Ground Lease Valuation and Analysis - January 2020 - VEIF Foundation
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January 2020 Ground Lease Valuation and Analysis Author: Mark McNamara
Ground Lease Valuation
and Analysis
Title: Ground Lease Valuation and Analysis
Author: Mark McNamara
Overview of Research
The problem of valuing leasehold interests in property has been troubling New Zealand (NZ) valuers
for many years. The main issue is the paucity of market comparable evidence. Conventional
techniques adopted by the valuation profession for estimating leasehold interests in NZ have been
criticised by the financial, legal and accounting professions together with the parties contracted to
the investment; the tenant and the landlord. A common criticism is they are irrational, because they
do not explicitly recognise growth. The lack of a logical basis often leads to inaccurate estimates of
value, leaving the lessee, lessor and advisors frustrated and bewildered.
To understand how this climate has come about, the literature and models introduced in the NZ
valuation profession to estimate partial interests are reviewed and their historical context described.
The extent of leasehold land currently in NZ is examined to gauge its size and importance in the NZ
property market. The categories of leasehold are further examined (i.e. commercial, residential and
rural), so a sense of the relative size in each sector is apparent. A sample of six conventional
leasehold models put forward by the NZ valuation profession are evaluated. Thereafter,
contemporary growth explicit models are proposed, drawing on research from UK professors
Andrew Baum and Neil Crosby, but adapting their modelling within the context of NZ. The research
paper aims to provide a valuation model with a logical and accurate basis for valuing partial
interests.
Key Words: Discounted Cash Flow (DCF); Future Value (FV); Ground Rent Percentage; Lessee’s Interest;
Lessor’s Interest; Present Value (PV); Present Value of Annuity (PVA); Net Present Value (NPV); Internal
Rate of Return (IRR); Target Rate of Return; Years Purchase (YP)
Jan 2020 3
Table of Contents
1 INTRODUCTION ................................................................................................................................. 9
1.1. AIMS AND OBJECTIVES ................................................................................................................ 9
1.2. IMPORTANCE AND RATIONALE ..................................................................................................... 9
1.3. PRACTICAL APPLICATIONS ........................................................................................................... 9
2 GROUND LEASE HISTORY.................................................................................................................... 9
2.1. HISTORY OF GROUND LEASES IN NZ.............................................................................................. 9
2.2. LAWS GOVERNING GROUND LEASES ............................................................................................10
2.3. CHANGES TO RENT REVIEW PATTERN ...........................................................................................11
3 LEASEHOLD IN NZ ...........................................................................................................................12
3.1. EXTENT OF LEASEHOLD ACROSS NZ.............................................................................................12
4 HISTORICAL LEASEHOLD VALUATION THEORY.......................................................................................15
4.1. INFLUENCE OF UNITED KINGDOM ...............................................................................................15
4.2. HISTORICAL THINKING IN NZ......................................................................................................16
5 CONVENTIONAL LEASEHOLD MODELS IN NZ........................................................................................17
5.1 UNDER-RENTED LEASEHOLD EXAMPLE ..........................................................................................17
5.2 EVALUATION OF CONVENTIONAL APPROACHES ..............................................................................22
5.3 CRITICAL ANALYSIS OF CONVENTIONAL APPROACHES .......................................................................24
5.4 SUMMARY ...............................................................................................................................28
6 FINANCIAL MATHEMATICS AND FORMULAE .........................................................................................28
6.1 THE REVERSE YIELD GAP .............................................................................................................29
6.2 TVM FORMULAE CRITICAL TO CONVENTIONAL LEASEHOLD MODELS...................................................32
7 CONTEMPORARY PERPETUAL LEASEHOLD VALUATION MODELS ................................................................38
7.1 LINCOLN APPROACH ..................................................................................................................39
7.2 SHORT-CUT DCF.......................................................................................................................47
7.3 REAL VALUE APPROACH .............................................................................................................49
7.4 EXPLICIT DCF APPROACH ...........................................................................................................52
8 CONTEMPORARY TERMINATING LEASEHOLD VALUATION MODELS ............................................................57
8.1 SHORT-CUT DCF.......................................................................................................................57
8.2 REAL VALUE .............................................................................................................................58
8.3 EXPLICIT DCF...........................................................................................................................59
8.4 SUMMARY ...............................................................................................................................61
9 LIMITATIONS OF CONTEMPORARY LEASEHOLD MODELS ..........................................................................61
9.1 SENSITIVITY OF VARIABLES ..........................................................................................................61
9.2 ANALYSIS AND VALUATION USING LEASEHOLD COMPARABLES ...........................................................63
9.3 DIVERGING GROWTH RATES ........................................................................................................73
10 CONCLUSIONS AND RECOMMENDATIONS...........................................................................................75
11 FURTHER RESEARCH .......................................................................................................................75
12 AUTHOR BIOGRAPHY ......................................................................................................................76
13 BIBLIOGRAPHY...............................................................................................................................77
14 ABOUT THE FOUNDATION ...............................................................................................................81
Jan 2020 4
List of Figures
1 Leasehold Land Area in NZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2 Auckland Leasehold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3 Canterbury Leasehold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4 Otago Leasehold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
5 Lessee's Interest Over Varying Unexpired Term - Harcourt Method . . . . . . . . . . . . . . . . . 24
6 Lessee's Interest Over Varying Unexpired Term - Auckland Method . . . . . . . . . . . . . . . . . 25
7 Lessee's Interest Over Varying unexpired Term - Gellatly Method . . . . . . . . . . . . . . . . . . 25
8 Lessee's Interest Over Varying Unexpired Term - Barratt-Boyes Method . . . . . . . . . . . . . 26
9 Lessee's Interest Over Varying Unexpired Term - Macpherson Method . . . . . . . . . . . . . . 26
10 Lessee's Interest Over Varying Unexpired Term - Statutory Method . . . . . . . . . . . . . . . . . 27
11 IRR for Fixed Interest Security . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
12 Timeline for an annuity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
13 Change of Present Value over time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
14 Change of Present Value over time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
15 Partial Interests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
16 Head Lessee's Income Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
17 Head Lessee's Income Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
18 Lessee's Interest Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
List of Tables
1 Categories of Leasehold Land in NZ (ha) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2 Variables and Model Framework, Conventional Leasehold Models . . . . . . . . . . . . . . . . . 24
3 Variables and Resultant Values for Conventional Leasehold Models . . . . . . . . . . . . . . . . . 28
4 10-Year Discounted Cash Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
5 DCF at 10% . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
6 Explicit DCF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
7 Sensitivity of Lessee's Interest. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
8 Gearing Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
9 Explicit DCF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
10 Explicit DCF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
11 Performance of comparable and subject at different rental growth rates . . . . . . . . . . . . 72
Jan 2020 5
Glossary
All Risks Yield A yield which incorporates risks and potential for growth. It is a
theoretical method of comparison rather than a return rate
recognising the time value of money where passing net income
and assessed market income differ and is analysed over the
period of time up to where net market income is realised. The
calculation of the all risks yield starts by analysing an implied
growth rate which requires a target rate of return assumption.
