• # NPV demystified

## by Patrick Sprouse • January 26, 2012 • CRE, Economics, Finance

Tenants working with brokers often are presented with financial spreadsheets breaking down potential deals or the financial implications of a few potential sites for lease. Usually somewhere close to the bottom, circled in red or highlighted (like the example on the right), is a dollar figure listed as the ‘net present value'(NPV)  of the deal(s). What does this mean to you the tenant? How are you supposed to digest this when you don’t use NPV in your normal course of business finances?

I’m going to demystify NPV a bit here; and hopefully provide a better understanding of what NPV actually is than most brokers providing financial breakdowns would (just ask if they are using a single-sum or multi-period cash flow PV formula and watch for the terror fill their eyes). A single sum formula only takes into account two time periods: the present (typically) and some future end date for the measured term. Multi-period formulas are in effect a sum of many single sum formulas.

Since most commercial leases are for more than one year, the multi-period formula is the one we’ll use. Its easiest to think of the multi-period present value formula as the present value of the expected cash flows of the lease.  So the formula would look something like this:

$NPV = {CF}_{1} + \frac{{CF}_{2}}{1+k} + \frac{{CF}_{3}}{{(1+k)}^{2}} + ... + \frac{{CF}_{T}}{{(1+k)}^{T-1}}$

CF = each year or term of the lease’s cash flow
k = is the discount rate (which I will touch on briefly)
T = term of the lease

CF is fairly easy to calculate; the revenues or payments of the lease including payments of building operating expenses, taxes etc. Obviously lease terms such as a triple net, or a full service can drastically impact the CF for the tenant or landlords. For a tenant, the lease revenues are recorded as outflows and operating expenses may be recorded as outflows or inflows depending on the above mentioned examples (full service, triple net, etc.). For a landlord, revenues are recorded as inflows, and operating expenses may be recorded either way per the service terms. It should be important to note, as a landlord, when looking at a property in the aggregate, the same formula can be applied, however cash flows before interest should be used, as including interest is the equivalent of adding the time value of money (TMV) twice into the equation (or there about).

The idea here is to create a sum of cash flows in today’s dollars (present value) so that the financial impacts of a given deal for a specific space can be accounted. But when comparing two or more deals, especially for tenants, the effective rent over the entire term is of even more value. For landlords, the effective rate has a double impact – not only does it tell the landlord the value of the lease, but the effective lease also goes into the calculation for the underlying value of the property: if the landlord is planning to sell, by understanding the NPV and EF a good broker will know how much flexibility a landlord actually has on rates, terms and concessions. To solve for the effective rent we have to find the equivalent level annuity payment of the NPV. Using the same definitions above the equation would look like this:

$EF = \frac{(NPV)*k}{(1+k)(1-\frac{1}{{(1+k)}^{T}})}$

The biggest question mark most people have is with the discount rate. Most people want a fixed rate to use, because finding and justifying a discount can be tricky, especially for people that do not actually use financial math often – which is true for most brokers. The old rule of thumb has been 10% – this is because 10% is an easy percentage to utilize making the financial rigor of NPV and EF calculations less intimidating – it is an easy way to create a what-if-analysis of a lease for things like comparison with other deals, concessions, tenant improvements, etc. If you do want to use financial rigor so as to increase the veracity of the model, you must find a discount rate to peg the financial analysis. For tenants, borrowing costs often make an accurate substitute. For landlords one might want to choose bonds that are secured through leases obligations – this will provide a good discount rate for pegging actual market values.

Also it should be noted that this NPV equation starts at year zero – not all NPV equations do – I began the one above at year zero because in most cases lease payments are made in advance opposed to in arrears (thus it begins with no discount to CF). I also chose to use annual cash flows, in some cases, such as when rents bump in mid year (ie. a 5% bump at month 6) a monthly cash flows for monthly rent would be the accurate more accurate equations. And lastly, when there are concessions and abatements cash flow to the landlord may start in the negative – and for the tenant the cash flows would begin in the positive.

Patrick Sprouse has over a decade of experience in the commercial real estate sector. Mr. Sprouse has held numerous positions in commercial brokerage, real estate technology and executive operations on regional, multi-market and national scales. Currently Mr. Sprouse is providing management and technology consulting service for a private real estate services company based in Washington, DC with over \$1.5 billion in 2015 revenue. Mr. Sprouse has an extensive background in business management, sales engineering, project management, software selection and business analysis as well as organizational change and brand management.

http://www.patricksprouse.com