this evaluation, it is important to analyze the anticipated cash flows that the company expects to receive from implementing projects.
When a company engages in capital expenditures, such as acquiring new equipment, expanding facilities, merging or consolidating with other companies, or initiating research and development programs, its goal is to generate future cash flow benefits. These expenses necessitate careful analysis and decision-making to determine the business activities that will enhance its value and financial stability (Evans, 2000, p.1).
Capital budgeting refers to the process of investing in capital assets. In order to evaluate these investments, companies need to consider the risks, costs, and benefits associated with a project. This implies that current expenses can have an impact on future value. Financial analysts commonly employ discounted cash flow (DCF) analysis to determine the present value of company projects. It is crucial to note that various financial analysts may have different assumptions regarding factors like project duration and company size (Evans, 2000, p.1).
Financial management focuses on the present value of assets, distinguishing it from accounting. The objective is to ensure that a business project generates future benefits by determining its present value. To achieve this, future cash flows are discounted to their present value. Discounting involves evaluating the value of a future amount in terms of today’s conditions. The disparity between future values and present values is influenced by the time value of money, which fluctuates over time due to inflation, uncertainty, and opportunity costs. Consequently, $100 will have diminished worth in the future as price levels rise (inflation). Furthermore, estimating future returns may be imprecise due to market dynamics. Nevertheless, $100 possesses greater worth in the present because it can be invested immediately and generate a return (Evans, 2000, p. 4).
The net-present value (NPV) and internal rate of return (IRR) are commonly used measures for evaluating investments. It is generally believed that higher IRRs and NPVs indicate greater potential profits than lower IRRs and NPVs. The calculation of NPV involves discounting a project’s cash flows at a specific discount rate over its lifespan. The formula for NPV is as follows:
According to Investopedia, the NPV (Net Present Value) of a project is determined by factors such as the initial cost/expenditures (C0), future cash flows/income (Ct), discount rate (r), and the time interval into the future when the income will be received or spent (t). If the NPV is positive, it indicates that the cash flows will also be positive, making the project worthy of acceptance.
If the NPV is equal to zero, the discount rate represents the internal rate of return (IRR). In essence, a higher IRR indicates a more favorable project as it signifies the rate of growth that a project can yield. While the estimated IRR may frequently deviate from the actual rate of return, it is consistently advisable for managers to invest in a project with a high IRR estimation. The utilization of IRR in obtaining the NPV aligns with the discounted cash flow method or DCF method.
The estimation of IRR is crucial when using NPV as a valuation method for firms. Incorrect estimation of IRR can result in incorrect or less profitable business decisions. IRR is obtained when NPV is set to zero and assumes that the project generates no interim/short-term cash flows, or that these cash flows can be invested at the actual IRR. This assumption is known as the reinvestment assumption of IRR. If the calculated IRR is higher than the true reinvestment rate for interim cash flows, the measure will overestimate the annual equivalent return from the project. As a result, the firm will not meet its expectations and the project may not contribute to solvency (Kelleher, 2004, p. 1-2).
The assumption of the internal rate of return (IRR) is that a project incurs initial expenses followed by future cash inflows. However, this may not always be the case as future cash flows, particularly in the last period, can be negative or involve expenses not accounted for in the initial outflow (Xiaojuan, 2005).
According to Baker (2006), if the income amounts received in each period (Ct) are higher than projected, a higher Internal Rate of Return (IRR) is required to bring the Net Present Value (NPV) back to zero.
The IRR is advantageous for business decision-making but can result in a significant capital budgeting mistake due to its assumption regarding reinvestment. When comparing mutually exclusive projects Y and Z, both with an IRR of 30%, the manager may mistakenly assume that both projects will generate future profit and value for the firm. However, this assumption disregards the varying reinvestment rates for interim cash flows. Project Z’s interim cash flows can only be reinvested at 8% of the cost of capital, whereas project Y’s cash flows can be reinvested in a subsequent project with a 30% return per time period. Consequently, project Y is clearly the superior choice since it has a growth rate of 41%, while project Z has a growth rate of only 8% annually (equivalent to a compound annual growth rate of 24% over 5 years) (Kelleher, 2004, p.2-3).
