42. Leaseholder/
Head lessee/
Tenant
Develops land
and leases on
wholesale/retail
Wholesale lessee
further improves
and partitions
Retail lessee
(sub-tenant) pays
lease rent to
head lessee
Pays ground rent
to freeholder
Ground lease
43.
44.
45.
46.
47.
48.
49.
50. Solution:
Profit Rent = FRV – Contract Rent =
= 250,000-100,000 = 150,000
Leasehold Value = YP n@dual rate * Profit Rent
= YP 8y@8%&3% * 150,000
= {1/(0.08+s)} *150,000
= 5.196 * 150,000
= 779, 400
NB: YP can be found from YP tables for term 8 y and 8% income yield and
sinking fund yield of 3%; alternately, one can use YP formula:
YP (dual rate) = 1/(i + s) , where i is the income yield and s is income yield of
sinking fund equal to y/[(1+y)^n-1], y is sinking fund accumulation rate
51.
52.
53.
54.
55.
56. 4.Valuation of Life Estate
Ramakrishna Nallathiga
Associate Professor
NICMAR University - Pune
57. Structure
Introduction
Types of Life Interests/Estates
Mortality Tables
Valuation Approaches
Application of Method
Exercises
Life interest of freehold
Life interest of leasehold
Life interest in a joint property
58. Introduction
Life estate comes with a bundle of property rights that
remain with the holder for his/her life
Therefore, life interest ceases to exist upon the death
of life holder and reverts to original grantor
Essentially, life interest exists in two forms:
during the life of the person holding it, or
the life of any other person holding it (life estate pur autre vie)
Unlike the case of freeholder/leaseholder, life estate is
not inheritable to legal heirs/ descendants
59. Types of Life Estate/Interests
Life interest may exist as either leasehold or freehold
properties; accordingly, it can be distinguished as
Lessee for Life
In this, the landlord grants a lease for life for a fixed number of
years
Life interest in leasehold property ceases to exist upon the
death of person or expiry of lease term (whichever earlier)
The lease can be terminated by the land lord/ lessor on the
death of person named in the lease (lessee)
Life estates holder (or, lessee) are subject to payment of rent
and any other conditions of letting
60. Types of Life Estate/ Interests
Tenant for Life
It is the same as freeholder, except that the ownership is for
the life of person holding the rights/estate
Although the life holder has ownership rights, he/she cannot
pass on or sell it
These rights go back to the ‘reversioner’ (grantor) or
‘remainderman’ (inheritor) after the death of life holder
Sometimes, contingent reversioner/remainderman is used to
mean a remainderman’s rights depend upon a contingent
event to take place e.g., remainderman outliving the tenant for
life
61. Mortality Tables
As the life estate is associated with life until the death
of estate holder, mortality tables are used for
computing the value of such interest in property
Mortality tables are normally developed in different
countries focusing on the average life span of persons
(rather than specific persons/groups as done by
insurers)
They reflect the probability of an average person
surviving until a referred age and, therefore, give an
indication of the life span of average individual
Among all the tables, Carl Isle Tables are popular and
developed for the UK but they can adopted with some
changes to suit domestic conditions like that of India
62. Valuation Approach
Mortality tables give the probability of survival of
average person until an age (of individual)
Valuation of Life holder rights is for the remaining age
of the holder (for average life expectancy)
Therefore, YP (Year’s Purchase) for life is the
accumulated rent/income multiplied by the probability
of survival and then discounted to the present
The product of present value and probability is also
termed as cumulative value, which we use in life
estate
Alternately, YP is also estimated by other means e.g.,
Jellicoe’s Formula
63. Valuation Approach
Jellicoe’s Formula
YP = [{1/(p+d)} -1 ]
Where,
p is the premium amount paid for participation in an
insurance policy of unit sum without any profits
d is equal to {i/(1+i)}
i is the income yield on the capital investment
For example, consider a 35 year old tenant with 8% income
yield, by examining the SBI life insurance premium tables
p = 0.02369 and d = 0.08/1.08 =0.074074, therefore
YP = {1/(0.02369+0.074074)}-1={1/0.097764}-1
= 10.2287-1 = 9.2287
64. Application of the Method
The valuation of life estate can be applied in four
different contexts
Valuation of life interest by tenant for life in freehold
Valuation of life interest by lessee for the life of leasehold
Value of reversion to a leasehold property upon the death of
tenant (as held by the reversioner or the remainderman)
Value of reversion to a freehold property after the death of
tenant for life
65. Exercise 1 (Life interest of tenant
and reversioner in freehold)
Valuation of property held by a life tenant aged 51 years is
required. It is a freehold property that fetches a net income of
Rs 10,000 per month. Assume an income yield of 10%
associated with such property. Also, find out the value to the
reversioner.
Note: YP for 51 year old has to be found using Carl Isle Tables
Solution:
Value (Tenant) = YP 51y@10% * Net Income
= 7.245 * 120,000 = 8,69,400
Value (Reversioner) = (YP perp@8% - YP51y@10%) *
Net Income
= (12.5-7.245)* 120,000 = 5.255*120,000
= 630,600
66. Exercise 2 (Life interest of reversion
and remainderman in a leasehold)
A 45 year old person has life interest in a leasehold
property with a lease term of 40 years at a net lease rental
of Rs 120,000 per annum. Assume an income yield of 8%
associated with the property
What is the present value of reversion to the property?
What is the present value to the heir of lessor aged 70 years?
