Property
Appraisal
Introduction
Introduction
• Definitions
• Appraisal
• Investment and
investors
• Appraisal techniques
• Summary
Definitions
• Market Value (value in exchange)
– Estimate of exchange price
– Relies on interpretation of market information
– Objective
• Worth (value in use)
– To a specific individual or group
– Usually involves consideration of personal
circumstances (risk and return) as well as market, e.g.
o financial resources available for a property acquisition,
including the split between debt and equity finance
o timescale for holding a property asset
o tax position, personal tastes and specific requirements of
the decision-maker
– Subjective
Definitions - IVS
• Investment Value or Worth “The value of property to
a particular investor, or a class of investors, for
identified investment objectives. This subjective
concept relates specific property to a specific investor,
group of investors, or entity with identifiable
investment objectives and/or criteria.”
Why might value and worth be different for the
same property?
Why might investors arrive at different appraisals
of worth?
What is Appraisal?
• A valuation is an objective comparison with evidence
from closely comparable properties
• An appraisal is an estimation of investment worth to
an investor by determining its risk and return
characteristics in relation to that investor
Market Valuation
Backward-looking; analysis of past
transactions
Appraisal of Worth
Forward-looking; forecast of cash-flow
Reasons for appraisal
• Acquisition
– Purchasing a property is one of the key times that Appraisal is
utilised
– Why will different parties pay different prices for the same
building?
•
•
•
•
Refurbishment/redevelopment
Financing arrangements
Ongoing performance
Disposal
Financial characteristics of
investments
• Investment = acquisition of asset(s) that are worth
more than their cost
• Nature of revenue receipt
– Fixed or variable income and capital value
• Liquidity
• Security of income and capital
– Nominal
– Real
Financial characteristics of
investments
• Conventional bonds
– long, short, medium or undated fixed interest debt investment
– gross redemption yield (GRY) = riskless nominal rate of return
– GRY on index-linked gilts = real risk-free rate of return
• Ordinary shares
– equity investment
– IRR unknown and must be estimated from anticipated cash flows
(unlike gilts)
– therefore shares involve risk -> premium above GRY
• Property
– Direct and indirect
– Commercial and residential
So who invests in property?
• Financial Institutions (general insurance
companies, life assurance companies and pension
funds)
• UK Property Companies
• Overseas Investors
• Traditional Estates and Charities
• Private Investors
• Limited Partnerships and Unit Trusts
Appraisal at Purchase
22-24 Queen Square,
Bristol
• Grade II listed terraced
office building. The
building was redeveloped
in 2007 and the Grade II
listed façade was retained
Sold to Invista December
2006 for £8.5m (4.87%)
Sold by Invista to Epic May
2008 for £6.2m (6.5%)
Appraisal at Purchase
1 Georges Square, Bristol
• Acquired in November 2004 by
Anglo Irish Private Bank for
£24,475,000 (6.20% NIY)
• Sold in May 2006 to Invista for
£29, 500,000 (4.95% NIY)
• Sold in September 2008 to IVG for
£21,915,000 (6.65% NIY)
• Sold in June 2010 to British Steel
Pension Fund for £25,375,000
(5.75% NIY)
1 Georges Square, Bristol
35,000
8.00
30,000
7.00
25,000
20,000
6.00
5.00
4.00
15,000
10,000
3.00
2.00
5,000
1.00
0
0.00
Price (£m)
Yield (%)
Summary
• Valuation is a market-based concept. An appraisal of
worth is an individual-based concept and represents a
means of assessing whether a price/valuation
represents ‘good value’ to an individual or group
•
A different information set is used to conduct
appraisals of worth, using more client-specific
information
• An appraisal of worth may vary more than a market
valuation as the financial estimation moves away from
an analysis of market information to greater
consideration of personal investor or occupier
requirements, using more sophisticated techniques
Property
Appraisal
Information Requirements
Introduction
• Properties are not frequently traded in
the open market and information
access is limited so valuers look at
comparable evidence to assess
market value (PV)
• Need to compare appraisals of worth
with asking price
• Example
– 43 Queen Square, Bristol…
Appraisal information
•
Economic indicators
– Output, (un)employment , movements in corporate profits (by sector),
money supply, public sector borrowing, inflation, interest rate
•
Market indicators
–
–
–
–
–
•
Rents, rental growth and depreciation rates
Redevelopment or refurbishment costs
Yields and forecasts of exit yields
Purchase and sale costs
Movements in market indices
Portfolio information
– Asset returns and correlations (to aid diversification)
– Sales and purchases
– Risk indicators
Property information
– Physical attributes (areas, ancillary space,
quality, improvements)
– Financial details (yield, rent passing, rental
growth, market rent and capital value)
– Legal terms (tenancies and lease details,
number of tenants, expiry dates, review dates,
voids, future leases)
– Outgoings and capital expenditure (vacancies,
voids, unrecoverable service and
management costs, letting, re-letting and rent
review costs, purchase and sale costs)
– Depreciation, costs & timing of redevelopment
and refurbishment, cost inflation
– Planning
– Taxation (Business Rates, VAT)
– Occupancy / holding costs (management,
review, purchase & sale costs)
– Dilapidations, service charge & other
payments for repairs and insurance if
leasehold
Client specific information
– Discount rate, taxation, loan / finance
– Holding period
Facts and variables in appraisal
Facts
Variables (assumptions)
Current Rents
Target rate of return
Covenant Strength of
Tenants
Estimated Rental Value
and Rental Growth
Prospects
Lease Expiries/Break
Clauses
Void Periods and other
anticipated expenditure
Areas
Holding Period
Exit Yield
Key investment appraisal
variables
Investment appraisal involves making explicit judgments (based on
evidence) about:
• Rent and rental growth
– Volatile over short term
– Little known about depreciation rates
– Expenditures
• Target rate or return
– Selection of risk premiums for individual properties is a grey area
• Holding period
– Longer period - more chance of error in selecting variables
• Exit value
– Prime yields fairly stable
Rent and rental growth
• Contractual rent will be known but market rent and future lease
terms must be estimated
• Associated variables:
– Timing of rent reviews
– Length of lease and existence of any break options (likelihood of
void periods)
– Management costs and taxation
– Financial impact of void periods
o How long will it take to let vacant space?
