The topic of replacement reserves is often confusing for commercial real estate professionals. How much should be set aside for replacement reserves? Should replacement reserves be included in net operating income? How do replacement reserves impact cap rates and value? In this article, we’re going to take a closer look at reserves for replacement, clear up the confusion, and also tackle some common misconceptions.
First, what are replacement reserves? Replacement Reserves are funds set aside that provide for the periodic replacement of building components that wear out more rapidly than the building itself and therefore must be replaced during the building’s economic life (short-lived items).
These components typically include the replacement of the roof, heating, ventilation, and air conditioning (HVAC) systems, parking lot resurfacing, etc. Note that replacement reserves do not include minor repairs and maintenance such as broken doorknobs or lightbulbs. These minor expenses are considered routine operating expenses, not irregular capital expenditures.
How much should be set aside for replacement reserves? As always, it depends. Typically, a commercial property will be inspected by a general contractor before acquisition. This will give you a good indication about what will need to be replaced over the intended holding period and allow you to work backwards into an appropriate replacement reserve amount. Additionally, many lenders will also require a replacement reserve to be set aside, usually in escrow, to cover major capital expenditures over the term of the loan.
Conventional wisdom says no, replacement reserves should not be included in the NOI calculation. This is what’s taught in many commercial real estate textbooks and even the highly respected CCIM courses. However, just because something is popular doesn’t make it right. As always, the decision to include, or exclude, reserves for replacement from NOI largely depends on the context.
One thing to keep in mind is that many sellers and listing brokers will intentionally exclude replacement reserves from their proformas to boost NOI, and thus improve valuation. Buyers, on the other hand, are typically much more conservative when creating a proforma. Recognizing this tension can be helpful before entering into any negotiations. Additionally, lenders will almost always include a reserve for replacement figure in their NOI calculations when determining the maximum loan amount. This makes sense from their perspective because lenders want to minimize risk and ensure the property’s cash flow is sufficient to repay the loan. Maintaining an adequate reserve for replacement gives a lender more comfort that a property can support the loan without relying on any capital injections or guarantor support.
Where context becomes particularly important is in understanding how market-based cap rates are calculated. You want to ensure you’re comparing apples to apples. For example, it’s common for appraisers to value a property using a market-driven cap rate based on comparable properties in the relevant submarket. However, if the market-driven cap rate you are applying to a stabilized NOI is derived from properties with reserves already netted out, then this obviously wouldn’t make sense to apply this cap rate to an NOI without reserves included. Let’s take a quick example to illustrate the difference:
As shown in the above simple proforma, replacement reserves are included in the NOI calculation. As such, the calculated net operating income is $750,000 and the resulting valuation based on an 8% cap rate is $9,375,000. Now, let’s take a look at what happens when we exclude replacement reserves from NOI:
As you can see, the resulting valuation is $10,000,000, which is an improvement of $625,000. This is certainly a significant difference in value that should not be ignored. Keep this in mind when working with seller provided proformas. Also, when reviewing third-party appraisals, this is usually a good item to take a closer look at.
Ultimately, the practice of capitalizing NOI without including any ongoing expenditures required to maintain market-based rents isn’t wise. These ongoing capital expenditures may include reserves for replacement, and even tenant improvement and leasing commissions required to keep the property occupied. A sophisticated investor will, of course, understand this and most certainly take it into account when determining value. As Warren Buffett famously asked:
Although Warren Buffett was referring to the misuse of Earnings Before Interest, Taxes, Depreciation, and Amortization (EBITDA), the same concept certainly applies to NOI and commercial real estate. Why would you determine value without considering all required expenditures to keep the property occupied and otherwise competitive?
Replacement reserves are an important line item in any commercial real estate proforma. Capital expenditures are necessary for maintaining a competitive and fully occupied property. Yet, many people gloss over the reserves for replacement line item and often exclude it completely from the NOI calculation. As shown above this can have a significant impact on a property’s valuation and as such it should not be ignored. Whether you include replacement reserves in NOI or not is largely based on context, but in either case your choice should be based on sound reasoning.
