Suggested solutions to
practical exercises
Chapter 3
1. £450,000 × 231.5/189.4 = £550,026.36
= value now if just kept pace with inflation
As actual value is £600,000 the real gain in value is £49,973.64
This is £49,973.64 × 100/£450,000 = 11.1 real percentage gain from original sum invested
2. Red Company dividend = 0.09 × 50p = 4.5 pence
Red Company yield = 4.5 × 100/72p = 6.25%
Blue Company dividend = 0.06 × £1 = 6 pence
Blue Company yield = 6 × 100/82p = 7.317%
Conclusion is that Blue Company is paying higher yield by 1.067%
3. £18,275 × 100/£400,000 = 4.569%
4. £5,244 × 100/(10,000 × £8.37) = 6.265%
5. £850,000 × 100/£17,000,000 = 5%
Chapter 4
1. (1+0.035)7 = 1.272279
2. 1.082512 = 2.589017
× £250 = £647.25
3. 1.058 × £3,000 = £4,432.37
4. 1.0510 × £22,500 = £36,650.13
5. Return on investment minus expected average inflation rate
= 4% – 2.6% = 1.4% real gain per annum
(1.0147 – 1) × £1,000,000 = £102,213.40 total real gain compared to just keeping pace with inflationary
increases
= £102,213.40 × 100/£1,000,000 = 10.22% total real gain on investment over the 7 years
6. 1.0619 × £17,000 = £51,435.19
1.0615 × £25,000 = £59,913.95
Total now = £111,349.14
For use in conjunction with Michael Blackledge, Introducing Property Valuation. Routledge: London.
© 2009 Michael Blackledge
2 Introducing Property Valuation: Suggested solutions to practical exercises
7. 1.082 × £6,500 = £7,581.60
× 1.075 = current value = £10,633.59
8 Amount of £1 for 7 years @ 4.5% = (1+0.045)7 = 1.36086
× £50,000 = £68,043
Amount of £1 for 3 years @ 4.5% =(1+0.045)3 = 1.141166
× £60,000 = £68,470
Therefore, total saved in account today = £136,513
9. 1.064 × 1.055 × £12,000 = 1.061 × 1.055 × £15,000 = Total now in account = £19,335.31
£20,292.88
£39,628.19
10.1.0455 × 1.0556 × £50,000 = £85,914.45
1.0556 × £70,000 = £96,518.99
In 6 years from now total saved = £182,433.44
11. To calculate future rents it is necessary to allow for compound interest at the estimated annual growth rate
to be added to the current market rent. This is found by using the Amount of £1 table. Thus future rents
will be:
In 5 years = £40,000 × A £1 in 5yrs @ 2%
= £40,000 × 1.1041 = £44,164 per annum
In 10 years = £40,000 × A £1 in 10yrs @ 2%
= £40,000 × 1.219 = £48,760 per annum
In 15 years = £40,000 × A £1 in 15yrs @ 2%
= £40,000 × 1.3459 = £53,836 per annum
12. PV is the inverse or reciprocal of the Amount of £1 formula. Thus if Amount of £1 (A) is found, the present
value for the same time period at the same interest rate will be 1/A or 1/(1+i)n.
13. 1/1.042526 = 0.338862
14. £8,500 × 1/1.0331 = £3,399.89
15. £220,000 × 1/1.0918 = £46,638.62
16. £42,000 × 1/1.068 = £26,351.32
17. PV for 8 years @ 5% = 1/(1+0.05)8 = 0.67839
× £100,000 = £67,839 needs to be invested now to reach the target amount required in 8 years from now.
18. PV of £80,000 in 4.5 yrs @ 4.85% = £80,000 × 1/(1.0485)4.5
= £80,000/1.237563 = £64,644.57
19. 28 months = 28/12 = 2.333 years
£11,500 × 1/1.042.333 = £10,494.43
20. The £300,000 will not be received for 2 years. Thus, its present value today at 9% all-risks yield will be:
£300,000 × PV £1 in 2 years @ 9%
= £300,000 × (1/1.092)
= £300,000 × 0.8417
= £252,510
SAY Sale Price now = £252,500
21. £450,000 × 1/1.072525 = £78,213.19
For use in conjunction with Michael Blackledge, Introducing Property Valuation. Routledge: London.
© 2009 Michael Blackledge
3 Introducing Property Valuation: Suggested solutions to practical exercises
22.£10,500 × 1/1.0353 = £9,470.40
£8,000 × 1/1.0358 = £6,075.29
£12,000 × 1/1.03513 = £7,672.85
Total current value =£23,218.54
23. £78,000 × 100/£1,000,000 = 7.8%
24. £320,000 × 100/£4,000,000 = 8%
25. Amount of £1 per annum for 8 years @ 6% = (1.068 – 1)/0.06
= 9.897468
× £4,000 = £39,589.87 now in the account
26.1.047 × £50,000 = £65,796.59
£5,000 × (1.046 – 1)/0.04 =£33,164.88
Total now in account = £98,961.47
Chapter 5
1. 0.04/(1.046 – 1) = 0.150762
2. £150,000 × 0.03/(1.0312 – 1) = £10,569.31 per annum
3. £50,000 × 0.045/(1.0457 – 1) = £6,235.07 per annum
4. £80,000 × 0.0325/(1.032515 – 1) = £4,223.09 per annum
5. £75,000 × 0.0425/(1.042518 – 1) = £2,858.01 per annum
6. Net of tax asf rate = 5.5% × (100 – 40)/100 = 3.3%
£45,000 × 0.033/(1.0339 – 1) = £4,375.66 per annum
7. £4,000 × (1.04756 – 1)/0.0475 = £27,037.05 saved so far
1.056 × £27,037.05 = £36,232.23 will have been saved in 6 years from now as a result of the money
already invested.
This leaves a shortfall of £100,000 – £36,232.23 = £63,767.77
£63,767.77 × 0.05/(1.056 – 1) = £9,374.96 per annum needs to be invested for next 6 years to reach target.
8. This requires use of two formulae or tables from Parry’s: the Amount of £1 and the Amount of £1 per
annum.
£2,500 invested per annum for the past 9 years @ 3.75% will now amount to: A £1 per annum for 9 yrs
@ 3.75% × £2,500
9
£2,500 × (1.0375 – 1)/0.0375 = £26,187.50
This sum will continue to attract interest at 4 per cent before tax per annum for the next 3 years. But,
investor pays income tax at 40 per cent. Thus net-of-tax (after deduction of tax) the investor will have 60
per cent of 4 per cent interest left, that is (100 – 40)/100 = 0.6 multiplier
0.6 × 4% = 2.4% net asf rate.
So, original investment in 3 years’ time will amount to:
£26,187.50 × A £1 for 3 yrs @ 2.4% = £28,118.61
Target sum required is £50,000, so ‘shortfall’ = £21,881.39
Annual investment per annum for next 3 years to meet this target is found by: annual sinking fund (asf) for
3 yrs @ 2.4% × £21,881.39
= 0.32546 × £21,881.39 = £7,121.51 per annum
For use in conjunction with Michael Blackledge, Introducing Property Valuation. Routledge: London.
© 2009 Michael Blackledge
4 Introducing Property Valuation: Suggested solutions to practical exercises
Conclusion: the investor needs to invest £7,121.51 per year for the next 3 years in order to achieve her
target of a total sum of £50,000 in 3 years from now.
9. 5% × (100 – 28)/100 = 3.6% net asf rate
£60,000 × 0.036/(1.03611.333 – 1) = £4,380.96 per annum
10. (1.1315 × 0.13)/(1.1315 – 1) = £0.154742 per annum
11. £160,000 × (1.1118 × 0.11)/(1.1118 – 1) = £20,774.86 per annum
12. £250,000 × (1.07525 × 0.075)/(1.07525 – 1) = £22,427.67 per annum
13. £25,000 × (1.1255 × 0.125)/(1.1255 – 1) = £7,021.35 per annum
14. £190,000 × (1.08520 × 0.085)/(1.08520 – 1) = £20,077.48 per annum
15. £240,000 × (1.072522 × 0.0725)/(1.072522 – 1) = £22,149.16 per annum/12 = £1,845.76 per month
16. £3,852.74/((1.087510 × 0.0875)/(1.087510 – 1)) = £24,999.99
In other words a £25,000 loan.
17. First find the annual repayments: £15,000 × (1.126 × 0.12)/(1.126 – 1)
= £3,648.39 per annum
Then divide by the annuity £1 will purchase for 3 yrs @ 12% or multiply by the years purchase single rate
for 3 yrs @ 12%:
£3,648.39/((1.123 × 0.12)/(1.123 – 1)) = £8,762.82
or £3,648.39 × (1.123 – 1)/(1.123 × 0.12) = £8,762.82 to repay loan early
Chapter 6
1. YP perp number from each of these all risks yields is:
a. 5% = 20
b. 6% = 16.667
c. 7% = 14.286
d. 9% = 11.111
e. 11% = 9.091
f. 12.5% = 8
2. ARY% represented by the following YP perp numbers is:
a. 5 = 20%
b. 8 = 12.5%
c. 10 = 10%
d. 14.23 = 7%
e. 16.667 = 6%
f. 25 = 4%
3. £200,000 × 100/6.75 = £2,962,962.96
SAY = £2,963,000
4. £80,000 × 100/8.5 = £941,176.47
SAY = £941,200
5. £1,200,000 × 8/100 = £96,000 per annum
For use in conjunction with Michael Blackledge, Introducing Property Valuation. Routledge: London.
