Chapter 6:Investment Method
Answers
Property Valuation, Second Edition. Peter Wyatt.
© 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd.
ARY INVESTMENT VALUATIONS
Rack-rented investment valuations
Answer 1
Market rent / £50,000YP in perp / @ / 7% / 14.2857
Valuation (gross of costs) / £714,286
Valuation (net of costs) / £675,448
Answer 2
Market rent / £500,000Less 10% for external repairs / -£50,000
Net market rent / £450,000
YP in perp / @ / 8% / 12.5
Valuation (gross of costs) / £5,625,000
Valuation (net of costs) / £5,319,149
Reversionary investment valuations
Answer 1
TermRent Passing / £50,000
YP / 4.00 Yrs / @ / 6% / 3.4651
Reversion
Market Rent / £60,000
YP in perp / @ / 6% / 14.2857
PV / 4.00 Yrs / @ / 6% / 0.7630
£653,738
Valuation (gross of costs) / £826,993
Valuation (net of costs) / £782,026
Answer 2
a) Term and Reversion Approach:
TermRent Passing / £10,000
YP / 4.00 Yrs / @ / 5% / 3.546
£35,460
Reversion
Market Rent / £15,000
YP in perp / @ / 6% / 16.667
PV / 4.00 Yrs / @ / 6% / 0.7921
£198,030
Valuation (gross of costs) / £233,490
Valuation (net of costs) / £220,794
b) Core and Top Slice:
CoreCore Rent / £10,000
YP in perp / @ / 6% / 16.667
£166,667
Top Slice
Top Slice Rent / £5,000
YP in perp / @ / 7% / 14.2857
PV / 4.00 Yrs / @ / 7% / 0.763
£54,492
Valuation (gross of costs) / £221,160
Valuation (net of costs) / £209,135
Answer 3
a) Term and Reversion:
TermRent Passing / £10,000
YP / 2.00 Yrs / @ / 8% / 1.7833
£178,330
Reversion
Market Rent / £125,000
YP in perp / @ / 9% / 11.1111
PV / 24.00 Yrs / @ / 9% / 0.842
£1,169,433
Valuation (gross of costs) / £1,347,763
Valuation (net of costs) / £1,274,480
b) Core and Top Slice
CoreCore Rent / £100,000
YP in perp / @ / 9% / 11.1111
£1,111,111
Top Slice
Top Slice Rent / £25,000
YP in perp / @ / 10% / 10
PV / 2.00 Yrs / @ / 10% / 0.8264
£206,612
Valuation (gross of costs) / £1,317,723
Valuation (net of costs) / £1,246,074
c) (Answer not available)
Equivalent Yield
Answer 4
Zone / Frontage / Depth / Ratio / ITZAA / 5 / 6 / 1 / 30
B / 5 / 6 / 0.5 / 15
C / 5 / 6 / 0.25 / 7.5
1st floor sale / 5 / 0 / 0.1 / 0
1st floor storage / 5 / 4 / 0.05 / 1
ITZA sq.m / 53.5
Rent ITZA sq.m / £2,500
MRV / £133,750
Apply comparable information to obtain MRV
TermRent Passing / £107,000
YP / 2.25 / yrs / @ / 6.00% / 2.0479
£219,126
Reversion
Market Rent / £133,750
YP in perp / @ / 6.00% / 16.6667
PV / 2.25 / yrs / @ / 6.00% / 0.8771
£1,955,259
Valuation (gross of costs) / £2,174,385
Valuation (net of costs) / £2,055,184
Leasehold interests with a fixed profit rent
Answer 1
Leasehold InterestRent received / £12,500
Less rent paid / £10,000
Profit rent / £2,500
YP / 8 Yrs / @ / 8% / 5.7466
Valuation (gross of costs) / £14,367
Valuation (net of costs) / £13,586
Rent received / £12,500
Less rent paid / £10,000
Profit rent / £2,500
YP / 8 Yrs / @ / 8% & 4% / 5.3043
Valuation (gross of costs) / £13,261
Valuation (net of costs) / £12,540
Sub-leasehold Interest
Market Rent / £16,000
Less rent paid / £12,500
Profit rent / £3,500
YP / 8 Yrs / @ / 8.5% / 5.6392
Valuation (gross of costs) / £19,737
Valuation (net of costs) / £18,664
Answer 2
a) Fixed Term Income Valuation
Dual rate YP:
= 3.7398 x 9,000= £33,658
The annual income must cover return on capital at 9% and a return of capital at 6% over the five year term. The capital value (price paid) is £33,658 and a 9% return is £3,029 per annum. The annual income is £9,000; £3,029 of this is return on capital at 9% so the remaining £5,971 is return of capital at 6%. The return on capital can be checked by compounding the five annual payments of £5,971 to see what they amount to:
Amount £1 pa:
= 5.6371 x 5,971= £33,659
Note that the dual rate introduces a different rate of return. Previously the investor’s return was on capital outstanding from year-to-year at the return on capital rate. The dual rate assumes a return on initial capital throughout. Thus the five amounts of £5,971 have to be assumed to be reinvested in a sinking fund accumulating at 6% pa.
