Wonky Ruminations About Present Value

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Everyone knows that a dollar received today is better than a dollar received a year from now. Many realize that it is advantageous to pay a dollar a year from now rather than pay it today. That’s the “time value of money.” It is also based on a pretty good, but not guaranteed, assumption that interest rates and inflation rates will be positive. Historically, that has been a good bet.

We’ve used the word “better” in the sense that most would understand, but “better” is actually in the eyes of the beholder. It is better for the recipient to get the dollar now, but that’s not the case for the payor. [Well, we’ve gotten that out of the way.]

So, which is better when it comes to paying or receiving monthly rent for a five year lease: (a) $12 per square foot of floor area throughout the term; or (b) $10 the first year, $11 the second year, $12 the third year, $13 the fourth year, and $14 the final year? After all, $12 per square foot is right in the middle, it is the average rent “figure” over the five year term.

There is no one answer, and that’s not because what is better for the landlord isn’t better for the tenant, and vice versa. The real reason is that to do the “calculation,” we need to settle on an “interest rate” or, more accurately, a “discount rate.” We’ll discuss the “discussion” later; for now, we’ll just say, “6%.” The calculation that we would be doing is directed to answering the question: “What would be the ‘Present Value’ of a stream of income received in the future.” Basically, we are asking, at the end of the day, how much money received, in hand, today and then invested at the discount rate (e.g., 6%) would be the same as getting a given stream of future payments (e.g., monthly rent) over the term of a lease?

Trust us for now, a flat rent of $12 per square for five years (60 monthly payments), for a 10,000 square foot space, at a 6% discount rate, is the economic equivalent of receiving (or paying) $518,818.83. Later, we’ll direct you to an on-line calculator that will do the math for you.

Using the same discount rate of 6%, getting (or paying) monthly rents for that 10,000 square foot space at the $10/$11/$12/$13/$14 rent schedule works out to be the same as receiving (or paying) $518,660.37.

That’s a pretty slim difference. So, our gut that charging the average rent in our case, $12 per square foot, for a $10/$11/$12/$13/$14 rent schedule, is pretty darn close in economic return. The difference in “Present Value” is only $158.46 in favor of the landlord over the entire five years.

“Wait a minute,” you might say: “That’s fine for 6%, but what if I could get 10% on my investment and thus I would be using a 10% discount rate?” This time, the answer would be that there is a $3,483.51 difference, now to the disadvantage of the tenant. That’s about 3/4 of a percent of the total amount involved. Yes, there is a difference, but it isn’t that great.

Is there a lesson to be learned from these examples? Ruminations thinks a simple one might be that it isn’t worth a lot of negotiation time or angst arguing about graduated rent schedules as contrasted with a fixed (average) rent, at least now from the bottom line, ultimate return point of view. Given that there are a lot of ways to structure a rent schedule to arrive at the same economic result, negotiation should be based on the cash flow needs of the negotiating parties.

Does this mean that reducing a future stream of payments to its “Present Value” will never be a decision factor or isn’t what really should be used to understand financial consequences? No, it doesn’t. If, for example, the rent schedule were not evenly graduated as it was in our example, you could have a measurable difference in outcome. So, when structuring any kind of alternate rent schedule, for whatever reason, though usually to match cash flow availability, you’d want to know the “equivalent” rent to whatever might have been the starting point. At the end of today’s posting, we’ll point you to a simple calculator that will get you some answers, identify its shortcomings, and make a suggestion for those who want to easily make these evaluations.

Present Value calculations are helpful in evaluating “free rent.” Milton Friedman is said to have said: “There is no such thing as a free lunch.” If you understand “Present Value,” you can figure out the cost of that “free rent-lunch.”

Where else might the use of a Present Value calculation be found? We’ve often used it in determining the remaining leasehold value of a lease in the allocation of condemnation proceeds between a landlord and its tenant. Leasehold value is the excess of a lease’s market rent over the lease’s stated rent. That difference, a monthly amount, has to be reduced to Present Value in order to know what portion of an eminent domain award belongs to the tenant (assuming it has successfully negotiated for it).

Another place the Present Value calculation “pops up” is in mortgage loan yield maintenance calculations. Again, the purpose is to figure out what lump sum payment, made now, would be the equivalent of a stream of future (mortgage) payments.

In a more complicated scenario, there are many joint ownership agreements that provide for enhanced distributions to one or more parties when one or more of the others have recovered their initial capital investments. To make this simple, imagine that there are two investors and one, the passive one, invested a million dollars. The agreement between that passive investor and the other owner who put in the “sweat” (read that: no money) is that the net cash flow would be split 50/50 once the passive investor got back its million dollars. What if there are no distributions for ten years when, all of a sudden, the passive investor gets a million dollars check? Is this the time when future distributions go 50/50? Well, every reader now knows that the passive investor isn’t “even.” That’s why one will see “preferred returns” in such arrangements. Sometimes, however, for reasons not relevant to understanding the Present Value concept, the use of a preferred return does not “balance” the scale.

