Depreciation and Effective Age

3. The published basis

The concept is not authored here. This paper operationalises Marshall & Swift’s extended life theory, published in the Marshall Valuation Service and its Section 97 depreciation tables, in a closed form of the author’s construction. Three propositions do the work:

1. Buildings age like people. The older a building gets, the greater its total life expectancy.
2. Correcting deficiencies lowers effective age and lengthens remaining life.
3. The published tables are empirical curves matched to actual sales and mortality data, and are explicitly not straight lines. This is where the straight line method fails.

Marshall & Swift state the lodging case directly, and this sentence justifies the whole approach:

A hotel is renewed continuously: a furniture, fixtures and equipment reserve funded out of revenue, maintenance spent every year, a brand product standard met periodically at the owner’s cost. A property renewed on that cycle does not accrue a year of effective age for every calendar year. That published statement is what the curve represents.

4. The form

Early years accrue nearly one for one. At a = 0 the slope is 1/λ, so a new building ages at close to calendar rate.

Effective age approaches the economic life without ever reaching it. As a grows, E(a) flattens and converges on L from below. That is what makes a 125 year old structure representable at all. The same visible outcome could be had by computing a straight line age and refusing any result above the economic life, but that produces a correct looking number by catching an incorrect one. The curve instead makes the impossible state unreachable: no input produces a negative remaining life, so there is nothing to catch and no special case a reader must know about to trust the figure.

Percent good is deliberately the plain ratio: the softening already lives in the curve, and a second shape here would soften the same effect twice.

5. What the hotel census says about how long hotels last

This section reports original research by the author. A census of the hotel universe carries 131,343 properties with both a construction year and a known operating status, and the question it answers directly is not how long a building lasts in the abstract but how often hotels of a given kind actually leave service.

Of those properties, these are the shares that have permanently closed.

The rate falls broadly as the scale rises, with one inversion between Upper Midscale and Upscale, and the span is more than fivefold. An economy hotel is roughly five times as likely to have left the operating universe as a luxury one. The finding holds independently within every construction frame, which is what makes it a property of the market position rather than of the building: in steel-framed stock the same walk runs from 0.5% at Luxury to 13.3% at Economy, in masonry from 2.1% to 11.5%, in wood frame from 1.4% to 9.2%.

Why this belongs in a paper about depreciation. Economic life is usually discussed as a property of construction, and construction is the part a table can describe. The census says the stronger signal is elsewhere. A luxury hotel is renewed because the position justifies the capital; an economy hotel at the same age, in the same frame, is far more likely to be closed than renewed, because the position does not. That is the same mechanism the curve in Section 4 describes, observed from the other end: what keeps a building in service is reinvestment, and what earns reinvestment is position.

What this study does not claim. It does not publish an economic life derived from the age of surviving hotels, and the reason is a confound worth naming rather than leaving for a reader to find. Ranked by the age its survivors reach, masonry appears to outlast steel. It does not. Masonry hotels are largely the 1900 to 1930 stock that was preserved and repositioned, while steel is modern build, so “how old do they get” is partly “when were they built”. Separating the two requires a hazard model that controls for construction vintage. That study is the next edition of this paper. Until it is run, no economic life is quoted from these percentiles.

The working schedule

Pending that model, L is taken from the life expectancy guidelines published in the Marshall Valuation Service, cited here as the craft reference the profession already uses and as a reasonableness check on the figures above rather than as the origin of the method.

Construction class describes the frame, a physical fact rather than a market opinion: A fireproof structural steel, B reinforced concrete, C masonry bearing walls, D wood or light metal frame. A stated economic life on the record is used in preference to the table; absent both a stated figure and a construction class, the method uses 50 years.