o Holding costs through void period
o Letting incentives and possible refurbishment costs to be allowed for
o Short-term lets...
Rent and rental growth
• Estimate rental value of
– New
– Existing
– Existing but refurbished
• Estimate rental growth rate
• Depreciation
5.00%
– Depreciation rate of existing property (% rent) 2.00%
– Depreciation-adjusted rental growth rate
2.94%
1 g 

 1
1 d 
NB. Capex of 0.5-1% p.a. means rent depreciation of 0.5-1%
p.a., rising to 2% p.a. with no capex...
Associated expenditures
•
•
•
•
Acquisition costs (% acquisition price).................................5.75%
Rent review costs (% new rent)............................................. 4-5%
Management costs (% income)............................................. 1-3%
Re-letting costs (% new rent)................................................7.50%
– Higher than rent review due to marketing and legal fees
• Lease renewal costs (% new rent).........................................5.00%
– No marketing costs
• Property tax / business rates
Forecasting and Depreciation
• Forecasting
– Forecasts of market rents and rental growth typically relate to prime
new business space in the locality concerned (i.e. no depreciation)
– National, regional and local level
– Usually based on econometric models of economy and property
market
– Property specifics are also vital
• Depreciation
– Don’t overlook or double-count!
– Think carefully about relationship between capex and depreciation
– If refurbishment expenditure is included in cash-flow then financial
benefit should be reflected in revenue (e.g. enhanced estimates of
rental value, growth rate or exit yield)
Discount rate or
target rate of return
• Must adequately compensate an investor for the risk taken
• Individual properties have individual target rates
• Portfolio construction can isolate property-specific risk from
market risk
• It is the cost of capital (an investment needs to compensate
investors for the use of their capital)
• Several ways of deriving it:
1. Risk-adjusted discount rate (RADR)
o Frequently used by investors and property analysts
2. Capital Asset Pricing Model (CAPM)
3. Weighted Average Cost of Capital (WACC)
4. Yield on client’s equity
1. Risk-adjusted discount rate
(RADR)
The target rate of return (TRR) required by an investor may be
derived from a ‘risk-adjusted discount rate’ (RADR), expressed
as:
TRR or RADR
Where:
=
RFR + RP
RFR is the risk-free rate of return or compensation for
loss of liquidity
RP is the risk premium or compensation for risk,
which comprises market risk (which cannot be
diversified away)
RADR derived by adding a risk premium to a ‘benchmark’ risk-free
rate
RADR components
a) Risk-free rate (RFR)
– Baseline defined by reference to the return from a low-risk
or riskless asset
– Typically the income yield on a medium / long dated gilt
b) Risk Premium
– Return to compensate for market and property-specific risks
associated with holding the specific property asset
– Need to decide which are best handled by building into the cash
flow and which should be incorporated by adjusting the RP
Risk Premium
• Difficult to estimate for individual property assets due to
– Paucity of data, confidentiality issues
– Uniqueness of assets and complexity of markets
– Overlap between risk factors
• Historically the UK long-term property RP = 2-6%
• Need to consider RP over different holding periods
• Need to distinguish long term (ave) RP from short term
sentiment re-ratings
• Group assets to determine property sector RP, then adjust to
reflect asset-specific risk
• Remaining costs (fees, management, dilapidation, etc.) are
handled in the cash flow
RADR limitations
a) Only one rate applied to all cash-flows so fails to distinguish
those parts of the cash-flow that are risky and those that are not
b) Heavily discounts distant cash-flows regardless of whether they
are actually more risky
c) Ignores the importance of diversification
2. Capital Asset Pricing Model
(CAPM)
• An investment’s expected return is a positive linear function of
risk (measured in terms of SD & variance)
• CAPM enables estimation of the target rate of return in the light of
returns available from ‘risk-free’ investments and market-related
risk factors of the investment under scrutiny
• Recognises that each investment has different market risk which
will influence its expected return
• Market risk is a special type of risk related to the contribution that
the asset makes to a well-diversified portfolio.
