Time Value of Money: A Beginner's Guide

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.

What is the Time Value of Money

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:

• More is better than less.
• Sooner is better than later.

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.

Compounding and Discounting: The Foundation For All Time Value of Money Problems

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.

The 5 Components of All Time Value of Money Problems

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.

The Key to Solving Any Time Value of Money Problem

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.

The Time Value of Money Timeline

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.

Consistency of Time Value of Money Components

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.

Cash Inflows vs Cash Outflows

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.

Financial Calculators and The Time Value of Money

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.

Time Value of Money Problems: The 6 Functions of a Dollar

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.

3 Basic Types of Compounding Problems

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.

3 Basic Types of Discounting Problems

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.

Time Value of Money Solutions Worksheet

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:

Conclusion

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/

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Internal Rate of Return (IRR): What You Should Know

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.

What is Internal Rate of Return (IRR)?

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.

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.

How to Calculate IRR

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.

How to Calculate IRR in Excel

The internal rate of return can be calculated using the IRR function in Excel:

To calculate IRR in Excel, you need:

• A set of evenly spaced cash flows. This is C2:C7 in the IRR Excel example above.
• At least one positive and one negative number in your set of cash flows. In the example above, the negative cash outflow occurs in year 0 and years 1-5 contain positive cash inflows.
• An optional guess to help the IRR formula in Excel. A guess is usually not necessary when calculating IRR in Excel. If the guess is omitted, then by default, Excel will use 10% as the initial guess. If the IRR can’t be found with up to 20 guesses, then Excel will return an error. In this case, a reasonable guess can be provided to the IRR function in Excel. For example, if you have monthly or weekly cash flows, then you may need to use a guess that is much smaller than the default 10%.

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.

IRR Meaning

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 vs CAGR

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.

What is a good IRR?

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 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.

• Option 1: Invest 100 at time 0 and get back 200 at time 1. This results in a 100% IRR, and a gross profit of 200-100 or 100.
• Option 2: Invest 1,000,000 at time 0 and get back 1,100,000 at time 1. This results in a 10% IRR, and a gross profit of 1,100,000 – 1,000,000, or 100,000.

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.

IRR Reinvestment Assumption Myth

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.

Conclusion

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/

Multifamily sellers: How to qualify a buyer before going under contract

Multifamily sellers: How to qualify a buyer before going under contract

Don’t waste time and opportunities: learn how to select the right buyer every time

As the seller of a multifamily asset, it’s crucial that the buyer you select is the best possible prospect for your property. Don’t waste time, money, and opportunities: you must ensure they’re qualified and can close and execute the contract as signed.

Keep reading to learn why it’s essential to qualify a buyer before going under contract on your multifamily property and how to do it.

Why do I need to qualify a buyer?

It’s important to close with the first buyer you select. If you don’t, each buyer after that will ask themselves, “What did that other buyer discover about this property that I am missing?”.

When you enter into a contract with a refundable deposit, you’re basically giving your chosen buyer a free option on your property for a period of time, typically 30–60 days. Before you proceed, you must be confident that they can close and execute the contract as signed.

What’s more, your tenants and staff will be disturbed throughout the contract process. To minimize the period of disruption, you should do all you can to ensure the transaction will close successfully at the end of the contract process.

As a seller, you’re required to provide due diligence information to the prospective buyer. When you qualify your buyer, you’ll greatly reduce the risk of wasting a lot of time and doing a lot of work only to not close on the property.

How do I qualify a buyer?

Before you sign the contract, make sure that your prospective buyer can provide certain items. Always ask them for the following:

– Proof of funds

– Lender pre-qualification

– A list of the other properties they own

– A list of the sellers and agents that they have worked with

For added reassurance, it’s recommended that you call the buyer’s lender to confirm their pre-qualified status. You can also call the agents, sellers, and buyers they’ve closed with in the past to enquire about how the transactions went.

Has the buyer toured the property in person before making an offer? Have they reviewed the due diligence information beforehand? If they have, this is a great sign. It’s proof that they have seen and have taken into account any issues with your property, and this greatly reduces the chances that they may later want to back out of the sale, saying they were unaware of the building’s condition. Be very wary of a buyer who doesn’t tour your property in person.