Solution: (In the second case the reversioner is remainderman)
V (reversion) = (YP 40y@8%&4%- YP 45y@8%)*120,000
= (11.05-9.52) * 120,000 = 1.53*120,000= 183,000
V (reversion) = (YP 45y@8%-YP 70y@8%) * 120000
= (9.52 – 5.41) * 120000 = 493,200
67. Valuation Approach to Life
Interest
Interest of
life tenant
Reversioner’s
interest
Death of Life
Tenant
Interest of
lessee for
life
Reversioner’s
interest
Death of
Lessee for Life
Lease
Term
Freehold Life Interest Leasehold Life
Interest
68. Exercise 3 (Life Interest in Joint
Property)
X and Y aged 42 years and 40 years respectively have become life tenants
of a trust property with an annual income of Rs 3,60,000. They have a
share each of 65% and 35% respectively. Assume an income yield of 8%
and 6% associated with their share of the estate.
What will be the value of life interest held by both? If the trust property
has been re-valued at 50,00,000 then what is the share of each person?
Solution:
X’s income = Share of X* Income = 0.65*360000 = 234,000
Y’s income = Share of Y * Income = 0.35*360000 = 126,000
Value of life interest of X = YP 42y@8%* 234,000
= 9.771*234,000 = 22,86,414
Value of life interest of Y = YP 40y@6%* 126,000
= 10.093* 126,000 = 12,71,718
After revaluation:
Share of X = [ 22,86,414/(22,86,414+12,71,718)]*50,00,000 = 32,12,480
Share of Y = [ 12,71,718/(22,86,414+12,71,718)]*50,00,000 = 17,87,520
69. References
S C Rangwala (2010), Valuation of Real Properties,
Charotar Publishing House, Anand
Chapter 9: Valuation of Life Estate
70. 5.Accounting for tax in
valuation of properties
Ramakrishna Nallathiga
Associate Professor
NICMAR University - Pune
72. Introduction
In the process of the valuation of investment
properties, we have been making use of rent income
of the property and associated yield
However, the rent income received at the hands of an
individual is subject to income tax, which will depend
upon the taxable position of the individual
Conventional position is that the tax position of
individuals vary widely and also nothing is gained
when valuing for sale is made on market by deducting
at an assumed rate
Therefore, it is imperative for us to account for the
effect of tax on valuation and arrive at those
valuations that are net of income tax
73. Introduction
As taxation of rent income alters the income cash flow
status for the individuals, it therefore alters the income
yield from such property.
One simple way is to adjust gross cash flows of rent
income taking into account of the tax rate of individual by
adjusting with ‘net tax factor’ (therefore, arriving at the
valuation for the individual)
Net income or yield = Gross income or yield * (1-t)
On other hand, if we are provided with cash flows that are
‘netted for tax’, or income yield is ‘net of tax’ then we can
‘gross up’ by making use of ‘gross tax factor’ to arrive at
market value
Gross income or yield = 1/(1-t) * Net income or yield
74. Approach to Valuation
In the case of freehold properties, the approach is the
same as valuation of perpetuity i.e.,
Work out the rent income netted after tax
Arrive at the income yield netted out for tax rate
In the case of leasehold properties, the approach
involves the following:
Workout the rent income netted after tax
Arrive at income yield netted out for tax rate
Sinking fund rate will not be affected by tax rate
75. Exercise 1
Valuation of freehold commercial property in a
suburban area that has been let recently at Rs 80,000
p.a. is required. The individual is subject to income
tax in the 30% tax slab. Assume 8% yield.
If the person has acquired the said property at market
value of Rs 9,00,000, is it above or below the
valuation for individual?
What is the value of the leasehold rights in the above
property if it were leased for a term of 9 years but at a
slightly higher yield?
76. Solution
Without tax effect:
V = 1/0.08 * 80,000 = 10,00,000 (Market Value)
With tax effect: (Value for the individual)
Tax adjusted net rent = (1-0.3)*80,000=56,000
Income yield after tax adjustment = 0.7*8 = 5.6%
(a) Freehold Value V fh = YP perp@5.6%*56,000
= 1/0.056*56,000 = 10,00,000
If the person bought the property at 900,000 mean he got
at bargain
(b) Leasehold value while considering yield of 9%
V lh = YP 9y@6.3%,3%*56,000
= 1/0.1691*56,000 = 5.91*56000
= 3,31,163
77. Exercise 2
Value on a gross and net basis of a leasehold
property with a rack rent of Rs 250,000 p.a. to be
received for 10 years is required. Leaseholder also
pays a ground rent of Rs 100,000 to the freeholder.
The property fetches an income yield of 10% along
sinking fund rate of 3% for an individual in tax slab of
20%.
What is the value of above leasehold property if the
profit rent received increases from Rs 150,000 to
250,000 after 5 years while others remaining same?