Source: Understanding Replacement Reserves in Commercial Real Estate
https://www.creconsult.net/market-trends/understanding-replacement-reserves-in-commercial-real-estate/
Being completely comfortable with the time value of money is critical when working in the field of finance and commercial real estate. The time value of money is impossible to ignore when dealing with loans, investment analysis, capital budgeting, and many other financial decisions. It’s a fundamental building block that the entire field of finance is built upon. And yet, many finance and commercial real estate professionals still lack a solid working knowledge of time value of money concepts, and they consistently make the same common mistakes. In this article, we take a deep dive into the time value of money, discuss the intuition behind the calculations, and we’ll also clear up several misconceptions along the way.
The time value of money is defined as the economic principle that a dollar received today has greater value than a dollar received in the future. What does the time value of money mean? The intuition behind the time value of money is easy to see with a simple example. Suppose you were given the choice between receiving $100,000 today or $100,000 in 100 years. Which option would you rather take? Clearly, the first option is more valuable for the following reasons:
No Risk – There is no risk with getting money back that you already have today.
Higher Purchasing Power – Because of inflation, $100,000 can be exchanged for more goods and services today than $100,000 in 100 years. Put another way, just think back to what $100,000 could buy you 100 years ago. $100,000 in 1922 would be the equivalent of roughly $1,700,000 today.
Opportunity cost – a dollar received today can be invested now to earn interest, resulting in a higher value in the future. In contrast, a dollar received in the future cannot begin earning interest until it is received. This lost opportunity to earn interest is the opportunity cost.
For these reasons, we can boil down the time value of money into two fundamental principles:
With this fundamental intuition out of the way, let’s jump right into the two basic techniques used in all time value of money calculations: compounding and discounting.
All time value of money problems involve two fundamental techniques: compounding and discounting. Compounding and discounting is a process used to compare dollars in our pocket today versus dollars we have to wait to receive at some time in the future. Before we dive into specific time value of money examples, let’s first review these basic building blocks.
Compounding is about moving money forwards in time. It’s the process of determining the future value of an investment made today and/or the future value of a series of equal payments made over time (periodic payments).
What’s the intuition behind compounding? Most people immediately understand the concept of compound growth. If you invest $100,000 today and earn 10% annually, then your initial investment will grow to some figure larger than the original amount invested. For example, in the illustration above $100,000 is invested at time 0 and grows at a 10% rate to $121,000 at time 2. We’ll go over the details of this calculation later, but for now just focus on the intuition. The initial investment compounds because it earns interest on the principal amount invested, plus it also earns interest on the interest.
Discounting is about moving money backwards in time. It’s the process of determining the present value of money to be received in the future (as a lump sum and/or as periodic payments). Present value is determined by applying a discount rate (opportunity cost) to the sums of money to be received in the future.
What’s the intuition behind discounting? When solving for the future value of money set aside today, we compound our investment at a particular rate of interest. When solving for the present value of future cash flows, the problem is one of discounting, rather than growing, and the required expected return acts as the discount rate. In other words, discounting is merely the inverse of growing.
So now that we have some basic intuition about compounding and discounting, let’s take a look at the 5 components of all time value of money problems. Why is it important to understand this? Because in every single time value of money problem, you’ll know four out of these five variables and will be able to easily solve for the fifth unknown variable. The 5 components of all time value of money problems are as follows:
Periods (n). The total number of compounding or discounting periods in the holding period.
Rate (i). The periodic interest rate or discount rate used in the analysis, usually expressed as an annual percentage.
Present Value (PV). Represents a single sum of money today.
Payment (PMT). Represents equal periodic payments received or paid each period. When payments are received they are positive, when payments are made they are negative.
Future Value (FV). A one-time single sum of money to be received or paid in the future.
Every single time value of money problem includes the above 5 components. Understanding this is critical because of one simple fact: if you can identify any 4 of the 5 components, then you can easily solve for the 5th. The key is to simply learn to identify the 4 known variables in a time value of money problem. Let’s revisit the example above to illustrate how this works.
Suppose you invest $100,000 today at 10% compounded annually. What will this investment be worth in 2 years?
