faculty of science Business School Sunk Costs and the Measurement of Commercial Property Depreciation W. Erwin Diewert (UBC and UNSW) and Kevin J. Fox (UNSW) Society for Economic Measurement Conference OECD, Paris July 22-24, 2015

faculty of science Background “…residential and non-residential structures and land pose significant challenges for national accountants and price statisticians.” Paul Schreyer (2009), “User Costs and Bubbles in Land Markets,” Journal of Housing Economics 18,

faculty of science Background Developments in property markets greatly influence: –economic growth, –monetary policy, –productivity measurement, –inflation measurement, –and hence welfare payments to the disadvantaged. Financial crises during the 20 th century were often triggered by commercial property price movements. For all its importance, there exist significant measurement challenges for national accounts producing key economic variables used in informing policy

faculty of science Summary This paper: –Formalizes a framework for measuring prices and quantities of capital inputs for commercial property. –Addresses problems with obtaining separate estimates of land and structure components, as required by the System of National Accounts, and as is important for tax purposes. –Addresses the problem of estimating structure depreciation taking into account the fixity of the structure. –Finds that structure depreciation is determined primarily by the cash flows that the property generates, rather than physical deterioration. –Provides a framework for determining the optimal life for a structure.

faculty of science What's different with commercial property? Commercial property buildings do not trade freely in second hand markets. Commercial properties are far from homogeneous. The usual user cost approach (Jorgenson, 1963, 1989) to the intertemporal allocation of initial fixed costs does not work in this context. Our approach builds on Hicks (1946) and Cairns (2013), taking into account the problem of amortizing property goodwill.

faculty of science The Commercial Property Project Purchase or construct a commercial property building ready at the end of period 0. We assume that the total actual cost of the structure at the beginning of period 1 is known: C S 0 > 0. Opportunity cost value of the land plot at the beginning of period 1: V L 0 > 0. The total initial cost of the commercial property, C 0, is then defined as C 0  C S 0 + V L 0.

faculty of science The Commercial Property Project Assume that the period t land prices V L t and land inflation rates i t satisfy the following equations, with 1+i t > 0 for all t: V L t = (1+i 1 )(1+i 2 )...(1+i t )V L 0 t=1,2,…. Assume that the beginning of period t cost of capital (or interest rate) that the investors face is r t > 0 for t = 1, 2,.... Assume that the building is expected to generate Net Operating Income (or cash flow) equal to N t  0, assumed to be realized at the end of each period t = 1, 2,...

faculty of science The Commercial Property Project The resulting expected discounted profit (  t ) for the investor group will then be defined as follows:  t   C S 0  V L 0 +  1 N 1 +  2 N  t N t +  t  t V L 0   t C D t where the  t and  t are defined recursively as follows:  1  (1+r 1 )  1 ;  t  (1+r t )  1  t  1 for t = 2, 3,... ;  1  (1+i 1 ) ;  t  (1+i t )  t  1 for t = 2, 3,.... –discounted cash flows:  1 N 1 +  2 N  t N t –plus the discounted expected land value of the property at end of period t:  t  t V L 0 –less the initial value of the structure at the beginning of period 1, C S 0 –less the market value of the land at the beginning of period 1, V L 0 –less expected discounted demolition costs,  t C D t.

faculty of science Choosing the Length of Life of the Structure Assume that the sequence of  t is maximized at t equal to T  1.  T   C S 0  V L 0 +  1 N 1 +  2 N  T N T +  T (V L T  C D T )  0. T is then the endogenously determined expected length of life for the structure. Note that the determination of the length of life of the structure is not a simple matter of determining when the building will collapse due to the effects of aging and use: it is an economic decision. Show that the eventual decline in the asset value of the property as the life of the building is extended depends entirely on the sequences of cash flows N t, demolition costs C D t, one period interest rates r t and one period expected land inflation rates i t.

faculty of science Period-by-Period Aggregate Asset Values, User Benefits and Depreciation Assume that the optimal length of life of the structure T has been determined and that the nonnegative discounted profits constraint holds. Sequence of project asset values and the changes in asset value over each time period. A 0   1 N 1 +  2 N  T N T +  T (V L T  C D T ) ; A 1  (1+r 1 )[  2 N 2 +  3 N  T N T +  T (V L T  C D T )] ; … A T  N T + V L T  C D T

faculty of science Period-by-Period Aggregate Asset Values, User Benefits and Depreciation Period t expected asset value change for the project:  t  A t  1  A t ; t = 1,...,T. In the zero discounted profits case where  T = 0, then  t can be interpreted as time series depreciation for the project. Period t cash flows N t : N t = (1+r t )A t  1  A t = r t A t  1 +  t This is not necessarily equal to user cost if profits are beyond the cost of capital. It can then be interpreted as a user benefit expression.