[Our last example.] Another place “Present Value” is used is in calculating damages arising out of a tenant’s breach that causes the lease to terminate. At least this is true in most jurisdictions and should be true in all jurisdictions. And, our “should be true” applies to states where mitigation by the landlord is required (most of them) as well as those states where the landlord can sit on its hands and seek to collect the full rent from the “departed” tenant. The difference is that in “mitigation” states, when it comes to the component of damages the ex-tenant must pay on account of the loss of rent, the ex-tenant is only liable for the amount that would be needed to cover the shortfall, if any, between what the “replacement” tenant is paying and the rent that the ex-tenant would have paid. [For the months where the landlord is really trying to re-let the leased space, but is unsuccessful, the ex-tenant needs to cover the entire rent; in many places, if the landlord “gives up,” the ex-tenant will only pay the shortfall, if any, between the terminated lease’s stated rent and the “market rent” for the space. That was a very, very shortened working explanation; there are many possible intervening factors. So, just take all of that as “the theory.”]

Now, if the ex-tenant just sends its check for the shortfall every month, today’s posting about Present Value has little application. But, if a particular landlord, like most landlords, doesn’t want to rely on an ex-tenant (who bailed out early in the first place) to pay the shortfall month after month, it will seek to get a lump sum judgment against the ex-tenant. Let’s say the stated rent was $10,000 a month and, with five years to go, the lease is terminated by reason of the tenant’s breach. Let’s also say that the space is immediately re-let for $9,000 a month (i.e., a $1,000 per month shortfall).

Now, with five years (60 months) to go, the total shortfall would seem to be $60,000. But only the $1,000 that gets paid today is really worth $1,000. The longer in time one has to wait to get a $1,000 payment, the less the Present Value of that $1,000 will be. In fact, the Present Value of $1,000 a month for 60 months is $51,882 (using a 6% discount rate) and $47,657 (using a 10% discount rate). Depending on which of the two discount rate examples a court would use, those figures would be the amount of the judgment, not $60,000.

Most readers, even though not themselves “running the numbers,” have already realized that the chosen “discount rate” can make a big difference in the “calculations.” To make that point a simple one, here are the outcomes for a series of discount rates based on ten years’ of monthly $1,000 payments (the first of which is due immediately – yes, it makes a slight difference not having to wait 30 days). Keep in mind that the cash received over the 120 payments would be $120,000. All of the following “Present Values” will be less: 2% = $108,711; 3% = $103,611; 4% = $98,837; 5% = $94,367; 6% = $90,178; 7% = $86,251; 8% = $82,565; 9% = $79,105; and 10% = $75,854. All readers will have to admit that the differences are significant.

One basic lesson that can be learned from the 2% – 10% listing above is that the higher the discount rate, the lower the Present Value. So, if a lease is going to have a discount rate for any purpose such as for calculating “accelerated” rent damages, tenants will want a higher discount rate than would landlords.

But, what is the “right” number. Sorry, that can’t be answered. Like a common response from a lawyer to a hypothetical question, “it depends.”

Here is the theory upon which it depends: “what investment return would be earned on the money if all were paid up front.” This turns the whole calculation on its head. Here’s how. If there is no mark-up or administrative fee, there is a one to one relationship between our descriptions of Present Value and how annuities are valued. We’ll make this simple. Look back at our example of receiving (or paying) $1,000 a month for 10 years (i.e., 120 months). We wrote that the Present Value of that series of payments, using a 6% discount rate, is $90,178. From an annuity viewpoint, if you invested $90,178 on day one at 6%, then immediately took $1,000, you could take 119 successive payments and, at that point, the money would have run out. Yes, making 120 successive monthly payments of $1,000 (applying a 6% discount rate) is the equivalent of paying $90,178 up front to someone who can earn 6% on the money.

So, what it depends on is the “alternate” opportunity for the money. If a landlord is earning 7% on its rental income (and that needs to take into account the payments made on the mortgage because the “leverage” is not part of the calculation – the rate is a blended one), then the landlord, to be fair, should be asking for a discount rate of 7%. In the “damage” calculation scenario, the tenant’s argument for a higher rate would be founded on the argument that the landlord could invest the amount of any judgment at more than 7%. When a tenant evaluates the Present Value of rent it might be paying, it would use its own investment return rate.

So, when Ruminations writes that “it depends,” Ruminations isn’t trying to weasel out. Every person has her or his investment rate and Citizens United has its own rate. Much like Joe Friday was reputed to have said, but never really did (“Just the facts, ma’am,”), that’s: “Just the facts, companion Ruminators”).

By the way, when evaluating the cost of a loan, the parties (each using their own interest or discount figures) can do a Present Value analysis. Even though a borrower may receive a $100,000 loan (that’s its “Present Value”), the principal payments made over time do not translate to paying back the same money, i.e., the present value of the returned principal is going to be less than $1,000. This isn’t the place to explain the interplay between interest rates and inflation rates (to get the  “real” interest rate), just keep in mind that while the borrower gets the full amount today, it pays the loan back, over time, with “cheaper” dollars. Call that: “inflation is a borrower’s friend” combined with the borrower earning money on what it borrows and in what it can reinvest.