First, we know that our present value (PV) is $100,000 since this is what we are investing today. Next, the rate (i) is given to us as 10%. Third, the number of periods (n) in this problem is 2 years. So that leaves 2 remaining variables out of the five: payment (PMT) and future value (FV). Which one out of the two do we know? While it wasn’t explicitly given to us, we do know that the payment (PMT) in this problem is zero. Whenever payment isn’t explicitly given to us, it’s implied that there is no payment. So, all that leaves us with is the future value (FV) component, which we can now easily solve. For now, don’t worry about actually doing the calculations. Instead, just focus on identifying the 4 known variables and the final 5th unknown.
Time value of money problems can always be visualized using a simple horizontal or vertical timeline. When you’re first learning how to solve time value of money problems, it’s often helpful to draw the 5 components of each problem out on a timeline, so you can visualize all the moving pieces.
As shown above, the 5 components of all time value of money problems (PV, FV, PMT, i, n) can be illustrated on a simple horizontal timeline. It’s also common to see a vertical timeline as well:
When drawing out a timeline for a time value of money problem, simply fill in the 4 known components, so you can clearly identify and solve for the unknown component. Here’s a timeline for the example compounding problem above, showing the 4 known components:
Note that it’s important to distinguish between a point in time and a period of time. The portion of time between “Time 0” and “Time 1” is collectively Period 1. However, “Time 0” and “Time 1” are each just specific points in time during Period 1. Time 0 is the beginning of Period 1, and Time 1 is the end of Period 1. In the same way, Time 1 is the beginning of Period 2 and Time 2 is the end of Period 2.
Before we dive into specific time value of money example problems, let’s quickly go over one of the most common roadblocks people run into. One of the most common mistakes when it comes to the time value of money is ignoring the frequency of the components. Whenever you are solving any time value of money problem, make sure that the n (number of periods), the i (interest rate), and the PMT (payment) components are all expressed in the same frequency. For example, if you are using an annual interest rate, then the number of periods should also be expressed annually. If you’re using a monthly interest rate, then the number of periods should be expressed as a monthly figure. In other words, n should always be the total number of periods, i should be the interest rate per period, and PMT should be the payment per period.
Note that most financial calculators have a “Payment Per Year” setting that attempts to autocorrect the consistency of the n and i components. If you’re just starting out with a financial calculator, it’s a good idea to ignore this functionality altogether. Instead, you can simply set the payments per year in the calculator to 1 (one) and then keep the n, i, and PMT components consistent. This will greatly reduce the errors and frustration you have with your financial calculator.
In time value of money problems, it’s also important to remember that negative and positive signs have different meanings. One helpful way to think about sign changes is as inflows and outflows of money. A negative sign simply means money is flowing out of your pocket. A positive sign means money is flowing into your pocket.
The above 5 components of every time value of money problem are the same regardless of how you decide to solve for the unknown. There are several popular financial calculators available, and all of them include the above 5 components as buttons. Teaching you how to use a financial calculator is beyond the scope of this article, but if you’re just getting started we recommend either the Hewlett Packard 10BII or the Texas Instruments BA II Plus. They both come with instruction manuals that include helpful tutorials.
Additionally, all time value of money problems can also be solved in Excel. Below, we provide you a solutions worksheet containing sample time value of money problems and answers. This will give you the exact formulas you can use in Excel to solve the most common time value of money problems.
With the above foundations out of the way, let’s dive into some time value of money practice problems. There are 3 fundamental types of compounding problems, and also 3 fundamental types of discounting problems. Together, these make up what’s commonly referred to as the 6 functions of a dollar.
These fundamental time value of money problems come up over and over again in finance and commercial real estate, so mastering them will go a long way towards strengthening your skill set. As mentioned, we are providing you with a solutions worksheet below containing answers to the following 6 time value of money problems. As you read through the questions, focus on identifying the 4 known components, and if you are already comfortable with a financial calculator, try solving them first before looking at the answers.