Annuity A series of payments of a fixed amount for a specified number
of years.
Bond A long-term debt of a firm. In common usage, the term bond
often refers to both secured and unsecured debt.
Capitalisation Rate The yield is price divided by net income. In the case of property
the income must be current market net rent.
Coupon Rate The stated rate of interest on a bond.
Discount Rate The interest rate used in the discounting process; sometimes
called the Target Rate of Return.
Discounted Cash Flow A method of ranking investment proposals, including the
internal rate of return method and the net present value
method.
Future Value The amount to which a payment or series of payments will
grow by a given future date when compounded by a given
interest rate.
Ground Rent The rent determined by the ground rent precentage multiplied
by the freehold land value.
Ground Rent Percentage Ground rent percentages are either prescribed in the ground
lease at a fixed percentage or set at market level at rent
review. In essence, a ground lease creates the obligation for
the lessee to pay a series of equal periodic rental payments
determined by the ground rental percentage multiplied by the
market land value. If the ground rent percentage is prescribed,
then the parties need to agree the land value only at review.
Where the ground rental percentage is not prescribed, then
the ground rental percentage and market land value at the
review date have to be agreed between the parties.
Jan 2020 6
Glossary
Growth Rate The average compound annual increase in projected rent.
Inflation Risk Free Yield (IRFY) The rate of return required on income at an interest rate
required for giving up capital, taking into account risks attached
to the investment but excluding any extra return for the effects
of future inflation. Wood termed this real return the inflation-
risk-free yield (IRFY).
Internal Rate of Return (IRR) The rate of return on an asset investment, calculated by finding
the discount rate that equates the present value of future cash
flows to the cost of the investment.
Lessee's Interest Lessee’s Interest is the present value of all future rent savings.
Lessor's Interest Lessor’s interest is the present value of the total rents received.
Modern Portfolio Theory (MPT) Markowitz (1959) developed a portfolio model that showed
how risk may be reduced within a portfolio by combining assets
whose returns demonstrated less-than-perfect positive
correlation. Markowitz received a Nobel Prize in 1990 for this
work and the model is termed Modern Portfolio Theory (MPT).
Net Present Value (NPV) A method of ranking investments. The NPV is equal to the
present value of future returns, discounted at the target rate of
return, minus the present value of the cost of the investment.
Option The right, but not the obligation, to undertake a specified
transaction within a set period.
Partial Interests Terminology referring to and/or lessee's, lessor's interests.
Present Value The value today of a future payment, or stream of payments,
discounted at the appropriate discount rate.
Rack Rent If current market rent is different from passing rent, full rental
value will apply when the lease expires or when the next rent
review takes place. The yield on the new figure is the
reversionary yield: the yield attained when the property
reverts to full rental payment. It is then said to be rack rented.
Real Return See Inflation Risk Free Yield (IRFY).
Jan 2020 7
Glossary
Sinking Fund A required annual payment designed to amortize a bond or a
preferred stock issue. The sinking fund may be held in the form
of cash or marketable securities, but more generally the money
put into the fund is used to retire some of the securities in
question each year.
Target Rate of Return This is the discount rate used in discounted-cash-flow valuations
(see Discount Rate). Different terminology was historically
suggested in the 1970's, e.g. the Marshall, 1976 'equated yield
analysis'. Baum and Crosby (2008) highlight this term was used
to "draw attention to the internal rate of of return/redemption
yield nature of the discount rate employed to distinguish it from
the all-risks yield or growth-implicit capitalisation rate used in
conventional valuations, now called the equivalent yield. This
terminology is now past its sell-by-date and the yield should
simply be called the target rate, hurdle rate or required rate to
align property terminology with other markets."
Years Purchase UK terminology equivalent to an annuity (see Annuity).
Note:
The opinions expressed within the research paper are of
the author.
The Valuers Education & Integrity Foundation invites
comments directly to: info@veif.org.nz
Jan 2020 8
1 Introduction
1.1. Aims and Objectives
To critically examine the application of conventional leasehold valuation models in NZ and suggest a
contemporary growth explicit model drawing on research from United Kingdom (UK) professors
Andrew Baum (Professor of Practice at Saïd Business School, University of Oxford) and Neil Crosby
(Professor of Real Estate, University of Reading).
The aim is to provide a
valuation model for
partial interests valuers
can use for accurate and
rational valuation
estimates that clients
can rely on.
1.2. Importance and Rationale
Leasehold valuations are important because they are used as a surrogate for transactions, due to the
paucity of market evidence in the sector and relied upon by the financial community for extending
finance together with parties investing in the sector. Conventional techniques adopted by the NZ
valuation profession for estimating leasehold interests have been criticised by the financial, legal and
accounting professions together with the parties contracted to the investment; the tenant and the
landlord. A common criticism is they are irrational because they do not explicitly recognise growth.
The lack of a logical basis often leads to inaccurate estimates of value, leaving the lessee, lessor and
advisors frustrated and bewildered. Leasehold valuation has become subject to greater scrutiny
from the parties with a vested interest due to the conventional valuation techniques failing to
address the changing economic environment affecting the sector. Therefore, the importance of the
research is to formulate a valuation model which is rational and accurate to restore confidence and
credibility in the valuation profession and property market.
1.3. Practical Applications
This research paper includes numerous examples demonstrating complex reversions both for
terminating and perpetually renewable leasehold property. The heart of it is the critical examination
of leasehold valuation models by unfolding a carefully reasoned approach to calculate both
leasehold interests. The lynchpin for any valuation pivots on two key criteria: one, a valuation
should be rational; two, a valuation should be accurate. It follows a rational approach that leads to
an accurate estimate.
