SPECIFYING AND CALIBRATING THE COST APPROACH LEARNING OBJECTIVES: After studying this chapter, a student should be able to: differentiate between the various costs that make up replacement cost new (RCN); discuss the differences between RCN for residential and non-residential properties; specify an equation for calculating the RCN of residential or non-residential properties; calibrate RCN using the comparative unit method and formula-driven cost models; develop cost-trend factors; and create a depreciation schedule and translate it into a formula. Chapter 4 discussed the determination of land values used in the cost approach and Chapter 5 discussed the theory and mechanics of the cost approach. This chapter discusses specification and calibration of residential and non-residential market-adjusted cost models used in mass appraisal. Specifying the Cost Approach The cost approach is based on the principle of substitution: a purchaser will pay no more for a property than the cost of acquiring land and constructing a substitute building of equal utility. The cost approach follows the structure of the general model developed in Chapter 3 (Equation 3.14): MV ' IV % LV Equation 6.1 which can be expanded, as shown earlier, to a market-adjusted hybrid cost model: MV ' k GQ[( k BQ EBA) % ( k LQ ELA) % EOA] Equation 6.2 where JGQ is the product of general qualitative components; JBQ is the product of building qualitative components (including depreciation); JLQ is the product of land qualitative components; EBA is the sum of building additive components; GLA is the sum of land additive components; and GOA is the sum of other additions additive components. The building and additions components (BQ, BA, and OA), except for depreciation, represent the supply side of the market and are calibrated from construction cost data. Depreciation and the other components represent the demand side and are calibrated from market data. The result, if done properly, is an accurate estimate of market value. 6.1
Chapter 6 Residential Improvements The first step in specifying cost models is to stratify improvements into homogeneous groups. There is usually a different market for each group. Potential purchasers of properties in one group are unlikely to consider a purchase from another group as an alternative. Residential properties are usually stratified by occupancy, storey height, and construction grade or wall type. A typical inventory is: C C C Occupancy One-family residential Two-family residential Three-family residential Four-family residential Storey height One storey One-and-one-half storeys Two storeys Two-and-one-half storeys Three stories Three-and-one-half storeys Wall type Wood frame or metal siding Brick or stone veneer Concrete block This classification structure implies seventy-two potential model types (4 6 3). One model would consist of single-family, one-storey houses of wood frame or metal siding; a second model would consist of single-family, one-storey houses with brick or stone veneer; and so forth. Next, the typical characteristics, or base specifications, of each model are specified. Using the unit-in-place or quantity survey method (Chapter 5), reproduction or replacement cost new is then estimated. In mass appraisal, however, these costs are converted to comparative unit costs. For residential structures, costs can usually be divided into horizontal, vertical, building addition, constant building component, qualitative, and other addition costs. Horizontal Costs Horizontal cost components are those related to area. Examples are floors and roofs. Total costs for such components are estimated by applying a price per square foot (or metre) to the applicable area. For example, if a building has 600 square feet of hardwood floors, the cost of which is $10.50 per square foot, the total cost is: $10.50 600 = $6,300 Most costs in residential buildings are horizontal. The sum of such costs for a house meeting the base specifications is the base rate for that model. 6.2
Specifying and Calibrating the Cost Approach Vertical Costs Vertical cost components relate to items that are physically vertical and tend to increase in direct proportion to linear feet (metres) or perimeter. Exterior walls and interior partitions are examples. These costs should be expressed per linear foot (or metre), with adjustments for atypical storey heights. Total costs for such components are estimated by multiplying the linear foot cost rate against the linear feet of the component and applying any required height adjustments. For example, if the cost of constructing a 9-foot, average quality brick veneer wall on wood frame is $85.00 per linear foot, the cost for a home with a 200-foot perimeter having this type of wall would be: $85.00 200 = $17,000 Vertical costs can be converted to horizontal costs by dividing total costs by square footage. In the above example, assuming