Half of the 6 functions of a dollar are compounding problems. These time value of money problems include finding the future value of a lump sum, the future value of a series of payments, and the payment amount needed to achieve a future value. Let’s dive into each of these problems with specific time value of money examples.
Future value of a single sum
This type of problem compounds a single amount to a future value. Here’s an example of this type of time value of money problem: What will $100,000 invested today for 7 years grow to be worth if compounded annually at 5% per year?
To solve this problem, simply identify the 4 known components and then use a calculator to find the 5th unknown component. In this problem, we know the present value PV is -$100,000 because it’s what’s invested today. It’s negative because it’s leaving our pocket when we put it into the investment. The number of periods N is 7 years, and the rate I is 5%. The N and I components are both expressed annually, so they are consistent. Knowing this, we can simply plug those 4 components into the calculator and solve for future value FV, which is $140,710.
Future value of a series of payments
This type of problem compounds an annuity to a future value. Here’s an example of this type of time value of money problem: If you deposit $12,000 at the end of each year for 10 years earning 8% annually, how much money will be in the account at the end of year 10?
To solve this problem, let’s first identify the 4 known components. We know that the payment amount PMT is -$12,000 because that’s what we are depositing at the end of each year. We also know that the interest rate I is 8% and the total number of periods N is 10 years. What about the present value? Well, because we aren’t starting with anything, our present value is simply $0. Again, in this problem the total number of compounding periods is expressed annually and so is the interest rate, so the n and i components are consistent. Now we can easily solve for the future value FV, which is the 5th remaining component.
Payments needed to achieve a future value
This type of problem compounds a series of equal payments into a future value and is also known as a sinking fund payment. Here’s an example of this type of time value of money problem: At a 7% interest rate, how much needs to be deposited at the end of each month over the next 10 years to grow to be exactly $50,000?
Let’s start by identifying the 4 known variables. We know that the rate I is 7%, and it is implied to be an annual rate. Next, we are given the total number of periods N which is 10 years, and finally the future value FV we are trying to achieve is $50,000. A quick check ensures that the rate and the number of periods are both expressed in years, but what about the payment frequency? The payment frequency in this problem is expressed monthly, so we are going to have to do some conversion to set this problem up correctly. Let’s convert everything to a monthly frequency so we are consistent with our payments.
To accomplish this, we can simply divide the 7% interest rate by 12 months to get .58% per month. Next we can multiply our 10-year analysis period by 12, since there are 12 months in each year, to get 120 total months. Now our N is 120 months, I is .58% per month, our FV is $50,000, and we can solve for a monthly payment PMT amount. Now we can simply plug these 4 known components in and solve for the payment PMT needed.
The other half of the 6 functions of a dollar involve discounting. These time value of money problems involve finding the present value of a lump sum, the present value of a series of payments, and the payment amount needed to amortize a present value such as a loan. Let’s dive into these discounting problems with some specific time value of money examples.
Present value of a single sum
This type of problem discounts a single future amount to a present value. Here’s an example of this type of time value of money problem: A U.S. savings bond will be worth $10,000 in 10 years. What should you pay for it today to earn 6.5% annually?
To solve this time value of money problem, let’s take a look at the 4 variables that we know. We are given the future value FV of $10,000, the number of periods N is 10 years, and the rate I is 6.5% per year. Both the rate and the number of periods are consistent, so we can now solve for the unknown present value PV.
Present value of a series of payments
This type of problem discounts an annuity (or series of equal payments) to a present value. Here’s an example of this type of time value of money problem: An insurance company is offering an annuity that pays $2500 per month for the next 20 years. How much should you pay for the annuity to earn 8% per year?
In this time value of money problem we know that the payment PMT is $2500 per month, the total number of periods N is 20 years, and the rate I is 8% per year. The rate and the total number of periods is consistent as annual figures at first glance. However, we also have monthly payments. So, we have to convert our annual number of periods (20 years) to 240 months, and also convert our annual rate of 8% to a monthly rate of .667. Now we can now easily solve for the present value PV.
Amount needed to amortize a present value
This type of problem determines a series of equal payments necessary to amortize a present value. Here’s an example of this type of time value of money problem: What are the monthly payments on a 30-year loan of $300,000 at an annual rate of 4.5% compounded monthly?