Prior knowledge of financial mathematics is assumed and the targeted audience is valuers, portfolio
managers, asset managers, property managers, academics of property, students of property, the
financial, accounting and legal professions, and parties linked with ground leases.
2 Ground Lease History
2.1. History of Ground Leases in NZ
Ground leases in NZ have a long history and their genesis extends back to 1840, when considerable
areas of land had been acquired by Māori and Europeans. Leasehold tenure has historically been
Jan 2020 9
the domain of larger non-profit organisations such as religious, educational and municipal bodies.
They were originally born from the need of early colonialists to own land and buildings, but because
both in freehold tenure were unaffordable, the land was leased and the improvements and lessee’s
interest in the land purchased (Knight 1994). This arrangement was affordable to the lessee and
provided a reasonable return to the landlord by way of ground rent from the land.
A ground lease creates the
obligation for the lessee to
pay a series of equal
periodic rental payments
determined by the ground
rental percentage
multiplied by the market
land value.
2.2. Laws governing ground leases
The Public Bodies Leases Act 1969 is the governing law for many ground leases and its predecessors
were the Public Bodies Leases Act 1908, the Public Bodies Leasing-Powers Act 1908 and the Public
Bodies Powers Act 1887. In the 1800’s, large areas of NZ were undeveloped and unprofitable,
however there was strong demand from settlers without significant amounts of capital for smaller
holdings and this was why the early statute was introduced. The settlers were mostly English who
were familiar with long leasehold. Large extents of endowment land, land owned by institutions,
local authorities, charitable trusts and public utilities (railways, harbour boards, schools), were also
available. Endowment land had limited liquidity whilst local authority, charitable and institutional
land owners had more latitude, with powers to enter into long term leaseholds.
The first phase of leasehold land in NZ was introduced by the Land Act 1877, aimed at the
agricultural sector and granted Licences for Pastoral Runs for a term of 10 years with right of
resumption (Eville, 1967). The 1882 Land Amendment Act introduced the perpetual lease, where
lands were offered via public tender at 5% of value. The terms of the lease provided 30 years, with
perpetual rights of renewal thereafter, a 21-year review pattern and fostered settlement of land for
those of limited capital.
The Land Act 1885 introduced the small grazing run lease where pastoral land no greater than 2,023
ha (subsequently increased to 8,092 ha) was granted for a 21-year term with perpetual successive
terms an option; ground rent set at 2.5% of capital value. The leases enabled husbandry of pastoral
and bush country, and large numbers were taken in Otago.
To encourage migration from towns to country where labour was needed, the village homestead
special tenure began in 1885. The scheme enabled Crown land up to 20.2300 ha to be purchased
under a perpetual lease. The introduction of the right to purchase came in 1892. A term of 25 years
was granted with the right of purchase after 10 years or lease into perpetuity.
A variation to Land Legislation in 1882 substituted a perpetual lease to a finite term of 999 years,
being a mechanism to compromise those who aspired to freehold and others advocating State
leasehold. Many of these leases still prevail. The tenure of small grazing was altered in 1907 in
perpetuity, with the renewable lease for a term of 33 years on settlement land and 66 years on
Crown land.
Jan 2020 10The Crown legacy in rural land
significantly moulded leasehold tenure
in NZ and its history paved the way for
pastoral run leases, small grazing run
leases and education reserve leases,
with terms between 21 and 66 years.
The Land Act 1924 smoothed over
legislation consolidating 78 Acts of
Parliament in respect to land.
By 1967, Crown Land held 45,627 leases and licenses, 6,175,547 ha in extent, comprising 2,446 ha of
urban land; 3,531 ha of commercial and industrial land; 2,568,894 ha of farm land; 3,389,840 ha of
pastoral and 210,836 ha of temporary licences and sundry tenures (Eville, 1967).
The Land Act 1948 became the dominant law governing lands, divided into twelve districts whilst the
Housing Division of the Ministry of Works controlled urban, commercial and industrial categories for
residential, business or factory sites. The distribution of land across the country varied greatly.
Otago administered in excess of 2,023,000 ha of Crown leasehold, in contrast to Auckland with the
smallest Crown leasehold area, 131,899 ha. However, Auckland’s focus was residential and
commercial land, highlighting the differing economic base between both regions.
Wall (1971) summed up the Wellington scene:
“It is interesting and perhaps significant that in New Zealand lessors are mainly public bodies
such as City Councils, Harbour Boards or Hospitals Boards and kindred religious and
educational institutions, with The Crown the largest lessor of all, while the private individual
has a relatively minor role as lessor. A brief study of the history of an individual area will
give the reasons for the establishment of the lessor. For example, with extensive
reclamation of Wellington Harbour around the turn of the century by Local Government and
the Harbour Board, there is a considerable amount of valuable central city land held by
these two Bodies while the New Zealand Railways is the lessor in an area previously
occupied by the old Te Aro Railway Station in the Wakefield Street area.”
2.3. Changes to rent review pattern
Wall (1971) also notes the period of 1969-70 saw a period of change in legislation effecting the
valuation of land. Changes included the Land Amendment Act 1970, dealing with Crown leasehold
under the Land Act 1948, where the perpetually renewable 33-year term was varied with an 11-year
rent review pattern, and the ground rent percentage decreased from 5.5% (5% if paid by the due
date) to 4.5% for the first 11 years and 4.5% thereafter, reducible to 4% if paid by the due date. The
important point here is the Legislature recognises an adjustment to the ground rent percentage is
necessary for the shorter 11-year review pattern in comparison to a longer 33-year review cycle to
reflect the benefit the lessee receives in the former. This is because where a longer rent review
pattern exists, the lessor requires a higher ground rent percentage in order to compensate for the
lost opportunity to obtain rental increases, which would arise where a shorter rent review interval
prevails. Here, the Legislature indicates the margin between an 11-and 33-year rent review pattern
is 1%. These margins are fuel for debate between valuers.
Jan 2020 11As noted, the Public Bodies Leases Act 1969 is considered the most important concerning ground
leases, controlling the creation, administration and renewal procedures. Section 26 focuses on
renewals of existing leases with the right to reduce rent review patterns to 5 yearly at the expiry of
the term. These changes resulted from the inflationary economy at this time and Jefferies (1991)
notes new terminating leases with 5 or 7-year review patterns evolved at this period.
