Investment Valuations

FLEXI-LEASES

Valuation of flexi-leases• Greater uncertainty requires valuers to consider probability of various outcomes:

– Will tenant renew short lease?– Will break be exercised?– Will there be a rent void, how long will it be?– What will terms of new lease be?– What will the covenant strength of the tenant be?

• Financial impact will depend on:– Length of lease– Terms of break– State of market

• Valuation issues:– Comparables harder to find– Temptation to focus on worst-case scenario– Risk of double-counting risk

• Valuation techniques:– ARY

• Yield adjustment• Insert rent void

– DCF• Short-cut• Full

– Modelling, probability analysis…

Valuation of flexi-leases- Yield adjustment

• A modern office property has just been let on a 15-year FRI lease at a market rent of £50,000 per annum with five-year rent reviews. There is a break option in the tenant’s favour in year five, just before the rent review (to prevent the tenant from using it as a bargaining tool). Comparable evidence suggests that rack-rented office investments let on 15-year FRI leases with five-year rent reviews to market rent sell at prices that generate initial yields of around 7%.

Market rent (£) 50,000

YP perpetuity @ 8% 12.5

Valuation (£) 625,000

Valuation of flexi-leases- Rent void using ARY

Market rent – first lease (£) 50,000 YP 5 years @ 7.5% 4.0459 202,950 Market rent – new lease (£) 50,000 YP perpetuity @ 7.5% 13.33 PV 6 years @ 7.5% 0.6480 432,000 Valuation (£) 634,950

On a standard lease a rent of £50,000 per annum and a yield of 7.5% would produce a valuation of £666,667

Valuation of flexi-leases- Rent void using DCF• Long-term gilts currently yield 8% and a typical property

risk premium is 2%• Assuming a target rate of return of 10% and an ARY of

7.5%, this implies a growth rate of 2.88% per annum

Year Net cash-flow (£)

Implied growth rate

of 2.88%

Estimated cash flow (£)

PV £1 @ target rate

of 10%

Discounted income (£)

1 50,000 1.0000 50,000 0.9091 45,455 2 50,000 1.0000 50,000 0.8264 41,322 3 50,000 1.0000 50,000 0.7513 37,566 4 50,000 1.0000 50,000 0.6830 34,151 5 50,000 1.0000 50,000 0.6209 31,046 6 0 0.0000 0 0.0000 0 7 50,000 1.1857 59,286 0.5132 30,423 8 50,000 1.1857 59,286 0.4665 27,658 9 50,000 1.1857 59,286 0.4241 25,143

10 50,000 1.1857 59,286 0.3855 22,858 11 50,000 1.1857 59,286 0.3505 20,780

11-perp 50,000 1.3666 911,065 0.3505 319,323 Valuation (£) 13.3333 635,723

OVER-RENTED PROPERTY

Over-rented property• Valuation issues

– Properties let at rent > market rent– Includes properties let at ‘headline’ rents

• Valuation techniques– ARY

• Value rent passing in perpetuity at an ‘adjusted’ ARY if the lease is long contains upward-only rent reviews and no break clause

• Because overage is more risky, use a modified core and top-slice (layer) method

– DCF• Allows explicit estimation of length of void period

Over-rented property- modified core and top-slice

Value a property let four years ago at a rent of £250,000 per annum on a 15-year lease with five-year upward-only rent reviews. The current market rent is £200,000 per annum. Comparable properties have recently sold for yields averaging 6%.

Core (market) rent (£) 200,000 YP in perpetuity @ 6% 16.6667 3,333,340 Top-slice (overage) (£) 50,000 YP 11 years @ 7% [a] 7.4987 374,935 Valuation (£) 3,708,275

[a] Gilt yield plus a 2% risk premium

But…

Over-rented property- modified core and top-slice

• There is a lack of evidence on which to base the overage yield

• No attempt has been made to estimate the length of time that the property will remain over-rented.