© 2009 Michael Blackledge
5 Introducing Property Valuation: Suggested solutions to practical exercises
6. Freehold valuation
Net income (MR) =
£150,000p.a.
× YP perp @ 7.5%
13.333
Market value =
£2,000,00
YP perp = 100/ARY
Client should offer £2 million for the freehold
7. Market rent (MR) = MV × ARY/100
Thus anticipated MR = £950,000 × 6.8/100
= £64,600 p.a.
8. Annual rate of return on property = All-risks yield (ARY)
ARY = MR × 100/MV
Thus: ARY = £175,000 × 100/£2.1M = 8.33%
9. (1.0915 – 1)/(1.0915 × 0.09) = 8.0606884
10. £60,000 × YP 3 yrs @ 7.25% = £156,743
SAY = £156,750
11. £87,500 × YP 2 yrs @ 11% = £149,846
SAY = £150,000
12. £200,000/£38,350 = YP for 10 yrs @ x% = 5.215123859
Look in Parry’s Tables for YP single rate and across the 10 years rows until a YP of this number or as close
to this as possible is found.
It will be seen that YP for 10 yrs @ 14% is 5.2161156 and is as close to number sought as to be of marginal
difference. Conclusion is that the investment has sold at a yield of close to 14 per cent.
13. YP single rate for 7 yrs @ 7.5%
= ((1.075)7 – 1)/((1.075)7 × 0.075) = 5.2966
Present value of £30,000 p.a. for 7 yrs @ 7.5% = £30,000 × 5.2966
= £158,898
SAY = £158,900
14. £2,000,000/YP 15 yrs @ 12% = £2M/6.8108645
= £293,648 per annum
15. 1/(1.136 × 0.13) = 3.694757903
16. £1,200,000/YP perp def 3 yrs @ 6% = £1,200,000/13.9936547
= £85,753 per annum
17. £400,000 × YP perp def 2 yrs @ 11% = £2,951,354
SAY = £2,9500,000
18. £60,000 × YP perp def 3 yrs @ 8% = £595,374
SAY = £595,000
19. YP 12 yrs @ 9% = 7.1607253
PV 4 yrs @ 9% = 0.7084252
YP × PV = 5.0728383 = YP for 12 yrs def 4 yrs @ 9%
20. YP single rate for 8 yrs @ 5%
= ((1.05)8 – 1)/((1.05)8 × 0.05) = 6.46321
PV for 2 yrs @ 5% = 1/(1.05)2 = 0.907029
For use in conjunction with Michael Blackledge, Introducing Property Valuation. Routledge: London.
© 2009 Michael Blackledge
6 Introducing Property Valuation: Suggested solutions to practical exercises
PV = £25,000 p.a. × YP for 8 yrs @ 5% × PV for 2 yrs @ 5%
= £146,558
SAY = £146,500
21. YP 8 yrs @ 7% = 5.9712985
PV 3 yrs @ 7% = 0.8162978
£90,000 × 5.9712985 × 0.8162978 = £438,692
SAY = £438,500
22. YP 5 yrs @ 5% = 4.3294767
PV 4 yrs @ 5% = 0.8227024
£70,000 × 4.3294767 × 0.8227024 = £249,330
SAY = £249,500
23. YP 25 yrs @ 8% = 10.6747762
PV 4 yrs @ 8% = 0.73502985
£300,000/(10.6747762 × 0.73502985) = £38,235 per annum
24. asf = 0.032/(1.0325 – 1) = 0.187603009
YP = 1/(0.08+0.187603009) = 3.73687875
25. £10,000 × YP for 7 yrs @ 10% + 4% = £44,129
SAY = £44,100
26. £26,500 × YP for 4 yrs @ 12% + 5% = £75,282
SAY = £75,300
27. Net asf rate = 7% × 0.6 = 4.2%
£25,250 × YP 7 yrs @ 14% + 4.2% (tax 40%) = £72,197
SAY = £72,200
28. Net asf rate = 6% × 0.8 = 4.8%
£39,000 × YP for 5 yrs @ 12% + 4.8% (tax 20%) = £112,352
SAY = £112,400
29. Net asf rate = 4.25% × 0.72 = 3.06%
Leasehold valuation
Rent receivable (market rent)=
£25,000 p.a.
Less rent payable=
£20,000 p.a.
Net profit rent=
£5,000 p.a.
× YP for 5 yrs @ 11.5% + 3.06% (tax 28%) 2.65752
Market value (assignment price) = £13,287
SAY = £13,300
30. Net profit rent =
£6,500 p.a.
× YP for 6 yrs @ 12% + 3.5% & tax @ 21% 3.1923 Market value (assignment price) = £20,750
31. YP for 6 yrs @ 9% + 3%= 4.0883492
PV for 3 yrs @ 9% = 0.77218348
YP for 6 yrs @ 9% + 3% (no tax) def 3 yrs = 3.15695571
32. YP for 10 yrs @ 11% + 3% (tax 30%)= 4.2623019
PV for 4 yrs @ 11% = 0.658730974
YP for 10 yrs @ 11% + 3% (tax 30%) def 4 yrs = 2.8077103
For use in conjunction with Michael Blackledge, Introducing Property Valuation. Routledge: London.
© 2009 Michael Blackledge
7 Introducing Property Valuation: Suggested solutions to practical exercises
33. Net asf rate = 6% × 0.6 = 3.6%
YP for 4 yrs @ 9% + 3.6% (tax 40%)= 2.0625805
PV for 2 yrs @ 9%= 0.84167999
YP for 4 yrs @ 9% + 3.6% (tax 40%) def 2 yrs = 1.7360323 × £42,00 = £72,900
Chapter 7
1. a. 4.7665397
b. 4.9733123
c. 4.8369963
2. £25,000 × 4.1904252 = £104,761
SAY = £104,750
3. 100 × (1.02254 – 1) = 9.308%
4. a.
£50,000 × 11.23136 = £561,568
SAY = £561,500
b. Net income=
× YP perp @ 6.25%
c.
£125,000
16.620
=
SAY =
p.a.
£2,077,533
£2.08 million
Net asf rate = 4% × 0.7 = 2.8%
Then using the formula, the YP can be calculated
£25,000 × YP for 5 yrs @ 9.5% + 2.8% (tax 30%) QIA = £70,371
SAY = £70,400
Chapter 8
1. a. 328 feet 1 inch (328’1”) or 109.36132 yards
b. 1,312 feet 4 inches (1,312’4”) or 437.4453 yards
c. 0.6213881 mile or 1,096.643 yards or 3,280 feet 11 inches (3,280’11”)
d. 3.1069409 miles or 5,468.2159 yards or 16,404 ft 6 in (16,404’6”)
2. a. 1,345.5328 square feet
b. 5,920.3444 square feet
c. 13,455.328 square feet
d. 123,789.02 square feet
e. 59.3032 acres
3. a. 3.81 metres or 38.1 centimetres or 3,810 millimetres
b. 5.0799997 metres
c. 7.0611997 metres
d. 6.4372 kilometres or 6,437.2 metres
e. 10.058125 kilometres
f. 44.25575 kilometres
g. 42.0888 hectares
h. 35.39625 cubic metres
For use in conjunction with Michael Blackledge, Introducing Property Valuation. Routledge: London.
© 2009 Michael Blackledge
8 Introducing Property Valuation: Suggested solutions to practical exercises
Chapter 10
1. Estimated market rent = 850 × £75 = £63,750 p.a.
ARY = MR × 100/MV
ARY = £63,750 × 100/£820,000
ARY = 7.77%
2. Comparable site has space for 1.5 × 33 = 49.5 dwellings
Site value per dwelling = £2,000,000/49.5 = £40,404
Subject has space for 1 × 40 = 40 dwellings
@ £40,404 each = £1,616,161
SAY = £1.62 million
3. MR = ARY × MV/100
MR = 5.25 × £3,000,000/100
Market rent = £157,500 per annum
/788 sq.m. = £199.87
SAY = £200 per sq.m. p.a.
4. Comparable = £217,000/3,100 = £70 psm
Thus rental value of subject = £70 × 2,750 sq.m. = £192,500 p.a.
5. Comparables:£185,000/600= £308.33 per sq.m. p.a.
£265,000/900= £294.44 per sq.m. p.a.