6. The softening parameter follows the property’s own reinvestment

λ controls how far the curve departs from the calendar. At λ = 1.0 it is neutral: still a curve, with no reinvestment tilt. Above 1.0 the property ages more slowly and below 1.0 faster, and the effect is substantial: the 125 year old structure that carries 45.9 effective years at λ = 1.0 carries 40.6 at λ = 1.5 and 31.6 at λ = 2.5. It is derived from two figures the record already carries, both checkable by a reader:

A hotel that reserves and maintains above market is the hotel Marshall & Swift describe as remodelled before the end of its useful life. One that under reserves ages faster, by the same arithmetic with the opposite sign.

λ is bounded to 0.5 through 2.5: reinvestment slows ageing and never stops it, so an unbounded parameter would let a generous reserve assumption erase a century of physical age. A value outside the bounds is refused rather than silently clipped. One further input tilts the same parameter, the property’s condition, and Section 9 sets out why it belongs there; the bound is applied to the tilted parameter, so no combination of reserve, maintenance and condition escapes it.

7. Renovations show as drops

A renovation does not change the curve. It moves the property’s position on it: a declared scope fraction removes that share of the effective age accrued to the date of the work, and accrual resumes along the same curve from the reduced position. Scope is stated per renovation, because all renovations differ and a year alone says nothing about what was done: 1.0 a gut back to new, 0.5 half the accrued effective age removed, 0.0 cosmetic, the position unmoved.

Plotted over a building’s life that is a sawtooth: a fall at each renovation and re accrual after.

Nothing in that row is capped, clipped or overridden. It is the equation at the stated inputs.

The sensitivity finding. Historic construction records for older structures are frequently ambiguous, and here they place construction anywhere between 1900 and 1929. Across that full twenty nine year disagreement the effective age moves 0.32 years, from 20.61 to 20.29, because the gut conversion dominates it; without the renovation recognised the same disagreement moves it 3.23 years. The lesson generalises: where a substantial renovation is recognised, vintage ambiguity is immaterial, and that is a measured result rather than an assertion.

8. One equation, two assets: the furniture, fixtures and equipment

The personal property is not a special case bolted on at the end. It is the same equation: same curve, same softening, same treatment of a renovation as a move along the curve. Exactly one input differs, the economic life, about 10 years for furniture, fixtures and equipment against 40 to 60 years for the building. The five to seven year figure often quoted is the MACRS depreciation period, a tax convention rather than a statement about how long a case good physically lasts.

A shorter life makes the curve bite far faster. At six chronological years it returns 5.65 effective years against a 50 year building life and 4.51 against a 10 year furniture life: close in years, but 45 percent of the life consumed against 11 percent.

A line refreshed on cycle never accrues much effective age. A line that is not refreshed accrues it quickly. Contributory value is then a product of two independently sourced figures:

Replacement cost new comes from the furniture, fixtures and equipment replacement cost benchmark, a distribution over 429 brand affiliations cut by service orientation. Percent good comes from the curve. Neither is derived from the other.

The cohort floor is n >= 100 observations. National, Limited-Service and Full-Service clear it. Extended-Stay at 43 and Select-Service at 38 do not. Those two are flagged as thin wherever used rather than quietly consumed, and the appraiser decides the fallback: ordinarily the property’s own history, with the band widened to bracket the subject so no spurious flag is raised.

9. Condition tilts the rate, not the answer

The remaining input is the property’s condition, and it enters as a multiplier on λ: the whole walk is re-run at a tilted rate rather than the answer adjusted afterwards. That placement is the more defensible reading as well as the simpler one, because a property in poor condition has been ageing faster all along, which is why it is in poor condition.

The default is average, the neutral tilt of 1.00: the curve exactly as derived, with condition saying nothing until someone says something. A default anywhere other than neutral would have every undeclared property quietly ageing at a rate nobody chose, on every assignment that never touched the field. Anything better or worse than average is a finding, and a finding is declared. Because the default asserts nothing, every tilt on the record is there because someone put it there and said why.