The main issue with the Internal Rate of Return (IRR) is that it assumes a reinvestment rate, which has a significant impact on the results. Even if adjusted to the company’s cost of capital, the actual IRR will still be lower than the estimated IRR. When the estimated IRR is only 10% higher than the true IRR, this impact becomes significant. However, adjusting the reinvestment rate to the cost of capital will yield a higher IRR compared to the project’s actual return because there will always be some margin of error when assuming cash flows are reinvested at an equal rate to the IRR (Kelleher, 2004, p. 3).
Having a net present value (NPV) of zero and experiencing multiple changes in the signs of cash flows lead to the existence of two internal rates of return (IRRs).
According to Investopedia, the internal rate of return (IRR) has been modified due to its drawbacks and potential for overoptimistic or incorrect decisions. This modification is known as the modified internal rate of return (MIRR), which assumes that all cash flows are reinvested at the company’s cost of capital. In simpler terms, MIRR represents the cost of capital expressed as a percentage.
The different types of capital incurring costs are based on the desired rate of return from investors who contribute funds to the company. By setting MIRR equal to the cost of capital, company managers aim to protect firm wealth and meet investor expectations. This modification also helps address the problem of multiple IRRs mentioned in COBA, USF Chapter 11, page 1.
MIRR addresses the reinvestment problem associated with IRR, but comparing mutually exclusive projects with differing durations and sizes can be difficult using MIRR (Gallinelli, 2008). To address this issue, Dunn and Carry (1997) propose adjusting the MIRR to provide rankings that align with the NPV of each project.
In order to provide examples and practical demonstrations, we will apply the concepts we have discussed to real-life scenarios. Currently, I am intending to purchase a big waffle-maker to help with the growth of my business making homemade biscuits at home.
To maximize profits and ensure business sustainability, there are two options to consider. Firstly, investing in a high-end waffle-maker priced at $3000 would allow the production of 20 uniquely designed waffles. While this option involves an initial cash outflow, it could lead to long-term benefits. However, there is a risk of additional costs for repairs or replacement if the waffle-maker malfunctions within three years. Alternatively, focusing on expanding the current biscuit production is another viable option.
If the net sales revenue or income stream that I will aim for each year from waffle-making is $1000, $1250, and $1500 respectively over a period of three years, we can calculate the Net Present Value (NPV) using the NPV equation:
The net present value (NPV) formula is expressed as follows: NPV = -3000 + 1000/(1+IRR) + 1250/(1+IRR)2 + 1500/(1+IRR)3.
If I use the Internal Rate of Return (IRR) in valuing the investment I am planning:
0 = NPV = -3000 + 1000/(1+IRR) + 1250/(1+IRR)2 + 1500/(1+IRR)3
The waffle-maker is very attractive to buy, with an IRR of 11%.
If I deposit my net profits in the bank and reinvest them with an 8% annual interest rate, it is said that my reinvestment rate will also be 8%. Additionally, since I am not borrowing money to acquire new capital, the financing rate is 0%. The MIRR formula takes into account the finance and reinvestment rates to solve the assumption of IRR. To calculate the MIRR, I can use MS Excel. By arranging the cash flows in sequence and using the formula =MIRR (year0:year4, 0, 8%), I obtained a result of 10% (Marshall School of Business, p. 12).
Although the IRR of the project is higher than the MIRR, which aligns with the theoretical view that MIRR is usually lower than IRR, this does not guarantee a positive return on cost of capital regardless of the measure chosen. It is crucial to also consider the option of not expanding the business and calculate the NPV to accurately evaluate potential future returns from the project. Ultimately, determining which valuation metric (IRR or MIRR) is better requires further consideration.