CAPM

E rn   rf  b p E rm   rf

Where
E(rn) =
expected return for a specific asset
rf
=
risk-free rate
b
=
amount of systematic risk (indicator of the
investment’s sensitivity to market
movements)
E(rm) =
expected market return (the reward for
bearing systematic risk)
CAPM example
Expected market return and variance: E(rm) and var(rm):
Scenario Prob (p)
Severe
recession
Mild
recession
Recovery
Strong
recovery
rm
p(rm) (rm –E(rm)) (rm –E(rm))2 p(rm –E(rm))2
0.2
-0.2
-0.04
-0.36
0.1296
0.02592
0.3
0.1
0.03
-0.06
0.0036
0.00108
0.4
0.3
0.12
0.14
0.0196
0.00784
0.1
0.5
0.05
0.34
0.1156
0.01156
E(rm) =
0.16
var(rm) =
0.04640
CAPM example
Expected asset return and its covariance with market
return: E(ra) and cov(ra, rm):
Scenario Prob (p)
Severe
recession
Mild
recession
ra
p(ra) (ra –E(ra)) (rm–E(rm)) p(ra –E(ra))(rm–E(rm))
0.2
-0.05
-0.01
-0.195
-036
0.01404
0.3
0.15
0.045
0.005
-006
-0.00009
Recovery
0.4
0.20
0.08
0.055
0.14
0.00308
Strong
recovery
0.1
0.30
0.03
0.155
0.34
0.00527
E(ra) = 0.145
covar(ra, rm) =
0.0223
CAPM example
Asset beta:
covra , rm 
ba 
= 0.0223/0.0464 = 0.48
var rm 
So the asset has a low beta coefficient indicating low volatility
(approx. 50% lower risk than the market)
Using the CAPM equation and assuming a RFR of 5%, we can
now calculate the expected target rate of return, E(rn)
E(rn) = 0.05 + (0.48)(0.16-0.05) = 0.1028 or 10.28%
3. Weighted Average Cost of
Capital (WACC)
• Discount rate (minimum expected rate of return) of an investment
is the ‘cost of capital’; it represents how much the company
should earn to break even
• WACC takes the cost of equity and after-tax cost of debt and
calculates an average, weighted according to the market values
of debt and equity
• Capital structure weights:
– Debt weight, w, is the market value of debt divided by the total
market value of debt and equity
– Equity weight is 1- w
Land Securities Capital structure weights
• MVs preferred but can use book values
– Equity = 6,636.6
– Debt = 2,923.1
• Equity weight
– 6,636.6/(6,636.6 + 2,923.1) = 69.4%
• Debt weight
– 2,923.1 /(2,923.1 + 6,636.6 +) = 30.6%
WACC formula
WACC = (1-w) re + w.rd (1 – t)
• Where w is the market value weight of debt, rd is the cost of debt,
t is the corporate tax rate and re is the geared cost of equity
• re can be estimated from CAPM
– E.g. if the b of the company is 1.35, rf is 6%* and E(rm) is 12.5%, then

E re   r f  b e E rm   r f

= 0.06 + 1.35(0.065) = 14.78%
– RFR is expressed gross of tax because firm must earn 6% after
taxes so shareholders can earn RFR of 6%.
WACC and tax
• Cash flows are after tax
• The WACC discount rate has to be consistent with cash flows
• Tax issues relate to debt
– Interest offers a tax shield = rd * tc
• It is as if the government reduces the cost of debt
– rd becomes rd (1 - t)
WACC example
• If the geared cost of equity is 14.78%, gross interest on debt is
9% , corporate tax is 40%, and with market value weights for
equity (we) of 0.3 and debt (wd) of 0.7, WACC can be calculated
as follows:
• WACC
= [0.3 x 0.1478] + [0.7(0.09(1 – 0.4)]
= 0.08214
Say 8.2%
WACC summary
• Represents discount rate to be used for
– Company projects
– With similar characteristics to existing investments
• What happens if investment has different risk/return profile?
– Subjective approach: adjust WACC by adding premiums or
deducting discounts depending on perceived risk (high, medium, low)
• The WACC is based on figures derived from the company and so
should only be used on projects with same financial structure as
the company
Holding Period of Investment
• Normally specified by client...
– Usually 3-5 or 10-15 years depending on type of investor
• ...or by fundamentals of the property
– influenced by lease terms (break clause, lease expiry)
– or by physical nature of property (redevelopment, voids)
• Longer hold period = greater risk of fluctuation of variables from
prediction, or reversion to long term trends?
Exit value
• Value of the property at the end of the holding period
• Usually capitalise the rent forecast at the end of the holding
period
• May reflect land values if demolition is anticipated
• May reflect refurbishment / redevelopment costs too
• Forecast building costs if refurbishment or redevelopment is
planned
Exit Yield
• Yield a purchaser would require for the property at the point of
(notional) sale
• Normally based on comparison with similar investments using
ARY approach
• Assume stability of market over holding period?