78. Solution
Gross profit rent = RR – GR = 250,000-100,000 = 150,000
Income yield = 10%
Sinking fund rate = 3%
Tax rate = 20%
(i) Solution A (Constant Profit rent)
V gross = YP 10y@10%,3%*150,000
= 5.341*150,000 = 801,150 (Market value)
V net = YP 10y@8%,3%*(150,000*0.8)
= 5.98*120,000 = 717,600 (Value for Individual)
(ii) Solution B (Increasing profit rent)
Profit rent during term = Rs 150,000
Profit rent after reversion = 250,000
79. Solution
Solution B (Revision after term)
V gross = V term + V reversion
= YP5y@10%,3%*150,000 + YP5y@12%,3%*250,000
*PVF5y@12%
= 5.341*150,000+3.58*250,000*PVF5y@12%
= 801,154+507,847 = 13,09,001
V net = YP5y@8%,3%*120,000+YP5y@9.6%,3%*200,000
*PVF5y@9.6%
= 5.98*120,000+3.917*200,000*0.6323
= 717,600+495,371 = 12,12,971
80. References
D Isaac and T Steley (2010), Property Valuation
Techniques, Macmillan Publishers, London
Chapter 13: Contemporary Methods of Valuation
81. Session 5: VALUATION OF
REVERSIONARY PROPERTIES
Ramakrishna Nallathiga
Associate Professor
NICMAR University Pune
83. Introduction
Commercial properties belong to a class of properties held
for reward on capital invested
One approach is to determine market value of property
based on the transactions in market place
An alternate approach is to consider the income from such
property and the capitalization (YP) that the properties of
similar class and category command to perform valuation
However, either approach does not account for
(a) changes in market conditions
(b) possible growth in income
Therefore, the property can be considered as ‘reversionary
freehold’ or ‘reversionary leasehold’ property that
Has been leased at below market rent with few years to expiry
Realises full market rent after expiry of lease period
85. Term and Reversion Method
In this method, the property is valued separately for
the contract rent of ‘term’ and at the full market rent
‘after reversion’
A lower yield is used for the ‘term’ than that after ‘reversion’
The rental income during term is also lower than that after
reversion
If the property fetches full market rent then the
valuation for term does not exist and it becomes
valuation of perpetuity in case of freehold rights and
valuation of lease in case of leasehold rights
The approach taken for valuation in this method is also
known as ‘vertical slicing’ approach
86. Term and Reversion Method
Contract Rent
Full market rent
Term Reversion
YP at x%
for k period
YP at y%
for n-k
period
PV of Re 1 @ z%
for k period
Contract Rent
Full market rent
Term Reversion
YP at x%
for k period
YP at y%
perpetual
PV of Re 1 @ z%
for k period
Freehold Properties Leasehold Properties
k k n
Ground rent
87. Hardcore Method
In this method, the property is valued separately for the
‘contract rent’ as well as for ‘incremental rent’
The property is expected to fetch assured ‘contract rent’ for ever or
for term and any rise in rent to FMV (or, incremental rent’ takes
place at the end of ‘term’ of contract
Therefore, contract rent is treated as perpetual income and rise in
income (or, rent increment) is deferred perpetual/ lease term
income in the valuation
The usual distinction of valuation of freeholds and
leaseholds for perpetual and lease term prevails
Therefore, the approach taken for valuation in this method
is also known as ‘horizontal slicing’ approach
88. Hardcore Method
Contract
Rent
Full market rent
Lease
Term
Deferred
lease term
YP at x%
for n period
YP at y% for n-k
period
PV of Re 1 @
z% for k period
Freehold Properties
Contract Rent
Full market rent
Perpetuity
Deferred
perpetuity
YP at x%
perpetual
YP at y%
perpetual
PV of Re 1 @
z% for k period
Leasehold Properties
n
k
k
Ground rent
89. Valuation of Reversionary
Freeholds - Exercise 1
Valuation of freehold interest in a commercial
establishment with a 25 years lease contract at Rs 5,000
monthly rent was required. The property was let about 5
years ago and full market rent is Rs 12,000. Assume the
rental income free of outgoings. Use hardcore method.
Solution:
V = V bottom slice + V top slice
V bottom slice = YP perp@4%* contract rent
= 25 * 60,000 = 15,00,000
V top slice = YP perp@6%*Incremental rent * PVF 5y@6%
= 16.67 * 84,000 * 0.74726 = 10,46,370
V = 25,46,370
90. Valuation of Reversionary
Freeholds - Exercise 2
Valuation of a freehold interest in a residential
property of good neighborhoods let to a tenant at the
monthly rent of Rs 10,000 is required. The lease term
is 7 years after which a full market monthly rent of Rs
25,000 is expected. Assume there are no outgoings.
Apply hardcore method.
V = V bottom slice + V top slice
V bottom = YP perp@4%*120,000 = 30,00,000
V top = (YP perp@6%-YP 7y@6%)* (180,000)
= (16.67-5.582)*180,000 = 19,95,840
V = 49, 95, 840
V top is deferred perpetuity accruing after term 7 years
91. Valuation of Reversionary
Leaseholds - Exercise 1
A residential guest house property is given on lease by
OYO, which has an unexpired term of 8 years with the
rent reserved at Rs 15,000 per month. OYO obtained the
house on 33 year lease at a ground rent of Rs 5,000 per
month. Subsequently, the property is proposed to be let
at full rental value of Rs 22,000 per month to a lessee for
a period of 25 years. What is the value of OYO’s
(lessee’s) interest in lease hold property?
V bottom slice = YP 33y@6%,3%*(15,000-5,000)*12
= 12.795*120,000 = 15,35,400
V top slice = (YP 33y@ 8%,3% - YP 8y@8%,3%)
*(7000)*12 = (10.183-5.196)*84,000 = 4,18,908
V for OYO (leasehold) = 19,54,308
92. Valuation of Reversionary
Leaseholds - Exercise 2
Valuation of a commercial leasehold establishment held by
person B is required. Person B obtained the leasehold
from person A at ground rent of Rs 1,000 per month for 50
years and improvised it. He/she had sub-let it at a rent of
Rs 10,000 per month to person C for a period of 20 years.
The full market rent of a similar property is Rs 15,000 per
month.