A prospective buyer who shows they’re motivated and wants to move quickly is also a great sign for a successful closing. The shorter the due diligence period, the better, and the larger the deposit, the better.

When you spend the time making sure your prospective buyer fulfills these criteria, you’ll put yourself in a great position to close successfully and ensure a quick and smooth transaction.

If you need help selling your multifamily property, eXp Commercial is here. Our objective as your multifamily advisor is to help you achieve your investment goals: from determining the listing price to selecting the best buyer and handling the sale process through to the closing, we’ll facilitate a smooth transaction for you.

 

Source: Multifamily sellers: How to qualify a buyer before going under contract

https://www.creconsult.net/market-trends/multifamily-sellers-how-to-qualify-a-buyer-before-going-under-contract/

Mason Square

Fully Equipped Car Wash For Sale
1250 Douglas Rd. | Oswego, IL | 3,750 SF | 6 Bays | 1.19 Acres
Mason Square Car Wash, a fully equipped and operational 6-bay carwash in southwest suburban Chicago’s Oswego, IL. Ideally located on an out-lot of the Mason Square Shopping Center along heavily trafficked Route 34, averaging 45,000 vehicles per day,
Listing Agent: Randolph Taylor 630.474.6441 | rtaylor@creconsult.net
https://www.creconsult.net/fully-equipped-car-wash-oswego-il-route-34/

Apartment Investing Case Study

In this article we are going to conduct an investment analysis on a 140 unit apartment building acquisition. We’ll walk through the process of forecasting cash flows and also explain the calculations needed to determine investment value. Read on as we take a deep dive into the world of apartment investing.

Apartment Investment Case Study Objectives

First, before we jump into the details of this investment analysis, let’s quickly go over our objectives. Here’s what we’ll accomplish in this case study:

• Forecast the before tax cash flows over a 5 year holding period for a 140 unit apartment building.
• Calculate the maximum supportable loan amount based on the debt service coverage ratio and the loan to value ratio.
• Calculate the gross rent multiplier.
• Calculate the cash on cash return.
• Calculate the debt service coverage ratio.
• Complete a discounted cash flow analysis to determine the levered and unlevered internal rate of return (IRR) and net present value (NPV).
• Stress test the vacancy rate to analyze how it impacts cash flow.
• Stress test the vacancy rate to analyze how it impacts the debt service coverage ratio.
• Stress test the loan interest rate to analyze how it impacts the debt service coverage ratio.

Apartment Investment Case Study Scenario

An investor is considering buying an apartment building with 140 units offered for sale at $16,500,000. The subject apartment building has the following unit mix: 

Additionally, the following assumptions are also being made by the investor in order to construct a 5-year cash flow proforma:

Vacancy and Credit Loss
In the current market, vacancy and credit losses are running at 9%. Due to the improving market conditions as well as the investor’s prior experience leasing and operating multifamily buildings, it’s expected that vacancy will steadily decline over the next 5 years to 5%.

Potential Rental Income
Potential rental income is based on the above unit mix. The 1-bedroom and studio rental rates are expected to increase at 2% annually. The 2-bedroom units are also expected to increase at 2% annually.

Financing
After a preliminary discussion with a relationship manager at a local bank it’s determined that a loan can be extended based on the lesser of a 1.25x debt service coverage ratio or 80% loan to value. Additionally, assuming the underwriting process doesn’t reveal any red flags, it’s expected that the loan will be based on a 20 year amortization and a 6% interest rate.

Operating Expenses
The following table breaks out historical operating expenses for the property as well as projected increases over the holding period.

Reserves for Replacement
In addition to the above operating expenses a reserve for replacement of $250 per unit will also be included in this analysis.

Sales Price and Cost of Sale
The projected sale price is estimated by applying a conservative 3% annual growth rate to the acquisition price of the property over the 5 year holding period. Additionally, a 6% cost of sale is factored into the net sales proceeds to account for selling costs.

Acquisition Costs
In addition to the $16,500,000 purchase price, an additional $50,000 is factored in to account for closing costs.

Discount Rate
For the purposes of this case study we’ll assume that the investor’s discount rate, or required rate of return, is 15%.

Apartment Investment Proforma

Using the above assumption we can now build a proforma for the proposed apartment investment property. This can be accomplished in Excel in a few hours, or in our case we did this entire analysis in less than 10 minutes.