• Important to consider impact of depreciation but don’t doublecount its effect on value by, say, reducing the forecast rent and
raising the exit yield
• Choice of exit yield is key when holding period < 20 years as
resulting exit value forms a substantial element of worth
Summary
• Rent and rental growth
– Growth
– Depreciation
– Associated costs
• Target rate or return
– RADR
– CAPM
– WACC
• Holding period
• Exit value
– Exit yield
– redevelopment
Property
Appraisal
Methods
Introduction
• Investment decisions involve choosing between different types
of investment with different characteristics
• Investment decisions are made against a background of risk
and numerous uncertain variables dependant upon future
events
• A rational basis to compare investment propositions (a
decision tool) is required that focuses on return / risk profile
• Must consider:
– Financial resources available (equity and debt)
– Project timescale
– Integration with existing portfolio
• Any mismatch between the market value or price of a property
investment and its worth to a particular investor should be
investigated
• A rational investor should buy an asset if its price is equal to or
below his assessment of worth
• The range of worth estimates is typically wider in the property
market than in the equities market where a great deal more
trading takes place on the more marginal differences between
price and worth
Methods
1. Simple screening:
a) Payback
b) Rate of return and yield
2. Project-only discounted cash-flows (DCFs):
a) Net Present Value (NPV)
b) Internal Rate of Return (IRR)
c) Capital Asset Pricing Model (CAPM)
3. Project-with-finance DCFs
a) Weighted Average Cost of Capital (WACC)
b) Flow to Equity (FTE)
1. Simple screening methods
a) Payback
• Measures time taken to recoup expenditure
• Widely used technique
• Simple to perform and interpret
• Favours investments where the greater cash-flow is received in
the early years because any income received after payback has
been attained is ignored
Payback: Example
Year
Property A
Property B
0
-100,000
-100,000
1
60,000
20,000
2
40,000
60,000
3
20,000
60,000
4
20,000
70,000
• Which is the best?
• Why?
Payback:
Example
Year
Property A
Property B
0
-100,000
-100,000
1
60,000
20,000
2
3
40,000
20,000
60,000
60,000
4
20,000
70,000
Net cash-flow
40,000
110,000
• A would be chosen because the payback is in 2 years despite the
total net cash-flow for B being much greater
Payback Limitations
• Views investments in the short term, only focusing on cash-flows
within the payback period; the shorter the payback the more
attractive the investment
• Fails to measure long-term profitability beyond the payback
period.
• Ignores the time value of money, the total return that can be
expected from the investment and volatility of that return
• The only justification for this method can be that as one projects
further into the future the more volatile returns are expected to be,
so it is better to have returns sooner
Discounted payback
• Variation of the payback method that considers the time value of
money by calculating how quickly a project recoups initial
expenditure in discounted (present value) terms
• It is really a version of the Net Present Value method (see later)
truncated to the payback year so cash-flows beyond this point
are, once again, ignored
• Payback method can be used as an initial screening device prior
to more sophisticated methods
b) Rate of return & Yield
• If an investment is correctly priced the expected (target rate of)
return will equal the actual return
• Obviously the actual return is not known as it is in the future but
we can look at past performance as a guide
• A simple but important measure of investment performance is the
ratio of net annual income to capital outlay, known as the
(income) yield
• Simple to calculate and can be compared to a ‘hurdle’ or target
rate of return set by the investor or compared to the investor’s
overall return on capital or WACC
Rate of return & Yield:
Theory
• Target rate of return, rn, comprises a risk-free rate, rf, a risk
premium, rp
rn
•
rf + rp
=
rn – g + d
=
rf + rp – g + d
And the yield, y, is
y
•
=
So if the market is correctly priced
rf + rp =
(required return)
=
y+g–d
(actual return)
Rate of return & Yield:
Application
Bond
Equity
Propert
y
rf +
4.5 +
rp
0
=
=
R
4.5
- g
- 0
4.5 + 6.3 = 10.8 4.5 + 3.2 = 7.7 -
3
1
= y
= 4.5
= 7.8
= 6.7
Rate of return & Yield:
Example
• An investor wishes to invest £5m and wants a 9% return
• A shop is available for £5m which has been let at £400,000 per
annum
• Annual rental growth is expected to be less than 1%
• Should the investor purchase this investment?
Rate of return & Yield:
Example
• An investor wishes to invest £5m and wants a 9% return
• A shop is available for £5m which has been let at £400,000 per
annum
• Annual rental growth is expected to be less than 1%
• Should the investor purchase this investment?
