Dr K Patel, Department of Land Economy, University of Cambridge 1

Investment Method (Continue)Leasehold Interests✦ Leasehold are more complex than freehold investments (a) because of their limited

lives, and (b) because their investment characteristics depend on the terms of bothhead lease and the sub-lease.

✦ Ultimately all leasehold interests must come to an end with nil value, consequentlyan investor holding to the end of a lease must suffer a capital loss

✦ Equity type long-leasehold investments may have substantial growth potential overmuch of their lives.

✦ The profit-rental income of a leasehold investment is the difference between therental income received from sub-tenant and the head rent payable to the landlord.

Dr K Patel, Department of Land Economy, University of Cambridge 2

Value profiles of freehold and leasehold investments

ValueValue

Total

Total

Building

Land

TimeTime

Freehold Leasehold

Dr K Patel, Department of Land Economy, University of Cambridge 3

Annual Sinking Fund✦ The annual sinking fund may be used to calculate the annual amount to be

set aside to meet a known future liability or expense.✦ This is the annual sum, SF, required to be invested at the end of each year to

accumulate to £1 in n years at i compounded interest.✦ Since the present value of £1 is the reciprocal of the future amount of £1, so

that the Annual Sinking Fund is the reciprocal of the Future Amount of £1pa. That is

1i)(1i SF n −+

=

Dr K Patel, Department of Land Economy, University of Cambridge 4

Example: The owner of an office block anticipates that he willneed to provide a new escalator in 10 years’ time at an estimatedcost of £50,000. If the capital can be invested at 8%compounded interest, what amount should be invested annuallyto meet his future liability?

£3,450 0.069 x £50,000

1 - (1.08)

0.08 £50,000 SF 10

==

���

�=

Dr K Patel, Department of Land Economy, University of Cambridge 5

Dual Rate YP✦ Dual Rate YP is used for calculating the capital value of income that is to be

received for a known limited period. This will occur in land and property withleasehold interests that will expire on a specific date.

✦ Dual Rate YP is based on the assumption that the investor would annually set asidea sum out of the income received. This would be invested as a sinking fund torecoup the original capital value at the end of the term. The YP must reflect the factthat the investor has a lower spendable income than in the case of the perpetualincome.

✦ Assume that the net interest on £1 to be i and the annual sinking fund to recoup £1 atthe end of the limited term to be SF. Then the total income from property worth acapital value of £1 = i + SF. Assume the capital value of a stream of income to be P.Then the annual income required is P(i+SF). ButCapital value = Net Income per annum x YPSo that

SF)(i1

SF)P(iP YP

���

�

+=�

���

�

+=

Dr K Patel, Department of Land Economy, University of Cambridge 6

Note: With the sinking fund calculation there are two different rates of interest(i) i is the rate of interest expected by the investor (known as the remunerative rate of

interest)(ii) the rate of interest for SF is a low, risk-free rate (an accumulative rate of interest).Example: Calculate the capital value of an income £2,000 per annum receivable for 12

years given that the remunerative rate of interest is 6% and the accumulative rate is3%.

Net income per annum £2,000YP for 12 yrs @ 6%, 3% = 7.096

Capital value £14,192

10.03)(10.03 0.06

1 12 −+

+=

Dr K Patel, Department of Land Economy, University of Cambridge 7

The effect of Tax on the sinking fund element of the Dual Rate YP✦ The Net Income receivable from property is normally taxable. In the case of the

leasehold interest, the income is for a limited period and is subject to tax.✦ In this case the sinking fund element is increased by multiplying by the adjustment

factor [1/(1-x)].✦ The Dual Rate YP formula is adjusted to take account of this tax as follows:

where x = rate of tax (in pence)/100

���

�

−++

=

x- 11

1i)(1i i

1 YP

n

Dr K Patel, Department of Land Economy, University of Cambridge 8

Example: Source Baum & CrosbyA corner shop & dwelling house in a good shopping centre in the town. Thefreehold is let on a 99 years lease expiring in 36 years time at a ground rent of £10pa.The head lessee let the shop 16 years ago on a 21 year FR lease at a rent of £100 pa.The premises are now worth a rent of £180 pa on a FR lease.(a) FreeholderGround rent £10YP 36 yrs @ 4% 18.9083