Solution:
V bottom slice = YP 50y@8%&3%* Profit Rent 1
= 11.253*(10,000-1,000)*12 = 12,15,324
V top slice = YP 30y@8%&3% * Incremental Rent *PVF
20y@8%
= 8.531*(15,000-10,000)*12*0.21455= 1,09,823
V = V top slice + V bottom slice = 13,25,147
93. References
S Datta, 2004, Valuation of Real Property, Eastern
Law House, Kolkata/New Delhi
Chapter 4 – Investment Method of Valuation
94. SESSION 7: EQUIVALENT YIELD
APPROACH TO VALUATION
Ramakrishna Nallathiga
Associate Professor, NICMAR - Pune
95. Structure
Introduction
Equivalent Yield Method
Equivalent Yield Assessment
Traditional Approach
Alternate Approach
Cash flows Approach
Exercise
Estimation of equivalent yield of a property
Usefulness of equivalent yield in estimating value
96. Introduction
An important approach taken towards valuation of
properties (both freeholds and leaseholds) under
investment approach is that
Rental income as well as yield remains constant during term
Rental income changes after reversion but remains constant
thereafter
Rental yield also changes after reversion but remains
constant thereafter
However, it is simple and more convenient if we use
same ‘yield’ both before and after reversion
Equivalent yield method uses this underlying principle
for Valuation of Properties
97. Equivalent Yield Method
In this method, the property
is valued by using the same
yield for all the incomes
This yield is the yield that
adjusts different yields of
different blocks
Therefore, it is obtained by
approximation using a trial
yield rate and then working
out the ‘equivalent yield
rate’ in iterative process
Contract Rent
Full market rent
Term Reversion
YP at x% for
k period
YP at x%
perpetual
PV of Re 1 @ x%
for k period
98. Equivalent Yield Method
Equivalent yield method gives us the overall yield from
reversionary property
This overall yield is nothing but a weighted average
yield of the yields of term and reversion respectively
It can also be considered as the internal rate of return
on the cash flows (with the assumption of constant rent)
used for term and reversion
The equivalent yield, in providing an overall yield,
means that reversionary property has a single yield
which can be compared with the yield of other
investment assets
It therefore helps property investors to know the overall
yield that can be compared with others
99. Equivalent Yield Assessment
Conventional Approach
In this approach, ‘term and reversion’/‘hardcore’ approach
forms underlying method, in which the value of reversionary
property is estimated using the principle of
Value of Property (V) = Value for Term +
(Deferred) Value after Reversion
Or, V = Value of bottom slice + Deferred Value of top slice
Valuation then follows the trial and error method to estimate
property values at different yield rates
Different trial rates that give either overestimate or
underestimate value of property need to estimated/worked
The equivalent yield is arrived from the interpolation of the
yields under different trials
100. Equivalent Yield Assessment
Alternate Approach
In this approach, the ‘annual
equivalent of gain’ (AEG) is first
estimated using a trial yield in the
formula
AEG = {(Gain on reversion*PV for
Term)/ YP for Term}
Equivalent yield is then estimated
using the formula
Ye = (Current income + Annual
equivalent gain) / Acquisition Price
We will stop at the point when the
estimate yield is ‘equivalent’ to
trial yield with which we began
Contract Rent
Term Reversion
YP at x% for
k period
YP at x%
perpetual
Gain on reversion
Annual Equivalent of Gain
for term
PV
101. Equivalent Yield Assessment
Cash Flow Approach
In this method, the rental income from investment
property in the form cash flows is estimated
These cash flows are discounted using present value
factors (at two different yields) to arrive at discounted
cash flows
Valuation then follows trial and error method to
estimate equivalent yield through interpolation
The equivalent yield thus arrived can be used to
estimate the values of term and reversion to further find
out the value of property
102. Exercise 1
The equivalent yield of an investment on a property in prime
location is required. The property has been acquired at a price
of Rs 35,00,000. It has been given on lease with an unexpired
term of 4 years at an exclusive rent of Rs 120,000 per annum.
The full rental value of the property is Rs 250,000 per annum.
Solution (Traditional Approach):
Let us assume an equivalent yield of 6% under trial 1
V1 = V bottom slice + V top slice
=YPperp@6%*120,000+YPperp@6%*130,000*PVF4@6%
= 16.67*120,000+16.67*130,000*0.7921
= 20,00,400+17,16,560 = 37,16,960
NB: The arrived value in trial 1 is more than acquisition price i.e., it is
an over estimate, therefore we use a higher trial yield in the next trial
103. Graphical explanation of interpolation
D1+
-D2
D1
D1+D2
ye
ye1
ye2
Ye = ye1+{D1/(D1+D2)}*(ye2-ye1)
104. Now, let us assume equivalent yield of 8% under trial 2
V2=YPperp@8%*120,000+YPperp@8%*130000*PVF4y@
6%
= 12.5*120,000+12.5*130,000*0.7921
= 15,00,000+12,87,162 = 27,87,162
The above value in trial 2 is less than acquisition value (35 L)
Therefore, equivalent yield lies in between the two trial yields,
which can be obtained by the means of interpolation
D1= 37,16,960-35,00,000 = 2,16,960
D2= 27,87,162-35,00,000 = -7,12,837
Eqvt yield = 6%+{D1/(D1+D2)}*(8%-6%)
= 6%+{216,960/(216,960+712,837)}*2%
= 6%+0.23*2% = 6.46%
105. Alternate Approach
Trial 1 @ yield of 6%
Gain on reversion (G) = YPperp@6%*FRV – Purchase Price
= 16.67*250,000-35,00,000 = 6,67,500
Annual Equivt Gain = G*PV4@6%/YP4y@6%
= 667,500*0.7921/4.212 = 1,25,529
Eqvt yield = (Curr Income+AEG)/Purchase Price
= (120,000+125,529)/35,00,000=7.01%
Trial 2 @ yield of 6.5% gives eqvt yield of 5.65%
Trial 3 @ yield of 6.25% gives eqvt yield of 6.7%
Trial 4 @ yield of 6.4% gives eqvt yield of 6.5%
Stop after trial 4 when trial yield and eqvt yield are same.
106. Usefulness of equivalent yield
Perform valuation of a similar property located in the area
using the above yield with unexpired lease term of 5 years
while assuming the contracted and market rents of Rs
1,00,000 per annum and Rs 2,00,000 per annum
respectively. The rental income is free of outgoings.