In this problem, we are given the total number of periods N of 30 years, a present value PV of $300,000, an annual interest rate I of 4.5% compounded monthly, and because this is a loan amortized over 30 years, it is implied that the future value FV is $0. After a quick check, it appears that the number of periods and the rate are actually expressed in different compounding periods, which of course presents a conflict. To resolve this, let’s adjust the n and i components so they are both expressed monthly. Using the formulas above, we can convert the total number of compounding periods to 30 x 12, or 360 months and the rate to 4.5% / 12, or 0.375% per month. Now we have our 4 known components and can easily solve for the present value.
As mentioned above, there are many ways to solve a time value of money problem, including financial calculators, regular calculators, software, and spreadsheets. While going over calculator keystrokes is outside the scope of this article, we did put together an Excel worksheet with solutions to the above 6 problems. You are welcome to download it for free here:
Time value of money concepts are at the core of valuation and other finance and commercial real estate topics. This article provides a solid foundation for understanding time value of money at an intuitive level, and it also gives you the tools needed to solve any time value of money problem. The time value of money is required as a basic building block in finance, and mastering these concepts will pay dividends for years to come.
Source: Time Value of Money: A Beginner’s Guide
https://www.creconsult.net/market-trends/time-value-of-money-a-beginners-guide/
The internal rate of return (IRR) is a widely used investment performance measure in finance, private equity, and commercial real estate. Yet, it’s also widely misunderstood.
The internal rate of return (IRR) is a financial metric used to measure an investment’s performance. The textbook definition of IRR is that it is the interest rate that causes the net present value to equal zero. Although the IRR is easy to calculate, many people find this textbook definition of IRR difficult to understand. Fortunately, there’s a more intuitive interpretation of IRR.
Simply stated, the internal rate of return (IRR) for an investment is the percentage rate earned on each dollar invested for each period it is invested.
We’ll walk through some examples of this more intuitive meaning of IRR step by step. But first, let’s take a closer look at the IRR formula.
The Internal Rate of Return (IRR) formula solves for the interest rate that sets the net present value equal to zero.
The IRR formula can be difficult to understand because you first have to understand the Net Present Value (NPV). Since the IRR is an interest rate that sets NPV equal to zero, what is NPV, and what does it mean to set the NPV equal to zero?
Simply stated, the Net Present Value (NPV) is the present value of all cash inflows (Benefits) minus the present value of all cash outflows (Costs). In other words, NPV measures the present value of the benefits minus the present value of the costs:
So, another way to think about the IRR formula is that it is calculating the interest rate that makes the present value of all positive cash flows equal to the present value of all negative cash flows. When this happens, then the net present value will equal zero:
This is what it means to set the net present value equal to zero. If we want to solve for IRR, then we have to find an interest rate that makes the present value of the positive cash flows equal to the present value of the negative cash flows.
Next, let’s walk through how to calculate IRR in more detail, and then we’ll look at some examples.
In most cases, the IRR is calculated by trial and error. This is accomplished iteratively by guessing different interest rates to use in the IRR formula until one is found that causes the net present value to equal zero.
A guess is used for the interest rate variable in the IRR formula, and then each cash flow is discounted back to the present time using this guess as the interest rate (often called the discount rate). This process repeats until a discount rate is found that sets the net present value equation equal to zero.
In the example above, the present cost is $100,000 as shown in Time 0. This is shown as a negative number when dealing with the time value of money because it is a cash outflow or cost. Each future cash inflow is shown on the vertical timeline as a positive number starting in Time 1 and ending in Time 5.
The IRR calculation repeatedly guesses the interest rate that will make the sum of all present values equal to zero. When this happens, the present value will equal the present cost, which will set the net present value equal to zero.
As you can imagine, guessing different interest rates over and over is a tedious and time-consuming process, so it is hard to calculate IRR by hand. However, the IRR calculation can be easily performed using a financial calculator or the IRR function in Excel.