£189Reversion to ERV £180YP perp. def 36 yrs. @ 5.5% 2.6455

£476Valuation £665

Dr K Patel, Department of Land Economy, University of Cambridge 9

(b) Head leaseholderRent received £100

Less Ground rent £10Profit rent £90YP 5 yrs @ 6%, 3% 4.0265

£362Reversion to ERV £180

Less Ground rent £10Profit rent £170

YP 36 yrs. def. 5 yrs. @ 7%,3% 7.923£1,346

Valuation £1,708

Dr K Patel, Department of Land Economy, University of Cambridge 10

(c) Sub-leaseholderERV £180

Less Rent paid £100Profit rent £80YP 5 yrs @ 8%, 3% 3.7264

Valuation £298

Dr K Patel, Department of Land Economy, University of Cambridge 11

Example: Dual Rate YP, tax-adjustedA leasehold interest has 20 years to run, subject to a fixed head rent of £100,000 pa. Thecurrent value is £200,000 pa, subject to 5-yearly reviews. Market evidence suggests afreehold capitalization rate k of 6% for this type of property.Rent received £200,000

Less Rent paid £100,000Profit rent £100,000YP 20 yrs @ 6%, 3%, tax 40% 8.195

i.e.1/[0.06+(0.03/((1.03)20 - 1)]x(1/0.6)£819,500

AnalysisYield = 6% x £819,500 = £49,170Sinking fund (gross) = £100,000 - £49,170

= £50,830Sinking fund (net) = £50,830 (0.60)

= £30,498x A £1 pa, 20 yrs @ 3% 26.8704Capital recouped £819,500

Dr K Patel, Department of Land Economy, University of Cambridge 12

Comments/Criticism✦ The capitalization rate (6% in the previous example): normally derived from

sales of comparable freehold and adjusted upwards to account for extra risk.✦ The accumulative rate of 3%: supposed to represent the net-of-tax return on

a guaranteed sinking fund to replace initial capital outlay on what is awasting asset.Bank deposits have earned considerably more than 3% safe rate since 1960.The initial capital outlay, regarded as an investment of cash ‘in a business’,is normally recouped out of investing in profit rents in similar investments.

✦ The tax adjustment: (40% in the previous example) counters the fact that anytax paying purchaser of the investment would lose a portion of his profit rentin tax. Without adjustment, the sinking fund would become inadequate.This may be the case for small-scale investors but not for tax exempt fundsor companies paying corporation tax.

✦ Trott 1980 in the RICS research report pointed out that different values ofthe three variables ( remunerative rate, accumulation rate and tax rate) maycombine to produce the same YP figure!

Dr K Patel, Department of Land Economy, University of Cambridge 13

Over-rented PropertiesIn the early 1990s rental values fell in nominal terms. According to IPD (1992) byMay 1992 70% of Central London offices were over-rented by an average of 35%.

Example: Baum & CrosbyA Central London office building is to be valued in June 1992. It was let on a 20-year FRI lease in 1990 with 5-year reviews passing rent of £2million pa. The ERVhas now fallen to £1million pa. The fully let rack rented capitalization is estimatedto be 8%. Gilts yielding approx. 10%.

Rent £2 m

ER £1 m

Years 17.75 Perpetuity

Dr K Patel, Department of Land Economy, University of Cambridge 14

Conventional approach: (i) capitalize the core income as if the property was fullylet at the appropriate ARY (ii) then capitalize the top-slice income for theunexpired term of the lease at a rate which reflects the fact that it is a fixed incomesupported by the upwards only rent review and is dependent on the tenant’s abilityto continue to pay the rent.Core incomeERV £1,000,000YP perp. @ 8% ARY 12.50

£12,500,000Top-slicePassing rent £2,000,000ERV £1,000,000Overage £1,000,000YP 17.75 yrs. @ 13% 6.8135

£6,813,459Valuation £19,313,459

Dr K Patel, Department of Land Economy, University of Cambridge 15

There are two problems with the conventional approach:✦ If the ARY implies long-term rental growth (which is the case with 8% yield) then ERV

may rise to exceed the passing rent before the lease expires. Therefore, it may be incorrectto capitalize the top-slice income for the whole of the unexpired term.

✦ Capitalizing the top-slice ignores the rental growth implied by the ARY.