a 2,100-square-foot building, the cost per square foot is: $17,000 2,100 = $8.10 This method is often used to build exterior wall costs into base rates, with adjustments provided for atypical area-to-perimeter ratios. Building Addition Costs Building additions are structures attached to the main living area, such as basements, garages, and porches. Their costs are usually expressed per square foot (or metre). Constant Building Component Costs For items whose costs are usually not related to size, such as bathrooms, fireplaces, and kitchen appliances, costs are expressed as lump sums, such as $10,000 for a bathroom or $1,000 for a water heater. The cost of such items varies with quality; for example, a flagstone fireplace costs more than a prefabricated one. Constant cost items are one major reason that horizontal building costs per square foot tend to decrease as size increases. As the costs of such components are spread over a larger area, their square foot cost decreases. Qualitative Cost Components These are percentage adjustments made to the primary structure (including attached additions) to reflect variations in quality and workmanship. They are usually referred to as grade adjustments in cost manuals. Other Additions Some structures or miscellaneous items are not attached to the primary residence. Examples include fencing, swimming pools, and outbuildings. Their cost may be calculated on a square foot (square metre), linear foot (metre), or lump-sum basis. However, unlike attached additions, they are treated independently from the primary structure, meaning that they do not receive the same qualitative adjustments. The combination of horizontal, vertical, attached, constant, qualitative, and other addition cost components yields replacement cost new (RCN). Mathematically, RCN ' [ k BQ (EBA H % EBA V % EBA A % EBA C )] % EOA Equation 6.3 6.3
Chapter 6 where JBQ is the product of building qualitative factors; GBA H is the sum of horizontal building component costs; GBA is the sum of vertical building component costs; V GBA is the sum of building addition (attached) costs; A GBA is the sum of constant building component costs; and C GOA is the sum of other addition (for example, outbuilding) costs. This formulation is the same as that of the general market-adjusted cost model in Equation 6.2, except that the additive building components have been broken down into horizontal, vertical, attached, and constant market-adjusted cost components. Once determined, RCN must be adjusted for depreciation and general qualitative factors. With these final adjustments, the market-adjusted cost model appears as follows: MV ' k GQ [(1 & BQ D ) RCN % LV] Equation 6.4 where BQ is a building qualitative adjustment for depreciation (several factors may apply to different D improvements) and LV is the land value before application of general qualitative adjustments (JGQ). Non-Residential Improvements Non-residential cost models operate on the same basic principles as residential ones, although stratification and cost components are somewhat different. Stratification is usually based on construction type, occupancy, and perhaps number of storeys or storey height. Construction types, similar to fire code classifications, reflect major differences in structural quality. Storey groupings capture cost variations inherent in building heights. The following represents a typical stratification scheme: C Structure type: Fireproofed steel frame (Class A) Fireproofed reinforced concrete frame (Class B) Masonry/steel frame (Class C) Wood/masonry/steel frame (Class D) C Storeys: 0-4 5-10 11-15 16-20 This scheme implies sixteen potential models (4 4) and accommodates most structures found in a typical assessment jurisdiction. Non-residential cost models contain the same six basic cost components found in residential properties, but there are some important differences in the format of the horizontal and vertical components. First, horizontal components are divided between structural and interior finish costs. This is necessary because many nonresidential buildings accommodate multiple tenants, each requiring a different interior finish. For example, a five-storey Class B structure with brick on block curtain walls might well have ground-level retail stores and upper-level offices and apartment units. Such a building would have one structural rate and many interior finish 6.4
