Table Of ContentProperty Valuation Tables
PROPERTY VALUATION
TABLES
Philip Bowcock BSc ARICS ARVA
©Philip Bowcock 1978
All rights reserved. No part of this publication may be reproduced
or transmitted, in any form or by any means, without permission.
First published 1978 by
THE MACMILLAN PRESS LTD
London and Basingstoke
Associated companies in Delhi Dublin
Hong Kong Johannesburg Lagos Melbourne
New York Singapore and Tokyo
British Library Cataloguing in Publication Data
Bowcock, Philip
Property valuation tables.
1. Real property -Valuation -Great Britain- Tables
I. Title.
333.3'32'0941 H D598
ISBN 978-0-333-23729-8 ISBN 978-1-349-15926-0 (eBook)
DOI 10.1007/978-1-349-15926-0
Disclaimer
The tables in this volume were typeset by computer
and although it is believed that a high level of
accuracy has been achieved neither the Author nor
the Publishers can guarantee that no error has
occurred.
This book is sold subject to the standard conditions of the Net Book Agreement.
To
Sheila
David John
Pauline Sandy
Paul Jonathan
CONTENTS
Introduction
Part I Standard tables
Table 1 Years' purchase, single rate 17
2 Years' purchase, dual rate 35
3 Years' purchase of a reversion to a perpetuity 133
4 Present value of £1 151
5 Annual sinking fund 167
6 Amount of £1 177
7 Amount of £1 per annum 191
8 Annuity £1 will purchase 201
9 Conversion factors: alternative income periods 211
10 Nominal and effective rates of interest 217
11 Gross and net income tax factors 221
Part II Discounted cash flow and inflation
Table 12 Rental equivalent on a lease 225
13 Rental equivalent on an annual tenancy 225
14 Years' purchase of an annual rising income 237
15 Rising annuity £1 will purchase 237
16 Capitalisation rates for perpetual incomes 249
17 Years' purchase for perpetual incomes: inflation risk-free
yields 261
18 Amount of £1 (annual effective basis) 273
Part Ill Life tables
Table 19 Years' purchase for a single life 279
20 Years' purchase for the longer of two lives 289
21 Single premium to secure £1 at death 323
22 Annual premium to secure £1 at death 329
23 English Life Tables No. 12 335
Part IV Miscellaneous information
Table 24 Units of measurement 341
25 Calendars 343
26 Financial trends of recent years 358
Appendix - References to recent articles on valuation theory 359
vi
PREFACE
Some justification is required for any addition to the many volumes of mathematical
tables in existence, and in the more restricted field of landed property valuation work
it is perhaps doubly necessary. Nevertheless the complexities of such work may require
a variety of techniques and data, and the present volume is offered in an attempt to
fill some gaps in existing material.
The principal difference between this volume and, so far as is known, any other
I ies in the consideration of the rate of interest. Hitherto in property valuation it has
been customary to regard a rate as being quoted on an annual effective basis, whereas
in practically all commercial activities the rate is quoted on the basis that interest is
added half-yearly - in other words, the effective period is six months and the annual
quotation is in fact a nominal rate. In order to provide for the first time a direct com
parison between property valuation and commerce, all interest rates are quoted on an
annual nominal basis assuming conversion half-yearly.
In these days of pocket electronic calculators it is relevant to consider the place
of valuation tables in practice, since most valuers will already possess a machine with
the ability to calculate factors (excluding life tables) at any desired rate of interest
or tax and for any number of years. However the complexity of many of the formulae
is such that many valuers will still wish to have a reference for checking their computa
tions.
The tables were computed and printed directly on a Wang 600 computing system
working to about 11 significant figures, and rounded to the nearest last significant
figure, 0.5 being rounded upwards. The printed output was then photographed for the
final production. As a check on accuracy numerous factors were also computed on a
Sharp 365 calculator working to 16 significant figures, which confirmed the original
calculations. The user may thus have reasonable confidence that the tables are an
accurate production from the given formulae, though it will be apprecic.ted that it is
impossible to guarantee complete accuracy in a work of this nature.
Although the final decisions on material were entirely my own I am indebted to
a number of people for their valuable suggestions and comments, and would parti
cularly like to express my appreciation to the following:
Professor M. J. A. Greaves BSc PhD FRICS, Department of Building and Estate
Management, Singapore University
Professor A. F. Millington BSc ARICS FRVA, Department of Land Economy,
Paisley Polytechnic
Professor J. N. Hunt BSc PhD DIC ARCS FRMetS FRAS FIMA, Department of
Mathematics, Reading University
Dr Ernest Wood BSc PhD FRICS, Department of Surveying, Liverpool Polytechnic
Mr. J. F. W. Baines BSc FRICS FRVA, Messrs J. F. W. Baines and Associates,
Chester
Mr. D. L. Epstein MSc ARICS, The English Property Corporation
Mr. W. A. C. A. Copp FIA, for advice on the life tables
Mrs. M.A. Colborne BSc ARICS, and Messrs Roger Emeny ARICS, and G. R. C.
Herd MSc ARICS FRVA, of my own Department
Mr. E. Hoffmann BA, Carmel College, for advice on the Jewish calendar
Mrs J. Orebi Gann of The Macmillan Press Ltd
I am also grateful to Her Majesty's Stationery Office for permission to reproduc~
the English Life Tables No. 12, and to Reading University for the use of computing
equipment.