A number of ground leases in New Zealand have a term of 21 years, are perpetually renewable with
either 7-or 21-year rent reviews and are sometimes referred to as Glasgow leases. Jefferies (1991)
provides a succinct summary in the March issue of the NZ Valuer’s Journal, describing how ground
leases have changed, particularly from the 1970’s onwards with shorter rent review patterns.
3 Leasehold in NZ
3.1. Extent of Leasehold across NZ
The combined area of NZ’s freehold and leasehold tenure is 26.13 million ha, of which 2.62 million
ha is leasehold, approximately 10% (Source: Quotable Value Ltd, 2019). There is a marked difference
in the distribution of leasehold land between the two islands, illustrated in Figure 1 below:
Fig 1: Leasehold Land Area in NZ
West Coast
Wellington
Waikato
Tasman
Taranaki
Southland
Otago
Northland
Nelson
Marlborough
Manawatu-Wanganui
Hawke's Bay
Gisborne
Chatham Islands
Canterbury
Bay of Plenty
Auckland
- 200,000 400,000 600,000 800,000
Land Area (ha)
561,545 ha of leasehold land is contained in the North Island, with 2,055,077 ha in the South Island.
Moreover, the extent of leasehold land varies from district to district. Canterbury and Otago have
the largest leasehold areas of 850,013 ha and 705,700 ha, respectively. By comparison, Auckland
has the smallest area at 211 ha.
However, the emphasis on leasehold land varies. A great deal of commercial and residential land is
prevalent in the Auckland area with very little agricultural leasehold land. Canterbury and Otago on
the other hand are dominated by the agricultural sector. Figures 2, 3 and 4 illustrate (source
Quotable Value Ltd).
Jan 2020 12Fig 2: Auckland Leasehold
Residential - Leasehold
Other - Leasehold
Auckland
Lifestyle - Leasehold
Industrial - Leasehold
Horticulture - Leasehold
Commercial - Leasehold
0 20 40 60 80 100
Land Area (ha)
Fig 3: Canterbury Leasehold
Utility - Leasehold
Specialist - Leasehold
Residential - Leasehold
Pastoral - Leasehold
Other - Leasehold
Canterbury Mining - Leasehold
Lifestyle - Leasehold
Industrial - Leasehold
Horticulture - Leasehold
Forestry - Leasehold
Dairy - Leasehold
Commercial - Leasehold
Arable - Leasehold
0 100000 200000 300000 400000 500000 600000
Land Area (ha)
Jan 2020 13Fig 4: Otago Leasehold
Utility - Leasehold
Residential - Leasehold
Pastoral - Leasehold
Other - Leasehold
Otago
Lifestyle - Leasehold
Industrial - Leasehold
Horticulture - Leasehold
Forestry - Leasehold
Dairy - Leasehold
Commercial - Leasehold
0 200000 400000 600000 800000
Land Area (ha)
In summary the ‘golden’ leasehold districts, Canterbury and Otago comprise approximately 60% of
total leasehold land in NZ. Leasehold land takes up 2.62 million ha and the pastoral sector makes up
approximately 65% as tabulated in Table 1 below:
Table 1: Categories of Leasehold Land in NZ (ha)
Arable 2,169
Commercial 4,499
Dairy 55,614
Forestry 537,262
Horticulture 3,855
Industrial 946
Lifestyle 8,099
Mining 2,129
Other 282,398
Pastoral 1,715,507
Residential 736
Specialist 2,257
Utility 1,150
Grand Total 2,616,621
Jan 2020 144 Historical Leasehold Valuation Theory
4.1. Influence of United Kingdom
Prior to the 1940’s, literature describing valuation approaches to leasehold valuation in NZ is sparse,
however, the approaches which did develop resemble the thinking described in UK textbooks which
date back to 1884 (Baum and Crosby, 1988). The following example (similar to Norris, 1884, 6)
illustrates the valuation approach to the three main interests in a property: the rack rented freehold;
the reversionary freehold and the leasehold.
Assume a suburban shop investment is leased at a net passing rent of $10,000 p.a. where the net
market income is $21,000 p.a. The next review is 2 years hence and all risks yields for a similar class
of property is estimated at 5.00%. Government 10 year-bonds average around 3%.
Rack Rented Freehold
Net Market Income $21,000
Capitalised in perpetuity @ 5%:
Valuation $420,000
deferred 2 years @ 5% $380,952
Reversionary Freehold
Contract Rent $10,000
PV $10,000, 2 years @ 5% $18,594
Reversion rent $21,000
Capitalised in perpetuity @ 5%:
$420,000
def erred 2 years @ 5% $380,952
Valuation $399,546
Leasehold
Net Market Income $21,000
Less: Contract Rent $10,000
Prof it rent $11,000
PV $11,000, 2 years @ 5%
Valuation $20,454
Note the valuation of the reversionary
freehold and leasehold interests are
such that the sum of the two always
equal to the total value of the freehold
in perpetuity (i.e. $399,546 + $20,454 =
$420,000). This concept stretched as
far forward to the rational model
(Sykes, 1981) to the point of being
indoctrinated into valuation.
The idea the ‘sum of the parts’ equal freehold is not accepted in contemporary leasehold valuation
because it assumes the lessee’s and the lessor’s target rate of return are the same (Baum and
Crosby, 2008, 199). There is a market perception the required return for a leasehold interest is
higher because leasehold is considered riskier to freehold, which implies the ‘sum of the parts’ is less
than freehold (Baum, Mackmin and Nunnington, 2017, 192). This point is taken further under
section 7.1.2 of this research paper.
Jan 2020 15Another idea which also evolved in the UK, and fortunately, has not been adopted by the NZ
valuation profession, is the concept of a sinking fund, where dual interest rates are adopted into the
calculations. The idea was the return of capital and on capital: the former justifying a lower rate to
recapture the leasehold investment which was considered a wasting asset with a finite investment
horizon. As this approach has not been adopted in NZ, further explanation is not necessary,
however interested readers should refer Baum and Crosby (2008).
4.2. Historical thinking in NZ
UK early conventional valuation theory reduced to a single target rate of return where the sum of
the lessee’s and lessor’s interests were understood to equate to freehold. A review of the valuation
literature in NZ (articles in The N.Z. Valuers’ Bulletin first published in 1941, changing to The New
Zealand Valuer in the late 1940’s, and later, New Zealand Valuers Journal) suggest a similar
interpretation here.