Specifying and Calibrating the Cost Approach (or occupancy) rates. Each occupancy rate would include costs for floor finish, ceiling finish, plumbing, and other features that depend on occupancy and would be applied against the number of square feet in each particular use. For example, interior finish costs applicable to a light warehouse may be as shown in Table 6.1. Table 6.1 Interior Finish Costs for a Light Warehouse Floor finish 10% vinyl tile $1.36 90% concrete with sealer Ceiling finish Gypsum board,taped & panelled 1.98 Interior partitions 8" concrete block, typical wall/floor 2.38 ratio Heating Suspended space heaters 1.43 Electrical/lighting Typical for occupancy 3.22 Plumbing Typical for occupancy 2.79 Total rate per square foot $13.16 Figure 6.1 Typical Occupancy Groups (Interior Finish Types) Store - one storey Department store Discount store Supermarket Shopping centre - mall Shopping centre - finished retail shell Shopping centre - Community Office building - one-storey, non-fireproof Office building - multistorey, fireproof Commercial airport terminal Private airport hangar Restaurant/cafeteria Drive-in/fast food Financial - main office Financial - branch office Appliance service/repair Service, paint, electrical repair, laundry Service station Automotive showroom Bus terminal Truck terminal Parking garage Wholesale outlet, produce outlet, manufacturing outlet Florist, greenhouse Auditorium, arena Bowling alley, skating rink Hotel Motel Light manufacturing Heavy industrial Food processing Warehousing Cold storage warehouse Dairy building Church Convent Rectory Private, elementary, secondary school Private college Private dormitory Private fraternity house Private hospital Nursing homes Mortuary, cemetery building, crematorium Club, lodge, union hall Yacht club Country club Library Public school Government-owned college Government-owned hospital Municipal building Movie theatre Stage theatre Typical interior cost rates for other occupancy groups can be computed in the same way and included in cost manuals. Figure 6.1 (above) lists occupancy groups found in many jurisdictions. To compute total horizontal interior costs, multiply the square feet of each occupancy group by the appropriate rate, make any required adjustments for atypical features, and sum the results. Vertical costs for non-residential properties are also divided between structural and interior costs. Vertical structural costs are a function of type of wall and materials. Typical costs should be determined for each wall type, for example, wood, masonry, and steel. The base wall cost for a building can then be computed as follows: 6.5
Chapter 6 Linear feet average floor height number of floors wall rate Assume, for example, that a building has a perimeter of 400 feet, a ground floor area of 10,000 square feet, 5 floors, and an average wall height of 10 feet per floor, implying a total floor area of 50,000 square feet (10,000 5). If structural building costs are $18.89 per square foot of wall area, total structural exterior wall costs are: 400 10 5 $18.89 = $377,800 or $7.556 per square foot of floor area ($377,800 50,000). The latter could be added to the structural rate applicable to the building and multiplied against the total square footage to compute a combined structural cost. Interior partitions are handled in the same way: Linear feet average partition height number of floors partition rate If a building is occupied by more than one group, the calculations should be repeated for each and totalled. As with structural costs, vertical interior costs can be combined with horizontal interior costs and expressed as square-foot rates in a cost manual. Important qualitative adjustments in non-residential cost models can include size-adjustment factors, area/perimeter ratios, heating and cooling, and other structural and interior building components. Building and storey height can also be accommodated in this manner as opposed to specifying separate base rates. Of course, non-residential cost models must also provide for items handled as lump sums and other additions, such as pools and recreation facilities, fencing, and outdoor lighting. Adjustments must be provided for nonstandard features and unusual floor heights. In summary, RCN of non-residential improvements can be calculated as follows: RCN ' [ k BQ (EBA S % EBA I % EBA A % EBA C )] % EOA Equation 6.5 where JBQ is the product of building qualitative factors; GBA S is the sum of structural components costs (including exterior walls converted to cost per square foot); GBA is the sum of interior finish components costs (including partitions converted to cost per square I foot); GBA is the sum of building addition (attached) costs; A GBA is the sum of constant building component costs; and C GOA is the sum of other addition costs. As with residential properties, RCN is depreciated, adjusted for qualitative factors, and added to the value of land and other (unattached) additions: MV ' k GQ [(1 & BQ D ) RCN % LV] Equation 6.6 where BQ is a building qualitative factor for depreciation. D 6.6