b) If a sinking fund is taken out in practice, tax may be payable on the interest earned so the gross accumulative rate must be reduced to a net accumulative rate. This is done by applying a tax adjustment factor (1-t) to the gross rate, where t = tax rate. Tax also affects income from property investments but, as tax positions of investors vary, net-of-tax comparisons may be meaningless. Therefore the remunerative rate is a gross rate. But the accumulative rate must replace capital outlay and the effect of tax cannot be ignored.
So, dual rate YP adjusted for tax:
In other words the sinking fund is ‘grossed up’ to allow for tax deduction and still recoup capital outlay.
DCF INVESTMENT VALUATIONS
Rack-rented freehold investments
Answer 1
Analysis of comparable:
£75,000 = 0.05 = 5% £1,500,000
The property is rack rented, i.e. the rent passing is equal to the Market Rent. Market evidence indicates that a 5% yield is appropriate for the subject property. Similar properties which are also rack rented are having their rents capitalised at 5%, therefore this would seem appropriate for the subject property.
Valuation:
Rent Passing/Market Rent / £50,000YP in perp / @ / 5% / 20
Valuation (gross of costs) / £1,000,000
Valuation (net of costs) / £945,627
In simple terms, the comparable sold for an income multiplier of 20, this is the best market evidence and therefore the same multiplier should be applied to the subject property.
Answer 2
Period / Rent / YP @ 9% / Future Value / PV @ 9% / NPV1 - 3 / £150,000 / 2.5313 / £379,694 / n/a / £379,694
4 - 6 / £161,534 / 2.5313 / £408,889 / 0.7722 / £315,737
7 - 9 / £173,954 / 2.5313 / £440,329 / 0.5963 / £262,554
10 - 12 / £187,329 / 2.5313 / £474,186 / 0.4604 / £218,328
13 - 15 / £201,733 / 2.5313 / £510,646 / 0.3555 / £181,553
16 - perp / £217,245 / 18.1818* / 0.2745 / £1,084,399
Total discounted value / £2,442,265
* YP in perpetuity @ 5.5%
Reversionary freehold investments
Answer 1
a)None of the above - £400,000*(1.03) = £412,000
b)None of the above - £400,000*(1.03)^6 = £477,621
c)£6,817,300
See below;
1 / £300,000 / £300,000 / 0.9259 / £277,7782 / £412,000 / £412,000 / 0.8573 / £353,224
3 / £412,000 / £412,000 / 0.7938 / £327,059
4 / £412,000 / £412,000 / 0.7350 / £302,832
5 / £412,000 / £412,000 / 0.6806 / £280,400
6 / £412,000 / £7,960,349 / £8,372,349 / 0.6302 / £5,276,000
d) All of the above statements are false
Answer 2
TermRent passing / 785,000
YP / 10 / yrs / @ / 7.00% / 7.0236
5,513,512
Reversion
MR / 750,000
Amt £1 / 10.00 / yrs / @ / 2.20% / 1.24
Projected MR / 932,443.47
YP in perp / @ / 5.0% / 20.0000
PV / 10.00 / @ / 7.0% / 0.50835
9,480,140
Valuation (gross of costs) / 14,993,651
Valuation (net of costs) / £14,178,393
FULL DCF, ARY & SHORT-CUT DCF VALUATIONS
Answer 1
Analysis of comparable evidence to calculate:
(a)MR of comparable property:
- Initial yield of 5%
- Sale price of £300,000 = £15,000 pa
(b)ERV of the subject property:
Comparable:
Zone / Width / Depth / Zone / ITZAA / 5m / 6m / 100% / 30
B / 5m / 6m / 50% / 15
Total / 45 sqm
Rental Value / £333.33 psqm ZA
Subject:
Zone / Width / Depth / Zone / ITZAA / 5m / 6m / 100% / 30
B / 5m / 6m / 50% / 15
C / 5m / 3m / 25% / 3.75
Total / 48.75 sqm
Rental Value / £16,250 pa
(c)To calculate growth rate implied by the initial yield of the comp given a target rate of return of 11% and a five year review pattern:
g=
g=1.06554564 – 1
g=0.06555 or 6.555%pa.