McGowan (1944) published three consecutive papers in the June, September and December issues
of The N.Z. Valuers’ Bulletin demonstrating fourteen examples where the solutions pivot on the
premise that all interests equate to freehold (recognise the calculations were governed by the then,
Valuation of Land Act 1925, S54 (since repealed)).
The Newman Case further solidified the notion. This case centered on the sale of a leasehold
property embodied under the Servicemen's Settlement and Land Sales Act 1943 and the fair
assessment of the lessee's interest. Archer, J stated:
"Notwithstanding these views, we are of opinion that the ascertainment of fair market value
of a lease in accordance with the principles expressed is far from a simple matter, and that it
is impossible to lay down any simple method of valuation for general adoption of Land Sales
Committees.
...the sum of the values of all the separate interests in a piece of land cannot be greater than
the capital value of the land. In a simple case, therefore, the interests of the lessor and
lessee cannot together be greater than the capital value, and conversely, the capital value
should be capable of division into the lessor's and lessee's interests respectively. There
appears to be ample authority for this proposition with which Blair, J., concurred in Valuer-
General v. Public Trustee (11). It follows that the ascertainment of the capital value of the
land affected is a valuable, if not a necessary starting-point where the value of a leasehold
interest is to be assessed. It also follows that the value of a leasehold can never exceed the
capital value of the freehold, and that the value assigned to a lessee's interest may always
be checked by considering whether the balance of the capital value is a reasonable sum to
be allowed for the interest of the lessor.”
The extension of this
thinking evolved, where
Jenkins (1950) proposed a
method of converting a
terminating to a perpetually
renewable lease, and the
calculation of new rent for
the perpetual interest.
Jan 2020 16Examinations reinforced the ‘sum of the parts’ theory, where an answer for an exam question on
leasehold (only one candidate completed the question) was set in the March 1956 issue of The New
Zealand Valuer and the editor urged students to closely study it.
Frizzell, R. (1972), a senior lecturer at Lincoln College at that time, put forward the proposition
Lessee’s Interest = Capital Value - Lessee’s value of Lessor’s Interest. However, he also
acknowledges the market worth of the lessor’s and lessee’s interests may not equate to capital value
of the property.
Jefferies, R. (1989) challenged this idea. Bell (1988, 104), sums up the ‘sum of the parts’ influence in
NZ:
“…the lessee’s interest has been capitalised at 10% and the rental is assumed to be due
annually in arrears. Generally, the rental would be due monthly in advance. In practice, the
lessee’s interest would be capitalised at a higher rate than 10% to reflect the diminishing
security of the asset. Nevertheless, the example illustrates a basic convention that has
arisen, namely that the value of all interests in a property when added together are equal to
the freehold value of the property when otherwise unencumbered. This convention has
come under question and might not always reflect the market circumstances. In essence,
however, the example does indicate that mathematically the total value of all interests is
equal to the market value of the property where all interests are discounted at the same
rate.”
The ‘sum of the parts’ theory was accepted by the author (McNamara, 1998). After years of
reflection, research and thought, I have abandoned this proposition and hopefully, it will become
clear to readers in the following sections of this research paper why.
5 Conventional Leasehold Models in NZ
The 1960’s through to the early 1970’s saw the development of numerous methods for estimating
lessee’s interests’ in NZ. For example, Gellatly (1966), Macpherson (1967) and Barratt-Boyes, B.A.
(1972) published their methods in The New Zealand Valuer and the March 1989 issue of The New
Zealand Valuers’ Journal (celebrating the fiftieth jubilee of the NZ Institute of Valuers’) reprinted
their articles, reinforcing the influence of their thinking. These together with the Auckland, Harcourt
and Statutory methods, influential at this time are summarised below:
1. The Harcourt Method
2. The Auckland Method
3. The Gellatly Method
4. The Macpherson Method
5. The Barratt-Boyes Method
6. Statutory Method
These approaches will now be critically examined, illustrated by an example.
5.1 Under-rented leasehold example
A rural property on a perpetually renewable 21-year term lease (reviewed at the same frequency)
with 18 years to run before the next review. Gilt edged rates (10-year NZ Government Bonds) are
Jan 2020 1712% and first mortgage interest rates are 15%. The Rack Rent Rate (market ground rental
percentage) for similar ground leases is 7% and the current market value for the land is $100,000.
The contract rent if $3,500 p.a.
This is an example of the term and reversion problem. The term is the present value of the rent
saving from the current time to the next rent review (or lease renewal). The reversion is the
perpetual right of renewal benefit, being the difference between the present value of the full rental
value 18 years hence and perpetual renewals thereafter, and rent savings that accumulate between
reviews due to the renewed rent being fixed between reviews. This pattern is illustrated in the
following graphic:
P
r
e
s
e
n
t
$7,000
v
a
l
$3,500
u
e
18 39 60 81 102 123 144
Years
In the graphic, the red and green are the term split between the lessor’s and lessee’s interests (rent
savings) respectively. The purple and blue represent the reversion partitioned into the lessor’s and
lessee’s interests respectively.
The conventional approaches to the valuation of the lessee’s interest for each of the methods are as
follows:
Harcourt Method
(i) Rental Benefit
Rental at gilt edged securities rate $x 1
Less contract rent $x 2
Benefit $x 3
PV of $x 3 at gilt edged discount rate for the number of years left in term.
(ii) Right of Renewal
Gilt edged rate % - rack rent % = x%
x% of Land Value (current market value) = $x 4
- $x 4 capitalised in perpetuity at gilt edged rate
- both capitalisation and discounting at gilt edged rates.
Jan 2020 18(i) Rental Benefit
Market return, $100,000 x 12% = $12,000
Contract Rent $3,500
Benefit $8,500
PV $8,500 p.a. for 18 years at 12%
$8,500 x 7.2497 = $61,622
(ii) Right of Renewal
12% - 7% = 5% x $100,000 = $5,000
$5,000 ÷ 12% =$41,667
$41,667 deferred 18 years @ 12% $5,418
Total lessee's Interest $67,040
Auckland Method (a variation on the Harcourt Method)
(i) Rental Benefit
Rack Rent rate $x1
Less contract rent $x2
Benefit $x3
PV of $x3 at gilt edged discount rate for the number of years left in term
(ii) Right of Renewal
Gilt edged rate % - rack rent % = x%
x% of Land Value (current market value) = $x 4
- $x4 capitalised in perpetuity at gilt edged rate
(i) Rental Benefit
Rack Rent, $100,000 x 7% = $7,000
Contract Rent $3,500
Benefit $3,500
PV $3,500 p.a. for 18 years at 12%
$3,500 x 7.2497 = $25,374
(ii) Right of Renewal
12% - 7% = 5% x $100,000 = $5,000
$5,000 ÷ 12% =$41,667
$41,666
Total lessee's Interest $67,040
This approach is described further on page 23.