Specifying and Calibrating the Cost Approach Calibrating Cost Models In mass appraisal, the cost approach often has the structure of the general hybrid model presented earlier in this chapter (Equation 6.1): which can be expanded to MV ' IV % LV MV ' k GQ [( k BQ EBA) % ( k LQ ELA) % EOA] Equation 6.7 where MV is the estimated market value; JGQ is the product of general qualitative variables; JBQ is the product of building qualitative variables; GBA is the sum of building additive variables; JLQ is the product of land qualitative variables; GLA is the sum of land additive variables; and GOA is the sum of other additive variables. The components of this model can be separated into replacement cost new (RCN), depreciation, land value, and general qualitative adjustments (shown previously in Equation 6.4): MV ' k GQ [(1 & BQ D ) RCN % LV] Equation 6.8 where BQ is a building qualitative factor for depreciation (D), and LV is land value before application of general D qualitative adjustments. The cost approach is developed in four steps: 1. determine the RCN, 2. estimate and apply depreciation, 3. estimate and add land value, and 4. apply any general qualitative adjustments (trend factors). Chapter 5 discussed important concepts in the cost approach and Chapter 4 discussed the theory underlying land valuation. The rest of this chapter addresses the calibration of the RCN for mass appraisal, the development of formula-driven cost models, the determination of cost-trend factors, depreciation analysis, and the application of market adjustment factors. Calibration of Replacement Cost New Costs used in mass appraisal are usually replacement costs, which represent the cost of constructing a substitute structure of equal utility based on current construction standards and materials. Replacement costs should include all direct and indirect costs, including materials, labour, supervision, architect's and legal fees, administrative expenses, overhead, and reasonable profit. Costs can be estimated by one of four methods: comparative unit, unit-in-place, quantity survey, and trended original cost (see Chapter 5 for a review of these). Mass appraisal uses the comparative unit method to find the "base" cost of a structure. Adjustments are then made for differences from base specifications using either the 6.7
Chapter 6 comparative unit or unit-in-place methods. Nevertheless, all costs should be derived from the quantity survey method. Commercially prepared cost manuals reflect such costs and many assessors use commercial manuals, making local adjustments as necessary (before using costs from commercial manuals, assessors should establish that they will not violate copyright protections). Assessors can also develop their own manuals from local quantity survey costs obtained from contractors and cost estimators. Labour and material costs should be separated from land and local demand-side factors, which are properly considered elsewhere in the cost approach. Derivation of cost tables from local cost data involves the following steps. 1. Determine the building types (models) to be included in the manual. These should include all building types commonly found in the jurisdiction. For residential property, building types can vary with occupancy (one-, two-, three- or four-family), construction grade, storey height, and wall type. Commercial property types usually vary with structure type (fire code classification) and number of storeys. 2. Determine typical building specifications for each model. These are referred to as base specifications. Figure 6.2 contains an example for a single-family, one-storey house of average construction. Building type Foundation Floors Figure 6.2 Sample Building Specifications One-storey frame, single-family, average quality. Continuous concrete perimeter footing and concrete or concrete block foundation under load bearing walls. Hardwood or carpeting, vinyl asbestos tile and ceramic tile; substantial subfloor and wood structure. Exterior wall Vinyl, wood, aluminum, partial medium-priced brick, or masonry. Average studs 2" 4" on 16" centre. Rafters 2" 6" on 24" centre or 2" 4" truss and joist 2" 8" on 16" centre. Roof Exterior-grade plywood or wood sheeting with medium-weight composition shingle or built-up with small rock roof cover. Interior Sheetrock taped and painted or inexpensive wood panelling; production-grade millwork and trim. Stock-type cabinets, hardware, and average-grade built-in features. Partitions ½" taped sheetrock on 2" 4" studs on 6" centre; 8' height. Heating/Cooling Average-grade forced air heating and cooling Electrical Romex or BX 110/220 volt circuits, adequate outlets, average-quality fixtures with some luminous fixtures in kitchen and baths. Plumbing Eight average-quality white or colour fixtures, 50-gallon hot water heater, laundry facilities, floor drain, and outside fixture. 3. Determine RCN for each model at various size levels. These costs should be quantity survey costs and can be obtained either from commercial cost services or from local builders, developers, and contractors. If the former, costs should be validated against local costs and adjusted as necessary. Remember to include all direct and indirect costs. 4. Plot cost per square foot against building size and determine their relationship. This can be done using a scatterplot, as in Figure 6.3. From the relationship, which is likely to be nonlinear, construct a cost table relating cost per square foot (base rate) to number of square feet. Fifty-foot increments will give a good approximation. Table 6.2 shows a cost table based on Figure 6.3. 6.8