Solution (Hard Core Method):
V=YPperp@6.5%*CR+YPperp@6.5%*IR*PVF5@6.5%
= 15.3846*100,000+15.3846*100,000*0.7835
= 15,38,460+12,05,385 = 27,43,845
Alternately, valuation can also be done using term & reversion
method which involves valuation of term and reversion
107. Exercise 3 (Assignment 2)
Consider a commercial property located in prime
urban area with an unexpired term of 5 years. The
contracted rent of property is Rs 10,000 per month
and the annual outgoings are Rs 20,000. The full
market rent of similar properties command Rs 25,000
per month whereas annual outgoings can be Rs
30,000. Workout the equivalent annual yield of such
property assuming that a comparable property has
been sold at Rs 20,00,000. Using estimated equivalent
yield assess the value of similar property with similar
term but with net rental incomes of Rs 150,000 and
250,000 respectively during term and after reversion
108. References
S Datta (2004), Valuation of Real Property:
Principles and Practice, Eastern Law House, Kolkata
Chapter 4: General principles of investment valuation
under Investment method
D Isaac and T Steley (2000), Property Valuation
Techniques, Macmillan Publishers, London
Chapter 7: Equivalent Yields
109. SESSION 8: DCF METHOD
OF VALUATION
Ramakrishna Nallathiga
Associate Professor, NICMAR - Pune
110. Structure
Accommodating Income growth
Approaches to Valuation
Traditional
Discounted Cash Flows (DCF)
DCF Approach
DCF Analysis
Measures of Investment Appraisal
NPV
IRR
Valuation with Income Growth
Exercises
111. Accommodating Income Growth
Valuation of Reversionary Freehold and Leasehold
properties traditionally is based on the assumption of
constant income from an investment asset
As investment properties are subject to lease/rent
revision at a periodicity, the income from property is no
longer constant but it varies over time
Valuation of Investment properties therefore needs to
accommodate lease/rent income growth into it
Valuation approach will vary depending upon whether
the rent/lease review is done annually or at a set
period in the rent/lease contract i.e., every 3-5 years
112. Approaches to Valuation
There are two major approaches taken towards
Valuation of reversionary freeholds and leaseholds
while accommodating the income growth
Traditional Approach
DCF Approach
Traditional approach uses horizontal/vertical slicing
approach with some modification to incorporate growth
However, it is the period of rent review which also
poses some difficulty in a straight forward approach
DCF method on other hand has little or no difficulty in
accommodating growth with annual or periodic rent
review
113. Traditional Approach
Under vertical slicing approach, the Value of Freehold
Property can be modified to include growth (g)
V = MR / y where y = r-g (r is target return rate)
Or, V = MR/(r-g)
If MR = 120,000; r=8%, g=3%; V=120,000/(8%-3%)
V = 120,000/0.05 = 24,00,000
NB: The above holds good so long that g < r
However, if the rent is set at a period p then the same
calculus of y changes to
y = r [1 – {((1+g)^p-1)/((1+r)^p-1)}
114. Exercise 1
Consider an investment property fetching a net income of Rs
10,000 per month given on 10 year lease. The freeholder
made rental agreement such that the income would grow at
3% per annum. Similar kind of properties give an investment
yield of 8%.
What is the value of freeholder’s rights?
V = 120,000/(0.08-0.03) = 24,00,000
If the rent is revised at 3% every three years what is the
value of freeholder’s rights?
y= 0.08 [1-{(1.03)^3-1}/{(1.08)^3-1}]=0.08(1-0.357)
= 0.05144~ 0.05 or 5%
V = 120,000/0.05144 = 23,32,815
115. DCF Approach
Cash flow is frequently used by business firms/projects
for assessing their business and cash flow appraisal is
done for making decision on business performance
Properties can also be considered as investment assets
that generate a series of cash flows and any investment
in property can also be subject to cash flow appraisal
Cash flow appraisal of properties is based on:
Present and future costs e.g., acquisition of land/building
and construction (negative cash flows)
Future receipts generated, in this case rents received from
letting of real property (positive cash flow)
Value received (or, cost incurred) on the disposal of real
asset (either positive or negative cash flow)
116. DCF Approach
Cash Flow Analysis is based on the treatment of cash
flows from the viewpoint of freehold property owner:
Income or revenues are treated as positive cash flows
Expenditure or outgoings are treated as negative
As cash flows occur at different points of time, a
Discounted Cash Flow (DCF) gives a better measure
of cash flows after discounting them to present day
DCF techniques that are used widely in project
appraisal for accounting for time value of money and
they can also be applied to the real properties that
generate cash flows
117. DCF Analysis
DCF technique is based on
calculating present worth of future
sums of money from property
To produce a DCF, the valuer has
at least three forms of discount
(interest) rate to choose from
The rate which has to be paid for
borrowing capital (borrowing rate)
The rate which could be earned if
the capital was invested elsewhere
(opportunity rate)
The rate of return that the investor
requires to compensate for risk
(target rate)
1-3 y 4-6 y 7-10 y
PV @ 8%
PV @ 8%
PV @ 8%
Perpetuity
PV @ 8%
118. Measures of Investment Appraisal
Two forms of DCF appraisal are used in investment analysis
Net Present Value (NPV)
Internal Rate of Return (IRR)
The NPV analysis is based on the summation of discounted
present value of all cash flows (both negative and positive)
A positive NPV implies that the property investment is
worthwhile (but other criteria may also be applied)
The IRR analysis is on the basis of rate of return from
investment at which the NPV of income equals the NPV of
expenditure i.e., rate which produces no net NPV
The IRR analysis is done in an iterative process with an
initial rate of return and then arrived through interpolation
119. Valuation with Income Growth
IRR (for all
cash flows)
IRR with no
growth
All Risks
Yield
Equivalent
Yield
IRR with
growth
Equated
Yield
Gilt Edged
Securities
Gross
Redemption Yield
120. Exercise 1
A shop property has been acquired at a price of Rs
20,00,000 by a freeholder and it was given on a 12
year lease to a leaseholder at an annual lease rental
of Rs 2,50,000 (on full repair and replacement terms)
which is also protected by a rent review of Rs 50,000
every three years.