Yield=
income / capital value
=
£400,000 / £5,000,000
=
0.08 or 8%
• The shop investment does not produce a sufficient return
Rate of return & Yield :
Example (continued)
• The shop investment has only been analysed in terms of its initial
return and the simple relationship between initial income and
price paid reveals nothing about future income and capital growth
prospects
• In the UK business properties typically let on leases incorporating
5 yearly rent reviews
• The IPD retail property index indicates that rents have been
growing at an average rate of 1.5% per annum
• Implied rental growth is 1.17% per annum
Rate of return & Yield:
Summary
• Like payback, the yield is simple to calculate and easy to
understand
• But it cannot account for financial magnitude of the investments
under consideration because it is a percentage measure
• The yield, like payback, ignores the time value of money and
ignores the concept of cash-flows
• Should only be used to screen investments prior to more detailed
appraisal
2. Project-only DCFs
• It is not necessary to account for financing when evaluating a
project
o the value of a project should not alter simply as a result of the
way that it is financed (Modigliani and Miller, 1958) (MM
hypothesis)
• It is okay to assume investment is wholly equity financed
o The funding decision is separate from the investment decision
but only in a world without tax...
o Financing only matters when tax is involved
Discounted Cash-Flow (DCF)
• A DCF shows the present values of all revenue (including rent,
premiums and sale price) and expenditure (including purchase
price and any periodic expenditure)
• The present value of a future sum, whether it is revenue or
expenditure, is dependent on the discount rate and the length of
time over which it is discounted: the higher the discount rate and /
or the longer the discount period, the lower the present value
• To assess investment worth:
– Estimate cash-flow
– Discount at target rate
DCF
• Can adjust the cash-flow in each period to account for changes in
inflation, rental growth, depreciation, refurbishment and
redevelopment expenditure, tax, financing, management and
transfer costs, etc.
• Allows direct comparison of investments because the cash-flows
are converted to a common denominator – present value
• Two widely used DCF decision tools
– Net Present Value (NPV)
– Internal Rate of Return (IRR)
a) Net Present Value (NPV)
• Sum of cash flows over holding period discounted at appropriate
discount (target) rate
• Present value of a capital profit, expressed as an absolute
number regardless of extent of cash flows needed to generate it,
over and above target rate of return
• If NPV positive, then return higher than target rate
66
Determinants of the
Target Rate of Return
•
Opportunity Cost of Capital (liquidity preference)
•
Inflation / growth
•
Risk
NPV:
Simple example
Year
Cash-flow
(£)
PV £1 @
10%
DCF (£)
0
-880,000
1.0000
-880,000
1
200,000
0.9091
181,820
2
400,000
0.8264
330,560
3
440,000
0.7513
330,572
4
220,000
0.6830
150,260
NPV
113,212
• Positive NPV signifies viability at 10% discount / target rate
NPV:
Comparison 1
Year
Cash flow
from
A
PV £1 @
10%
DCF
Cash flow
from
B
PV £1 @
10%
0
-140,000
1
-140,000
-140,000
1
-140,000
1
60,000
0.9091
54,546
20,000
0.9091
18,182
2
40,000
0.8264
33,056
40,000
0.8264
33,056
3
20,000
0.7513
15,026
40,000
0.7513
30,052
4
40,000
0.6830
27,320
60,000
0.6830
40,980
5
40,000
0.6209
24,836
60,000
0.6209
37,254
NPV
14,784
NPV
19,524
NPV:
Comparison 2
Year Property A
Property B
0
-750,000
-750,000
1
90,000
-500,000
2
90,000
70,000
3
90,000
70,000
4
90,000
90,000
5
70,000
90,000
6
70,000
90,000
7
-500,000
90,000
8
2,000,000
2,000,000
Net Total
1,250,000
1,250,000
563,303
323,484
NPV
• 2 investments which have
same net total cash-flows but
timing of payments is
different
• NPV will be higher if majority
of cash flows are received
early on
NPV:
Benefit-to-cost ratio
• If capital outlays are different, calculate NPV as a proportion of
PV of total costs and choose the project with the highest
Year
0
1
2
3
Income from
Investment A
-50,000
30,000
20,000
15,000
PV£1 @
10%
DCF
1
0.9091
0.8264
0.7513
-50,000
27,273
16,528
11,270
NPV
PV total costs
NPV/PV Total Costs
Income
from
Investment
B
-70,000
40,000
30,000
20,000
PV£1 @
10%
DCF
1
0.9091
0.8264
0.7513
-70,000
36,364
24,792
15,026
5,071
50,000
NPV
PV total costs
6,182
70,000
10.14%
NPV/PV Total Costs
8.83%
NPV:
Inflation rate as the discount rate
• If inflation rate is used as the
discount rate then it is
possible to determine
whether an investment
meets the minimum
requirement of transferring
purchasing power through
time
Year
Cashflow
Discount /
Inflation
Rate (4%)
DCF
0 -200,000
1.0000 -200,000
1
15,000
0.9615
14,423
2
20,000
0.9246
18,492
3 200,000
Net
35,000
0.8890 177,800
NPV
10,715
Constructing a real estate
cash-flow
Period
Income
(£)
Net
Cash
Flow (£)
Growth
rate
Real
Discounte
YP 5 yrs PV £1 @
Cash
d income
@ 16%
16%
Flow (£)
(£)
Initial outlay
-£100,000
0-4
12,000
12,000
1.0000
12,000
3.2743
1.0000
39,292
5-9
12,000
12,000
1.2763
15,315
3.2743
0.4761
