Valuation Theory, the Marshallian Synthesis and Implications to Mark-to-

Market Measurements

Terry V. GrissomProfessor of Real Estate University of

Washington and Lecturer in Real Estate University of Ulster

Process• Problem : Economic Foundation of Valuation

Techniques and Implications to Theory of Equivalence or Hierarch of Process

• Theory: ValueValuationAppraisal

• Empirical: Fit of ModelEquivalence vs. HierarchyComparative & Statisticalmark-to-market

Theory• Value Theory [Marhsal (1890/1979) (Friday (1922), Ratcliff (1961, 1965,

1972),Wendt (1974) Grissom (1981,1985, 1986), McParland, McGreal and Adair (2000), Odileck and Unsal, (2009) DeLisle &Grissom (2010)],

• Valuation Theory [Marhsal (1890/1979), Mertzke (1927), Babcock (1932), Bonbright (1937), Schmutz (1948), Wendt (1956), Ratcliff (1961, 1965, 1972a), Babcock (1968), Wendt (1974), Graaskamp (1979), Grissom (1981, 1985, 1986). Grissom et al (1987), Grissom & Diaz (1991), Moore (1992), Wincott et al (1996), Scott (1996), Crosby (1999), Crosby and Murdock (1999), Sharpiro et al (2009), Parli & Fisher (2010), DeLisle &Grissom (2010)],

• Appraisal Theory [Mertzke (1922), Schmutz (1948, 1956), Kinnard (1966) Ratcliff (1964, 1965, 1972b), Wendt (1974), Graaskamp (1979), Grissom (1981, 1985, 1986) Diaz (1990), Grissom and Diaz (1991), Pomykacz (2009), DeLisle and Grissom (2010)

Value Theory• Value Determinants

• Value Premise/Principles

• Statistical Concepts (Colwell,1979) (Gini, 1922)(Kummerow 2002)(Grissom 1986)

• Equilibrium Concepts (Marshall 1890)

Valuation Theory

Measurement and Base:

• Traditional –Property Base

• Statistical – Data Set or Market Base (Grissom, Robinson, Wang 1987)

• Equilibrium – Conditioned Set or Market BaseCannaday and Colwell (1981a, 1981b)

Appraisal Theory

Appraisal Analysis comprised of two general decision tools (Moore, 1992):

• Methods of standards and measurement; objective• Decision tools

Standard/Objectives – (subjective/judgment)Logic: Theory of Equivalence

HierarchyEvaluation Base

Figure 1Marshallian Valuation Construct and Market Structure

P

Q

DSR

SM SSRSI

SL

DI

DL

DSR’

PM

PSR

PI

Market Constructs of Approaches• Momentary/current price in Short Run Equation:

premised on Supply and Demand

• Price is a function of size/quantity and rent Where:

Conditional on and inverse relationship of price and quantity

MssoM QRqP |

SMO

MRQP

sMooM RPQ

Market Constructs of Approaches• The momentary market is altered by shifts in current supply

considering modifications as per land use succession conditions:• This is estimated by the rate of growth in supply based on the

neo-classical theorem as formulated by Robinson (1962). This theorem influences various long-run impacts on current expectations across input markets. The variables per market used in this study are conditioned on the weighted effects of growth expectations (SR)as functions of asset market calculus relative to the long-run normal growth rate:SSR = h(SM, SR, QSR|PSR, PM)

Market Constructs of Approaches

Short Run Pricing incorporating growth/change considerations and impacts:

Change/growth rate:

= gSR = h(

Expected Short-Run Price:

)))()( LRLRI

LRI

LRI

I ggg

gggg

g

SRSRSRSmE PSmQiP )(|

Market Pricing Constructs of Approaches

siISISISI VPV ||

tRoNOI

Vi

ii |

NOI = f(R, Ro|t, GIM)And NOI = net operating income ( rent less all expenses

and deductions)OER = operating expense ratio, derived from OER = 1-(Ro

X GIM) to derive a market developed operating expense ratio (OER). See Triece equation

GIM = a gross income multiplier (Price Gross Income/rent).