Specifying and Calibrating the Cost Approach Table 6.2 Relationship between Cost per Square Foot and Number of Square Feet Square Feet Cost per square foot 800 $67.60 850 66.78 900 66.01 950 65.28...... 2,250 55.87 Figure 6.3 Scatterplot of Cost per Square Foot 5. Develop adjustments for variations from base specifications. Adjustments can take the form of multipliers per square foot, other per unit costs, or lump sum dollar costs. Multipliers are computed by dividing costs per unit of a structure having (or not having) the feature by the base rate. Assume, for example, that $62.95 per square foot is the base rate for a structure without air conditioning. If the comparable cost per square foot for a structure with air conditioning is $67.11, the appropriate multiplier is 1.066 ($67.11 $62.95). Conversely, if the base specifications include air conditioning, then the appropriate multiplier for a building without air conditioning would be $62.95 divided by $67.11, or 0.938. Multipliers are more efficient in cost algorithms than additive adjustments and easier to maintain. However, some adjustments, may be better made on a per-square-foot (or metre) basis, depending on whether the feature affects value per square foot (metre) additively or interactively (multiplicatively). Other adjustments, for example, those for a fireplace or hot tub, are constant and must be handled as dollar amounts that often depend on the quality of the feature. 6.9
Chapter 6 6. Test the schedules by applying them to buildings of known cost. If estimated costs are inconsistent with actual costs, review cost data used in the analysis and make necessary adjustments. Estimated costs must reflect actual local costs. Sometimes this can be achieved by adjustments to base rates. Formula-Driven Cost Models Formula-driven cost models speed computer processing and facilitate cost updating. As indicated above, many per-unit adjustments found in cost manuals can be converted to multipliers, which are easier to maintain and update. To derive a formula-driven cost model from the local market, proceed as outlined above, determine base cost for benchmark properties, and, where possible, express cost relationships as multipliers. For a simple example, consider Table 6.3, which shows base construction costs for twelve benchmark properties based on grade, square feet, storey height, and wall type. The base property (designated by an asterisk) is a 1,500 square foot, grade C, one-storey house with wood siding. The other benchmarks have been selected so as to isolate differences attributable to each construction feature: five differ only in construction grade, three differ only in size, two differ only in storey height, and one differs only in wall type. To obtain the base rates for each benchmark, simply divide base construction costs by square feet. For the base home, this yields $84,560 1,500 = $56.37. To obtain cost multipliers for the other benchmark properties divide their base rates by that of the base property. Table 6.3 Derivation of Cost Formula Square feet Base Base rate Multiplier Grade Storey Wall (SQFT) cost (cost SQFT) (base rate 56.37) A 1 Wood 1,500 66,556 44.37 0.787 B 1 Wood 1,500 75,450 50.30 0.892 *C 1 Wood 1,500 84,560 56.37 1.000 D 1 Wood 1,500 93,198 62.13 1.102 E 1 Wood 1,500 106,162 70.77 1.255 F 1 Wood 1,500 126,350 84.23 1.494 C 1 Wood 1,000 62,130 62.13 1.102 *C 1 Wood 1,500 84,560 56.37 1.000 C 1 Wood 2,000 102,700 51.35.911 C 1 Wood 2,500 118,902 47.56.844 *C 1 Wood 1,500 84,560 56.37 1.000 C 1½ Wood 1,500 82,740 55.16 0.979 C 2 Wood 1,500 82,110 54.74 0.971 *C 1 Wood 1,500 84,560 56.37 1.000 C 1 Brick 1,500 87,346 58.23 1.033 GRADE SQFT STOREY WALL *Base property (1) Cost = SQFT base rate size adjustment storey adjustment wall adjustment (2) Cost = SQFT 56.37 grade adjustment size adjustment storey adjustment wall adjustment Example for 2,000 square foot, grade D, 1½-storey, brick home: (1) Cost = 2,000 62.13 0.911 0.979 1.033 = $114,481 (2) Cost = 2,000 56.37 1.102 0.911 0.979 1.033 = $114,462 Note that although there are 144 possible combinations of construction features (6 4 3 2), the base value of any building can be found directly from its base rates and applicable cost multipliers. One can multiply the square feet of the subject building by the base rate corresponding to its grade, followed by the adjustment factors for size, storey height, and wall type (see first example at bottom of Table 6.3). Or, one can multiply the square feet of the subject building by the base rate of the base property, $56.37, and adjustment factors for grade, size, 6.10