faculty of science Period-by-Period Aggregate Asset Values, User Benefits and Depreciation The initial project cost, C S 0 + V L 0, can be distributed across the T time periods before the building is demolished by the series of period-by- period cost allocations N t*  0 where the discounted value of these cost allocations (to the beginning of period 1) is equal to the project cost:  1 N 1* +  2 N 2*  T N T* = C S 0 + V L 0. If  T = 0: N t*  N t for t = 1,2,...,T  1and N T*  N T + V L T  C D T. → If N t is distributed back to the owners at the end of each period t and the end-of-period T market value of the land plot V L T less demolition costs C D T is also distributed to the owners at the end of period T, then the present value of the resulting sequence of distributions will just be equal to the initial project cost.

faculty of science Decomposition of Asset Values into Land and Non-Land Components If expected discounted profits  T are equal to zero, can decompose property values, user costs and time series depreciation amounts into land and structure components. Aggregate asset values: A t = V L t + V R t Cash flow (user cost): N t = U L t + U R t Change in asset values (depreciation):  t =  L t +  R t

faculty of science Decomposition of Asset Values into Land, Structure and Goodwill Components If expected discounted project profits are positive define an intangible goodwill asset: V G 0  A 0  C S 0  V L 0 =  T > 0. Then V R 0 = V G 0 + C S 0, and the shares of the initial goodwill asset and structure cost in initial non-land asset value are s G 0  V G 0 /V R 0 ; s S 0  C S 0 /V R 0 = (1  s G 0 ). decompositions become: A t = V G t + V S t + V L t N t = U G t + U S t + U L t  t =  G t +  S t +  L t

faculty of science Decomposition of Asset Values into Land, Structure and Goodwill Components U G t  s G 0 U R t ; U S t  (1  s G 0 ) U R t V G t  s G 0 V R t ; V S t  s S 0 V R t  G t  V G t  1  V G t ;  S t  V S t  1  V S t ; Decompositions become: A t = V G t + V S t + V L t N t = U G t + U S t + U L t  t =  G t +  S t +  L t

faculty of science Decomposition of Values into Price and Quantity Components The decomposition of land values into price and quantity components is reasonably straightforward since the quantity of land is constant over the life of the project: P L t  V L t ; Q L t  1 Period t user cost price and quantity of project land: p L t  (1+r t )V L t  1  V L t ; q L t  1 ; Goodwill does not have to be decomposed into price and quantity components if it is simply regarded as a repository for pure profits.

faculty of science Decomposition of Values into Price and Quantity Components The decomposition of structure values into price and quantity components is more complex — changing quality of structure over time. Let P S t* be an appropriate exogenous construction price index for the end of period t. End of period asset price and quantity (in constant quality units of measurement) for the project structure: P S t  P S t* ; Q S t  V S t /P S t*

faculty of science Decomposition of Values into Price and Quantity Components Decomposition of the period t user cost value for the structure into price and quantity components is fairly simple: p S t  [r t  i S t + (1+i S t )  t ]P S t  1* ; q S t  Q S t  1 Note that p S t has the same as traditional user cost

faculty of science Conclusions Our approach can be viewed as providing objective depreciation rates for the structure of commercial property. Provides a decomposition of aggregate capital into land, structure and goodwill components. Novelty of the approach includes taking into account: –the fixity of the structure, –the endogeneity of the useful life of the structure.

faculty of science Conclusions Three major conclusions: –Taking account of fixity of the structure does not lead to a dramatically different measurement framework compared to traditional approaches; still obtain user costs for the structure that look familiar. –The pattern of time series depreciation allocations is largely determined by the cash flows that the property generates over the lifetime of the structure. Cash flow patterns are likely to be very different across different property classes, posing measurement problems and indicating that traditional depreciation models are unlikely to be adequate. –The proposed framework requires much data for implementation, which are unlikely to be available. Further assumptions are needed to provide a practical framework. But the framework does capture many realities of the commercial property market, thus advancing our understanding.