Intermediate Valuation Phase:

Where:

Hayek: Supply price /roundabout discounting affects

Market Pricing Constructs of Approaches

RVPV DiDDIDII ||||

The intermediate equilibrium value (VI|E) occurs where VI|D - VI|

S = 0; in the equation form where:

[I|D - D VI|D + Ri|D] - [I|S + S VI|S] = 0

Using the relationship VI|D - VI|S = 0; then Equation 5 is restated as:[I|D - I|S] + VI|E (S- D) + Ri|D = QVI|E

 

VI|E = QVI|E - Ri|D -[I|D - I|S]

(S- D)

Demand Pricing conditioned on price and rent associations:

Market Pricing Constructs of ApproachesLong Run considerations (distributive theory):• SLR = f(|R, L|w, K|i, |)|,

Where: = land as a factor of production compensated by rent R, a market price for the use of land or a cost in the process of production/construction L = labor compensated with a wage (w) K = capital receiving a return of (i) and = entrepreneurship, which is compensated with profit, which is treated as a cost of production in the creation or development of an asset. The factors are conditional on the level of total resources and the state of choices of development technology, , efficient, inefficient, sustainable or traditional.

Market Pricing Constructs of Approaches

• The ability to link long-term normal price and cost supports the form of the long-run supply and demand schedules based on Demand and Supply Equations respectively:

LRiDLRDDLRDLR RPQ |||| Demand

SLRSSLRSLR PQ ||| Supply

Equilibrium State:

P LR|S - P LR|D = 0

Empirical• Fit of Theory/Model-Equilibrim: Table 2a/b

and Figures 2-7• Statistical Distributions- E(V), Ve, Vp: Table 3

relative to Equilibrium values• Tests of Equality (Marhall’s Time Frames)

Theory of EquivilenceHierarchy : Table 4

• Comparative Statics and Marginal Distributions (Mark-to-Market): Table 5

$275-280 $274

Market Momentary

Short-Run

Intermediary Long Run

E(V)|M SR LR

Ve|Md SR LR

Vp|MoSR LR

Risk(SR)SR LR

Atlanta $150.00 $142.65 $146.30 $144.50 $144.92$125.58 $148.57$141.31$153.84$177.21 $144.60

$145.91 $124.82 $148.05$141.34 $151.41$176.77 $142.74

$149-150$130-133 $147$141-142$140-145$176-177 $144

$3.84$6.40 $ 2.77$1.36$0.62$1.64 $15.96

Austin $136.50 $118.00 $123.00 $120.00 $ 72.18 $117.54$ 89.21$128.85$145.81$151.65 $119.62

$ 72.30 $115.81$ 85.18$126.85$142.76$151.96 $127.45

$ 72.50 $109$ 70-75$110-120$140-143$151-153 $ 75

$ 0.46$16.16 $ 7.54$13.73$ 6.50$ 0.85 $30.18

Boston $329.00 $289 $301.50 $295.00 $243.00 $263.33$171.49$267.01$313.50$321.65 $255.55

$243.50 $265.85$172.85 $283.55$309.83$319.50 $267.70

$180-190 Bi-$200-225 modal$300-325$300-305$310-320 $316

$27.40$19.85 $24.19$44.57$15.58$13.56 $60.15

Equilibrium Values Statistical Values

Valuation Theory Model Tests-Empirical

100

120

140

160

180

200

220

90000 110000 130000 150000 170000 190000

$150.00

$144.50$146.30

SmS(I)

S(L)

S(L)'

S(I)'

Atlanta: Marshallian Synthesis of Valuation Approaches and Market Structure

SaleComps Income

Cost Approach

P

Q

D(L)

D(L)'

D(I)

D(I)'

D(sr)

D(sr)'

Valuation Theory Model Tests

40

80

120

160

200

240

740007600078000800008200084000860008800090000

$136.50

$120.00

$123.00

D(L)

D(L)'

D(I)

S(M)

S(I)

S(L)

S(L)'

D(sr)

D(I)'D(sr)'

Austin Marshallian Synthesis of Valuation Approaches and Market StructureP

Q

Valuation Theory Model Tests

120

160

200

240

280

320

360

400

190000 200000 210000 220000 230000 240000 250000

$329.00

$301.50$295.00

S(L)

S(L)'

D(L)

D(L)'

S(m) S(I)

S(I)'