Many valuers capitalise the overage for the whole period that the tenant is contracted to pay it, but the market rent may overtake the contract rent before the end of the lease and part of the overage is capitalised twice – the property will be over-valued

(End of lease)

Top layer capitalised at overage yield

Bottom layer capitalised at ARY

Income that is capitalised twice

Rent

0 1 6 11

Projected market rent

Time

Over-rented property- Short-cut DCF

Using a growth rate of 5.57% per annum (implied from ARY of 6% and target rate of 11%) the market rent will grow to the following amounts at the next two rent reviews:

£200,000 x (1+0.0557)1 = £211,140£200,000 x (1+0.0557)6 = £278,868

So market rent overtakes contract rent between first and second rent reviews.The growth-explicit short-cut DCF valuation is as follows…

Term (contract rent) (£) 250,000 YP 6 years @ 11% 4.2305 1,057,625 Reversion to market rent (£) 200,000 FV 6 years @ 5.57% 1.3843 YP in perpetuity @ 6% 16.6667 PV 6 years @ 11% 0.5346 2,466,828 Valuation (£) 3,524,453

The valuation is lower than the layer approach above because double-counting has not occurred

Over-rented property- Short-cut DCF

• Drawback of growth-explicit DCF is the lack of evidence to support rental growth rate

• Target rate may need to be adjusted to reflect covenant strength of tenant, length of remaining lease term and extent of overage

• In between reviews rent is only subject to tenant (default) risk and if the contract rent is very high in comparison to market rent for long periods (e.g. beyond the first rent review) then it is exposed to a greater degree of tenant risk. As such it may be more characteristic of a corporate bond-type investment issued by the tenant

IPD provide time series over 1, 5 and 10 years epochs by sector,

location & type

VALUATION UNCERTAINTY

Introduction• A valuation is not a permanent part of the property• Analysis of market data only suggests what happened in the past and it

is for the valuer to interpret these data to assess current market value• Values can be difficult to assess due to

– Heterogeneity of property– Paucity of market information – Large number of inputs / assumptions

• Disparity in valuations of the same property is valuation variance• Discrepancy between a valuation and exchange price is valuation

inaccuracy• Valuation uncertainty acknowledges the fact that valuation variance

and inaccuracy are inevitable and influenced by type and location of property

Valuation accuracy• RICS / IPD annual study…• Ave difference of 10.9% (9.6% when weighted by sale price) between sale

prices and ‘adjusted’ valuations in IPD UK Annual Databank• 63.8% within +/-10%• 88.5% within +/-20%• 75% transaction prices > valuation (ave 6% higher) Why?

– MV definition precludes bids by special purchasers– Vendors may selectively dispose of properties– Vendors actively present assets to market– Growth assumptions in analysis not picking up true picture– Valuers conservative and backward-looking

• IPD contains prime properties so evidence more consistent; non-prime may include more variation and more incentives…

Valuation variance• How much variance?

– 9.53% from the mean valuation of each property (Hutchison et al, 1996)• Why?

– Client pressure, esp. mortgage lending vals (Kinnard et al, 1997)– Knowledge of the asking price or pending sale price (Gallimore and

Wolverton, 1997)– ‘Behavioural characteristics’ of the valuer (Bretten and Wyatt, 2001)

• Solution?– Red Book now contains stricter guidelines regarding

• external pressure• QA• Conflicts of interest

Variance and themargin of error• A means of establishing whether a valuer has been negligent?

– Singer & Friedlander v John D Wood and Company, 1977: +/-10% around the subsequent transaction price (or some other notion of ‘correct’ market value) would be permissible.

– In 38 High Court valuation negligence cases between 1977 and 1998• +/-10% (26.1%)• between 10% and 14.99% (30.4%).

• Why? (Crosby et al, 1998)– Expert witnesses are unfit to present themselves as ‘experts’– The margin of error principle and the ‘brackets’ applied are too onerous– Expert witnesses are being ‘influenced’ to produce a valuation to suit their

client’s need• But how is the ‘correct’ valuation reached?• The courts fail to examine the processes involved and focus instead on

the outcome

Valuation uncertainty• Current reporting (RICS GN5):

– Single estimate plus comment on• cause of the uncertainty and the degree to which it is reflected

in the reported valuation• robustness of the valuation, perhaps noting the availability and

relevance of comparable market evidence• Potential quantitative measures:

– Sensitivity analysis– Scenario testing and discrete probability modelling– Simulation and continuous probability modelling

Sensitivity analysis• Examines the degree of change in the valuation caused by a pre-

determined change in an input variable– One variable at a time

• Usually 10-20% either side of expected value but can be more realistic– Look at equivalent yield spreadsheet…

• £200k p.a. contract rent• £250k p.a. market rent• 7.96% equivalent yield

• Can see which inputs have greatest impact– Usually the ARY– Usually focus on downside shifts

Market information:All risks yield (ARY) 8.00%Market rent (£) 250,000Explicit growth rate 2%

Property information:Years to reversion (term) 4Term (contract) rent (£) 200,000Rent review period 5