Specifying and Calibrating the Cost Approach storey height, and wall type (second example at bottom of Table 6.3). In the second case, no table look-ups are required and the entire formula can be updated by simply changing the base rate of the base property, as long as no major changes occur in construction practices or in the relative cost of building components. The example is simplified in that there are no other quality adjustments, no "other additions" (basements, garages, and so forth), and only four size categories. However, it is likely that other quality adjustments (such as for heating or cooling systems) can also be expressed as multipliers and added to the formula (some adjustments may best be left in per-square-foot or per-square-metre format). Other additions should be handled separately: their value should be found as the product of size, value per unit, and any applicable quality adjustments, and the result added to that for the primary building area. For example, to find the value of a garage, multiply its size by value per unit and any quality adjustments. Then add the computed value to that of the main structure. Constant costs (for example, a water heater) require table look-up and their results, too, should be added. Although at first glance it may appear that many benchmark properties of different sizes must be identified, say at fifty square foot intervals, this is not so. Instead, size adjustments (SIZEADJ) can be derived through a model that captures the relationship between benchmark size adjustment factors and square foot. One simple nonlinear model of this type is: SIZEADJ ' b 0 SQFT b 1 Equation 6.9 where b is a constant, and b is an exponent expressing the degree of the size adjustment. 0 1 Values for b 1 of less than 1.00 indicate that as building sizes increase, costs per square foot decrease. The farther from zero, the greater the resulting adjustment. The values of b 0 and b 1are found through a multiplicative or loglinear regression of SIZEADJ on SQFT. For example, loglinear regression on size of the four size multipliers from Table 6.3 (1.102, 1.000, 0.911, and 0.844) yields the equation: SIZEADJ ' 8.284 SQFT &.29086 Equation 6.10 which produces the adjustment factors shown in Table 6.4. Table 6.4 Size Adjustment Factors Derived by Loglinear Regression Model-indicated Square Feet Benchmark Multiplier Adjustment Factor 1,000 1.102 1.111 1,100 1.080 1,200 1.053 1,300 1.029 1,400 1.007 1,500 1.000 0.987 1,600 0.969 1,700 0.952 1,800 0.936 1,900 0.922 2,000 0.911 0.908 2,100 0.895 2,200 0.883 2,300 0.872 2,400 0.861 2,500 0.844 0.851 6.11
Chapter 6 Equation 6.10 can be used to find the appropriate size adjustment for any building size. For example, for a 1,733-square-foot house: -.29086 SIZEADJ = 8.284 1,733 = 0.947 Expressing size adjustments in this way speeds calculations and produces smooth, continuous adjustments without interpolation. Size adjustments can be extracted from existing cost manuals by a similar method. Assume, for example, that the typical, or base, property for a particular construction class has 1,500 square feet and construction costs vary as shown in columns 1 and 2 of Table 6.5. The base rate is $63.80 with size adjustments computed as shown. Table 6.5 Derivation of Size Adjustment Square Cost per Base Size feet square foot rate adjustment 800 $74.60 $63.80 = 1.169 850 73.60 63.80 = 1.154 900 72.80 63.80 = 1.141 - - 1,450 64.40 63.80 = 1.009 63.80 63.80 = 1.000 63.20 63.80 = 0.991-58.60 63.80 = 0.918 58.20 63.80 = 0.912 57.80 63.80 = 0.906 ö1,500 1,550-2,400 2,450 2,500 Again, the table could be approximated with a formula to smooth adjustments and speed calculations. In any case, cost models in the form of multipliers or equations can be updated annually by simply adjusting the base rate of the benchmark property to reflect current costs (see below). Size and other percentage adjustments need only be reviewed periodically, say every three or four years. Cost-Trend Factors Once determined, construction costs must be periodically updated. One way to do this is to repeat the six steps above; another is to develop cost-trend factors. The latter is easier, and acceptable as long as no major changes occur in construction practices or the relative costs of building components. Several major publishers of construction cost data report cost indexes for various building types. To apply such an index, simply divide the index corresponding to the assessment date by the index corresponding to the date of construction costs found in existing manuals; the formula is: F ' I c I b Equation 6.11 where F is the appropriate cost-trend factor, I is the current cost index (as of the assessment date), and I is the c b base index for existing costs. To update base costs multiply them by the appropriate cost-trend factor. 6.12