Therefore, the implied growth rate is 6.555%
Valuation:
Years / Rent / Growth @ 6.56% / Projected Rent / YP @ 11% / PV @ 11% / PV0 - 2 / £10,000 / 1.0000 / £10,000 / 2.4437 / 1.0000 / £24,437
3 - 7 / £16,250 / 1.2098 / £19,659 / 3.6959 / 0.7312 / £53,128
8 - 12 / £16,250 / 1.6618 / £27,004 / 3.6959 / 0.4339 / 343,305
13 - / £16,250 / 1.2828 / £37,096 / 20.000 / 0.2575 / £191,042
Valuation (gross of costs) / £311,912
Valuation (net of costs) / £294,952
Answer 2
a) Full DCF Valuation
Comparable (28 Stall Street)
Zone / Width / Depth / Zone / ITZAA / 7m / 6m / 100% / 42
B / 7m / 6m / 50% / 21
C / 7m / 5m / 25% / 8.75
Total / 71.75 sqm
Rental Value / £265.50 psqm ZA
Subject (24 Stall Street)
Zone / Width / Depth / Zone / ITZAA / 8m / 6m / 100% / 48
B / 8m / 6m / 50% / 24
C / 8m / 3m / 25% / 6
Total / 78 sqm
Rental Value / £20,709 pa
Initial yield estimate:
From the comparable it can be estimated that the initial yield is 6% (£19,050pa/£317,500).
Annual growth rate estimate:
The annual growth rate implied by an initial yield of 6% and a target return of 11% given a 5 year rent review pattern is calculated using the formula: g = 0.05571 or 5.57%pa
DCF Valuation:
Years / Rent / Growth @ 6.56% / Projected Rent / YP @ 11% / PV @ 11% / PV0 - 2 / £16,000 / 1.0000 / £16,000 / 2.4437 / 1.0000 / £39,099
3 - 7 / £20,709 / 1.1766 / £24,366 / 3.6959 / 0.7312 / £65,848
8 - 12 / £20,709 / 1.5430 / £31,954 / 3.6959 / 0.4339 / £51,243
13 - 17 / £20,709 / 2.0234 / £41,903 / 3.6959 / 0.2575 / £39,879
18 - / £20,709 / 2.6534 / £54,949 / 16.667 / 0.1528 / £139,940
Valuation (gross of costs) / £336,008
Valuation (net of costs) / £317,738
b) ARY Check with traditional method:
TermRent Passing / £16,000
YP / 3.00 Yrs / @ / 5% / 2.7232
£43,571
Reversion
Market Rent / £20,709
YP in perp / @ / 6% / 16.6667
PV / 3.00 Yrs / @ / 6% / 0.8396
£289,802
Valuation (gross of costs) / £333,373
Valuation (net of costs) / £315,246
Alternatively, short-cut DCF:
TermRent Passing / £16,000
YP / 3.00 Yrs / @ / 11% / 2.4437
£39,099
Reversion
Market Rent / £20,709
Amt £1 / 3.00 Yrs / @ / 5.57% / 1.1766
YP in perp / @ / 6% / 16.6667
PV / 3.00 Yrs / @ / 11% / 0.7312
£296,946
Valuation (gross of costs) / £336,045
Valuation (net of costs) / £317,773
Answer 3
77 High Street MR£27,282 pa
81 High Street ARY9%
Target rate12%
Growth rate 3.55% pa
a) Term and Reversion ARY method:
TermRent Passing / £22,000
YP / 2.00 Yrs / @ / 8% / 1.7833
£39,233
Reversion
Market Rent / £27,282
YP in perp / @ / 9% / 11.1111
PV / 2.00 Yrs / @ / 9% / 0.8417
£255,147
Valuation (gross of costs) / £294,380
Valuation (net of costs) / £278,374
b) Short-cut DCF:
TermRent Passing / £22,000
YP / 2.00 Yrs / @ / 12% / 1.6901
£37,182
Reversion
Market Rent / £27,282
Amt £1 / 2.00 Yrs / @ / 3.55% / 1.0723
YP in perp / @ / 9% / 11.1111
PV / 2.00 Yrs / @ / 12% / 0.7972
£259,114