Term & Reversion method:Term yield 7.00%Reversion yield 8.00%

Equivalent Yield method:Equivalent yield 7.96%

Core & Top-slice method:Core yield 8.00%Top-slice yield 8.50%DCF method (short-cut and full):Target rate of return 10.00%Implied growth rate 2.33%Exit yield 8.00%

Key VariablesMarket rent (£) 250,000

YP in perpetuity @ 8% 12.5000

Valuation (£) 3,125,000

Valuations

Year Net cash-flow (£)

Growth rate of 2.33%

Estimated cash flow

(£)

PV £1 @ target rate of 10%

Discounted

income

1 250,000 1.0000 250,000 0.9091 227,273

2 250,000 1.0000 250,000 0.8264 206,612

3 250,000 1.0000 250,000 0.7513 187,829

4 250,000 1.0000 250,000 0.6830 170,753

5 250,000 1.0000 250,000 0.6209 155,230

6 250,000 1.1221 280,526 0.5645 158,349

7 250,000 1.1221 280,526 0.5132 143,954

8 250,000 1.1221 280,526 0.4665 130,867

9 250,000 1.1221 280,526 0.4241 118,970

10 250,000 1.1221 280,526 0.3855 108,155

10-perp 250,000 1.2591 3,934,728 [a]

0.3855 1,517,008

Valuation (£) 3,125,000

Term (contract) rent (£) 200,000

YP for initial term of 4 years @ 7.96% 3.3150

662,995

Reversion to estimated MR (£) 250,000

YP in perpetuity deferred 4 years @ 7.96% 9.2457

2,311,416

Valuation (£) 2,974,411

Term (contract) rent (£) 200,000

YP for initial term of 4 years @ 10% 3.1699

633,973

Reversion to estimated MR (£) 250,000

Compounded over 4 years @ 2.33% pa 1.0965

PV £1 4 years @ 10% 0.6830

YP in perpetuity @ 8% 12.5000

2,340,481

Valuation (£) 2,974,454

Term (contract) rent (£) 200,000

YP for initial term of 4 years @ 7% 3.3872

677,442

Reversion to estimated MR (£) 250,000

YP in perpetuity @ 8% 12.5000

PV £1 4 years @ 8% 0.7350

2,296,968

Valuation (£) 2,974,411

Core rent (£) 200,000

YP in perpetuity @ 8% 12.5000

2,500,000

Top-slice: uplift to estimated MR (£) 50,000

YP in perpetuity @ 8.5% 11.7647

PV £1 4 years @ 8.5% 0.7216

424,455

Valuation (£) 2,924,455

Sensitivity Analysis

Variable % Change Value Change Valuation % Change

MR

-5% 237,500 2,858,840 -3.89%

- - 2,974,411 -

-10% 225,000 2,743,269 -7.77%

ARY

+5% 8.36% 2,826,143 -4.98%

- - 2,974,411 -

+10% 8.76% 2,691,038 -9.53%

Sensitivity analysis of reversionary freehold valuation(ARY equivalent yield)

Sensitivity Analysis

Sensitivity analysis of reversionary freehold valuation(Short-cut DCF)

Variable % change Value change Valuation % change in valuation

TRR

+5% 9.50% 2,970,854 -0.12%

- - 2,974,454 -

+10% 9.00% 2,967,146 -0.25%

MR

-5% 237,500 2,857,430 -3.93%

- - 2,974,454 -

-10% 225,000 2,740,406 -7.87%

RentalGrowth

-5% 2.21% 2,963,420 -0.37%

- - 2,974,454 -

-10% 2.10% 2,953,408 -0.71%

Sensitivity of CV of £17,500 p.a. rent to changes in ARY and TRR

exit yield of 10% exit yield of 8% exit yield of 8%

rental growth @ 5%pa rental growth @ 5%pa rental growth @ 3%pa

Yield / Return ARY Value Target rate value 1 Target rate value 2 Target rate value 3

1% £1,750,000 £1,112,204 £1,227,730 £878,797

2% £875,000 £923,973 £1,014,277 £734,949

3% £583,333 £773,236 £843,994 £619,474

4% £437,500 £651,933 £707,508 £526,294

5% £350,000 £553,829 £597,579 £450,703

6% £291,667 £474,081 £508,600 £389,047

7% £250,000 £408,915 £436,212 £338,478

8% £218,750 £355,383 £377,016 £296,766

9% £194,444 £311,167 £328,348 £262,163

10% £175,000 £274,447 £288,120 £233,288

11% £159,091 £243,780 £254,685 £209,051

12% £145,833 £218,024 £226,739 £188,586

13% £134,615 £196,271 £203,249 £171,202

14% £125,000 £177,792 £183,391 £156,348

15% £116,667 £162,006 £166,507 £143,580

16% £109,375 £148,444 £152,068 £132,541

17% £102,941 £136,726 £139,651 £122,941

18% £97,222 £126,546 £128,910 £114,546

19% £92,105 £117,653 £119,568 £107,163

20% £87,500 £109,843 £111,397 £100,637

Capital value of a £17,500 pa rental income using a range of ARYs and a range of target rates of return assuming 1) rental growth at 5% pa & an exit yield after 25 years of 10%, 2) growth 5% & exit yield 8% and 3) growth 3% &

exit yield 8%)