Subject property’s floor area is mid-way between these two comparables and it appears the market has made
a quantum adjustment for their respective sizes. Thus adopt average of the two comparable rents:
750 × £301.39 per sq.m. = £226,040
SAY market rent of office = £226,000 per annum
6. Analysis of ITZA
Zone A 16.5 × 6 = 99 @ x =
99
Zone B
16.5 × 6 = 99 @ 0.5x =
49.5
Zone C
16.5 × 6 = 99 @ 0.25x =
24.75
Zone D 16.5 × 2 = 33 @ 0 as non NIA =
0
GF Ancillary 16.5 × 7 = 115.5 @ 0.05x =
5.775
LG Sales =
260 @ 0.1x =
26
Mezz Sales =
270 @ 0.125x =
33.75
1st Flr stock =
302 @ 0.04x =
12.08
TOTAL ITZA (sq.m.) =
250.855
@ £60,000/sq.m
Market value= £15,051,300
SAY= £15 million
(on assumption VP value or property let at current market rent)
7. The return frontage will add to the value, but there is no single agreed approach on how this should be
assessed. It is possible to adopt a diagonal zoning method, working from the front corner of the unit and
using an average of the two zone A rental rates. The shop area will then be divided into triangular and
trapezium-shaped zones rather than rectangles. Alternatively, zoning can take place from both frontages
and highest figure per square metre adopted where zones overlap. However, this can lead to overvaluation.
More simply a percentage addition can be made as an ‘end allowance’ after the unit has been zoned in the
conventional fashion from the highest zone A rental frontage. It is also essential the ITZA rental used has
been derived in the same way as the method employed to value the subject premises.
Possible analysis of floor area (note 10 sq.m. deducted from zone C square measurements to allow for
non-NIA area):
For use in conjunction with Michael Blackledge, Introducing Property Valuation. Routledge: London.
© 2009 Michael Blackledge
9 Introducing Property Valuation: Suggested solutions to practical exercises
Zone
Frontage Depth Area Value
ITZA
A
12.5
6
75
1
75
B
12.5
6
75
0.5
37.5
C
12.5
4
40
0.25
10
Ground floor ancillary
130 0.05
6.5
Mezzanine floor sales
105 0.125
13.125
1st floor ancillary
285 0.04
11.4
Lower ground sales
170 0.1
17
Lower ground ancillary
150 0.04
6
ITZA =
176.525
Add end allowance for
Return frontage @ say 10%
17.6525
Total ITZA =
194.2
Total rent p.a. SAY =
£350,000
Rent psm ITZA p.a. =
£1,802.47
This rental assessment would apply if the subject was on the same terms as the comparables. However, there
are differences that require further adjustment:
Discount for longer lease length of 21 years= – 5%
Increase for longer rent review periods = +3%
Reduction for restrictive user clause = – 10%
Total of these adjustments =
– 12%
Reduce calculated rental by this amount = £350,000 × 0.88 = £308,000
Conclusion: recommended rent at review around £308,000 per annum.
8. A/E = cost of work/YP for number of years over which cost is to be ‘written off ’.
= £200,000/YP 20 yrs @ 11%
= £200,000/7.9633
= £25,115 per annum
Such a calculation is needed to calculate annual depreciation for accounts purposes or to find out what a
capital expenditure would equate to on an annual basis. It will be used when finding the ‘equivalent rent’
or ‘net effective rent’ for a property (as defined in RICS Red Book Valuation Information Paper No. 8:
The Analysis of Commercial Lease Transactions) from its ‘headline rent’. The headline rent is the sum
payable by the tenant, but this ignores the value of any ‘incentives’ incorporated in the lease agreement.
For comparison purposes and to find the ‘true’ market rent it is necessary to find the ‘equivalent’ rent (see
Chapter 16 for more information).
9. a.
b.
c.
£175,000/YP for 7 yrs @ 6% = £31,348.63 per annum
£185,000/YP for 5.5 yrs @ 7.25% = £41,976.92 per annum
Net asf rate = 5% × 0.72 = 3.6%
£225,000/YP for 8 yrs @ 9% + 3.6% & tax @ 28% = £54,651.38 per annum
10. Annual equivalent = Capital sum/YP
= £125,000/YP for 15 yrs @ 8%+3%(tax 40%)
AE = £125,000/5.8958
= £21,202 per annum
Chapter 11
1. YP perp deferred 2 yrs @ 6.2% = 1/((1.062)2 × 0.062) = 14.3007
PV = £90 × 750 sq.m. × YP perp def 2yrs @ 6.2% = £965,297
SAY value = £965,000
For use in conjunction with Michael Blackledge, Introducing Property Valuation. Routledge: London.
© 2009 Michael Blackledge
10 Introducing Property Valuation: Suggested solutions to practical exercises
2. Leasehold valuation
Rent receivable (market rent)=
£32,000 p.a.
Less rent payable=
£25,000 p.a.
Net profit rent =
£7,000 p.a
× YP for 4 yrs @ 9.50%
+ 3.0% & tax @ 40%
2.027 Market value (assignment price)= £14,188
SAY = £14,200
Freehold valuation
Term
Net income=
£25,000 p.a.
× YP for 4 yrs @ 7.00%
3.387
£84,680
Reversion to market rent
Net income=
£32,000 p.a.
× YP perp def 4 yrs @ 8.00%
9.188
= £294,012
Market value = £378,692
SAY = £379,000
• Freehold ARY on reversion assumed at 1.5 per cent lower than leasehold ARY as better investment
• Term yield reduced by 1 per cent to reflect additional security of income compared to market rent
3. Net asf rate = 5% × 0.72 = 3.6%. Say round down to 3.5%.
Leasehold valuation
Rent receivable (market rent)=
£250,000 p.a.
Less rent payable=
£200,000 p.a.
Net profit rent=
£50,000 p.a.
× YP for 5 yrs @ 8.50%
+ 3.5% & tax @ 28%
2.907
Market value (assignment price) = £145,348
SAY = £145,000
4. Net asf rate = 3.5% × 0.8 = 2.8%. SAY round down to 2.5% as next nearest in tables.
Leasehold valuation
Rent receivable (market rent)=
£100,000 p.a.
Less rent payable=
£50,000 p.a.
Net profit rent=
£50,000 p.a.
× YP for 5 yrs @ 7.00%
+ 2.5% & tax @ 20%
3.249
Market value (assignment price) = £162,439
SAY = £162,500
5. Analysis of the comparables:
Bannister House: £200/sq.m. but slightly smaller than subject although has 15 year term + 5-yearly rent
reviews
Coe House: £179.10/sq.m. but somewhat larger than subject and a straight 5 year term
Thus use say £195/sq.m. as current MR on subject property; giving market rent of £321,750 per annum
Freehold valuation of subject
Term
Net income
£250,000 p.a.
× YP for 3 yrs @ 6.5%
2.648 = £662,119
Reversion to market rent
£321,750 p.a.
× YP perp def 3 yrs @ 7.5%
10.733 = £3,453,281
Market value = £4,115,400
SAY = £4,110,000
For use in conjunction with Michael Blackledge, Introducing Property Valuation. Routledge: London.
© 2009 Michael Blackledge
11 Introducing Property Valuation: Suggested solutions to practical exercises
Initial yield = £250,000 × 100/(MV+purchase costs)
Assume costs @ 6% then initial yield = £250,000 × 100/£4,356,600
= 5.74%
Reversionary yield = £321,750/MV = 7.83%
Equivalent yield found from tables, formula or simple DCF/interpolation:
Years
Income × YP = DCF
1-3
£250,000
4-perp
£321,750
Calculated at 7.5% and say 6.5% and then results interpolated to find yield. Using conventional methods,
this can be achieved as follows:
Freehold valuation @ trial rate equivalent yield of 7.5%
Term
Net income
£250,000 p.a.
× YP for 3 yrs @ 7.5%
2.601
= £650,131
Reversion to market rent
Net income
£321,750 p.a.
× YP perp def3 yrs @ 7.5%
10.733 = £3,453,281
Market value = £4,103,412
SAY = £4,100,000
Freehold valuation at trial rate equivalent yield of 6.5%
Term
Net income
£250,000 p.a. × YP for 3 yrs @ 6.50%
2.648
£662,119
Reversion to market rent
Net income
£321,750 p.a.
× YP perp def 3 yrs @ 6.50%
12.736 = £4,097,853
Market value = £4,759,972
SAY = £4,760,000
‘True’ or ‘Target’ MV found from above = £4.11 million
MV @ 7.5% yield =
£4.1 million
MV @ 6.5% yield =
£4.76 million
Difference between MVs at two trial rates = £0.66 million
Difference between target MV and
MV at higher trial rate =
£0.01 million
Difference between the two trial rates = 1%
Thus equivalent yield = 7.5% – ((0.01 × 1%)/0.66) = 7.5% – 0.015%
= 7.48%
To prove this is correct, insert it back into a conventional valuation:
Freehold valuation
Term
Net income
£250,000 p.a.
× YP for 3 yrs @ 7.48%
2.601
£650,368
Reversion to market rent
Net income
£321,750 p.a.
× YP perp def 3 yrs @ 7.48%
10.768 £3,464,447
Market value = £4,114,815
SAY = £4,110,000
For use in conjunction with Michael Blackledge, Introducing Property Valuation. Routledge: London.
© 2009 Michael Blackledge
12 Introducing Property Valuation: Suggested solutions to practical exercises
6. First, assess the current market rent for each property:
Unit 1 measures 1,000 sq.m.