23,876
10-14
12,000
12,000
1.6289
19,547
3.2743
0.2267
14,508
15-19
12,000
12,000
2.0789
24,947
3.2743
0.1079
8,816
20-Perp
12,000
12,000
2.6533
31,840
9.0909*
0.0514
14,874
Net Present Value (NPV)
£1,365
*YP perpetuity at exit yield of 11%
Constructing the cash-flow:
Tranching income
b) Internal Rate of Return (IRR)
• Rate at which cash flow is discounted to give an NPV of 0
– Income discounted to equate with expenditure
– It is where the discount rate equals the IRR
• Rate generated internally by the cash flow of the investment
– 'Internal' denotes that the rate is asset-specific rather than derived
from comparable evidence or a market rate
– NPV & IRR make different assumptions about the reinvestment rate
• IRR is a % amount whereas NPV is a money amount
• IRR higher than target rate signifies viability
75
IRR (reinvestment rate)
• IRR cannot be calculated directly because as the number of cashflows increases so does the complexity of its polynomial
expression, with multiple roots
• Also, projects with +ve and –ve cash-flows can have > 1 IRR
• Use interpolation or iteration instead
IRR:
Interpolation



Year
Cashflow
0
1
2
3
4
-880,000
200,000
400,000
440,000
220,000
PV £1 @
15%
(TR1)
1.0000
0.8696
0.7561
0.6575
0.5718
NPV1
Present
value
-880,000
173,920
302,440
289,300
125,796
+11,456
PV £1 @
16% (TR2)
1.0000
0.8621
0.7432
0.6407
0.5523
NPV2
Present
Value
-880,000
172,420
297,280
281,908
121,506
-6,886
IRR lies between 15% and 16%
If NPVs are plotted on a graph against discount rates a
curved line depict exact IRRs
We can interpolate a straight line between these two
rates to determine where NPV = 0, so long as we have a
positive and a negative NPV to work from
IRR:
Interpolation
NPV (£)
Actual (non-linear) relationship
between NPV and discount rate
+11,456
Assumed (linear) relationship
between NPV and discount rate
IRR estimate
x
0
-6,886
15%
True IRR
16%
Discount
rate (%)
IRR:
Interpolation
Using similar triangles, we can interpolate a linear estimate of the
IRR between the two trial rates
NPV1
x  TR2  TR1  
NPV1  NPV2
Where
TR1 = lower trial rate
NPV1 = NPV at lower trial rate
TR2 = higher rate
NPV2 = NPV at higher rate
and + and - signs are ignored
11,546
x  1%
 0.63%
18,432
Therefore IRR estimate is 15% + 0.63% =15.63%
IRR:
Interpolation example
•
Freehold office investment recently let on an full repairing and
insuring (FRI) lease with 10 years left
•
Price is £1m, current rent is £100,000p.a., expected to rise to
£125,000p.a. at next rent review
•
At the end of the lease the property could be refurbished at a cost
of £1.5m and would then expected to sell for £3m (these are
forecasts, not current values). The refurbishment is expected to
take a year to complete
Using 10% trial rate
Yr
0
1
2
3
4
5
6
7
8
9
10
11
Income and Costs
£(+)
Purchase Price
Rental Income
Refurbishment
Rental Income
Rental Income
Rental Income
Rental Income
Rental Income
Rental Income
Rental Income
Rental Income
Sale Proceeds/
Refurb Costs
Net Present Value
100,000
100,000
100,000
100,000
100,000
125,000
125,000
125,000
125,000
125,000
3,000,000
£(-)
Net Flow
1,000,000
1,000,000
100,000
100,000
100,000
100,000
100,000
125,000
125,000
125,000
125,000
125,000
1,500,000
1,500,000
PV @
10%
1.0000
0.9091
0.8264
0.7513
0.6830
0.6209
0.5645
0.5132
0.4665
0.4241
0.3855
0.3505
DCF
1,000,000
90,910
82,640
75,130
68,300
62,090
70,563
64,150
58,313
53,012
48,188
525,750
£199,047
Using 15% trial rate
£(+)
Yr
0
1
2
3
4
5
6
7
8
9
10
11
Income and Costs
Purchase Price
Rental Income
Rental Income
Rental Income
Rental Income
Rental Income
Rental Income
Rental Income
Rental Income
Rental Income
Rental Income
Sale Proceeds/
Refurb Costs
Net Present Value
100,000
100,000
100,000
100,000
100,000
125,000
125,000
125,000
125,000
125,000
3,000,000
£(-)
Net Flow
1,000,000
1,000,000
100,000
100,000
100,000
100,000
100,000
125,000
125,000
125,000
125,000
125,000
1,500,000
1,500,000
PV @
15%
1.0000
0.8696
0.7561
0.6575
0.5718
0.4972
0.4323
0.3759
0.3269
0.2843
0.2472
0.2149
DCF
1,000,000
86,960
75,610
65,750
57,180
49,720
54,038
46,987
40,863
35,538
30,900
322,350
-134,104
Interpolate IRR
IRR = TR1 + [(TR2 – TR1) x
NPV1
]
NPV1 + NPV2
= 10 + [(15 – 10) x
199,043
]
134,091+ 199,043
= 10 + [5 x 199,043 ]
333,134
= 10 + 2.9875
= 12.99%, say 13%
Year
IRR:
Iteration
• Rent is £12,000 pa with 5 year
rent reviews
• ARY is 11% and rental growth is
6% pa
• Asking price is £100,000
• Using the IRR function, the IRR
of this investment is found to be
11.25%
NB. IRR function in Excel assumes
1st cash flow is period 0
Income Growth
rate (6%
per
annum)
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
20-perp
IRR
Real
Cash
Flow
-100000
12000
12000
12000
12000
12000
12000
12000
12000
12000
12000
12000
12000
12000
12000
12000
12000
12000
12000
12000
12000
12000
1.0000
1.0000
1.0000
1.0000
1.0000
1.3382
1.3382
1.3382
1.3382
1.3382
1.7908
1.7908
1.7908
1.7908
1.7908
2.3966
2.3966
2.3966
2.3966
2.3966
3.2071
12000
12000
12000
12000
12000
16059
16059
16059
16059
16059
21490
21490
21490
21490
21490
28759
28759
28759
28759
28759
349869a
11.25%
Property Risk
Analysis
What is risk?