Jan 2020 19Gellatly Method
(i) Rental Benefit
Mortgage Return on Land Value $x 1
Less contract rent $x 2
Benefit $x 3
PV of $x 3 at Mortgage Rate for the number of years left in term
(ii) Right of Renewal
Mortgage % - rack rent % = x%
x% of Land Value (current market value) = $x 4
- $x 4 capitalised in perpetuity at mortgage rate
- discounted at mortgage rate
(i) Rental Benefit
Market return, $100,000 x 15% = $15,000
Contract Rent $3,500
Benefit $11,500
PV $11,500 p.a. for 18 years at 15%
$11,500 x 6.1280 = $70,472
(ii) Right of Renewal
15% - 7% = 8% x $100,000 = $8,000
$8,000 ÷ 15% =$53,333
$53,333 deferred 18 years @ 15% $4,310
Total lessee's Interest $74,782
Barratt - Boyes Method
(i) Rental Benefit
Rack Rent rate $x1
Less contract rent $x2
Benefit $x3
PV of $x3 at Mortgage Rate for the number of years left in term
(ii) Right of Renewal
Mortgage % - rack rent % = x%
x% of Land Value (current market value) = $x 4
- $x4 capitalised in perpetuity at mortgage rate
- discounted at mortgage rate.
Jan 2020 20(i) Rental Benefit
Rack Rent, $100,000 x 7% = $7,000
Contract Rent $3,500
Benefit $3,500
PV $3,500 p.a. for 18 years at 15%
$3,500 x 6.1280 = $21,448
(ii) Right of Renewal
15% - 7% = 8% x $100,000 = $8,000
$8,000 ÷ 15% =$53,333
$53,334
Total lessee's Interest $74,782
Macpherson Method
(i) Rental Benefit
Rack Rent rate $x 1
Less contract rent $x 2
Benefit $x 3
PV of $x 3 at Mortgage Rate for the number of years left in term
(ii) Right of Renewal
2% of Land Value = $x 4
PV factor $1 in perpetuity at mortgage rate = a
PV factor $1 for term remaining at mortgage rate = b
Difference c
(i) Rental Benefit
Rack Rent, $100,000 x 7% = $7,000
Contract Rent $3,500
Benefit $3,500
PV $3,500 p.a. for 18 years at 15%
$3,500 x 6.1280 = $21,448
(ii) Right of Renewal
PV of 1$ in perpetuity @ 15% 6.6666667
PV of 1$ deferred 18 years @ 15% -6.1279659
0.5387008
$2,000 x 0.53870079 = $1,077
Plus rental benefit $21,448
Total lessee's interest $22,525
Refer to page 23 for further explanation of this approach.
Jan 2020 21Statutory Method
- Incorporated in section 122 of the Land Act 1948.
- Used for assessing 'goodwill' when freeholding (i.e. lessor's interest).
Method
(i) Calculate Land Rent as at the date of valuation.
(ii) Subtract contract rent from land rent to arrive at rental benefit.
(iii) Treat rental benefit as an annuity discounted at rate of land rent for period
of term left to run.
Assumptions
21- year perpetually renewable lease
18 years left in term.
Contract rent: $3,500
Land Exclusive of Improvements $100,000
Land Rent: 5.0% of land value
Land Rent: $5,000
Rental benefit = $5,000 - $3,500 = $1,500
PV $1,500 p.a. for 18 years @ 5% = $1,500 x 11.6896 = $17,534
Therefore, lessor's interest = $100,000 - $17,534 = $82,466
5.2 Evaluation of Conventional Approaches
Harcourt Method: There are a number of major flaws in this valuation method. The rental benefit in
the term grossly overstates the market ground rent by multiplying the current market land value by
the Gilt Edged rate which is 12%; 5% above the Rack Rent rate of 7%, or an over estimate of $5,000.
The rental benefit is discounted to present value (PV) at the Gilt Edged Rate. In the term and
reversion approach, it may be argued that the term portion of the rental benefit is very secure.
Being less than current market rent, the lessee enjoys a profit rent and the PV of this portion is
calculated at the Gilt Edged rate. Despite this, the resultant rental benefit is over-valued because
the market rent is incorrectly assessed from the Gilt Edged Rate instead of the Rack Rent Rate.
The right of renewal benefit is calculated as the difference between the Gilt Edged Rate and Rack
Rent Rate, capitalised in perpetuity at the Gilt Edged Rate and deferred at the Gilt Edged Rate. It is
not logical to assume the right of renewal benefit represents the difference between the Gilt Edged
Rate and Rack Rent Rate. There is no growth assumed in the calculation.
Auckland Method: The Auckland Method addresses the issue highlighted in the Harcourt Method,
correctly calculating the market ground rent, multiplying the Rack Rent Rate by the current market
land value. The resultant present value of the term rental benefit is therefore significantly lower
than the Harcourt Method, being a smaller profit rent discounted to PV at the Gilt Edged Rate.
The right of renewal benefit adopts the same parameters to the Harcourt Method however the
capitalised profit rent is not deferred. This off-sets the lower value of the term rental benefit
($36,248) by increasing the reversion right of renewal benefit by the same difference. Accordingly,
resultant lessee’s interests of both the Harcourt and Auckland Methods are the same. Difficulties
arise from the right of renewal benefit not being deferred. Regardless of the period to expiry or
review, the right of renewal benefit stays constant at $41,667, assuming all other parameters remain
unchanged. Effectively, the time value of money is ignored with this assumption, which does not
reflect reality and has the effect of the Harcourt and Auckland methods, giving the same answer.
Jan 2020 22Gellatly Method: The Gellatly Method has an identical framework to the Harcourt Method. The
overstated market rent is amplified where the market ground rent is calculated by multiplying the
current market land value by the difference between the First Mortgage Rate (15% which is higher
than Gilt Edge Rate: 12%) and the Rack Rent Rate. The same criticisms described under the Harcourt
Approach apply to the Gellatly Method. In essence, the Gilt Edge Rate is substituted by the First
Mortgage Rate under the Gellatly Method.