Assess the investment worthiness of the shop property
by the freeholder. (NB: Assess based on eqvt yield)
Also, find the value of leasehold (lessor’s interest) as
well as freehold interests of the property.
123. Solution 1 (contd..)
Now, we know that the equivalent yield lies in
between 10 and 12%.
We interpolate and find it in the same manner as
we did for reversionary properties
ye = 10%+{95559/(95559+115784)}*(12-10%)
= 10% + 0.45*2% = 10%+0.9% = 10.9%
The investment in this property is attractive, as it
gives an income yield of 10.9% when compared to
the yield of government bonds (7.15%) or the yield
of long term deposit in banks (6.5%)
124. Solution 2
S
No.
Time
period
Cash
Flow (Rs)
PVF @
10.5%
YP
3y@
10.5%
Discounte
d Cash
Flow (Rs)
1 1-3 250,000 1 2.465 616,250
2 4-6 300,000 0.7411 2.465 548,089
3 7-9 350,000 0.5493 2.465 473,927
4 10-12 400,000 0.4071 2.465 401,436
5 > 12 450,000 0.3017 9.524 1,293,000
Lesser’s Interest
Value of Leasehold =
V1+V2+V3+V4
= 20,39,702
Freehold Interest
Value of Freehold =
V1+V2+V3+V4
+V5(perpetuity)
= 33,32,702
NB: Rack rent of the property grows by Rs 50,000 at then
end of lease term i.e., 12 years, and it becomes perpetual
rent and thereby perpetuity 12th year onwards
125. Exercise 2 (Assignment 3)
An investor into property is confronted with two real properties, of
which he has to choose one. The two real properties have
different cash flows as shown below. Suggest the worthy
investment property based on NPV
Year (s) Description Property 1 Property 2
0 Purchase of Property 20,00,000 22,00,000
1-3 Initial Rental income 40,000 pa 30,000 pa
4-6 Revised Rental Income 50,000 pa 50,000 pa
7-9 Revised Rental Income 60,000 pa 70,000 pa
10-12 Revised Rental Income 65,000 pa 75,000 pa
12 Disposal of Property 18,00,000 19,00,000
126. Present Value of Cash Flows of
Property 1
Year
(s)
Cash Flow YP @10% PVF @10% PV of Cash Flow
0 -20,00,000 1 1 -20,00,000
1-3 40,000 2.487 1 99,480
4-6 50,000 2.487 0.7513 93,424
7-9 60,000 2.487 0.5645 84,235
10-12 65,000 2.487 0.4241 68,558
>12 15,00,000 1.0 0.3186 4,77,900
NPV of DCF 1 -11,76,403
127. Present Value of Cash Flows of
Property 2
Year
(s)
Cash Flow YP @10% PVF @10% PV of Cash Flow
0 22,00,000 1 1 -22,00,000
1-3 30,000 2.487 1 74,610
4-6 50,000 2.487 0.7513 93,424
7-9 70,000 2.487 0.5645 98,274
10-12 75,000 2.487 0.4241 79,105
>12 19,00,000 1.0 0.3186 6,05,340
NPV of DCF 2 -12,49,247
128. References
Peter Wyatt (2011, Property Valuation,
Chapter 5 – Property Investment Valuation
D Isaac and T Steley (2000), Property Valuation
Techniques, Macmillan Publishers, London
Chapter 3: Discounted Cash Flow
129. SESSION 9: EQUATED YIELD
APPROACH TO VALUATION
Ramakrishna Nallathiga
Associate Professor, NICMAR - Pune
130. Structure
Introduction
Growth in rental income
Equated Yield
Criteria for Investment
Equated Yield Assessment
Formula approach
Cash flow approach
Growth explicit approach
Exercises
131. Introduction
Traditional approach to the Valuation of Commercial
properties as investment assets follows assumption of
constant income and yield from investment properties
However, in the real world, rental income from real
properties keeps on rising due to the inflation forces.
Therefore, it is appropriate to account for the growth in
rental income for performing valuations, which can be in
terms of
I. absolute rise as incremental amount
II. annual/ periodic growth rate
Apart from DCF analysis, where the annual cash flows
reflect rental income growth, another approach could be
based on the ‘equated yield’ approach, which accounts
for the future growth of rental income
132. Types of Rental Income Rise/ Growth
Linear (Incremental Rise) Non-linear (Growth)
Revised Rent (R1) = Original Rent
R0*+ Increment (k)*n
Revised Rent (R1)= Rent (R0)*(1+g)^n for
compounding growth
= R0*(1+g*n) for simple growth
133. Investment Approach towards Valuation
Valuation of
Commercial
Properties
Conventional
Approach
Term & Reversion
Method
Hardcore Method
Modified Approach
(Reversionary
Properties)
Alternate Approach
Discounted Cash
Flow Method
Equated Yield
Method
134. Equated Yield
Equated yield is the yield on investment that takes into
account of the future growth (of rental income)
Equated yield is different from the ‘all risks yield’ of
reversionary properties, where an increase in income on
reversion to market rent is estimated at present value
Equated yield can be assessed based on
Formula approach
Cash Flows approach
Growth explicit approach
Equated yield assessment helps in aiding investment
decision on acquiring a real property by comparing it
with other/ similar class of investment assets
135. Criteria for Choice of Investment Return
An investment decision is made on the basis of the return
from it vis-à-vis other investment assets
Return from an investment have three major components:
Time preference element, which refers to the postponement of
consumption to a later date
Inflation element, which refers to the fall in money value due to
macro factors
Risk premium element, which refers to a premium/ mark-up
associated with investment with high risk
The relationship between them can also be expressed as
(1+ market interest rate) = (1+inflation rate) * (1+ real interest rate) *
(1+ risk premium rate)
Or (1+e) = (1+g) (1+i) (1+r)
136. Equated Yield
Equated yield refers to that yield of the investment
property which takes into account of growth in rental
income associated with the property
Equated yield is also referred to as the target rate or
market rate and is given by the following relation:
(1+ market rate) = (1+inflation rate) * (1+ real rate)
(1+e) = (1+g) (1+i) or i = 1- {(1+e)/(1+g)}
For example, if real rate 8%, growth rate 5% give market rate 14.5%
NB: This holds good so long that all of them are annual rates
When the growth is not annual, then the relationship
between equated yield and income yield are as follows
137. Equated Yield Assessment - Formula
In this approach, following variables are used in the
analysis of the equated yield
i. Initial Yield (or ARY) (i)
ii. Annual growth rate of rent (g)
iii. Rent review period (n)
iv. Equated yield (e)
The relationship between them can be expressed as
i = e – e [ {1+g)^n – 1}/{1+e)^n – 1} ] or
= e [1 – {1+g)^n – 1}/{1+e)^n – 1} ]
Valuation follows that of perpetuity in the case of
freeholds and that for term in the case of leaseholds
138. Exercise 1
A client is interested in investing in a shop property
which gives a rack rent of Rs 100,000 p.a. He/she
seeks valuer’s advice on purchase price of property.