Unit 2 measures 2,000 sq.m.
Unit 3 measures 1,500 sq.m.
Comparables indicate rentals of £55 to £60 per sq.m. for similar units. Quantum adjustments to allow for
differing sizes of units normally show higher rentals per sq.m. for smaller floorspaces. Thus adopt: £60 per
sq.m. for unit 1, £55 for unit 2 and £57.50 for unit 3.
Estimated market rents:
Unit 1 = £60,000 p.a.
Unit 2 = £110,000 p.a.
Unit 3 = £86,250 p.a.
Freehold valuation of Unit 1
Term
Net income
£50,000
× YP for 1.5yrs @ 7.00%
1.379
Reversion to market rent
Net income
£60,000
× YP perp def 1.5yrs @ 7.00%
12.907
=
Market value =
SAY =
p.a.
£68,934
p.a.
£774,422
£843,356
£843,000
Note: term yield not reduced as term income only marginally ‘more secure’ than reversionary income (i.e.
rent in term is only £10,000 less and is still 83 per cent of market rent) so little difference in risk involved.
Freehold valuation of Unit 2
Term
Net income
£100,000 p.a.
× YP for 1yrs @ 7.00%
0.935
£93,458
Reversion to market rent
Net income
£110,000 p.a
× YP perp def 1yrs @ 7.00%
13.351
= £1,468,625
Market value = £1,562,083
SAY = £1,562,000
Note: term yield not reduced as term rent only slightly ‘more secure’ than reversion being only £10,000
(approximately 9 per cent) lower.
Freehold valuation of Unit 3
Term
Net income
£85,000
× YP for 0.33yrs @ 7.00%
0.315
Reversion to market rent
Net income
£86,250
× YP perp def 0.33yrs @ 7.00%
13.970
=
Market value =
SAY =
p.a.
£26,811
p.a.
£1,204,937
£1,231,749
£1,232,000
Note: no adjustment made to term yield as term rent is virtually same as reversionary rent and is thus
considered an equal risk rate.
For use in conjunction with Michael Blackledge, Introducing Property Valuation. Routledge: London.
© 2009 Michael Blackledge
13 Introducing Property Valuation: Suggested solutions to practical exercises
As remaining term is so short, a simpler valuation would be:
Net income (market rent) =
× YP perp @ 7%
£86,250 p.a.
14.286
Market value = £1,232,167
SAY = £1,232,000
Total value of freehold interest in the estate held by ABC Investments =
Unit 1 MV =
£843,000
Unit 2 MV =
£1,562,000
Unit 3 MV =
£1,232,000
Total market value SAY = £3.64 million
Leasehold valuation of XYZ’s interest in Unit 1
Rent receivable (market rent)
£60,000 p.a.
Less rent payable
£50,000 p.a.
Net profit rent
£10,000 p.a.
× YP for 1.5yrs @ 8.25% + 3.0%
& tax @ 21%
1.087
Market value (assignment premium) = £10,870
SAY = £11,000
Leasehold valuation of RST’s interest in Unit 2
Rent receivable (market rent)
£110,000
Less rent payable
£100,000
Net profit rent
£10,000
× YP for 1yrs @ 8.25% + 2.5%
& tax @ 28%
0.68
Market value (assignment premium) =
p.a.
p.a.
p.a.
£6,800
Leasehold valuation of DDP’s interest in Unit 3: The rent paid by the tenant is virtually the market rent and
there are only four months left to run on the lease, so the lease will have no saleable value. No valuation
required.
7. Analysis of comparables
The basis of this is to obtain a basic breakdown (£ per sq.m.). Then see how the comparable differs from
the subject property and adjust accordingly. The location of all the comparables is the same as the subject
building (as they are in the same road) and so no adjustment is needed for this aspect.
Features of subject property:
• Three-storey building, but this does not pose any special problem as there is a lift.
• Built 15 years ago – if not refurbished this would be viewed as an older building and could be more
difficult to let on the open market.
• Secondary office district so it is necessary to be looking for secondary ARYs not prime.
• Occupied by a PLC, so quite a good covenant, which means a slightly lower yield, could be accepted.
• Maintained to a good standard and has double-glazing, lift and central heating, so reasonably good for
its age.
• Ten years without review means that this is not so good from the landlord’s viewpoint as, although the
income may be quite ‘safe’, there would also be no increases to keep pace with inflation.
• IRL (internal repairing lease) terms mean the landlord has to pay for external and structural repairs,
insurance and management.
For use in conjunction with Michael Blackledge, Introducing Property Valuation. Routledge: London.
© 2009 Michael Blackledge
14 Introducing Property Valuation: Suggested solutions to practical exercises
Analysis of Ascot House comparable
£85,000/945 sq.m = £89.95 per sq.m. p.a.
Differences to subject
Built 4 years later
Adjustment
25 yr term
Rent reviews
Add say 5% to this comparable rent as such a long term is not favoured by tenants
nowadays and the 10 year periodleft on the subject lease is more attractive
No rent reviews are mentioned, so assume they are standard 5-yearly. Add say 5%
to allow for no review on subject property which would lead to landlord seeking
higher rent to offset loss of income over next 10 years
Size/quantum
FRI terms
This year letting date
Air conditioning
Nil; similar age
Comparable is 26% larger; say add 3% for quantum for subject
Nil; rent on review/lease renewal of subject will either be on FRI terms OR IRL
less outgoings which will = net FRI rental value anyway
Nil; assume no significant change in market since let
Better than subject; say deduct 10%
Adjusted comparable: for subject, the rental value needs adjustment by say +3% = £92.65/sq.m.
Analysis of Sandown House comparable
£102,400/1,170 sq.m = £87.52 per sq.m. p.a.
Differences to subject
5-storey building
Adjustment
Built 4 years later
Nil; similar age
Lease term
5-yrly RRs (assumed)
Size/quantum
FRI terms
This year rent review
2 storeys more than subject. Not a drawback providing the building has a lift. This
is not stated, but can be assumed
Lease has 10 years unexpired; the same as the subject building, so nil adjustment
Add say 5% to allow for no review for 10 years on subject
Comparable 56% larger; say add 5% for quantum for subject
Nil; rent on review/lease. Renewal of subject will either be on FRI terms or IRL
less outgoings will = net FRI rental value anyway
Nil; assume no significant movement of market since let
Adjusted comparable: for subject, the rental value needs adjustment by say –10% = £96.27/sq.m.
In addition, the freehold sale last week provides evidence of the ARY. The rental receivable by the landlord
is the market rent as at this year, so assume is up-to-date if market not changed since letting.Thus: ARY =
(£102,400/£930,700) × 100 = 11% i.e. this is the freehold ARY when MR is payable for this building.
Analysis of Chester Court comparable
£73,750/680 sq.m = £108.45 per sq.m. p.a.
Differences to subject
Built 1 year later
Adjustment
Lease term not known
5-yrly RRs (assumed)
Assume as new lease this will be for currently common 5-year term for an older
building; as subject lease is twice this length and less attractive to a tenant say
deduct 5%
Add say 5% to allow for no review for 10 years on subject
Size/quantum
IRI terms
Let this year
Poor condition
Nil; similar age
Comparable 28% smaller; say deduct 5% for quantum allowance on subject
As rent on review/lease renewal of subject will either be on FRI terms or IRL
less outgoings will = net FRI rental value, theoutgoings on this comparable
need to be deducted; say deduct 15% (10% external & structural repairs + 5%
management)
Nil; current market evidence providing no significant change in market since let
Subject is better; say add 10%
Adjusted comparable: for subject, the rental value needs adjustment by say –10% = £97.60/sq.m.
For use in conjunction with Michael Blackledge, Introducing Property Valuation. Routledge: London.
© 2009 Michael Blackledge
15 Introducing Property Valuation: Suggested solutions to practical exercises
Summary of comparable analysis
All the above are only suggestions on how percentage adjustments could be allocated. There is considerable
room for differences in opinion on the percentages used and the method of analysis used.
Also quite a lot more information needs to be found on each comparable, if possible, to ascertain why the
figures differ between each building and what qualitative factors this may be due to – it is never possible to
have too much evidence!
Unadjusted comparables show: £89.95, £87.52 and £108.45. Straight average of these figures is £95.30/
sq.m. although one comparable is considerably out-of-line with the others and there is a temptation to
disregard this and just average the remaining two – but this would be wrong! Having made qualitative and
quantitative adjustments, the adjusted comparables are: £92.65, £96.27 and £97.60. These are a lot more
consistent and logical and the straight average of these is £95.50/sq.m. Two of the comparables are higher
than the strict average, thus the figure of £96.00/sq.m. will be adopted for the subject building.
market rent valuation = 750 sq.m. × £96.00 = £72,000 per annum
Capital valuations
The all-risks yields will need to be used in the calculations, based on any market evidence that can be
obtained. The best and most direct evidence is provided by the sale of Sandown House last week.Taking
account of this evidence and the location and secondary nature of property, etc., an ARY of 11% for the
freehold and 13% for the leasehold calculations can be adopted (i.e. 2% added to freehold for leasehold in
absence of any direct leasehold yield evidence).
a. Existing freehold valuation
Term
Gross income
£70,500
Less outgoings:
Ext/struct reps @ say 10% MR
£7,200
Insurance
£6,000
Management @ 5% rent
£3,525
£16,725
Net income
£53,775
× YP for 10 yrs @ 10%
6.1445
Reversion
Net income
£72,000
× YP perp def 10 yrs @ 11%
3.2016
Capital value =
SAY =
p.a.
p.a.
p.a.