Finally I would like to thank my wife and family for their encouragement and
particularly for help with checking and proof reading.
P.B.
April 1978 Department of Land Management
and Development,
Reading University
vii
INTRODUCTION
INTRODUCTION
The place of mathematical formulae in valuation
Possibly the one certain fact about valuation is that the future is uncertain and assump
tions made at the time of valuation about future trends are most unlikely to materialise
exactly as envisaged. Nevertheless some consideration of the future is inherent in any
valuation, and in accepted valuation theory compound interest is invariably used as a
basis for finding the present equivalent of future value. This can only be an approxi
mation to the state of affairs existing in any particular case, but approximation will
obviously be improved where the mathematical model corresponds as closely as
possible with the facts of life.
Thus, as rents are almost invariably received quarterly in advance, it is appropriate
to base the tables on this assumption, and those tables which are related to an annual
payment (years' purchase, annuity, sinking fund and amount of £1 per annum) all
follow this principle. Conversion factors are provided for use where rents are not
received on this basis in order to make the tables as versatile as practicable. In practice
it is thought that there will be comparatively few occasions on which a conversion
will be required.
Selection of Tables
It would be quite impossible to include all conceivable tables in any single volume,
and the choice has been made in relation to (a) the needs of the traditional approach
to valuation; (b) the requirements of techniques which have come into prominence
during the last few years: and (c) the demands of students and teachers. Some of these
of course conflict, and the selection must be at best a compromise.
Rates of interest generally have small increments in those cases where computa
tion from first principles is relatively tedious. Thus basic tables generally run from 1%
to 15% at Y..% intervals, though with restrictions where the magnitude of the factors is
too large or too small to be included within the format adopted. Where appropriate
rules have been included to allow for the extension of periods of years if needed.
Other works have included a variety of tables which are not included here primarily
because of the limitations of size. Some of these can be derived quite easily from the
tables herein and the appropriate rules will be found in the introduction to each Part.
It is standard practice in mathematical tables to include the relevant formulae and
these are given together with the underlying assumptions at the beginning of each
section. Some examples are given in certain cases of the use to which a table may be
put, but it is beyond the scope of this volume to consider whether any particular use
is appropriate in a given market situation. Reference should be made to other texts
and writings in current periodicals for opinions on particular methods of dealing with
valuation in practice.
It has been assumed that valuers are likely to require about four significant figures
of accuracy for most purposes. This inevitably means that some factors are given with
more than this, for instance the Present Value of £1 has seven for a substantial part of
the table. It is not envisaged that valuers are likely to require this degree of accuracy
for most purposes. In some cases it is impractical to give even four figures, but such
cases are generally confined to extreme values of years or interest rates, which are
unlikely to be of great importance.
Notation
There is no standard system of notation within the discipline of property valuation
though the actuarial profession has for many years used a system recognised inter
nationally which is generally unfamiliar to British valuers. In order to make notation
as comprehensive as possible, formulae are given in two forms in the preamble to each
Part: first the actuarial style, and secondly that found in the majority of property
valuation texts.
2
The following symbols are used in the second style of formula:
j Nominal annual rate of interest
r Effective annual rate of interest
s Effective annual sinking fund rate
t I nco me tax rate, expressed as a decimal
g Effective annual growth rate
f Effective annual inflation rate
n Number of years
m Number of payments or conversions per annum
k Nominal capitalisation rate for incomes in perpetuity where growth and
inflation are implicit in the choice of rate.
TN 1 - t, giving an income net of tax from gross income.
T G - 1- giving gross income from income net of tax.
1 - t
The effective rate of interest
It is customary to quote rates of interest 'per annum' since this is a convenient unit of
time, and as a percentage of the capital value since this is again more convenient in use
than a decimal fraction. (When dealing with formulae of course it is necessary to use
the decimal fraction form.) Since interest rates for the majority of commercial pur·
poses assume that interest is paid half-yearly however, it is necessary to consider precisely
what is meant by 'per annum'.
Consider a bank loan starting on 1 January at a quoted rate of 10% per annum. It
is the practice of banks to charge interest each half year, and the situation at the end
of the first year will be as follows, assuming no payment is made to the bank at the
end of the first six months:
Loan £1000
Interest @ 5% for 1st half year 50
Outstanding loan, 1 July 1050
Interest for 2nd half year 50.50
Total outstanding at year end 1102.50
Th e tota I .m terest c ha rge m. re I at1. on to t he ong.1 .n a I I oan .IS 10 2·50 or 10 . 25°to'.
1000
It can readily be seen that if interest were added more frequently than twice a year
the effect would be to increase the annual rate still further. Thus it is important to
quote the number of times per annum that interest is added to capital or 'converted'.
In practice it is found that banks, stock exchange securities and most other forms of
large-scale lending are quoted on the basis of an annual nominal rate (10% in the above
example) with half-yearly payments of interest or income. The true annual effective
rate for a half-yearly conversion is calculated from the formula
r=(1+~)2 -1
This formula is discussed in several standard texts but rarely is it actually used for
valuations. Nevertheless the investor will be concerned with comparisons between
investments, and a true comparison can only be made if the same yardstick is being
used. In order to make possible direct comparisons this formula is applied to all quoted
rates of interest in this volume; hence the rate at the head of each column is the nominal
3