The target yield is 13% and similar property a
compound growth rate in income of 5% p.a. The
rent is reviewed after every 5 years.
Consider valuation of freehold rights as well as
leasehold rights (for a lease term of 40 years).
139. Exercise 1
Solution 1:
ARY(i) = 0.13*[ 1-{(1.05)^5-1}/{(1.13)^5-1}]=0.0873
The ARY (8.73%) is good and higher than fixed income
instruments like bonds or term deposits so can invest
Solution 2:
Value of freehold = YP perp@8.75%*NR
= 1/0.0875 * 100,000 = 11,42,857
Value of leasehold = YP 40y @8.75%,3%*NR
= 1/[0.0875+{0.03/(1.03^40-1)}]*NR
=9.92434*100,000 = 9,92,434
140. Equated Yield Assessment – Cash Flows
Equated yield method is based on the Discounted Cash Flows
(DCF) approach towards valuation of properties, which
incorporates the rental growth within DCF framework
According to the DCF method
NPV = Σ Rn/ (1+i)^n – C
Where Rn is rental income flow in year n, and C is the Sale
price of comparable property in market; i is IRR
The IRR is worked out on trial basis in the above with a chosen
rate as the equated yield and the growth associated with it is
calculated using the formula (growth explicit approach):
(1+a)^r = [(YP perp @ i) – (YP-r @ e)] / [YP-perp @ i *PVr@e]
where
a- rate of rental growth; r – rent review pattern of comparable property
i– rate of capitalization of property (rack rental yield); e- equated yield
141. Exercise 2
Consider a commercial property that has been leased at
an annual exclusive rent of Rs 120,000 with a 5 yearly
rent review for a lease period of 25 years. Rents are
growing at 10% annual rate in the area. Comparable
properties are also being sold at Rs 20,00,000.
What is the equated yield of the property? Based on
that do you suggest investing in such property.
For the above equated yield, if the rent review period is
reduced to 3 years then what growth is required while
assuming an initial yield of 6%?
144. Graphical explanation of interpolation
NPV1+
NPV 2 -
NPV1
NPV1+NPV2
ye
ye1
ye2
Ye = ye1+
(NPV1/NPV1+NPV2)*(ye2-ye1)
145. Solution 1 (contd..)
Now, we know that the equivalent yield lies in between
10 and 12%. We interpolate and find it in the same
manner as we did for reversionary properties
ye = 10%+{274600/(274600+174600)}*(12-10%)
= 10% + 0.6*2% = 10%+1.2% = 11.2%
The investment in this property is attractive, as it gives
an income yield of 11.2% when compared to the yield
of government bonds (7.15%) or the yield of long term
deposit in banks (6.5%)
146. Solution 2
It is given that the income yield or ARY(i) is 6%, rent
review period (r) is 3 years and equated yield (or,
target rate) (e) is arrived at 11.2% (~11%), the growth
rate required can be calculated from the following
formula
(1+g)^r = (YPperp@i –YPr@e)/(YPperp@i*PVr@e)
(1+g)^3 = (16.6672-2.4437)/16.6672*0.7311
(1+g)^3 = 1.1671
1+g = 3√ 1.1671 = 1.0528
Or, g = 5.28%
147. Extension to another property valuation
Let us consider valuing another property with a
different initial rent of Rs 100,000 and same rental
growth as computed but different rental review
period of 7 years leased for 21 years
We will compute the initial yield for the given rental
growth term structure at 4.637%
Value of the property V = YP perp@6.647%*CI
= 15.044 * 100,000
= 15, 04, 400
148. Growth explicit valuation
Revision
Term (years)
Annual Rack
Rent (Rs)
PVF@11% YP 7y@11% PV of Rent
1-7 100,000 1 4.7122 471,220
7-14 140,710 0.4816 4.7122 319,365
14-21 197,993 0.2633 4.7122 245,654
>21
(perpetuity)
278,596 0.1117 X 31,119X
100,000 X = 1,036,239+ 31,119 X
Or 31,119 X – 100,000X = 10,36,239
Or 68,881 X = 10,36,239
Or X = 15.044
Initial yield (y) = 1/ YP perp = 1/x = 6.647 %
149. References
S Datta (2004), Valuation of Real Property:
Principles and Practice, Eastern Law House, Kolkata
Chapter 4: General principles of investment valuation
under Investment method
D Isaac and T Steley (2000), Property Valuation
Techniques, Macmillan Publishers, London
Chapter 4: Interest rates and yields
Chapter 5: Equated Yields
150. 10. RISK & UNCERTAINTY IN
INVESTMENT VALUATION
Ramakrishna Nallathiga
Associate Professor, NICMAR Pune
151. Structure
Introduction
Individual Vs Portfolio Risk
Risk and Composition of Interest Rate
Theory of Risk and Its application
Risk adjusted discount rate
Risk adjusted cash flows
Property Investment Risks
Property Risk Evaluation
Property Risk Management
152. Introduction
Investment properties are subject to risks and
uncertainty associated with many aspects of them
While risk can be expressed in measurable terms of
probability, uncertainty cannot be done so
Financial management theory suggests three broad
categories of risk:
Business risk, which arises due to the uncertainty of future
income flows based on the nature of the firm’s business
Financial risk, which arises from the method of financing of
investment
Liquidity risk, which is the uncertainty introduced by the
availability of access to the secondary market for an
investment
153. Introduction
Baum and Crosby (1995) also differentiate
between real and monetary risks, which refer to the
risks associated with real and money income
They categorise various investment assets based on
it Degree of Risk Real Terms Money Terms
Low Index linked gilts
Inflation linked
bonds
Bank deposits
Fixed deposits
Medium Equities
Properties
Index linked gilts
Inflation linked
bonds
High Bank deposits
Fixed deposits
Property
Equities
154. Individual Vs Portfolio Risks
Risk is also distinguished between individual
property investments and a portfolio of properties