£330,420
p.a.
£230,515
£560,935
£561,000
b. Existing leasehold valuation
Rent receivable (MR on FRI terms)
Add outgoings
Rent receivable on IRL terms
Less rent payable
Net profit rent
× YP 10 yrs @ 13% + 3% (tax 28%)
£72,000 p.a.
£16,725 p.a.
£88,725 p.a.
£70,500 p.a.
£18,225 p.a.
3.982
= £72,565
SAY = £72,500
c. Freehold valuation with VP
Net income (MR)
× YP perp @ 11%
£72,000 p.a.
9.0909
= £654,545
SAY= £654,500
Freehold with VP minus (present freehold + present leasehold)
= £654,500 - (£561,000 + £72,500) = £21,000
For use in conjunction with Michael Blackledge, Introducing Property Valuation. Routledge: London.
© 2009 Michael Blackledge
16 Introducing Property Valuation: Suggested solutions to practical exercises
Thus there is a small potential ‘marriage value’ from the merging of the leasehold and freehold interests
(covered in Chapter 16). This is the release of potential latent additional value through the tenant purchasing
the freehold and then being in possession of a property that could sell for more than the combined total of
the present freehold and leasehold interests.
8. Valuation of head leasehold interest
Term
Rent receivable=
£47,500 p.a.
Less rent payable=
£ 1,500 p.a.
Net profit rent
=
£46,000 p.a.
× YP 2 yrs @ 11% + 4.5%
(tax 30%) 1.2368
= £ 56,893
Reversion
Rent receivable: 1,000sm @ £60 =
£60,000 p.a.
Less rent payable=
£ 1,500 p.a.
Net profit rent =
£58,500 p.a.
× YP 20 yrs def 2 yrs @ 12%
+ 4.5% (tax @ 30%) 4.8157
= £281,718
Capital value = £338,611
SAY = £338,500
Notes
• Term yield 1 per cent lower to reflect term rent receivable is much lower and more secure than reversion
rent.
• The subject property has a ‘standard’ office content of circa 10 per cent GIA. A much higher office
content could warrant a higher overall rental rate per sq.m. or a valuation on an ‘excess office’ basis,
where comparables have been obtained from buildings with approx. 10 per cent content. This ‘excess’
approach would be to value all office content in excess of 10 per cent at a higher rate per sq.m. (usually
1.5 or 2 times the standard industrial/warehouse rental rate).
Valuation of sub-leasehold interest
Rent receivable (FRI terms)= £60,000 p.a.
Less Rent payable (FRI terms)= £47,500 p.a.
Net profit rent= £12,500 p.a.
× YP 2 yrs @ 12%+4.5% (tax 21%) 1.3532
Capital value = £16,915
SAY= £17,000
On next rent review, sublessee will pay MR and will have no profit rent; value of interest is thus over next
2 years only.
9. Head leasehold valuation
Term
Rent Receivable
Less Rent Payable
Net profit rent
× YP for 4 yrs @ 8.00%
+ 2.5% & tax @ 28%
£225,000 p.a.
£25,000 p.a.
£200,000 p.a.
2.413
= £482,545
For use in conjunction with Michael Blackledge, Introducing Property Valuation. Routledge: London.
© 2009 Michael Blackledge
17 Introducing Property Valuation: Suggested solutions to practical exercises
Reversion
Rent receivable
£240,840 p.a.
Less rent payable
£25,000 p.a.
Net profit rent
£215,840 p.a.
× YP for 12 yrs @ 8.00%
+ 2.5% & tax @ 28%
5.535 × PV 4 yrs @8.00%
0.735
= £878,082
Market value (assignment price) = £1,360,627
SAY = £1,361,000
10. Comparable rent = £67.50 per sq.m. p.a. However, this property is considerably larger than the subject, so
adjust for quantum and adopt say £70 for subject premises: £70 × 1,300 = £91,000 per annum.
Freehold valuation
Term
Net income=
£60,000 p.a.
× YP for 7 yrs @ 8.00%
5.206 £312,382
Reversion to market rent
Net income=
£91,000 p.a.
× YP perp def 7 yrs @ 9.00%
6.078
£553,112
Market value = £865,495
SAY = £865,000
Equivalent yield approach: freehold valuation
Term
Net income =
£60,000 p.a.
× YP for 7 yrs @ 8.91%
5.048 £302,891
Reversion to market rent
Net income=
£91,000 p.a.
× YP perp def 7 yrs @ 8.91%
6.175
£561,939
Market value = £864,831
SAY = £865,000
Nominal equivalent yield = 8.91% (annually in arrear)
Hardcore or layer approach: freehold valuation
Hardcore
Net income =
£60,000
× YP perp @ 8.38%
11.933
Top slice
Net income=
£31,000
× YP perp def 7 yrs @ 10.38%
4.826
Market value =
SAY =
p.a.
£715,990
p.a.
£149,600
£865,590
£865,000
For use in conjunction with Michael Blackledge, Introducing Property Valuation. Routledge: London.
© 2009 Michael Blackledge
18 Introducing Property Valuation: Suggested solutions to practical exercises
Freehold valuation: quarterly in advance basis
Term
Net income=
£60,000 p.a.
× YP for 7 yrs @ 8.45%
5.395
£323,714
Reversion to market rent
Net income=
£91,000 p.a.
× YP perp def 7 yrs @ 9.45%
5.953
£541,686
Market value = £865,399
SAY = £865,000
Equivalent yield approach QIA: Freehold valuation
Term
Net income=
£60,000 p.a.
× YP for 7 yrs @ 9.36%
5.260
£315,623
Reversion to market rent
Net income=
£91,000 p.a.
× YP perp def 7 yrs @ 9.36%
6.041
£549,767
Market value = £865,389
SAY = £865,000
True equivalent yield = 9.36% (quarterly in advance)
The ARY has been found from annually in arrear analysis of comparables and must be reused in the same
way so that devaluation and revaluation are on the same basis. The yields used in each of the other valuations
should similarly be derived from analysis using the same approach as the valuation method. For example, a
quarterly in advance yield must be found by both analysing and then valuing using this approach. The above
uses an adjusted QIA yield to find the same capital value calculated from the conventional approach. If the
same ARY was used as found from annually in arrear analysis, an overvaluation will result.
Freehold valuation: quarterly in advance basis but using unadjusted annually in arrear ARY
Term
Net income=
£60,000 p.a.
× YP for 7 yrs @ 8.00%
5.464
£327,851
Reversion to market rent
Net income=
£91,000 p.a.
× YP perp def 7 yrs @ 9.00%
6.416
£583,890
Market value = £911,741
SAY = £912,000
11. An insurance assessment is needed to find the annual premiums that will be payable:
Site clearance and preparation SAY
Construction costs: 1,550 × £1300
Professional fees @ say 12% costs
=
Cost of alt accom for say 2 yrs rebuilding
period for 1,220 sq.m. @ £130 psm MR
Plus allowance for inflation @ say 3%
Insurance sum @ 35p per £100 = £8,816 p.a. premium
£30,000
£2,015,000
£241,800
£2,286,800
£158,600
£2,445,400
£ 73,362
£2,518,762
For use in conjunction with Michael Blackledge, Introducing Property Valuation. Routledge: London.
© 2009 Michael Blackledge
19 Introducing Property Valuation: Suggested solutions to practical exercises
Freehold valuation
Term
Gross income
£110,000 p.a.
Less outgoings:
Repairs & decs @ 5% MR =
£7,930
Insurance =
£8,816
Management @ 4% rent=
£4,400
=
£21,146 p.a.
Net income
£88,854 p.a.
× YP for 5 yrs @ 5.50%
4.270
£379,432
Reversion to market rent
Net income
£158,600 p.a.
× YP perp def 5 yrs @ 6.50%
11.229 £1,780,909
Market value = £2,160,341
SAY = £2,160,000
Notes:
• Rent will be increased to MR in 5 years’ time when lease expires.
• Rent on reversion can be taken to FRI basis as even if relet on internal repairing terms the net figure after
deduction of outgoings should equal FRI MR.
• ARY on term reduced by 1 per cent as term income lower than reversionary income and thus more
‘secure’.
12. Leasehold valuation
Rent receivable (market rent on FRI terms) = £85,000 p.a.
Add outgoings =
£9,550 p.a.
Market rent on existing lease terms =
£94,550 p.a.
Less rent payable =
£55,000 p.a.
Net profit rent =
£39,550 p.a.
× YP for 4 yrs @ 10.00%
+ 3.0% & tax @ 28%
2.315
Market value (assignment price) = £91,555
SAY = £92,000
Freehold valuation
Term
Gross income =
£55,000 p.a.