The internal rate of return can be calculated using the IRR function in Excel:
To calculate IRR in Excel, you need:
The reason Excel requires evenly spaced cash flows is that IRR calculates a periodic interest rate. To calculate a periodic rate, cash flows must occur regularly over the same period of time. For example, an annual IRR will require cash flows that occur annually and a monthly IRR will require cash flows that occur monthly.
The XIRR function in Excel is commonly used to calculate a return on a set of irregularly spaced cash flows. Instead of solving for an effective periodic rate like the IRR, the XIRR calculates an effective annual rate that sets the net present value equal to zero.
Memorizing IRR formulas and calculations is one thing, but truly understanding what IRR means will give you a big advantage. Let’s walk through a detailed example of IRR and show you exactly what it does, step-by-step.
Suppose we are faced with the following series of cash flows:
This is pretty straightforward. An investment of $100,000 made today will be worth $161,051 in 5 years. As shown, the IRR calculated is 10%. Now let’s take a look under the hood to see exactly what’s happening to our investment in each of the 5 years:
As shown above in year 1 the total amount we have invested is $100,000 and there is no cash flow received. Since the 10% IRR in year 1 we receive is not paid out to us as an interim cash flow, it is instead added to our outstanding investment amount for year 2. That means in year 2 we no longer have $100,000 invested, but rather we have $100,000 + 10,000, or $110,000 invested.
Now in year 2 this $110,000 earns 10%, which equals $11,000. Again, nothing is paid out in interim cash flows, so our $11,000 return is added to our outstanding internal investment amount for year 3. This process of increasing the outstanding “internal” investment amount continues all the way through the end of year 5 when we receive our lump sum return of $161,051. Notice how this lump sum payment includes both the return of our original $100,000 investment, plus the 10% return “on” our investment.
This is much more intuitive than the common mathematical explanation of IRR as “the discount rate that makes the net present value equal to zero.” While technically correct, it doesn’t help us all that much in understanding what IRR actually means. As shown above, the IRR is clearly the percentage rate earned on each dollar invested for each period it is invested. Once you break it out into its individual components and step through it period by period, this becomes easy to see.
IRR can be a helpful decision indicator for selecting an investment. However, there is one critical point that must be made about IRR: it doesn’t always equal the compound annual growth rate (CAGR) on an initial investment.
Let’s take an example to illustrate. Suppose we have the following series of cash flows that also generates a 10% IRR:
In this example, an investment of $100,000 is made today and in exchange we receive $15,000 every year for 5 years, plus we also sell the asset at the end of year 5 for $69,475. The calculated IRR of 10% is the same as our first example above. But let’s examine what’s happening under the hood to see why these are two very different investments:
As shown above in year 1 our outstanding investment amount is $100,000, which earns a return on investment of 10% or $10,000. However, our total interim cash flow in year 1 is $15,000, which is $5,000 greater than our $10,000 return “on” investment. That means in year 1 we get our $10,000 return on investment, plus we also get $5,000 of our original initial investment back.
Now, notice what happens to our outstanding internal investment in year 2. It decreases by $5,000 since that is the amount of capital we recovered with the year 1 cash flow (the amount exceeding the return on portion). This process of decreasing the outstanding “internal” investment amount continues all the way through the end of year 5. Again, the reason our outstanding initial investment decreases is that we are receiving more cash flow each year than is needed to earn the IRR for that year. This extra cash flow results in capital recovery, thus reducing the outstanding amount of capital we have remaining in the investment.
Why does this matter? Let’s take another look at the total cash flow columns in each of the above two charts. Notice that in our first example the total cash flow was $161,051 while in the second chart the total cash flow was only $144,475. But wait a minute, I thought both of these investments had a 10% IRR?! Well, indeed they did both earn a 10% IRR, as we can see by revisiting the intuitive definition of IRR:
The Internal rate of return (IRR) for an investment is the percentage rate earned on each dollar invested for each period it is invested.
The internal rate of return measures the return on the outstanding “internal” investment amount remaining in an investment for each period it is invested. The outstanding internal investment, as demonstrated above, can increase or decrease over the holding period. IRR says nothing about what happens to capital taken out of the investment. And contrary to popular belief, the IRR does not always measure the return on your initial investment.