Condition need not come from an inspection. It may be read from a walk through, from conversations with the operator, or from records provided, and it must carry its source, because “excellent, per the asset manager” and “excellent, observed” are different strengths of evidence. That is where an asymmetry matters: no comparable sale is ever inspected, so a comparable’s condition rests on a renovation year in a sales book, while the subject is the one property actually walked at a known date.

The building and the furniture, fixtures and equipment carry separate condition statements, and both default to average. They genuinely differ: a soft goods refresh leaves excellent furniture in an older plant, and a structural programme the reverse. One shared word would force one of them to be misstated, and an appraiser who saw the difference would express it by adjusting a renovation scope instead, hiding a condition judgement in a field that means something else.

The tilt itself is bounded to 0.5 through 2.0, and the tilted λ is then held to the 0.5 through 2.5 bound of Section 6, so no composite of the two escapes the range stated there. A word outside the scale or a number outside the bounds is refused rather than clamped. A condition constant out of range does not look wrong on a page; it quietly moves every year of the walk.

The condition statement moves the answer by a knowable amount, in one direction, for a stated reason, and the report records the word, its source and the tilt it carried.

10. Limitations

The replacement cost new data is dateless. It carries one current replacement cost new figure per brand affiliation, with no time series and no market key, so it has no date of value ceiling and no market resolution. It must not be presented in a retrospective valuation as an as of cutoff figure, and what it supplies is a current national read rather than a local one. A market resolved, date ceilinged edition is a known open item.

The two coefficients that scale the reinvestment inputs into λ are authored. The functional form comes from the published extended life concept and the inputs are measured from the record, but the weights applied to them have not been calibrated against published research. They are stated defaults, overridable per assignment, and should be read as considered judgement rather than an empirical result.

A comparable’s condition at its own sale is a low confidence statement, resting on a renovation year in a sales book. Condition adjustments drawn from that comparison are less certain than adjustments drawn from measured facts such as room count or transaction date, and are weighted accordingly.

The curve models ordinary renewal, not every circumstance. Deferred maintenance, functional obsolescence and external obsolescence are separate diagnoses, addressed on their own terms and disclosed rather than folded into the effective age.

11. Data and inputs

Two figures in this paper are measured rather than assumed. The permanent closure study in Section 5 is run across the hotel census, the count of the hotel universe carrying both a construction year and an operating status. The benchmark in Section 8 is a furniture, fixtures and equipment replacement cost master spanning 429 brand affiliations, cut by service orientation and pooled into percentiles with outlier robust band edges.

That pairing is the point. A formula on its own is a shape without a scale, and a data set on its own is a scale without a judgment. The data supplies the scale, the appraiser supplies the judgment, and the method in this paper is where the two meet.

Subject specific inputs, being the construction class, the construction and renovation chronology, the declared renovation scopes, any stated condition of the building or of the furniture, fixtures and equipment together with its source, the reserve percentage and the property operations and maintenance ratio, are drawn from the record of the individual assignment and are stated in the body of the report this addendum accompanies.

Every constant described here is a stated default, and a value stated on the record for a specific assignment is used in preference to any default. Figures 1, 2 and 4 are reproducible from the equation in Section 4 and the inputs printed in each caption. Figure 3 and the cohort table reproduce the benchmark distribution.

Horwath HTL: Hospitality Valuation & Advisory Services

Horwath HTL provides specialized hotel valuation, litigation support, and real estate advisory across the Americas. Our US valuation practice delivers independent, audit-ready appraisals, financial reporting valuations, property tax appeal assessments, and transaction due diligence for hotel owners, lenders, institutional investors, and law firms.

Bryan Younge, MAI, ASA, FRICS is Managing Partner, USA with Horwath HTL, specializing in complex hotel valuations, expert witness testimony, and real estate advisory. He leads the firm’s US practice, advising global hotel brands, ownership groups, lenders, and counsel on portfolio valuations, tax appeals, litigation support, and high-stakes hospitality transactions. To discuss your U.S. hospitality valuation or advisory requirements, contact Bryan at byounge@horwathhtl.com or reach out to your local Horwath HTL office.