•
•
•
•
Risk is uncertainty regarding the expected future
rate of return from an investment
It is perceived in terms of security of capital,
security of expected income and liquidity
More risky an investment is perceived to be, less
attractive it is and thus less valuable; this translates
to a higher yield / return
Main concerns are
–
–
–
probability of making a loss
estimating most likely (capital and income) return
estimating variability of returns
Types of risk
• Systematic risk
– affects all investments
– caused by inflation, economic cycles, interest rate
fluctuations, etc.
– cannot be diversified away
•
Unsystematic risk
– affects specific investments
– caused by business, financial or liquidity risks
– can be diversified (or can it?) using a portfolio of
investments
Sources of property
investment risk
• Tenant risk
– Non-payment of rent or other contractual obligations
• Sector and geographical risk
– See return characteristics of property sectors and regions
– ‘Lumpiness’ of property investment accentuates this type of risk
– International diversification can ameliorate some of this type of risk
• Structural risk
– Future expenditure
– Prime much less prone
• Legal risk
– landlord and tenant legislation
– fiscal policy
• Planning
– Ownership
– other legislation; Sunday trading
• Location risk
Risk analysis
•
Despite widespread use of DCF appraisal
techniques, risk measurement is rare
•
Competition, globalisation and securitisition
pressures on property to align with other investment
classes
•
Traditionally, ARY accounts for risks associated
with a property investment
•
Investors are starting to quantify risk and allow for it
separately using methods used to analyse nonproperty investments
Risk-return analysis
1. Expected Net Present Value (ENPV)
Calculate NPV for each option using expected values for
variables in the cash flow. The likelihood of these values
being obtained are then quantified using probability
analysis
Period
Cash flow Discount rate 7%
DCF(£)
(£)
0 (1750000)
1
1750000
1
60000
0.9345
56070
2
80000
0.8734
69872
3
2000000
0.8160
1632000
NPV
7942
ENPV
Assume previous cash flow has probability of 40% and and that the
following outcomes and associated probabilities are deemed possible:
Period
0
1
2
3
4
NPV
(7% discount rate)
Period
0
1
2
3
NPV
(7% discount rate)
Cash flow (£)
(1750000)
50000
70000
90000
2000000
(42,895)
Probability 20%
Cash flow (£)
(1750000)
70000
90000
2000000
(26,021)
Probability 20%
Period
0
1
2
3
4
NPV
(7% discount rate)
Period
0
1
2
3
NPV
(7% discount rate)
Cash flow (£)
(1750000)
40000
60000
80000
2000000
(69,126)
Probability 10%
Cash flow (£)
(1750000)
80000
100000
2000000
(44,100)
Probability 10%
ENPV
Outcome (£)
(69,126)
(42,895)
7,942
26,021
44,100
Total
Probability
0.10
0.20
0.40
0.20
0.10
1.00
NPV x Probability
(6,913)
(8,579)
3,177
5,204
4,410
Expected NPV (2,701)
• Positive NPV using point estimate has become a negative
ENPV using probabilities
• Probability estimates are subjective but the process does focus
the mind on likelihood of achieving predicted returns
• Not a true measure of risk as it does not measure variation, just
a prediction for expected return, e.g. consider the two options
below
ENPV
Option A
NPV
(200)
300
500
ENPV
Probability Prob. x NPV
0.2
(40)
0.6
180
0.2
100
240
Option B
NPV
150
250
300
Probability
0.2
0.6
0.2
Prob. x NPV
30
150
60
240
Identical ENPVs but very different volatilities (150 for B and 700 for
A with a negative possibility)
Risk-return analysis
2. Probability analysis
Use Standard Deviation (SD) to evaluate risk
probability
probability
Option A
0.6
Option B
0.6
0.2
0.2
-200
300
500
outcome
150
250
300
outcome
Probability analysis
• SD for A is £233.24 and for B is £48.99 so B is less volatile
• ‘Coefficient of variation’ allows investments with different ENPVs
to be compared:
CoV = SD/ENPV
Risk-return analysis
3. Sensitivity analysis
• Examines change in NPV / IRR caused by changes
in key variables
• Usually a margin of 10-20% either side of the
expected values of key variables (rent, yield, etc) is
tested
• More sophisticated analysis may use more realistic
variations in the key variables or use different %
changes depending on the variable
• Does not consider the likelihood of particular