Specifying and Calibrating the Cost Approach When published cost indexes do not adequately reflect local costs, appraisers must develop their own cost-trend factors. The steps are as follows: 1. Define a benchmark building for each construction class. This building should be of typical size and correspond to the base specifications. 2. Identify the required materials and labour to construct the benchmark property (Table 6.6, columns 1 and 2). 3. Using the quantity survey method, estimate base and current unit costs (columns 3 and 4). 4. For each component, multiply number of units by base unit costs and current unit costs to obtain total costs (columns 5 and 6). 5. Sum the results to obtain total direct building costs. Indirect costs can be analysed the same way and added to direct costs. Often it is reasonable to assume that indirect costs will increase in the same proportion as direct costs. Finally, divide total current costs by total base costs to obtain the appropriate cost-trend factors to use in updating base rates. In Table 6.6, the cost adjustment is calculated as 1.164. Table 6.6 Derivation of Construction Cost Index (1) (2) (3) (4) (5) (6) Base Current Base Current Item Quantity unit cost unit cost total cost total cost Materials Concrete block/100 15 $85.00 $112.00 $1,275 $1,680 Lumber/1,000 board feet 18 339.00 450.00 6,102 8,100 Cement/cubic yard 30 26.10 33.00 783 990 Gravel/cubic yard 20 12.00 16.50 240 330 Plumbing 1 8,340.00 9,300.00 8,340 9,300 Iron and steel 1 6,750.00 7,560.00 6,750 7,560 Electrical wiring 1 4,315.00 4,485.00 4,315 4,485 Labour Common labourer/hour 300 12.60 14.50 3,780 4,350 Carpenter/hour 300 17.60 21.00 5,280 6,300 Mason/hour 75 18.40 23.20 1,380 1,740 Plasterer/hour 100 17.85 19.50 1,785 1,950 Plumber/hour 150 18.00 20.70 2,700 3,105 Painter/hour 125 17.20 18.92 2,150 2,365 $44,880 $52,255 Cost adjustment factor = $52,255 $44,880 = 1.164 If adjustments to base rates are expressed as multipliers, they will usually require no adjustment. If they are expressed in lump sums or dollars per unit, they should be updated by comparing current and base costs for the items. Construction costs can usually be trended in this way for several years. Periodically, however, base specifications and construction costs should be updated to reflect current construction technology and practices. 6.13
Chapter 6 Depreciation Analysis As discussed in Chapter 5, depreciation is the accrued loss in value due to physical wear and tear and functional and economic obsolescence. Depreciation represents the difference between RCN and market value and, as such, must be derived from the market. Many published cost manuals have tables indicating depreciation or "percent good" based on the type and age of structures. Such tables may be unrealistic for the local market and should be used with caution. Depreciation can vary by structure type and construction quality. Because location is so important to value, it may also be necessary to specify separate schedules for different geographic areas. In mass appraisal, depreciation schedules should reflect typical physical deterioration and include separate adjustments for functional and economic obsolescence. However, it is also important that appraisers have the ability to override depreciation schedules or assign additional depreciation as necessary for individual parcels. Depreciation schedules can be extracted from the market by correlating sales prices, less the value of land and miscellaneous structures, with effective age. Success depends on the reliability of the data used in the analysis. The steps are as follows: 1. Stratify sales by building or construction type. The sales should include only arm s-length sales adjusted as necessary for atypical financing, personal property, and time. Sales involving mixed-use parcels should be excluded. 2. Subtract the value of land and miscellaneous structures to obtain residual building values. Properties with extreme land-to-building ratios should be excluded. 3. Divide by RCN to obtain percent good (%GOOD). Mathematically: %GOOD ' SP & (LV % OV) RCN Equation 6.12 where S is the sale price, LV is land value, and OV is the value of other improvements. 4. Plot percent good against effective age, or plot accrued depreciation (1 - %GOOD) against effective age (see Figure 6.4). If effective age is not available, use actual age and exclude improvements with unusual renovations or deferred maintenance. 5. Fit a curve to the data. This is best accomplished with graphics or statistics software. Multiplicative MRA or a curve-fitting algorithm can be used. 6. From the curve, construct a percent good or accrued depreciation table. A table constructed from the data in Figure 6.4 might look like Table 6.7, with factors shown for ten-year increments in columns (2) and (4). 6.14