£0

£200,000

£400,000

£600,000

£800,000

£1,000,000

£1,200,000

£1,400,000

£1,600,000

£1,800,000

£2,000,000

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

%

Valu

e

ARY Value

Target rate value 1

Target rate value 2

Target rate value 3

Scenario testing

• Examines impact of simultaneous changes in input variables– Pessimistic– Realistic– Optimistic

• Look at rack-rented FH valuation using full DCF…– £250k p.a. MR– 10% TRR– 8% ARY/Exit yield– 2.33% p.a. implied growth rate– Use ‘scenarios’ option on the ‘tools’ menu…

• As with sensitivity analysis, no real sense of probability

Scenario testing• Discrete probabilities

– Subjectively derived– Not a proper measure of

variation (variance, standard deviation)

• Simplistic way of dealing with uncertainty

– Table shows two properties with the same weighted ave valuation but…

Property 1 Property 2

Valuation(£)

Prob-ability

Weightedvaluation

Valuation(£)

Prob-ability

Weightedvaluation

2,800,000 2% 56,000 -80,000 5% -4,000

3,000,000 18% 540,000 2,000,000 20% 400,000

3,125,000 60% 1,875,000 3,500,000 50% 1,750,000

3,200,000 15% 480,000 3,700,000 20% 740,000

3,300,000 5% 165,000 4,600,000 5% 230,000

Weighted average valuation (£)

3,116,000 Weighted average valuation (£)

3,116,000

Continuous probability modelling• Look at central tendency (mean, median, mode) and variation

(variance, standard deviation) in valuations (dependent variable)• Ask 50 valuers to value two properties:

– Property 1: mean = £3.2m, sd = £0.5m– Property 2: mean = £3.5m, sd = £1m

• Coefficient of variation = sd/mean (a measure of spread relative to the mean)

– Property 1: CoV = 15.63%– Property 2: CoV = 28.57%

• Property 1 is less volatile by sd and CoV measures• Need more data and need to assume valuations are normally

distributed• But this isn’t what happens in practice – instead we have one

valuation but variations in inputs…

Simulation

• How does variation in valuation inputs (the independent variables) affect the valuation?

• Use simulation program to– assign probabilities to inputs– run simulations of combinations of input values based on their

probability of occurrence– produce a probability distribution of valuation figure (with stats

that summarise this distribution: mean, sd, confidence range)• Involves a series of steps

1. Build valuation model and identify key input variables…– Short-cut DCF with and without a void at a break in year 5– ARY/Exit yield, MR and void period

Simulation2. Ascribe probability distributions to key inputs

– Break void: triangular distribution (most likely = 0.25 yrs, min = 0 yrs, max = 1.5 yrs)

– MR: normal distribution (mean = £50k, sd = £5k)– ARY: triangular distribution (most likely = 8%, min = 6.5%, max = 9%)

Normal(50000, 5000)

Valu

es x

10^

-5

Values in Thousands

0

1

2

3

4

5

6

7

8

35 40 45 50 55 60 65

< >5.0% 5.0%90.0%41.78 58.22

Triang(0.065, 0.08, 0.09)

Values in Thousandths

0

10

20

30

40

50

60

70

80

90

60 65 70 75 80 85 90 95

5.0% 5.0%90.0%69.33 86.46

Triang(0, 0.25, 1.5)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

-0.2

20

0.23

5

0.69

0

1.14

5

1.60

0

5.0% 5.0%90.0%0.137 1.194

Simulation– Construct correlation matrix…

3. Run simulation– Distribution of valuation outcomes generated by sampling

combinations of input values selected according to their probabilities of occurrence

4. Output

450 537.5 625 712.5 800

5% 90% 5% 530.6959 729.9083

Mean=623238.3

Distribution for Valuation (£)/R26

Valu

es in

10^

-6

Values in Thousands

0

1

2

3

4

5

6

7

Mean=623238.3

450 537.5 625 712.5 800