The Excel calculator determines the Net Present Value (NPV) to be 1221.60 when using the Internal Rate of Return (IRR) as the discount rate r. Alternatively, if we use the Modified Internal Rate of Return (MIRR) as the discount rate, the project’s total return will be 6912.09. Both NPV values are positive, indicating that purchasing the waffle-maker is likely to result in a positive return in the future and is therefore considered a good investment. This analysis focuses solely on determining if the investment will yield positive returns and does not consider alternative strategies like increasing production without buying a waffle-maker. The theory behind MIRR, IRR, and NPV applies when evaluating a single project or comparing different projects of similar scales and durations. If another investment option is introduced, such as hiring a baker, these valuation measurements remain valid. In this scenario, selecting the project with a higher NPV would be preferred. Cary and Dunn (1997) proposed methods for adjusting IRR and MIRR when faced with varying initial outflows and cash inflows in different projects.
Regarding the main question of this paper, we must choose between IRR or MIRR.
In our simple example, the Internal Rate of Return (IRR) is higher and the Net Present Value (NPV) is lower. Relying solely on IRR to make a conclusion may lead the decision maker to overly optimistic assumptions about higher returns.
Although the MIRR may have a lower value than the IRR, the project’s actual return is higher. In decision-making, managers usually rely on the IRR as a rule of thumb, but academicians often prefer the MIRR because they acknowledge that these two measures are distinct and necessitate different interpretations. The MIRR specifically deals with the impractical assumption of unlimited reinvestment of capital in the IRR, thereby offering a more realistic representation of real-life scenarios. It is crucial to exercise caution regarding assumptions since they can create an illusory depiction of reality.
The decisions made by a firm have various impacts on them, whether in the short-term or long-term. When selecting a project for capital budgeting, the company must consider its effects on both present and future value. This can contribute to the firm’s solvency or lead to bankruptcy. The valuation of a firm provides stakeholders with insight into its financial capabilities. Overestimating or underestimating its value can result in suboptimal business activities. The same principle applies to project valuations. Considering economic conditions and the firm’s capabilities, it is crucial for the company to invest in activities that generate positive NPVs or those with the highest NPV among available options. Accurate estimation of NPV requires using an appropriate discount rate or rate of return.
MIRR is superior to IRR as it takes into account more realistic assumptions, offering insights into the genuine mechanics of accurate business activity valuation. Ultimately, accurate valuation contributes to informed decision-making, emphasizing the crucial need for proper estimation of the ‘real’ internal rate of return.
References
Baker, Samuel L. (2006, September 26). “Perils of the Internal Rate of Return.” Retrieved October 21, 2008, from http://hspm.sph.sc.edu/COURSES/ECON/invest/invest.html
Cary, David, Dunn, Michael. (1997). Adjustment of Modified Internal Rate of Return for Scale and Time Span Differences. Academy of Accounting and Financial Studies, 2, 57-63.
The author of the article “Course 3: Capital Budgeting Analysis” is Evans, Matt H. The article can be found at the website http://www.exinfm.com/training/pdfiles/course03.pdf.
Gallinelli, Frank (2008). NPV, IRR, FMRR, MIRR, CpA – Stirring the Alphabet Soup of Real Estate Investment (Part 2). Retrieved October 21, 2008.
Investopedia. (2008). Retrieved October 21, 2008, from www.investopedia.com
Kelleher, John C., MacCormack, Justin J. authored an article titled “Internal rate of return: A cautionary tale” in August 2004. The article was published in The McKinsey Quarterly and is available at http://mdm.gwu.edu/forman/IRR%20A%20Cautionary%20Tale.pdf. It comprises four pages.
Marshall School of Business: University of Southern Carolina offers a course in Excel 2000 Intermediate. Information Resources for this course can be found at http://www.marshall.usc.edu/assets/003/5240.pdf
The text is a reference to a publication titled “Possible Approaches to the valuation of a firm” by Mendel University of Agriculture and Forestry in 2004. The publication was featured in Agricultural Economics – Czechoslovakia and can be found on pages 204-206.
Xiaojuan, Grace (2005, October 13) has created a PowerPoint lecture presentation. The presentation can be retrieved from econ.uscb.edu.ppt and was accessed on October 22, 2008.
