Kevin Dowd 28 August 2018
A number of our readers continue to be puzzled about why Dean and I have been insisting (see, e.g., here, here and here) that the net rental or q rates used for NNEG valuations should be positive.
This point matters because we are interested in how NNEG valuations are affected by deferment property prices.
The deferment property price is the price we would pay now to receive possession of the property in some future period t.
We would assert that, as a general rule, the deferment property price will always be less than the current property price, i.e., we would pay less for deferred possession. The demonstration of this claim goes as follows:
Let q0, q1, q2, …. be the set of net rental rates for a property from now, period 0, to forever. These net rental services are the use-benefits we get from living in a property (e.g., the benefits of having a roof over our heads) or the rental incomes we could obtain by renting the property out. Let us assume that these are all positive. After all, zero or negative rental rates do not make much sense.
Let A be the set of those net rental rates q0, q1, q2, …. for periods 0 to forever.
Let B be the set of net rental rates q10, q11, q12, …. for periods 10 to forever.
Let C be the set of net rental rates q0, q1, …. q9 for periods 0 to 9.
Since the sets of rentals are positive and hence valuable, then the prices of A, B and C should be positive. By the ‘law’ of zero arbitrage, the price of A should also be equal to the sum of the prices of B and C. But since the price of C is positive, it must follow that the price of B < the price of A, i.e., the deferment price must be less than the current price.
How might one challenge this conclusion?
One can hardly challenge zero arbitrage, except for fleeting moments: arbitrage opportunities do not stay unexploited for long.
The only other potential challenge is to argue that the rental rates are or could be negative.
So let’s consider possible examples of negative rentals.
One is where the property and the land which it stands are utterly polluted, possibly beyond any repair. Chernobyl comes to mind: even if the land could be restored to a usable state, the costs of doing so would be prohibitive. In this case, all q0, q1, q2, … are negative and will be indefinitely. The property and the land itself are then abandoned.
Fortunately, this type of situation is rare.
A less extreme case is where the property is uninhabitable and repair would be uneconomic, but the land itself is valuable. Parts of Detroit come to mind as Dean has suggested here. You could then say that the net rental proceeds were negative for the current property, but this situation would not last. In this case, the property would be sold off and demolished, and the site redeveloped. A positive rental stream would then eventually be restored.
A third and less severe case is where the property needs repair and repair is economically feasible, or where you have tenants from Hell. The property might not generate any current net rental, but it could be repaired or the tenants evicted and a positive rental stream restored. This situation is not uncommon, but is still exceptional or relatively infrequent, in that it does not apply to most properties most of the time.
The general case is that most properties most of the time generate a positive net rental stream. Therefore, when looking for a general rule to assess deferment value, the only sensible rule is to assume a positive rental stream – and a positive rental stream implies that the deferment price will be less than the current property price.
A positive rental stream also puts a lower bound on the cost of the NNEG. To give an example, in my base case calibration set out in Asleep at the Wheel – with a 70 year-old male, a 40% loan-to-value ratio, etc. and a stream of zero q rates, then my ERM NNEG model gives a NNEG valuation of just over 23% of the amount loaned. For the given calibration, this valuation is the absolute minimum one should get, and even this valuation will be too low because it presumes that the net rentals are zero when they should be positive.
This absolute minimum valuation is also much higher than those one gets if one uses the implied negative q rates that some ER firms appear to be using.