Less outgoings:
Repairs & decs @ 5% MR =
£4,250
Insurance @ 3% MR =
£2,550
Management @ 5% rent =
£2,750
=
£9,550 p.a.
Net income = £45,450 p.a.
× YP for 4 yrs @ 7.50%
3.349 = £152,227
Reversion to market rent
Net income= £85,000 p.a.
× YP perp def 4 yrs @ 8.50%
8.489
= £721,574
Market value = £873,801
SAY = £874,000
13. When comparables and subject property to be valued are on different lease terms, adjustments must be
made to bring them all on to a common basis, otherwise the comparison is not like-with-like. It is usually
simpler to convert everything to FRI (full repairing and insuring) terms, as these are the most common.
For use in conjunction with Michael Blackledge, Introducing Property Valuation. Routledge: London.
© 2009 Michael Blackledge
20 Introducing Property Valuation: Suggested solutions to practical exercises
a. The landlord will view the rent collected as not net and need to deduct outgoings from it – for IRT this
will be external and structural repairs/decorations, insurance and management.
b. From the tenant’s viewpoint it is necessary to consider what the building is worth if it was sublet at
MR on IRT. A prospective tenant would be prepared to pay more than the MR calculated on FRI
terms since they are not responsible for some of the matters a tenant on FRI would be. That is they are
‘saving’ money on not having to pay out for those outgoings and this would be reflected in them being
prepared to pay more rent in the first place. This can be equated to the MR on FRI terms PLUS the
value of the outgoings they are NOT responsible for, which are those the landlord IS responsible for
summarised above. Once this is done the remaining figure will be the MR on IRT basis. Even better, of
course, is to find comparables also let on IRT basis and then it is a more straightforward comparison!
14. Valuation of leasehold interest in high street shop
Rent receivable (market rent on FRI terms)
£70,000
Add outgoings
Repairs & decs @ 5% MR =
£3,500
Insurance @ 3% MR=
£2,100
Management @ 5% rent =
£2,500
£8,100
Market rent on existing lease terms
£78,100
Less rent payable
£50,000
Net profit rent
£28,100
× YP for 4 yrs @ 7.50%
+2.5% & tax @ 28%
2.442
Market value (assignment price) =
SAY =
p.a.
p.a.
p.a.
p.a.
p.a.
£68,625
£69,000
Notes:
• ‘Outgoings’ are added back to bring comparable value in line with internal repairing only terms as under
existing lease.
• Spot figures or assumptions on percentage of rental value need to be adopted as no other evidence
available.
Chapter 12
1. Equated yield approach: freehold valuation
Assumed annual rental growth rate =
Equated yield (annually in arrear) =
True equated yield (quarterly in advance) =
Years
Income p.a.
PV factor
1 to 5
£80,000 3.791 6 to 10
£92,742 2.354 11 to 15
£107,513 1.462 16 to 20
£124,637 0.907 21 to 25
£144,489 0.563 26 to perp*
£167,502 1.231 GPV =
SAY =
3.00%
10.00%
10.66%
DCF
£303,263
£218,294
£157,132
£113,106
£81,416
£206,130
£1,079,342
£1,080,000
* Income capitalised @ ARY of 7.5% found from formula in Secton 12.4 to reflect continued future rental growth but then discounted
at equated yield.
2. Equated yield approach: freehold valuation
Assumed annual rental growth rate =
Equated yield (annually in arrear) =
True equated yield (quarterly in advance) =
2.50%
9.00%
9.53%
For use in conjunction with Michael Blackledge, Introducing Property Valuation. Routledge: London.
© 2009 Michael Blackledge
21 Introducing Property Valuation: Suggested solutions to practical exercises
Years
Income p.a.
PV factor
1 to 3
£420,000 2.531 4 to 6
£452,294 1.955 7 to 9
£487,071 1.509 10 to 12
£524,522 1.165 13 to 15
£564,853 0.900 16 to perp*
£608,285 4.128 GPV =
SAY =
DCF
£1,063,144
£884,065
£735,150
£611,320
£508,347
£2,511,240
£6,313,265
£6,316,000
* Income capitalised @ ARY of 6.65% found from Formula 2.1 to reflect continued future rental growth but then discounted at
equated yield.
3. a. Using formula in Section 12.4, implied annual rental growth = 2.29% per annum.
b. Using equated yield formula the all risks yield = 5.86%.
4. Freehold valuation
Term
Net income =
£50,000 p.a.
× YP for 3 yrs @ 7.00%
2.624
£131,216
Reversion to market rent
Net income =
£75,000 p.a.
x YP perp def 3 yrs @ 8.00%
9.923
£744,218
Market value = £875,434
SAY = £875,000
Equated Yyeld approach: freehold valuation
Assumed annual rental growth rate =
Equated yield (annually in arrear) =
True equated yield (quarterly in advance) =
Years
Income p.a.
PV factor
1 to 3
£50,000 2.465 4 to 8
£81,955 2.774 9 to 13
£95,008 1.684 14 to 18
£110,140 1.022 19 to 23
£127,682 0.620 24 to perp*
£148,019 1.258 GPV =
SAY =
3.00%
10.50%
11.23%
DCF
£123,256
£227,347
£159,979
£112,574
£79,216
£186,164
£888,537
£889,000
* Income capitalised @ ARY to reflect continued future rental growth but then discounted at equated yield.
Shortcut DCF valuation
Current rent= £50,000 p.a.
× YP for 3 yrs @ 10.5%
2.4651235
= £123,256
plus
Market rent = £75,000 p.a.
× A £1 for 3 yrs @ 3%
1.092727
=
£81,955
× YP perp @ 8%
12.5
× PV for 3 yrs @ 10.5%
0.7472316
= £765,492
Market value = £888,748
SAY = £889,000
For use in conjunction with Michael Blackledge, Introducing Property Valuation. Routledge: London.
© 2009 Michael Blackledge
22 Introducing Property Valuation: Suggested solutions to practical exercises
The three appraisals produce slightly different values, but a variation of £14,000 at this value level is
comparatively small. Assume final value adopted is around mid-way between the conventional and DCF
valuations, say at £880,000, and then the variation between the appraisals is less than 1.6 per cent.
5. Term
Net income
£72,000
× YP for 2 yrs @ 7%
1.808
Reversion to market rent
Net income
£84,000
× YP perp def 2 yrs @ 8%
10.717
Market value =
SAY =
Assumed annual rental growth rate = 3%
Equated yield = 10.5% (annually in arrear)
Years
Income p.a.
PV factor
1 to 2
£72,000 1.724 3 to 7
£89,116 3.065 8 to 12
£103,309 1.861 13 to 17
£119,764 1.129 18 to 22
£138,839 0.686 23 to perp £160,953 1.390 GPV =
SAY =
p.a.
£130,177
p.a.
£900,206
£1,030,383
£1,030,000
DCF
£124,125
£273,170
£192,224
£135,264
£95,182
£223,686
£1,043,651
£1,044,000
Again, there is some relatively small variation in values between the different approaches. The difference of
£14,000 is not too significant at this value level (less than 1.36 per cent of lowest value found).
Conclusion: freehold market value is around £1.037 million.
6. The two open market comparables need to be analysed to arrive at the estimated market rent (MR) for the
subject building now.
Macduff House = £300000/1500sq.m. = £200/sq.m. p.a.
Macbeth House = £575000/3200sq.m. = £179.69/sq.m. p.a.
Interpolating between these figures to take into account ‘quantum adjustment’ as floor area of subject
property is 2,200 sq.m., an estimated MR of £191.60/sq.m. is taken. With 10 years until rent review on the
subject property, against five-yearly pattern on comparables, it is possible to argue that a small increase in
this amount could be used.
Note when current lease expires, it is assumed building will be relet on ‘normal’ five-yearly rent reviews and
this is reflected in the DCF analysis.
Market rent of subject building = 2200 × £191.60 = £421,520
SAY = £421,500 p.a.
a. Freehold valuation
Term
Net income=
£320,000 p.a.
× YP for 3 yrs @ 7.00%
2.624
£839,781
Reversion to market rent
Net income=
£421,520 p.a.
× YP perp def 3 yrs @ 8.00%
9.923
£4,182,702
Market value = £5,022,483
SAY = £5,022,000
For use in conjunction with Michael Blackledge, Introducing Property Valuation. Routledge: London.
© 2009 Michael Blackledge
23 Introducing Property Valuation: Suggested solutions to practical exercises
b. Equivalent yield approach: freehold valuation
Term
Net income=
£320,000 p.a.
× YP for 3 yrs @ 7.98%
2.578
£824,969
Reversion to market rent
Net income=
£421,520 p.a.
× YP perp def 3 yrs @ 7.98%
9.953
£4,195,515
Market value = £5,020,484
SAY = £5,022,000
Nominal equivalent yield = 7.98% (Annually in arrear)
True equivalent yield = 8.39% (Quarterly in advance)
Equated yield approach: freehold valuation
Assumed annual rental growth rate = 2.50%
Equated yield (annually in arrear) = 10.18%
True equated yield (quarterly in advance) = 10.86%
c. Years
Income p.a.