Barratt-Boyes Method: The Barratt-Boyes Method is another version of the Gellatly Method (just as
the Harcourt and Auckland methods are). The Gilt Edge Rate is substituted with the First Mortgage
Rate and in all other respects, the mechanics of the calculation mirror the Auckland Method. The
off-set between the term and reversion is $49,024, being higher than the Harcourt and Auckland
Methods due to the First Mortgage Rate being higher than the Gilt Edge Rate. The method lacks any
real rationality, as with the Auckland Method, where the right of renewal benefit remains constant
at $53,333.
Macpherson Method: The term of the Macpherson Method is identical to the Auckland and Barratt-
Boyes Methods, calculating the market ground rent by adopting the Rack Rent Rate and applying the
First Mortgage Rate to calculate the PV of the profit rent in the term. The First Mortgage Rate is
adopted on the assumption it reflects the opportunity cost to the lessee (i.e. the substitute for
ground rent is first mortgage funding).
The right of renewal benefit in the reversion is different to all the approaches discussed thus far.
The calculation takes the difference between the First Mortgage Rate factor into perpetuity and the
PV factor of the term at the First Mortgage Rate. This difference is then multiplied by $2,000, which
is difficult to understand. The Macpherson Method prescribes little value to the right of renewal
benefit.
Statutory Method: As with all the methods, the Statutory Method assumes no inflation, so therefore
there is no increase in the lessee’s interest over the unexpired term of the lease. In all future
renewals, the market ground rent and contract rent are assumed to be equal and rental benefits
arriving to future terms are ignored (i.e. there is no right of renewal benefit in the calculation). The
method uses a discount rate of 5% which is artificially low, and the contract rent is set at 4.5% of the
Land Exclusive of Improvements (a variation to what defines land value, LEI). The valuation date of
the LEI is effective from the commencement date or renewal date of the lease.
A summary of the variables and framework of the six methods are set out in Table 2 overleaf:
Jan 2020 23Table 2: Variables and Model Framework, Conventional Leasehold Models
Har Auck Gell B.B Mac Stat
Rental GE RR MR RR RR LR
Benefit - CR - CR - CR - CR - CR - CR
Discount Rate GE% GE% MR% MR% MR% LR%
Right of Renewal GE - RR GE - RR MR - RR MR - RR $2,000
Capitalisation P p GE Pp GE Pp MR Pp MR Pp - UT
Discount Rate GE% MR% MR%
Key
GE = Gilt Edged Rate Har = Harcourt Method
RR = Rack Rent Auck = Auckland Method
MR = Mortgage Rate Gell = Gellatly Method
LR = Land Rent B.B. = Barratt - Boyes Method
Pp = Capitalisation in perpetuity Mac = Macpherson Method
UT = Unexpired Term of Lease Stat = Statutory Method
CR = Contract rent
5.3 Critical analysis of conventional approaches
To illustrate the issues highlighted, an analysis of the term and reversion values assuming an
unexpired term of 1 year, 2 years, 3 years and consecutively through to 20 years unexpired has been
undertaken for each method. The results for the Harcourt and Auckland Methods are graphed in
Figures 5 and 6 below and overleaf:
Fig 5: Lessee's Interest Over Varying Unexpired
Term - Harcourt Method
$70,000
$60,000
Present Value
$50,000
$40,000
$30,000
$20,000
$10,000
$0
0 5 10 15 20 25
Unexpired Term (years)
Term Reversion
Jan 2020 24Fig 6: Lessee's Interest Over Varying Unexpired
Term - Auckland Method
$50,000
$40,000
Present Value
$30,000
$20,000
$10,000
$0
0 5 10 15 20 25
Unexpired Term (years)
Term Reversion
In Figure 5, the reversion declines inversely with the length of unexpired initial term, in contrast to
the perpetual right of renewal benefit which increases as the unexpired term lengthens which is
intuitively what you would expect. In Figure 6, the Auckland Method’s reversion stays constant
regardless of the unexpired initial term (and always higher than the term). Clearly the reversion
should decrease in value where the unexpired term is long but the approach does not make this
adjustment. The term increases where the unexpired initial term is longer. Despite these disparate
patterns, the lessee’s interest equates for both methods regardless of the unexpired term.
The same relationship is evident where the Gellatly and Barratt-Boyes Methods are analysed and
compared, Figures 7 and 8 below and overleaf:
Fig 7: Lessee's Interest Over Varying unexpired
Term - Gellatly Method
$80,000
$70,000
$60,000
Present Value
$50,000
$40,000
$30,000
$20,000
$10,000
$0
0 5 10 15 20 25
Unexpired Term (years)
Term Reversion
Jan 2020 25Fig 8: Lessee's Interest Over Varying Unexpired
Term - Barratt-Boyes Method
$60,000
$50,000
Present Value
$40,000
$30,000
$20,000
$10,000
$0
0 5 10 15 20 25
Unexpired Term (Years)
Term Reversion
The Macpherson Method has a similar pattern to the Harcourt and Gellatly Methods however there
is no real logic to the results, as noted previously (Figure 9).
Fig 9: Lessee's Interest Over Varying Unexpired
Term - Macpherson Method
$25,000
$20,000
Present Value
$15,000
$10,000
$5,000
$0
0 5 10 15 20 25
Unexpired Term (Years)
Term Reversion
D'Arcy (1972) was critical of both the Macpherson and Gellatly methods (based on the Harcourt
method):
“But I would question the validity of both methods, because at the date of renewal it gives
the same value to the right of renewal (ROR), irrespective of the length of the term. I think
it is generally agreed that all other things being equal, the value of the ROR on a 21 year
lease is worth more than the ROR on say a 7 year lease.”
Finally, the Statutory Method is illustrated in Figure 10 overleaf, where there is no lessee’s interest
allocated to the reversion (right of renewal benefit). This means there is no lessee’s interest in the
land where the lease is near to expiry/renewal.
