# How The Time Value of Money Applies to Commercial Real Estate Valuation

# How The Time Value of Money Applies to Commercial Real Estate Valuation

So much of commercial real estate valuation revolves around discussions about cap rates, price per square foot, or just the total price paid. Some of the more in-depth approaches to valuation such as the internal rate of return (IRR) and net present value (NPV) are often taught to students and analysts esoterically without conveying an intuitive understanding of the fundamental concept that underlies the IRR and NPV approach: the time value of money (TVM).

Even when using sophisticated Excel models that include the “=IRR()” or “=NPV()” functions there usually isn’t a good understanding of what’s going on behind the scenes. In this article we’ll dig into the concept of the time value of money and then show some examples of why it’s so important to understand why the timing of cash flows on an investment matter so much.

## Foundations of the Time Value of Money

In its most simplistic definition, the time value of money states that the value of a dollar is highly dependent on when that dollar is received. For example, a dollar is worth more today than it will be worth one year from now (or two years, three years, etc. – theoretically even one day from now). This is true with the exception of a deflationary period where the value of a currency is actually falling over a period of time.

There are several reasons why the value of money is dependent on when it is received:

**Inflation**– The long term average inflation rate in the United States is around 3.0%, give or take. Based on this inflation rate, to buy what you could buy with $1.00 today, you would need $1.03 one year from now. Given this, the purchasing power of a $1.00 bill is higher today than it will be at some point in the future. Thus, the preference should be to receive that $1.00 bill today.**Risk**– If you receive a dollar today, there is no risk. However, there is always some risk that you won’t receive that $1.00 in the future for some reason.**Reinvestment Potential**– A dollar received today can be reinvested in another investment. If you receive that dollar a year from now, you will have lost the opportunity to earn a return on that dollar over the previous year.

With this definition in mind, it makes sense that we try to maximize the amount of money we receive in the near-term vs. the long-term. The answer, however, isn’t always to receive money today rather than at some point in the future. If someone offers you a very large return on a dollar in the future, it may be worth considering whether to forego that dollar today for a much larger sum in the future after considering the risk of the investment and other factors. In order to determine whether an investment is worth making (to forego spending a dollar today vs. investing it for a future return), we need to look at two concepts that are fundamental to the time value of money: discounting and compounding.

## Compounding

We’ll start with compounding because it’s the most natural. Compounding is the concept of how money grows over time. It’s about determining what a dollar today will be worth in the future. Most people are familiar with how a savings account works: you place money in the bank and the bank pays you a certain amount of interest on that account each year. Let’s use a simple example to illustrate.

In the table above, we’ve invested $1.00 at a 3.0% interest rate. The table shows how that $1.00 grows over time as it earns a 3.0% return each year it is invested (we’ve expanded the number of decimal places to give a better idea of how that $1.00 is growing). The important thing to note about compounding is that the interest earned on a previous year also earns interest the following year. For example, during the first year the $1.00 invested earns a return of 3.0%. In the second year, that $1.00 initial investment also earns a return of 3.0%, but this year the previous interest earned of $0.03 also earns a 3.0% return (in this case it’s around $0.0009). So in five years we have almost $1.16 cents from our initial $1.00 investment.

## Discounting

Discounting is a little less common as a concept, but arguably much more important in commercial real estate valuation. The idea of discounting is that you have an amount of money that you expect to receive in the future and you want to know what that money is worth today. In other words, you want to know what the present value of a dollar received in future dollar is.

Much like compounding, you need to know what rate to discount that future dollar. The discount rate is determined by market forces, risk, and the investors required rate of return (more about discount rates here). Before we get into the specifics of discounting, it would be helpful to look at a simple example. We’ll use the template from the compounding example above and apply different discount rates to a series of cash flows to determine the present value of those cash flows based on different discount rates.

The first example below shows a series of cash flows over a five-year period (for illustration purposes, the cash flows are based on a 10% annual growth rate of one dollar).

For each year in the table, the investor expects to receive that amount of money in the future ($1.10 one year from now, $1.21 two years from now, etc.) for a total sum of $6.72 cents over the five-year period. According to the present value formula, the investor could pay $5.00 for this investment to achieve an annualized rate of return of 10.0%. Below are two examples of the same table, but this time with different discount rates applied (8.0% in the top table and 12.0% in the bottom table). As you can see, the present value today of the top table with a discount rate of 8.0% is $5.2847, which is higher than the present value of $4.7384 for the 12.0% discount rate.

Let’s look just at year one first and then break down each year so it’s clear what’s happening.

In the table on the far left, in year one the investor expects to receive $1.10 from the investment. If the investor requires a return of at least 10.0% on their investment, what can the investor pay for the future $1.10 cash flow? It’s $1.00. However, in the middle table the investor requires a return of only 8.0%, so the investor can afford to pay $1.0185 for the future receipt of $1.10. Finally, in the table on the far right, if the investor requires a return of 12.0% on their investment, the investor can pay only $0.9821 for the $1.10 received in one year. The relationship here is that the higher the return the investor requires, the less they can pay for the same series of cash flows.

Let’s now look at what happens with the cash flow from each year using a discount rate of 10.0%.

Essentially, what discounting does is find the amount that needs to be compounded at a given interest rate in order to receive a future amount. Looked at it this way, discounting is the inverse of compounding.

## Applications in Commercial Real Estate

As discussed above, discounting is more likely to be used in commercial real estate than compounding, at least within valuation applications. The Net Present Value (NPV) and Internal Rate of Return (IRR) valuation methods rely heavily on discounting the projected future cash flows into an estimate of current value.

One of the reasons discounting is used more heavily in real estate is because cash flows are more heavily affected by lease contracts and market forces than by other factors that are under the control of the investor. For example, if an investor purchases an office property with leases in place over the next five years, the cash flows are going to be fairly predictable. At this point, the investor needs to apply a valuation method to determine how much those cash flows are worth at the investors’ required rate of return.

In situations with less certain cash flows, investors will still attempt to predict the future cash flows of the property and use the same valuation methods to arrive at an acceptable current purchase price.

## Nuances of Time Value of Money

In the first section of this article, we argued that the timing of a cash flow is an important concept of the time value of money. The two tables below illustrate how the timing of cash flows impact the potential value of an investment.

Notice that both tables have the same discount rate of 10.0%. In the top table, the investment receives cash flows of $1.20 in the first three years and only $1.10 in the last two years. In the bottom table, the series of cash flows is reversed with the investment receiving $1.10 in cash flow in the first two years and $1.20 in the last three years. The total cash flow received by the investor is the same, but more cash is received earlier in the investment in the top table than it is in the bottom table. The result is that the investment with higher cash flows earlier in the investment has a higher present value ($4.4186) vs. the investment with the higher cash flows later in the investment period ($4.3754)

Although the difference in the two amounts used in this example are small, in larger investments the difference could be millions of dollars.

Also notice that higher cash flows earlier in the investment hold period allow the investor to re-invest those proceeds in other investments and earn a return on top of the returns achieved from the initial investment (earning interest on interest). In real estate, the investor can use the cash flows to pay dividends to partner investors, reinvest in improvements to the property itself, use as equity for the purchase of other properties, or use it for any other investment and thus compound earlier returns.

### Conclusion

Real estate is not day-traded. It’s owned for years and sometimes decades. Understanding the value that a property holds based on the cash flow it will generate over time is a hugely important factor in successful real estate investing. The concept of the time value of money and its implications for the value of real estate should be well understood by anyone attempting to enter the real estate investment world.