PV factor
DCF
1 to 3
£320,000 2.479 £793,278
4 to 8
£453,931 2.821 £1,280,609
9 to 13
£513,581 1.737 £892,323
14 to 18
£581,070 1.070 £621,767
19 to 23
£657,427 0.659 £433,244
24 to perp*
£743,819 1.344 £1,000,031
GPV =
£5,021,252
SAY =
£5,022,000
* Income capitalised @ ARY to reflect continued future rental growth but then discounted at equated yield.
7. Freehold valuation
Term
Net income
× YP for 3 yrs @ 6%
Reversion to market rent
Net income
× YP perp def 3 yrs @ 7%
£250,000 p.a.
2.673
= £668,253
£300,000 p.a.
11.661
= £3,498,419
Market value = £4,166,672
SAY = £4.2 million
Equivalent yield approach: freehold valuation
Term
Net income
£250,000 p.a.
× YP for 3 yrs @ 6.95%
2.627
= £656,679
Reversion to market rent
Net income
£300,000 p.a.
× YP perp def 3 yrs @ 6.95%
11.762
= £3,528,532
Market value = £4,185,211
SAY = £4.2 million
For use in conjunction with Michael Blackledge, Introducing Property Valuation. Routledge: London.
© 2009 Michael Blackledge
24 Introducing Property Valuation: Suggested solutions to practical exercises
Nominal equivalent yield = 6.95%
True equivalent yield = 7.26% (quarterly in advance)
Hardcore or layer approach: freehold valuation
Hardcore
Net income
£250,000 p.a.
× YP perp @ 6.70%
14.925
= £3,731,343
Top slice
Net income
£50,000 p.a.
x YP perp def 3 yrs @ 8.70%
8.949
= £447,468
Market value = £4,178,811
SAY = £4.2 million
Hardcore or layer approach using equivalent yield:
Freehold valuation
Hardcore
Net income
£250,000 p.a.
× YP perp @ 6.95%
14.388
£3,597,122
Top slice
Net income
£50,000 p.a.
× YP perp def 3 yrs @ 6.95%
11.762 £588,089
Market value = £4,185,211
SAY = £4.2 million
Equated yield approach: freehold valuation
Annual rental growth rate = 3 %; equated yield = 9.6 %
Years
Income p.a.
PV factor
1 to 3
£250,000 2.504
4 to 8
£327,818 2.909 9 to 13
£380,031 1.839 14 to 18
£440,560 1.163 19 to 23
£510,730 0.736 24 to perp*
£592,076 1.735 GPV =
SAY =
DCF
£626,117
£953,635
£699,062
£512,447
£375,649
£1,027,157
£4,194,067
£4.2 million
* Income capitalised @ ARY to reflect continued future rental growth but then discounted at equated yield.
For use in conjunction with Michael Blackledge, Introducing Property Valuation. Routledge: London.
© 2009 Michael Blackledge
25 Introducing Property Valuation: Suggested solutions to practical exercises
Chapter 13
1. 5,120 × £2,000 = £10,240,000
1,500 × £200 = £300,000
800 × £120 = £96,000
Total construction costs = £10,636,000
2. a.
Zone A = 8 × 6 = 48 sq.m. @ £2,000 = £96,000
Zone B = 8 × 6 = 48 sq.m. @ £1,000 = £48,000
Zone C = 8 × 4 = 32 sq.m. @ £500 = £16,000
Grnd flr ancillary = 8 × 4 = 32 sq.m. @ £100 (1/20) = £3,200
1st floor sales = 80 sq.m. @ £200 (1/10) = £16,000
1st floor ancillary = 80 sq.m. @ £80 (1/25) =
£6,400
Market rent per shop = £185,600p.a.
GDV:
Offices MR=
£562,500 p.a.
× YP perp @ 6%
16.666
= £9,374,999
Shops MR =
£2,227,200 p.a.
× YP perp @ 5.25%
19.0476
= £42,422,814
= £51,797,813
GDV SAY = £51.75 million
b. Letting fees @ 10% of MR = £278,970
Sales fees @ 3% GDV = £1,552,500
3. a.
b.
c.
d.
e.
((1.07)2 – 1) × £15M/2 = £1,086,750
((1.075)2 – 1) × £15M/2 = £1,167,188
((1.08)2 – 1) × £15M/2 = £1,248,000
((1.0825)2 – 1) × £15M/2 = £1,288,547
((1.09)2 – 1) × £15M/2 = £1,410,750
4. a.
b.
c.
d.
e.
((1.07)1.75 – 1) × £11.5M/2 = £722,759
((1.075)2.25 – 1) × £11.5M/2 = £1,016,076
((1.08)1.667 – 1) × £11.5M/2 = £787,102
((1.0825)2.833 – 1) × £11.5M/2 = £1,447,839
((1.0775)3.083 – 1) × £11.5M/2 = £1,487,862
5. £5,000,000 × PV 2.25 yrs @ 8% = £5,000,000 × 0.841 = £4,205,005
£4,205,005/1.05 = £4,004,767
Site value SAY= £4 million
6. £3,250,000 risk and profit = 20.96% GDV
= 26.53% costs
For use in conjunction with Michael Blackledge, Introducing Property Valuation. Routledge: London.
© 2009 Michael Blackledge
26 Introducing Property Valuation: Suggested solutions to practical exercises
7. See example residual method valuation illustrated below:
Freehold industrial development
Gross Development Value:
Market Rent =
x YP perp
£807,500
16.000
=
Less Costs of Development:
Compensation to site's existing occupiers =
Demolition of existing buildings =
Site clearance/remediation/preparation =
Other initial/miscellaneous/contingency costs =
Construction costs:
industrial/distribution units
constructable floor area in sq.m. =
@ construction cost per sq.m. =
surface parking and loading areas
constructable floor area in sq.m. =
@ construction cost per sq.m. =
landscaping
constructable floor area in sq.m. =
@ construction cost per sq.m. =
Arch, QS & other prof. fees as % of const. costs
Agents & Legals on letting as % of MR
Agents/Legals on investment sale as % of GDV
Finance charges on costs over devt. period @
Developer's Risk & Profit:
as % of costs
as % of GDV
Less Site Purchase finance over devt. period @
Less site purchase costs @
£
£
£ 12,920,000
SAY =
£
12,920,000
1,390,000
Total Costs =
Balance =
=
=
=
Site Value =
SAY =
£
£
£
£
£
£
£
11,318,262
1,601,738
139,231
1,462,507
82,783
1,379,724
1,370,000
= per hectare:
£
796,512
£
£
£
£
70,000
200,000
9500 m ²
£775.00 /m ²
Costs =
£
7,362,500
7000 m ²
£50.00 /m ²
Costs =
£
350,000
0
£0.00
Costs =
12
10
3
6.25
£
£
£
£
£
90,000
936,300
80,750
387,600
451,112
m²
/m ²
%
%
%
%
1,489,239
1,292,000
SAY =
6.25 %
6 %
£
8. First analyse retail ITZA and market rents for each shop unit.
Zone Front
Depth
Area
Value
ITZA
A
7.5
6
45
1
45
B
7.5
6
45
0.5
22.5
C
7.5
5
37.5
0.25
9.375
1st F Ancillary
130
0.02
2.6
Total ITZA =
79.5
Total Rent = £143,000 p.a.
Rent psm ITZA p.a. =
£1,799.31
For use in conjunction with Michael Blackledge, Introducing Property Valuation. Routledge: London.
© 2009 Michael Blackledge
27 Introducing Property Valuation: Suggested solutions to practical exercises
Then provide residual valuation using all information provided and making reasoned assumptions where
necessary as illustrated below:
Offices
Gross Development Value:
Market Rent =
x YP perp
£528,000
14.286
=
£
7,542,857
SAY =
£
7,540,000
£ 23,833,333
SAY =
£
23,830,000
£
£
£
£
£
£
£
20,398,782
10,971,218
1,343,472
9,627,746
629,853
8,997,893
9,000,000
Retail units
Gross Development Value:
Market Rent =
x YP perp
£1,430,000
16.667
=
Less Costs of Development:
Compensation to site's existing occupiers =
Planning fees =
Site clearance/remediation/preparation =
Promotion and marketing costs =
Other initial/miscellaneous/contingency costs =
Construction costs:
Offices
constructable floor area in sq.m. =
@ construction cost per sq.m. =
Retail units
constructable floor area in sq.m. =
@ construction cost per sq.m. =
Arch, QS & other prof. fees as % of const. costs
Agents & Legals on letting as % of MR
Finance charges on costs over devt. period @
Developer's Risk & Profit:
as 15% of costs
as 10% of GDV
Less Site Purchase finance over devt. period @
Less site purchase costs @
£
£
£
£
£
£
£
150,000
15,000
70,000
100,000
500,000
4700 m ²
£1,900.00 /m ²
Costs =
£
8,930,000
3100
£1,500.00
Costs =
13
10
7.75
£
£
£
£
4,650,000
1,765,400
195,800
1,142,582
£
2,880,000
Total Costs =
Balance =
=
=
=
Site Value =
SAY =
m²
/m ²
%
%
%
2,627,817
3,137,000
SAY =
7.75 %
7 %
Conclusion is that proposed purchase price of £7 million is reasonable.
a. £4,880,000 would be total available for risk and profit
b. This equals 27.86% of the costs.
c And 15.56% of the total GDV.