D(sr)D(I)

D(I)'

D(sr)'

PBoston Marshallian Synthesis of Valuation Approaches and Market Structure

Q

Valuation Theory Model Tests

0

40

80

120

160

200

240

280

320

360

300000 320000 340000 360000 380000 400000 420000

D(sr)'

D(L)'

D(I)'

S(L)

$237.00

$197.00

$252.00

Los Angeles Valuation Approaches and Market StructureP

Q

D(sr) S(m)

D(I)D(L)

S(I)

S(L)'

S(I)'

Valuation Theory Model Tests

60

80

100

120

140

160

180

24000 26000 28000 30000 32000 34000 36000 38000

$118.50

$112.50

$135.50

D(sr)

S(m)D(I)

S(I)

S(L)D(L)

D(L)'

D(I)'

D(sr)'S(L)'S(I)'

Nashville Valuation Approaches and Market StructureP

Q

Valuation Theory Model Tests

0

100

200

300

400

500

88000 92000 96000 100000 108000 116000

$279.00

$259.00$230.00

S(m)

D(L)

D(L)'

D(I)D(sr)

D(I)'

D(sr)'

S(I)

S(L)

S(I)'S(L)'

San Francisco Valuation Approaches and Market StructureP

Q

Appraisal Theory: Equivalence vs Hierarchy• Empirical Analytics suggest Equivalence concept is weaken• Samuelson and Comparative Statics (1946-1947): offers

statistical critique of comparative statics in relation to marginal analysis. This offers support for or rejection of observations.

This is achieved in a 3 step process where: • Samuelson builds on Stigler’s argument that a goods

endogenous attributes are proportional to the quantity of the M good itself. This allows the price of the goods to be used to make maximum/minimum decision calculations. Goods can be specified by unique value determinants and attributes in the form:

11

1 MQM i

n

ii

Appraisal Theory: Equivalence vs HierarchyM1 is a minimum aggregated productivity attribute measurement allowed or acceptable per asset. A1iQi is the attribute quality measurement observed per unit in the market. •The assumptions of the endogenous attributes as defining the asset or good allows the price or cost estimate to specified as Pi = C|P1Q1+C|P2Q2…C|PnQn.

•This allows the cost combination in two price situations to be compared to the extent Pi Pj and deduce the level of price changes associated with optimal changes in quantities associated in each price situation.

Appraisal Theory: Equivalence vs Hierarchy• In this context the corresponding price and quantity changes in the

momentary market are stated as PM and QM and PSR and QSR in the short run market.

• The price-quantity pairings in the intermediate and long run markets are indicated by I and LR. By definition:

PMQSR PMQM and PSRQM PSRQSR

• Adding these inequalities and rearranging terms produces: (PSR-PMR)(QSR-QM) = P1Q1P2Q2…PnQn 0

This equation allows the comparison of the equilibrium positions in a comparative static format. This enables a direct comparison of the equilibrium positions as specified for the momentary, short-run, intermediate and long-run market pricing points.

Paasche/Laspeyres Indices

Appraisal Theory: Equivalence vs Hierarchy• With the assumption of constant utility (U), the price

differences can be carried further to a dynamic construct consider the integral format:

The above equation reflects a Hicksian demand construct, as such for the equivalence theorem to hold, the Hicksian demand structure has to hold across market periods, while a hierarchy format is consistent with the Marshallian construct with additive utility inferred. The test is determined by the percentage difference of the value estimate from the current market standardized as one (1), with the test statistic of 1-.

0|)]()([)]()([1

0

UdttQtQtPtP SRIt

t

SRI

Conclusions• Good Fit of Models across Economic phases• Strong argument for hierarchy of valuation techniques (given the

partial equilibrium construct that underlies the appraisal process based on the economics of the Marshiallian synthesis.

• though reconciliation process is reasonable, for it to hold significant procedure and assumptions must be developed in Sharpiro et al (2009)

• Mark-to-market standards supported if perspectives are designated as • Potential to condition pro-cyclical concerns• Suggest the focus on using market rather than subject as base of

analysis (or integration: See Grissom, Robinson and Wang (1987)• Further benefits to be gained by employing calculus of variation

construct and error correction models as alternative to structural equilibrium procedure