Specifying and Calibrating the Cost Approach Figure 6.4 Percent Good and Depreciation Plots Table 6.7 Percent Good and Depreciation Tables Percent good table Depreciation table (1) (2) (3) (4) (5) Percent depreciation derived Effective age Percent good Effective age Percent depreciation by multiplicative regression 0 100 0 0 0 10 85 10 15 15.5 20 75 20 25 24.5 30 67 30 33 32.1 40 60 40 40 38.9 50 55 50 45 45.1 60 50 60 50 50.9 70 45 70 55 56.4 Mechanics aside, the success of these procedures rests on the accuracy of the data used in the analysis, including land values and effective age estimates. The accuracy of land values should be verified from ratio studies and adjusted to the market as necessary. For individual parcels, when effective age estimates are too high, too much depreciation will be applied. On the other hand, if effective age estimates are too low, too little depreciation will be applied. Depreciation tables, like cost tables, can be stored as equations. In the present example (Figure 6.4), a simple multiplicative regression of percent depreciation (%DEP) on effective age (EFFAGE) yields the following: %DEP ' 0.0335 EFFAGE 0.6646 Equation 6.13 6.15
Chapter 6 Equation 6.13 gives the benchmark depreciation factors shown in column (5) of Table 6.7. These results are similar to the table values from which they were derived, and the table values could be adjusted to achieve an exact match. Of course, the equation could be similarly applied to structures of any given effective age and the resulting tables included in the agency's cost manual. Market Adjustments The final step in the cost approach is ensuring that estimated values are consistent with the market. This is particularly important because the cost approach separately estimates land and building values and uses replacement costs, which reflect only the supply side of the market. Market adjustments can be developed in several ways and can take several forms. Ratio studies can be used to evaluate appraisal accuracy by selected property strata (Chapter 11). Within the cost approach, stratification by construction class helps evaluate the accuracy of base rates, stratification by size groups indicates whether cost models appropriately reflect economies of scale (principle of decreasing returns), and stratification by age groups helps monitor the accuracy of depreciation schedules. Ratio studies for vacant land indicate whether land values are accurate. Finally, ratio studies by neighbourhood help evaluate the need for neighbourhood adjustments. One should always attempt to tailor adjustments in this manner rather than apply across-the-board adjustments. However, standard adjustments are appropriate when equity among property groups has been established. In addition to ratio studies, multiple regression analysis (MRA) and feedback can help to calibrate the cost approach to the market. Again consider the simple general cost model: MV ' IV % LV Equation 6.14 This model can be calibrated using linear MRA, with the constant constrained to zero: SP ' (b 1 IV) % (b 2 LV) Equation 6.15 where SP is sale price, and b and b are coefficients, or multipliers for buildings and land respectively. 1 2 If land and improvement values reflect the current market, the coefficients b 1 and b 2 will be close to 1.00. Values significantly above 1.00 indicate under-appraisal, and values significantly below 1.00 indicate overappraisal. For example, a value of 1.40 for b 1 and 0.90 for b 2 indicates that land values need to be increased by 40 percent and building values decreased by 10 percent. This basic model can be refined as follows: SP ' (b 1 RCN) & (b 2 DEP) % (b 3 LV 1 ) % (b 4 LV 2 ) %... % (b p LV n ) Equation 6.16 where DEP is accrued depreciation and LV, LV,..., LV equal land value if the parcel is in the specified 1 2 n neighbourhood, and zero otherwise. Again, all coefficients should be close to 1.00. Where they are not, procedures should be reviewed and adjustments considered. A hybrid model that could be used to similar effect is: SP ' (LV b 1 % IV b 2 ) b NBHD1 3 b NBHD2 4... b NBHDn p Equation 6.17 6.16
Specifying and Calibrating the Cost Approach The neighbourhood variables are general qualitative binary variables coded 1 if the property is in the neighbourhood and 0 if it is not. Nonlinear MRA or feedback can be used to calibrate the model. Again, all coefficients should be close to 1.00. Summary This chapter concludes the discussion of the cost approach in mass appraisal. Chapter 5 set the stage for the using the cost approach and this chapter discussed specifying and calibrating cost models. You should note that we will not be leaving the cost models completely behind as many of the performance evaluation tools and techniques discussed in detail in later chapters will be used to test and evaluate cost models. However, for the next two chapters we will focus on the direct (sales) comparison approach. 6.17