Valuation (gross of costs) / £296,296
Valuation (net of costs) / £280,185
LEASEHOLD INVESTMENTS
Answer 1
a)Since the rent review is in one month, grow the current rent for 5 years at 2% p.a. to determine likely market rent. There is one more review due in five years’ time, and both leases will expire in ten years’ time. Therefore the projected future rental income from sub-lease is:
Amount of £1 @ 2%...
For 5 years1.104
For 10 years 1.219
Projected rent at forthcoming review: £246,210
Projected rent at subsequent review (in 5 yrs):£271,816.
Target Rate of Return Say, 11% (7% +4%)
(gilt yield plus mark up for property risk premium plus leasehold interest)
Periods / Income / Less head rent / Cash flow / YP single rate / PV £1 / PV1 – 5 / £246,210 / £10,000 / £236,210 / 3.650 / 1 / £862,167
6 – 10 / £271,816 / £10,000 / £261,816 / 3.650 / 0.580 / £554,264
Total / £1,416,431
b)Dual rate without tax due to tax exempt status of pension fund:
VARIABLE / ANALYSISRemunerative rate / ARY marked up by 1 to 2%, say 1½% = 10½%
Accumulative rate / Base lending 4.75%; sinking fund may pay no more than say 3%
YP dual rate / 10½%, 3%, 10 years
Profit rent / Inflated rent less head rent = £236,210 p.a.
YP dual rate multiplier / 5.202
Value of head lease / £1,228,785
(c)Comparison of two valuations:
DCF has produced higher value partly because has built in rental growth at next review. Dual rate method heavily dependent on adjustment to remunerative rate, which is subjective, and method is flawed because using freehold yield and uses sinking fund at unrealistically low rate to mimic a freehold investment.
Answer 2
a)Lease expires in 20 years time, sub-let on a 25 year lease five years ago, therefore, 20 years unexpired and the rent was recently reviewed.
Amount of £1= 1.0155
=1.0773
YP Single Rate =
= 3.433
Years / Current Rent / Rental growth@ 1.5% / Projected
Income / Head
Rent / Cash
Flow / YP @ 14% / PV £1
@ 14% / PV
0-4 / £345,000 / 1 / 1 / £15,000 / £330,000 / 3.433 / 1 / £1,132,890
5-9 / £345,000 / 1.0773 / 1.0773 / £15,000 / £356,669 / 3.433 / 0.519 / £635,487
10-14 / £345,000 / 1.1605 / 1.1605 / £15,000 / £385,398 / 3.433 / 0.270 / £357,229
15-19 / £345,000 / 1.2502 / 1.2502 / £15,000 / £416,349 / 3.433 / 0.140 / £200,106
Valuation / £2,325,712
b)Dual rate calculation:
Adjust freehold ARY upwards to reflect additional risk of a LH investment
YP dual rate at say 13% remunerative rate and 4% accumulative rate, no tax, 20 years unexpired
Profit rent = £345,000 - £15,000 = £330,000 p.a.
YP dual rate = 1 = ? x £330,000 = £?m
0.13 + [ 0.04 ]
[(1.04)20 -1]
c)Comment on difference between the valuations:
- Cash flow gives higher value???
- Cash flows from LH investment dealt with differently.
- Refer to use of TRR and LH target rate.
- Dual rate uses growth equivalent yield reduced by sinking fund component.