A good IRR is one that is higher than the minimum acceptable rate of return. In other words, if your minimum acceptable rate of return, also called a discount rate or hurdle rate, is 10% but the IRR for a project is only 8%, then this is not a good IRR. On the other hand, if the IRR for a project is 18%, then this is a good IRR relative to your minimum acceptable rate of return.
Individual investors usually think about their minimum acceptable rate of return, or discount rate, in terms of their opportunity cost of capital. The opportunity cost of capital is what an investor could earn in the marketplace on an investment of similar size and risk. Corporate investors usually calculate a minimum acceptable rate of return based on the weighted average cost of capital.
Before determining whether an investment is worth pursing, even if it has a good IRR, it is important to be aware of some IRR limitations.
IRR can be useful as an initial screening tool, but it does have some limitations and shouldn’t be used in isolation. When comparing two or more investment alternatives, the IRR can be especially problematic. Let’s review some disadvantages of IRR you should be aware of.
IRR and timing of cash flows
The internal rate of return for an investment only measures the return in each period on the unrecovered investment balance, which can vary over time. That means the timing of the cash flows can impact the profitability of an investment, but this won’t always be indicated by the IRR. Recall the two IRR examples discussed above:
The first investment on the left produces cash flow each year, while the second does not. Although both investments produce a 10% IRR, one is clearly more profitable than the other. The reason is that in the first investment, the unrecovered investment balance changes from year to year, while in the second investment it does not.
As a result, the IRR could conflict with other measures of investment performance, such as the equity multiple or net present value. This is one reason why the IRR can be useful as an initial screening tool, but shouldn’t be used in isolation.
IRR ignores the size of the project
The IRR also does not account for the magnitude of a project. That means the project with the highest IRR won’t necessarily be the project with the highest profit. For example, consider the following two options.
Even though option 1 has a higher internal rate of return, option 2 has the highest profit. This can happen because IRR ignores the size of the project.
Multiple IRRs
When a stream of cash flows has more than one sign change, then multiple IRRs can exist. For example, consider the following scenario:
When you calculate an IRR on these cash flows, you actually get multiple solutions! The reason this occurs has to do with Descartes’ rule of signs concerning the number of roots in a polynomial. This means that the number of positive IRRs can be as many as the number of sign changes in the cash flows.
The Modified Internal Rate of Return (MIRR) was designed to solve the multiple IRR problem and many other limitations of IRR as well.
One of the most commonly cited limitations of the IRR is the so-called “reinvestment assumption.” In short, the reinvestment assumption says that the IRR assumes interim cash flows are reinvested at the same rate as the IRR.
The idea that the IRR assumes interim cash flows are reinvested is a major misconception that’s unfortunately still taught by many business school professors today.
As shown in the step-by-step approach above, the IRR makes no such assumption. The internal rate of return is a discounting calculation and makes no assumptions about what to do with periodic cash flows received along the way. It can’t because it’s a DISCOUNTING function, which moves money backwards in time, not forward.
Should you consider the yield you can earn on interim cash flows that you reinvest? Absolutely, and there have been various measures introduced over the years to turn the IRR into a measure of return on the initial investment, such as the Modified Internal Rate of Return (MIRR).
This is not to imply that the IRR doesn’t have some limitations, as we discussed in the examples above. It’s just to say that the “reinvestment assumption” is not among them.
The Internal Rate of Return (IRR) is a popular measure of investment performance. While it’s normally explained using its mathematical definition (the discount rate that causes the net present value to equal zero), this article showed step-by-step what the IRR actually does. What is IRR? Once you walk through the examples above, this question becomes much easier to answer. It also becomes clear that the IRR isn’t always what people think it is. That is, IRR isn’t always the compound annual growth rate on the initial investment amount. IRR can be useful as an initial screening tool, but it does have several limitations and therefore should not be used in isolation.
Source: Internal Rate of Return (IRR): What You Should Know
https://www.creconsult.net/market-trends/internal-rate-of-return-irr-what-you-should-know/