Of course, choosing the “investment rate” and then its corollary, the “discount” rate or factor, is not a science. Even if there were no competing parties (e.g., a prospective landlord and its prospective tenant) negotiating over the rate, each seeking to settle on one more favorable to itself, there is no one correct number. So, don’t look to Ruminations to make the task any easier. We know it isn’t the “cost of living,” the prime rate or some Treasury rate. It might be something closer to a mortgage rate index for some applications or a “cap” rate (expressed the “other” way) for others. Courts, when reducing a rent-damages judgment to Present Value may use the legal interest rate for judgments, even though that’s not a rate designed for the same economic purpose.

So, how does one calculate a “Present Value” if needed or wanted? There is a mathematical formula, but it is one that looks like something from an advanced algebra book. So, most people take advantage of existing calculators. Those who are already calculating Present Values in their present lives are already using calculators of their own choice. Those who want to put a toe in the water might want to look at this pretty easy-to-use one: SIMPLE PRESENT VALUE CALCULATOR.  You can find it by clicking: HERE. When it pops up, you’ll see an example using a 6.5% discount rate. It answers the following question: “What is the present value, on Today’s Date, of 120 monthly $1,000 payments if the first payment is made on the listed First Cash Flow Date. Try it; hit “Calc.”

If you have a graduated payment problem, such as the rent going up each year, you’ll want to do two sets of calculations. First, for each rent level, you’ll want to calculate the present value of that year’s rent as if it were the first year of the lease. You’d use 12 payments with the first payment (Cash Flow Date) being the same date as “Today’s Date.” That will tell you the Present Value of one year’s payments as of the first day of the payment year. Then, for each year after  the first year (years 2, 3, 4, etc.), you’d tell the calculator that there was one payment being made in the same amount as you figured out for that year, but this time the “Cash Flow Date” would be date the first rent payment for that year is actually due. Lastly, you’d add up the results for all of the years in the lease.

What we’ve described is a somewhat time-consuming task, but not a complicated one. If you want to do a lot of these calculations, especially if it’s something you’d like to do regularly, then “spreadsheet” skills will come in handy. For example, Microsoft Excel has a Present Value function. It will do those calculations for you, and is described: HERE. http://tinyurl.com/ltydlpc. If you (or a friend) have basic Spreadsheet design skills, you can easily design one that fits your exact needs. There are also commercially available products. We don’t tout these, but will point you to Leasematrix so that you can see the kind of product that is available.

Of course, if any reader already has such a spreadsheet or other calculator she or he would like to share with colleagues, please post a link or other information in the Comments box below.

[We will be reserving the right to change any of the numbers in today’s posting if, after the intoxicants wear off, they seem to be calling out for correction.]



  1. Howard Burns says

    whatever interest rate is charged for late payments, default etc. should be the discount rate used to calculate future unpaid rent due. As a aside, and I will admit somewhat off topic, note the wonderful State of Calif (and perhaps other states too?) which assumes it will acheive a 7% compounded rate of return on pension funds invested yet if a city or county wants ‘out’ of the State pension system, discounts their required payment using only a 2.5% discount rate, making a massive penalty to try to withdraw from a failing pension system. A good study in differing NPV rates.

  2. David Graham says

    Ruminations, this is great post. More people need to understand the fundamental role of the time value of money in the commercial real estate industry. You’ve written a wonderfully accessible piece (again).

    You rightly said: “But, what is the ‘right’ number. Sorry, that can’t be answered.”
    Totally agree. However, there is most certainly a wrong number.

    And, in some states, the legislature picked the wrong number. I applaud the California legislature for including in the landlord remedy statute a present-value concept of the stated rent’s excess over market rate. However, sadly, it picked the wrong number. See California Code, Civil Code – Civ § 1951.2(b). The difference in the rents for the remaining periods “is computed by discounting such amount at the discount rate of the Federal Reserve Bank of San Francisco at the time of award plus 1 percent.”

    Here’s the problem: two very different meanings for the same technical word “discount rate.” Discount rate is the rate at which a stream of future cash flows is discounted to present time, which is today’s topic. This is the investment industry definition.

    Alas! “Discount rate” is also the minimum interest rate charged by the U.S. Federal Reserve to lend to other banks, i.e. short-term bank-to-bank lending. This is the banking industry definition, which has absolutely nothing to do with commercial real estate or valuing future cash flows from an investment.

    The discount rate used on cash flows varies depending on a variety of factors, as you said. But, the San Francisco Fed discount rate is set by policy, and is currently fixed at 1.75% per annum. So, according to the statute, a damage award would be the future difference between stated rent over market rent, discounted to present at 2.75%. As you well said, a lower discount rate results in a higher present value.

    From my perspective, the California legislature erred in its definition and made inflated landlord damage awards the law of the land. I suggest that enlightened lease negotiators (1) keep copying the Calif. statute, but (2) change any default remedies provision to a discount rate of at least “WSJ prime rate plus x%.”

    p.s. full disclosure: I am the son of a commercial landlord.

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