Now that we have a 5 year proforma, let’s take a look at what the maximum supportable loan amount is based on these cash flows. Using the above 1.25x DSCR and 80% LTV assumptions we get the following:

As shown above, the maximum loan analysis based on year 1 proforma NOI is about $12,250,000. Assuming we can get this loan amount approved at the 6% rate amortized over 20 years, this is the updated proforma:

You’ll notice that the debt we added to the property reduced our cash flow significantly, however, this also reduces our equity requirement and therefore improves yield. We’ll discuss this in more detail below, but first let’s take a look at some quick ratios:

Year 1 cash on cash return is 6.14%. At first glance this is well below our target rate of return of 15%, However, because the cash on cash return only takes into account a single year instead of the entire holding period, the IRR and NPV below will be much more relevant for our purposes.

The gross rent multiplier is 7.58x, which taken by itself doesn’t mean much. However, assuming we have some other submarket data to compare this to we can check whether or not it’s in line with comparable properties. The important take away here is to check whether or not the gross rent multiplier is abnormal, and if so, to further investigate why.

The debt service coverage ratio is in line with the bank’s requirement of 1.25x and improves over the holding period. This is partially due to our assumption of increasing occupancy over our investment horizon, as well as increasing rental rates. We’ll stress test these assumptions further below, but at first glance the DSCR is adequate for this deal.

Finally, the breakeven occupancy on this property is just under 79%. This means total vacancy can go up to 21% and the property will still produce enough cash flow to cover expenses and debt service. Good to know.

Apartment Discounted Cash Flow Analysis

Screening this property with the above ratios is a good starting point, but ultimately a full discounted cash flow analysis should be completed to determine IRR and NPV:

As you can see above, the levered internal rate of return comes in at 18.65%. While the above Year 1 cash on cash return didn’t meet our required rate of return of 15%, the full discounted cash flow analysis shows that the yield on this investment comfortably exceeds our target return. In fact, the net present value tells us that we can pay about $650,000 over the asking price and we’ll still achieve our target yield. This can come in handy during negotiations, especially in a competitive bidding situation.

Apartment Investment Sensitivity

So after a quick first pass it appears that this potential acquisition meets our target yield based on some reasonable assumptions. However, what if our assumption of a declining vacancy rate, from 9% in Year 1 to 5% in Year 5, turns out to be overly optimistic? Let’s take a look at what we deem to be a worst case scenario – that the market vacancy rate actually deteriorates after we acquire the property to 15%, rather than the current 9%. How will this impact our IRR?

While a worse than expected vacancy rate does reduce our cash flow, it turns out that we’d still achieve our target yield of 15%. What about the debt service coverage ratio? Will a higher than expected vacancy rate violate our 1.25x DSCR loan covenant? Let’s take a look at what happens to the debt service coverage ratio as we move from a 6% vacancy rate all the way up to a 20% vacancy rate:

As shown above, in Year 1 we actually can’t support a 1.25x DSCR requirement at a vacancy rate of 10%. While this does improve over the holding period, this could be problematic for us if the market turns out worse than expected. This could also be discovered during the loan underwriting process, resulting in a lower loan amount or stronger loan covenants. This information might come in handy during negotiations.

Next, let’s take a look at how sensitive our DSCR is to our loan interest rate. This is useful in understanding how much wiggle room there is in negotiating the interest rate with our bank, as well as understanding how capital market conditions might affect the buyer of our property at the end of the holding period.

As shown above, 6% appears to be the upper limit loan interest rate based on Year 1 cash flow. Once the rate gets beyond 6% it starts eating into our 1.25x DSCR requirement. However, in subsequent years, assuming we hit our projections, the property can support a much higher interest rate based on the same loan amount. This provides some cushion toward the end of our holding period, in case the then prevailing market conditions change and interest rates rise.

Conclusion

While there are several different angles you can look at when underwriting a potential acquisition, this simple case study illustrates a few core concepts. First, sizing up a loan amount based on proforma cash flow. Second, calculating and interpreting several quick but useful ratios. Third, understand whether or not an acquisition meets a target yield. And finally, understanding how changes in our assumptions affect our resulting cash flow and underwriting ratios. While there are several additional layers of analysis we can dive into for a property like this, the above analysis gives us a good starting point for screening this particular property.