outcomes
Risk-return analysis
4. Scenario Modelling
• Combine possible values for key variables into
scenarios and examine effect on IRR / NPV
• Usually best, worst and realistic scenarios
• Focus on pessimistic scenario due to assumption of
risk aversity
• Can assign probabilities to scenarios
Scenario
Optimistic
Realistic
Pessimistic
FRV (£)
25,000
24,000
23,000
rental
growth (%)
ARY when Value (£)
sold (%)
9
4.25 578,000
8.25
4.35 525,000
7.5
4.5 459,000
Scenario modelling
Scenario
Probability
0
1
2
3
IRR
Boom
Normal
Recession
0.2
0.6
0.2
(10,000)
(10,000)
(10,000
5,500
5,000
4,000
6,000
5,500
4,000
6,400
6,000
4,000
37.8
28.8
9.7
Expected return = (0.2)(37.8) + (0.6)(28.8) + (0.2)(9.7)
= 26.8%
Scenario modelling
Economy
Boom
Steady
Slump
Probability
0.30
0.40
0.30
Estimated
Development
Return
35%
20%
5%
Scenario modelling
Return
35%
20%
5%
Probability
x
0.30
x
0.40
x
0.30
Expected Return
=
=
=
=
10.5%
8.0%
1.5%
20.0%
And
(Return – mean return)2 x Probability
(35% - 20%)2 x
0.30
=
67.5
(20% - 20%)2 x
0.40
=
0
( 5% - 20%)2 x
0.30
=
67.5
Expected Risk
=
135
= 11.62%
Risk-return analysis
5. Simulation
• Subjectively estimate values and associated probability
distributions for each key variable
• Computer program randomly selects a combination of
values in accordance with their probabilities and performs
appraisal (e.g. NPV / IRR calculation)
• Selection repeated many (1000) times with each value of
each variable selected according to its assigned
probability
• Mean snd standard deviation of the NPV/IRR calculates
and pattern of results graphically portrayed
Simulation
• @Risk or Crystal Ball
• Can enter ranges, standard deviations, correlations,
etc to model mean, variation
• e.g Rental value and exit yield standard deviations
based upon comparable ranges, growth forecast
ranges based on standard errors of forecasts, costs
based upon BCIS current costs and forecast ranges,
depreciation rate ranges based on past studies?
Basic process
• Build spreadsheet model
• Run simulation
• Analyse results
Defining model assumptions
• Types of data cells
– Assumption cells (numbers not formulae)
– Forecast cells
• Determine appropriate probability distribution for each
stochastic variable
• Define assumptions
• Specify correlations
Run simulation
• Forecast chart
– Can input % uncertainty, level of required figure...
Simulation parameters
• ERV refurbished 110,000 (SD 5,000)
• ERV existing 100,000 (SD 5,000)
• Exit yield 7.25% (SD 0.5%)
• Cost of refurbishment £750,000 (SD £50,000)
• Rental value growth 5% (SD 1%)
• Depreciation rate 2% (SD1%)
• Refurbishment cost growth 5% (SD 2%)
Simulation results
Forecast: Net Present Value
1,000 Trials
Frequency Chart
5 Outliers
.020
20
.015
15
.010
10
.005
5
.000
0
-£651,965
-£317,545
£16,876
£351,297
£685,717
Simulation results
Summary:
Display Range is from -£656,496 to £685,214
Entire Range is from -£956,130 to £755,757
After 1,000 Trials, the Std. Error of the Mean is £8,137
Statistics:
Trials
Mean
Median
Mode
Standard Deviation
Variance
Skewness
Kurtosis
Coeff. of Variability
Range Minimum
Range Maximum
Range W idth
Mean Std. Error
Value
1000
£15,920
£13,115
--£257,315
£66,211,084,541
-0.19
3.25
16.16
-£956,130
£755,757
£1,711,887
£8,137.02
Risk Free Rate Comparison
• What is the chance of getting less than the risk free
rate or return of 5%?
• Redo Appraisal at a 5% RF discount rate gives an NPV
of £674,357
• But real question is what chance of getting less than
5%?
• Answer is over 90% chance of beating 5%,
• 1SD means 84% chance of beating target which is
good enough even for risk averse investor
Risk Free Rate Analysis
Output at risk free rate
Statistic
Forecast values
Trials
1,000
Mean
£733,276
Median
£711,941
Mode
Standard Deviation
Variance
Skewness
Kurtosis
Coeff. of Variability
--£514,088
£264,286,052,100
0.06391
3.28
0.70108
Minimum
-£970,856
Maximum
£2,535,205
Mean Std. Error
£3,506,061
Risk analysis - summary
• Investors primarily concerned with level of return,
typically measured against a benchmark
• Less concerned with assessment of volatility of
returns
• Risk is regarded as the chance of not achieving
benchmark return
• Main measure of risk is standard deviation and focus
is always on downside potential