Markowitz (1959) developed a portfolio model for
risk to a portfolio of investments that can also be
applied to property investments, which proposes
that there are systematic and unsystematic risks
Construction of a well balanced portfolio of
property investments gives rise to the reduction of
unsystematic risks but not systematic risks
155. Individual Vs Portfolio Risk
Modern Portfolio Theory sees investment decision as a
tradeoff between risk and expected return
However, property investment, unlike equity investment,
does not offer opportunity to reduce risk through
diversification
The major types of risks encountered by a property
investor are the risks associated with:
Income flow
Future outgoings
Capital value
Market value
156. Risk and Composition of Interest rate
As discussed earlier, the market interest rate is made up
of (a) time preference element (ii) inflation premium (iii)
risk premium
The relationship can be expressed as:
(1+i) = (1+e) (1+g) (1+r) or,
i = (1+e) (1+g) (1+r) - 1
A risk free return (RFR) thus equals (1+e) (1+g) – 1
Therefore, i = (1+RFR) (1+r) – 1 or,
i = 1+r+RFR+rRFR-1 = r+RFR+rRFR
It can also be simplified to i = r+RFR
157. Theory of Risk and Its Application
There are two approaches to the inclusion of risk in a
discounted cash flow method of valuation
Risk-adjusted discount rate approach
Risk adjusted cash flows
Risk adjusted discount rate approach
Here it is assumed that the cash flows are fixed and a risk
element is incorporated into discount rate
Risk adjusted cash flows approach
A risk element is incorporated into cash flows in this
approach and discount is made using risk-free discount rate
158. Risk Adjusted Discount Rate
In this analysis, no distinction is made between NPV
approach and IRR as investment selection criteria
The rates of return used in the DCF calculation will
depend upon the specific investor (or, client) – most
important is the equity yield rate that applies to equity
proportion of the investment after excluding debt
Once equity yield is specified, it possible to estimate
the present worth of the equity position.
This rate can be based on the rate of return that equity
capital appliers expect to receive, therefore comes
close to opportunity cost principle
159. Risk Adjusted Discount Rate
The rate of return embodies three factors – time preference,
inflation premium and risk premium i.e.,
I = RFR + r (risk premium)
The above uses target rate of return (which is expected to
be equal to market rate) but there is still the risk in the
estimation of inflation which is not included
The return required of a project can also be taken from
Capital Asset Pricing Model (CAPM), which states
I = RFR + β (Im – RFR)
Where Im is the required rate of return of project of avg
risk and Rm equals to Im-RFR is the risk premium
β adjusts the mean risk for the relative riskiness of the
project under consideration
160. Risk Adjusted Cash Flows
In this expected value of cash flow is compared with a
range of possibilities by comparing the probable
distribution around the expected level with normal statistical
distribution
This can be done through examining the variance, which is
equal to the sum of squares of the differences between the
normal expected values and the probability distribution
This analysis has probability built into it and using this we
can compare the actual outcome with expected outcome.
Once the risk is built into the cash flows, the discount rate
can be applied to level of out come at the risk free rate
161. Property Investment Risks
Baum and Crosby (1995) also identify a number of
possible risks that could affect property investments:
Tenant risk
Sector risk
Structural risk
Legislation risk
Taxation risk
Planning risk
Legal risk
162. Property Risk Evaluation
Risk evaluation aids the decision making process
and helps the investor to answer questions of:
What is the expected return or the most likely outcome?
What is the probability of making a loss as measured
against a target return, cost of borrowing or alternate
investment return? Alternatively, what is the probability
of exceeding the return?
What is the variability or spread of returns in relation
to the expected return? Low volatility (risk) is traded off
against return.
163. Property Risk Management
There are different means of individual property
risk management (Waldy 1991):
More intuitive/rational choice of ARY
More explicit approaches like sensitivity analysis
(changing input values) and scenario testing (risky
situations from different inputs)
Risk adjusted discount rates that provide premium for
risk
Certainty equivalent techniques that use probability
and remove downward risk to work out risk free cash
flows
164. To Sum Up
Properties, like the projects, are also prone to risk/
uncertainty associated with several elements e.g., cash flows,
inflation and market rate for discounting
Property investment risks can also be distinguished as
individual property risk as well as portfolio risks
Property investment risk sources are different from those of
project investments and financial investments
Risk theory helps to include risk through approaches either
that adjust cash flows or discount rate
Risk evaluation aids decision making by examining the
probability, variability/spread and expected outcome
Risk management involves making use of evaluation tools
and utilizing approaches that include risk
165. References
D Isaac and T Steley, Property Valuation
Techniques, Macmillan, London
Chapter 11: Risk