 

Source: Apartment Investing Case Study

https://www.creconsult.net/market-trends/apartment-investing-case-study/

Difference Between Market Value and Investment Value in Commercial Real Estate

Value is traditionally defined as the power of a good to command other goods or services when exchanged. Within this broad definition of value, there are various types of value given to real property, such as investment value, market value, insurable value, assessed value, liquidation value, or replacement value. In this article we’ll go over different types of real estate value, and then zero in and focus on the difference between investment value and market value, which is often confused by commercial real estate professionals.

Types of Real Estate Value

First of all, let’s briefly go over several common types of commercial real estate value, then we’ll dive into the difference between investment and market value and clarify with an example.

Market Value is what’s typically meant when referring to a property’s value and is the value used for loan underwriting purposes. The Appraisal Foundation has a specific definition for market value as published in the Uniform Standards of Professional Appraisal Practice (USPAP). According to the Appraisal Foundation, market value is the most probable price a property would bring in a competitive and open market under all conditions requisite to a fair sale, with the buyer and seller each acting prudently and knowledgeably, and assuming the price is not affected by undue stimuli.

Investment Value refers to the value to a specific investor, based on that investor’s requirements, tax rate, and financing.

Insurable Value – This covers the value of the portions of a property that are destructible for the purposes of determining insurance coverage.

Assessed Value – Assessed value is the value determined by the local tax assessor to levy real estate taxes.

Liquidation Value – Liquidation value establishes the likely price that a property would sell for during a forced sale, such as a foreclosure or tax sale. Liquidation value is used when there is a limited window for market exposure or when there are other restrictive sale conditions.

Replacement Value – This is the cost to replace the structure with a substitute structure that is identical or that has the same utility as the original property.

A property can have any of the above types of value at any given time, with no two values necessarily being the same. This is an important point to remember when trying to understand the value of a commercial real estate property. This is especially true when determining market value and investment value.

Approaches to Market Value

Market value is what’s determined by an appraisal. During the commercial loan underwriting process, most lenders will require a third-party appraisal in order to determine a market value estimate, which is then used to find an appropriate loan amount and collateral value.

How do appraisers determine market value? First, before a market value can be estimated by an appraiser, the highest and best use for the property must be determined. The highest and best use is the legal use of a property that yields the highest present value. This process usually begins with evaluating the zoning laws to understand the legally permitted uses for the property.

Once the legally permitted uses are understood, the physically possible uses are then considered, within the bounds of the zoning ordinances. This takes into account the physical limitations of the property such as topography, size, layout, etc.

Finally, the financial feasibility is considered for all of the uses that are legally permissible and physically possible. The financially feasible use that produces the highest financial return is the highest and best use.

Once the highest an best use is determined, the appraiser can then determine market value. Appraisers may use three basic approaches to estimate market value: the sales comparison approach, the cost approach, and the income approach, using either the Direct Capitalization Method or the Discounted Cash Flow Model. We discuss each of these approaches in detail here, but below we’ll briefly summarize.

Sales Comparison Approach
The sales comparison approach links the value of a property to prices that recent buyers have paid for similar properties. In reality no two properties are exactly alike, but this approach can provide a reasonable estimation of value when there is a large quantity of recently sold comparable transactions.

Income Capitalization Approach
The income based approach to market value derives property value from the income it produces. The two methods used to value a property based on income are the direct capitalization method and the discounted cash flow valuation method.

Cost Approach
The cost approach bases value on the cost of reproducing a property, less any accrued depreciation. Accrued depreciation can come from three sources: physical deterioration, functional obsolescence, and external obsolescence. Once the replacement cost is determined and the accrued depreciation is netted out, the cost is added to the value of the land to determined an appropriate value based on cost.

Reconciliation of Value
In a full appraisal the above values are typically reconciled by using a weighted average to determine the final value estimate. For example, it may be determined that a higher weight should be given to the income approach because the available comparable sales data is weak, and as such this would be reflected in the final reconciled market value.

Approaches to Investment Value

While the market value process is usually used in appraisals for loan underwriting purposes, when deciding how much to pay for a property, investors also consider how much a property is worth. Investment value is the amount that an investor would pay for a specific property, given that investor’s investment objectives, including target yield and tax position.