If it is assumed that the overage is eliminated by the review in 12.75 years time, then theterm of 12.75 years could be valued at a risk-free rate subject to a risk premium and thereversion valued at the ARY.Term rent £2,000,000YP 12.75 yrs @ 13% 6.0731

£12,146,170Reversion to ERV £1,000,000YP perp. def. 12.75 yrs @ 8% 4.685

£4,685,513 £16,831,683

Dr K Patel, Department of Land Economy, University of Cambridge 16

Shortcomings✦ There is a problem with the yield choice on the reversion in that the 8%

yield (in the previous example) implies that rental growth is anticipatedevery 5 years. The PV relates to the behaviour of the ERV in the waitingperiod. The ERV grows continually and therefore the reversion should bedeferred at a lower yield to imply a better growth potential.

✦ Theoretically the growth potential of reversionary properties is greaterthan for the fully let properties. However, the market does not perceivereversions in this light and it is rear for a reversionary property to bevalued at an equivalent or average yield which is lower than the all risksyield of the fully let property.

Dr K Patel, Department of Land Economy, University of Cambridge 17

Purchases with a Special Interest: A purchaser who can afford to pay more thanother investors because of creation of marriage value.Marriage value will occur if: (i) two or more legal interests are merged in the sameproperty (ii) two or more adjacent pieces of land in separate ownership are mergedinto one ownership.Example: Nos 1, 2 & 3 Church Street are shops with living accommodation over asfollows

No. Freeholder Net rack Occupier & Details of any lease rental value pa type of shop

1 Mr D £3,000 Mr D (Grocer)

2 Mr H £3,500 Mr W Let to Mr W on an internal repairing (Hardware) lease with 5 yrs. unexpired at a rent

of £2,500 pa 3 Mr S £3,300 Mr B Let to Mr B on an internal repairing

(book shop) lease with 10 yrs. unexpired at a rent of £3,000 pa

Dr K Patel, Department of Land Economy, University of Cambridge 18

Mr D plans to acquire freehold interests in shops 2 & 3. The shops would cost£25,000 to alter and convert into a supermarket, giving a net rack rental of £16,000pa. Value all the interests, and advise Mr D as to the gain he will enjoy by themerger of interests.Value of the supermarket assuming a freehold yield of 7%Net rack rental value pa £16,000YP in perp. @ 7% 14.28

£228,480Less cost of alteration £25,000Capital Value £203,500 (approx)

Shop No. 1 Mr D’s interest assuming a freehold yield let at a rack rent of 8%Net rack rent pa £3,000YP in perp. @ 8% 12.5Capital value £37,500

19

Shop No. 2 Mr H’s interest assuming a freehold yield let at a net rack rent of 8% andexternal repairs & insurance cost of £440 pa.Unexpired term lease in 5 yrs.Rent pa £2,500

Less external repair pa £440Net Income £2,060YP 5 yrs @ 15% 3.352

£6,905ReversionNet rack rental value pa £3,500YP perp. Def. 5 yrs @ 8% 8.507

£29,774Capital value £36,700 (approx)Mr W’s interest assuming a leasehold yield of 9%, external repairs & insurance cost of £440pa, sinking fund of 2 ½ % and tax 30%.Rack rental value £3,500

Less external repairs & insurance pa £440Less rent paid pa £2,500

Profit rent £1,440YP 5 yrs. @ 9%, 2½% & tax 30% 2.764Capital value £4,000 (approx)

20

Shop No.3 Mr S’s interest assuming a freehold yield of 8% let on a net rack rent and externalrepairs & insurance cost of £400 pa.Unexpired term of lease is 10 yrs.Rack received pa £3,000

Less external repairs & insurance pa £440Net income pa £2,600YP 10 yrs. @ 15% 5.019Capital value £13,049ReversionNet rack rental value pa £3,300YP in perp. Def 10 yrs @ 8% 5.79

£19,107Capital value £32,150 (approx)

Mr B’s interest assuming a yield of 9%, external repairs & insurance of £440 pa, sinking fund of2 ½ % and tax 30%.Net rack rental value pa £3,700

Less external repairs & insurance £400Profit rent £700YP 10 yrs @ 9%, 3% and tax 30% 4.597Capital value £3,200 (approx)

Dr K Patel, Department of Land Economy, University of Cambridge 21

SummaryValue of the supermarket £203,500LessMr D’s interest £37,500Mr H’s interest £36,700Mr W’s interest £4,000Mr S’s interest £32150Mr B’s interest £3,200

£113,550Marriage value £89,950

Mr D will enjoy a gain on the merger of the interests of £89,950. Hecan use this surplus to ‘over-bid’ any other investors who may wish topurchase the interests in shops 2 and 3.