These two rates are frequently run together, so which is to be preferred?
A trick question!
The answer is that they are mathematically identical, but they are defined differently.
Let’s start by some clarifying definitions.
The net rental rate is the rate that the landlord receives after deducting for void, management costs and maintenance costs.
The deferment rate is the discount rate applied in the deferment price formula, reflecting the foregone income or use during the deferment period. A more precise definition of the deferment rate is the discount rate that when applied to the freehold price of vacant possession results in the price of deferred possession. The deferment rate itself is not directly market observable, but it can be estimated as a function of market variables.
A First Principles Analysis
Let d be the current net nominal annual rental, the current time being the beginning of the year. (We use ‘d’ here because the approach we are using derives from the dividend discount model, where ‘d’ is used to refer to (nominal) dividends.) ‘Net’ means the gross or headline rental paid by tenants, less the costs incurred by the lessor such as management, maintenance and the expected costs of void or empty periods while the property is being re-let. Then we shall show that
(1) d/S=q
where d is the net rental as above, with the current time being the beginning of the rental year; S the estimated ‘spot price’, i.e., the freehold value of vacant possession estimated as the market value of an identical or similar property not encumbered by a leasehold; and q the deferment rate as defined above.
Then assuming that the value of the property is the present value of all net rental receipts, which is what a market participant would reasonably assume, the following equation holds:
(2) S=d × y × (1+y+y^2+y^3…) = d × (y+y^2+y^3…) = d × y/(1-y)
Where y = (1+g)/(1+r+π), r is the risk free rate, π is the risk premium required by investors in residential property, and g is growth of net income (e.g., dividends or net rental, not property price). 1 So for any rental cashflow period we project the year-end net rental by the expected growth rate g, then discount back by the investor required cost of equity r+π.
Rearranging, it follows that
(3) d/S=(1-y)/y
We now want the deferment value R_n, i.e., the value of the property minus the lost net rental for n periods:2
(4) R_n=d×y×(y^n+y^(n+1)…)
Assume that there is no term structure to cost of equity or growth. The following equation is then true:
(5) R_n = d ×y × (y^n+y^(n+1)…) = d × y × (1+y+y^2…) × y^n=Sy^n
i.e.,
(6) R_n = Sy^n
Define q as the discretely compounded discount rate applied to spot S such that:
(7) R_n = Sy^n = S(1+q)^(-n)
Hence
(8) y = 1/(1+q).
From (3), substituting 1/(1+q) for y:
(9) d/S = (1-y)/y = (1+q)(1-1/(1+q)) = (1+q)-(1+q)/(1+q) = q
and hence
(10) d/S= q
which was to be proved. Therefore we can estimate the deferment rate using observable values for the value of vacant possession, S, and a value of the previous net rental amount .
Observe that (10) holds true whatever growth rate we choose, and whatever interest rate and risk premium are required by investors.
Which is really strange, too.
Professor Tunaru (2019, p. 50) states, “For risk-management calculation purposes then, it is very important to have an accurate measurement of q. Lack of data availability and long-term horizon makes this exercise extremely difficult, if not practically impossible.”
This claim seems plausible. Who could predict unobservables such as dividend growth, risk premia and so on?
Yet we can calculate by a simple formula using observable variables!
(Based on Chapter 7 of our new report.)
- (2) follows from applying the discount dividend model (e.g., Gordon, 1959) with property prices and rentals taking the place of stock prices and dividends. See, e.g., https://en.wikipedia.org/wiki/Dividend_discount_model.
- I.e. where lost rental = d×(y^0+y^1+⋯+y^(n-1)).