Because investment value depends on an investor’s investment objectives, investment value is unique to the investor. As such, different investors can apply the same valuation methods and still come up with different investment values. Investors can choose from a variety of valuation methods when determining investment value, unlike appraisers who have to adhere to strict procedural guidelines. The following are the most common measures of investment value:

Comparable Sales (Comps) – This is the same sales comparison approach mentioned above that is used by appraisers. Typically investors will compare similar properties on a per square foot or per unit basis.

Gross Rent Multiplier – This is a simple ratio that measures investment value by multiplying the gross rents a property produces in a year by the market based Gross Rent Multiplier (GRM). The gross rent multiplier is usually derived from comparable properties within the same submarket.

Cash on Cash Return – The cash on cash return is another simple ratio used to determine investment value. It’s calculated by taking the first year’s proforma cash flow before tax and dividing it by the total initial investment.

Direct Capitalization – This is the same direct capitalization approach mentioned above that is used by appraisers. Capitalizing the income stream of a property is a very common and simple way to determine both market and investment value for a commercial property.

Discounted Cash Flow – The discounted cash flow model is used to find an internal rate of return, net present value, and a capital accumulation comparison. While the simple ratios above are quick and easy, they do come with several built-in limitation that are solved by a discounted cash flow analysis.

Investment Value vs Market Value

As shown above, market value is essentially the value of a property in an open market and is what’s determined by an appraisal. Investment value, on the other hand, is determined by an individual investor based on that investor’s unique investment criteria and goals.

Let’s take a quick example to illustrate this difference. Suppose an individual investor is contemplating the acquisition of a small apartment building and has projected the following cash flows:

As shown above, using the investor’s discount rate of 10%, the property generates a levered NPV of $210,820. This property is under contract with a total purchase price of $1,200,000 but the above analysis implies the investor could pay up to $1,410,820 and still achieve the target yield. Check out the intuition behind IRR and NPV to learn more about how this works.

The above levered analysis assumes that the investor can obtain a $960,000 loan (80% loan to value), amortized over 20 years at 5%. But suppose that during the underwriting process the bank orders a third-party appraisal and it comes in at $1,000,000 rather than the $1,200,000 the investor is paying. This also reduces the supportable loan amount to $800,000 (based on an 80% LTV) rather than the anticipated $960,000. Unfortunately, in this scenario it turns out that the seller refuses to sell for less than $1,200,000. In other words, this is an above market transaction where the investment value is higher than the market value. Does it still make sense to do the deal?

Let’s take a look at what the new cash flows look like to the investor in this new loan scenario:

As shown above the new loan amount reduces the yield to 16% from 22%. But this still exceeds the investor’s required return of 10%. So, does it make sense to do the deal? As always, it depends.

In most cases the investment value and the market value should be approximately equal, but sometimes these two values will diverge. On the one hand investment value can be higher than market value. This can happen when the value to a particular buyer is higher than the value to an average, well-informed buyer. For example, this might be the case when a company expands to a new building for sale across the street, paying more than market value in order to keep competitors out of the sub-market. The additional value over and above the market value provides a strategic advantage and therefore might be justified. In the case of an investor, investment value could sometimes be higher than market value due to favorable financing terms or tax treatment that is non-transferable.

On the other hand, investment value can be lower than market value. This might be the case if the particular asset class in question is not a property type that you specialize in. For example, if you are primarily a multifamily developer, then decide to evaluate a site for possible hotel development, your internal investment value may be less than the market value due to the steeper learning curve costs involved. Additionally, investment value could be lower than market value if you require an above-average return based on your existing portfolio mix. In these cases it can sometimes be tempting to pursue a deal even though investment value is less than market value. In these cases think carefully before getting distracted by something that might not make sense.

Conclusion

The safest policy is of course to make sure a transaction makes sense both from an investment value perspective as well as a market value perspective. Keep in mind that investment value is much more subjective than market value, and as such it can be abused. To avoid falling victim to investment value abuse, it’s best to always estimate market value whenever a relevant market exists.  Be especially skeptical if someone claims that investment value differs from market value in a way that supports his or her sales pitch. They might be right, but as the saying goes, trust but verify.

 

Source: Difference Between Market Value and Investment Value in Commercial Real Estate

https://www.creconsult.net/market-trends/difference-between-market-value-and-investment-value-in-commercial-real-estate/