Jan 2020 26Fig 10: Lessee's Interest Over Varying Unexpired
Term - Statutory Method
$25,000
$20,000
Present Value
$15,000
$10,000
$5,000
$0
0 5 10 15 20 25
Unexpired Term (Years)
Term Reversion
The Statutory Method is used for assessing “goodwill” when freeholding. Goodwill is not business
goodwill but infers the lessee’s interest in the land. In the example, the offer the Crown (Lessor)
would extend to the lessee to freehold the property would be calculated as follows:
PV $1,500 p.a. for 18 years @ 5% = $1,500 x 11.6896 = $17,534
Therefore, lessor's interest = $100,000 - $17,534 = $82,466
Despite the method’s short comings, it is easily understood and still widely used by the valuation
profession outside the brief of the Land Act 1948, under which the approach is governed.
A common practice is to calculate the market ground rent by multiplying the Rack Rent Rate by
current market land value. The rental benefit is discounted to PV at the Gilt Edged Rate whilst the
reversion (right of renewal benefit) is estimated by multiplying a percentage (analysed from sales
evidence; say 25%) by the Land Value. The calculation would typically be as follows:
(i) Rental Benefit
Rack Rent, $100,000 x 7% = $7,000
Contract Rent $3,500
Benefit $3,500
PV $3,500 p.a. for 18 years at 12%
$3,500 x 7.2497 = $25,374
(ii) Right of Renewal
$100,000 x 25% = $25,000
Total lessee's Interest $50,374
A summary of the results from the six conventional leasehold valuation methods are set out in Table
3 overleaf:
Jan 2020 27Table 3: Variables and Resultant Values for Conventional Leasehold Models
Har Auck Gell B.B Mac Stat
Rental 12% 7% 15% 7% 7% 5%
Benefit $61,622 $25,374 $70,472 $21,448 $21,448 $17,534
Discount Rate 12% 12% 15% 15% 15% 5%
Right of Renewal 5% 5% 8% 8% $2,000
Capitalisation 12% 12% 12% 15% 15%
Discount Rate 12% 15% 15%
Benefit within initial term $61,622 $25,374 $70,472 $21,448 $21,448 $17,534
+ ROR Benefit $5,418 $41,666 $4,310 $53,334 $1,077 $0
Lessee's Interest $67,040 $67,040 $74,782 $74,782 $22,525 $17,534
Lessor's Interest $32,960 $32,960 $25,218 $25,218 $77,475 $82,466
The results indicate a wide variation in lessee’s interest, where the Gellatly and Barratt-Boyes
Methods answers are approximately 70% higher than those of the Macpherson Method.
5.4 Summary
All methods ignore inflating rack rents in the term and reversion components of the calculation. The
Harcourt and Gellatly methods look at alternative investments to arrive at rent benefits in the term
component which overstate the rental benefit. To off-set the spike in the term, the reversion is
adjusted by further irrational means so the total sum is not overextended. The right of renewal
benefit is assumed to confer benefits due to rack rent rates always being below interest rates. All
methods ignore inflating rent benefits in subsequent terms.
Frizzell (1972) was critical of these methods, highlighting the exclusion of future increases in
economic rents and lamented the indoctrination of past methods contained in the repealed Section
45 of the Valuation of Land Act:
“I feel that many valuers like myself, who
have been indoctrinated in the past with the
methods contained in the repealed Section
45 of the Valuation of Land Act (a method
which works admirably in a situation of non-
inflating land values and in selection of an
appropriate discount rate), are reluctant to
re-examine appropriate methods for use
today.”
Before presenting growth explicit models which address the issues noted, the following section
introduces formulae and aspects of financial mathematics which are important to understand, so to
conceptualise Explicit Discounted Cash Flow and Short-cut DCF approaches.
6 Financial Mathematics and Formulae
The main purpose of this section is to explain the mathematics of annuities which will be used
extensively to apply contemporary leasehold valuation models. Value is essentially the present
value of future benefits, which centres on the proposition that $1 in the hand today is worth more
Jan 2020 28than $1 one year thereafter because $1 could be invested, earning interest worth more than $1
currently. This represents the time value of money (TVM).
There are many texts explaining TVM. This research paper does not add to the tally but hones in on
specific formulae which are critical to contemporary leasehold valuation models. In particular, it
shows that allowing for constant rental growth, which is a closer approximation of what actually
occurs in practice, is very straightforward.
Before presenting these formulae, the context leading up to their development is described.
6.1 The reverse yield gap
To understand the development of contemporary leasehold valuation techniques, a grasp of the
context in which the previous changes occurred is necessary. The early 1900’s was an era which had
little to no inflation. This led to leases with long terms and equally long rent review periods. The
aim was stability over the long term and minimum vacancy.
Property was considered, by contrast to other investment media (bonds, shares, debentures, fixed
interest deposits), to be relatively illiquid and therefore the yield expected was generally 1 to 2%
higher than that generated from long term government bonds. To a great extent, both types of
investment were comparable: the common element they share is cash flow, and their respective
cash flow profiles are not that dissimilar. Pairing these characteristics, a bond’s coupon resembles
property rent and a property’s reversion compares to a bond’s redemption, however the major
difference is the illiquidity of property.
Crosby (Baum and Crosby, 2008) undertook a detailed examination of how valuation techniques
evolved during the twentieth century. The conclusions of this analysis were that the models evolved
through various stages, caused by valuers’ attempts to adapt for changing economic circumstances.
In this context, comparisons between investments were made on the basis of the all risks yield.
Recognise the internal rate of return and all risks yield were the same in this environment. To
illustrate the point, consider the following example comparing a fixed interest security bond and the
property valued above. The fixed interest security is purchased for $100 at a yield of 3% and held to
redemption. The all risks yield is 3% (3 ÷ 100) which is also the internal rate of return, calculated as
follows:
Fig 11: IRR for Fixed Interest Security
Years 0 1 2 3 4 5 6 7 8 9 10
Cash flows -100 3 3 3 3 3 3 3 3 3 103
-0
-100 -100 x (1+.03)
-1
2.91262136 3 x (1+.03)
-2
2.82778773 3 x (1+.03)
-3
2.74542498 3 x (1+.03)
-4
2.66546114 3 x (1+.03)
-5
2.58782635 3 x (1+.03)
-6
2.51245277 3 x (1+.03)
-7
2.43927453 3 x (1+.03)
-8
2.3682277 3 x (1+.03)
-9
2.2992502 3 x (1+.03)
-10
76.6416732 103 x (1+.03)
0 NPV is zero at a 3% discount rate (the IRR)
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