For use in conjunction with Michael Blackledge, Introducing Property Valuation. Routledge: London.
© 2009 Michael Blackledge
28 Introducing Property Valuation: Suggested solutions to practical exercises
Chapter 14
1. Gross receipts
£225,000
Less purchases
(£85,000)
Gross profit
£140,000
Less working expenses
£65,000
Net profit
£75,000
Less proprietor’s share @ 50%
£37,500
Balance= £37,500
Return on proprietor’s capital:
Fixed assets
£35,000
Stock
£7,000
Cash
£4,500
Total capital
£46,500
Interest @ say 5%
0.05
= Remaining balance for rent + rates = Less business rates =
Rental value= Value of land and buildings
Rental value= × YP perp @ 8%
Capital value= SAY = £
Value of ‘goodwill’ = share × 1.5
= £37,500 × 1.5 =
£2,325
£35,175
(£9,000)
£26,175 p.a.
£26,175 p.a.
12.5
£327,187
327,000
£56,250
Total value could be assessed as land and buildings, goodwill and fixed assets = £418,250
As a check, compare to gross receipts: £418,250/£225,000 = 1.858 YP
This is within range of other comparable properties, but on higher side of figures achieved, so may wish
to consider reducing multiplier on goodwill and/or increase ARY as at 1.5 YP total value would only be
£337,500.
2. Gross receipts:
Room lettings
Average occupancy rate =
66%
Weekly charge per room =
£450
Total receipts from room lettings =
£930,150
Fitness room/gymnasium lettings
£9,600
Functions rooms lettings
£62,400
Restaurant/coffee shop/bar takings
£69,600
Total gross receipts:
£1,071,750
Less Purchase of new equipment
£60,000
Less general working expenses
£416,000
Net Profit
£595,750
Less proprietor’s share including
interest on proprietor’s capital
£327,663
Rent + Rates =
£268,088
Less estimated annual rates
£43,000
For use in conjunction with Michael Blackledge, Introducing Property Valuation. Routledge: London.
© 2009 Michael Blackledge
29 Introducing Property Valuation: Suggested solutions to practical exercises
Market rental value of completed
development = Market rent SAY =
× YP perp @ 8%
£225,088 p.a.
£225,000 p.a.
12.5
Market value (capital value) = £2,812,500
(of completed development)
SAY = £2,800,000
SAY land value = 40 per cent of completed development value as city centre site (but comparables needed
to support this), then market value of site = £1,120,000 (/0.3) = £ per ha: £3,733,333
SAY =£3,700,000 per hectare
Chapter 15
1. Depreciated replacement cost valuation
Construction costs: 1,000 sq.m @ £900 psm =
£900,000
Site works; say =
£60,000
Allowance for any necessary adjustments &
additions say =
£50,000
=
£1,010,000
Date of replacement assumed as valuation date (now)
and no allowance to cost needed for this aspect
Allowance for professional fees
and statutory fees say @ 12% =
Allow for short-term finance over half the
construction period @ say 7% =
Gross Replacement Cost (excluding VAT) =
£121,200
£87,668
£1,218,868
Say useful life of building is 60 years total. Therefore, unexpired useful life is 30 years. Say allow 50% for
simple ‘straight-line’ depreciation to reflect age, obsolescence and existing repairs required of £125,000.
Thus 50% of £1,218,868 + site value = current capital value 50% of GRC =
£609,434
Site value: 0.182 ha @ say £2.5M per ha =
£455,000
(from comparables)
=
£1,064,434
Conclusion: asset value of existing building = SAY £1.064 million.
Chapter 16
1. YP single rate for 4.5 yrs @ 6%
= ((1.06)4.5 – 1)/((1.06)4.5 × 0.06)
= 3.84417
PV for 0.5 yrs @ 6%
= 1/(1.06)0.5
0.971286
PV = £50,000 p.a. × YP for 4.5 yrs @ 6% × PV for 0.5 yrs @ 6%
= £186,689
SAY = £186,700
For use in conjunction with Michael Blackledge, Introducing Property Valuation. Routledge: London.
© 2009 Michael Blackledge
30 Introducing Property Valuation: Suggested solutions to practical exercises
2. Calculation of MR on FRI terms disregarding value of improvements.
From landlord’s viewpoint
MR on IRT= £25,000 p.a.
Less outgoings:
Repairs @ say 5% MR =
£1,250 p.a.
Insurance @ say 2.5% MR =
£ 625 p.a.
Management @ say 6% rent =
£1,500 p.a.
= £ 3,375 p.a.
MR on FRI terms (excl imps) = £21,625p.a.
Note: external and structural repairs only as tenant responsible for internal repairs.
From tenant’s viewpoint
MR (improved) on FRI terms =
Less Annual equivalent of improvements:
£25,000/YP 25yrs @ 11%+3% (tax30%)
= £25,000/6.7032=
MR on FRI terms (excl imps) =
£26,000 p.a.
£ 3,730 p.a.
£22,270 p.a.
SAY parties prepared to split difference 50/50
Therefore agreed MR on FRI terms excluding
value of improvements = £21,950; SAY = £22,000 p.a.
Valuation of Grant’s present interest
Rent receivable IRT
=
Less rent payable IRT
=
Net profit rent
=
× YP 3yrs @ 11%+3%
(tax 30%) Capital value = £25,000 p.a.
£15,000 p.a.
£10,000 p.a.
1.7477
£17,477
Note: leasehold yield assumed as 1 per cent higher than freehold yield.
Valuation of Grant’s proposed interest
Term
Rent receivable (MR on FRI) =
£26,000
Less rent payable =
£x
Net profit rent
=
£26,000 – x
× YP 5yrs @ 11%+3% (tax30%) 2.6380
=
Reversion
Rent receivable (MR on FRI) =
£26,000
Less rent payable=
£22,000
Net profit rent =
£ 4,000
× YP 20yrs @ 11%+3% (tax30%)
× PV 5yrs @ 11%
3.6371
=
Less cost of improvements =
Value =
p.a.
p.a.
p.a.
£68,588 – 2.638x
p.a.
p.a.
p.a.
£14,548
(£25,000)
£58,136 – 2.638x
Assessment from tenant’s viewpoint
• Present interest should = Proposed interest
• Therefore: £17,477 = £58,136 – 2.638x
• Therefore: x (proposed rent) = £15,413 p.a.
For use in conjunction with Michael Blackledge, Introducing Property Valuation. Routledge: London.
© 2009 Michael Blackledge
31 Introducing Property Valuation: Suggested solutions to practical exercises
• The maximum rent which the tenant would be prepared to offer under the new lease would be
£15,400p.a.
Valuation of landlord’s present interest
Term
Gross income =
£15,000 p.a.
Less outgoings:
Repairs @ say 5% MR * =
£1,250 p.a.
Insurance @ say 2.5% MR = £ 625 p.a.
Mangmnt @ say 6% rent = £ 900 p.a.
=
£ 2,775 p.a.
Net income =
£12,225 p.a.
× YP 3yrs @ 9%
2.5313
= £ 30,945
Reversion
Gross income
=
£25,000 p.a.
Less outgoings:
Repairs @ say 5% MR * =
£1,250 p.a.
Insurance @ say 2.5% MR = £ 625 p.a.
Mangment @ say 6% rent = £1,500 p.a.
=
£ 3,375 p.a.
Net income =
£21,625 p.a.
× YP perp def 3yrs @ 10% 7.513
= £162,468
Capital value = £193,413
* External and structural repairs only as tenant responsible for internal repairs
Valuation of landlord’s proposed interest
Term
Net income =
£x p.a.
× YP 5yrs @ 9%
3.8896
= £3.8896x
Reversion 1
Net income =
£22,000 p.a.
× YP 20yrs def 5yrs @ 9.5%
5.597
= £123,152
Reversion 2
Net income
=
£26,000 p.a.
× YP perp def 25yrs @ 10% 0.92296
= £23,997
Capital value = £147,149 + 3.8896x
Assessment from landlord’s viewpoint
• Present = proposed values
• Therefore: £193,413 = £147,149 + 3.8896x
• Therefore: x (rent required) = £11,894 p.a.
• Landlord requires a minimum rent under the new lease of SAY £12,000 p.a.
Conclusions
Difference between tenant’s and landlord’s figures = £15,400 – £12,000 = £3,400.
Tenant can afford to pay more than the landlord requires, so the deal is viable.
The exact figure agreed will depend on the bargaining power and negotiating ability of the two sides.
However, after negotiation, say a 50/50 split of the difference between the parties is agreed, then a rental
of around £13,700 p.a. is likely to be mutually acceptable under the new lease.
SAY agreement is reached at £13,700p.a.
Again in this instance, both landlord and tenant are better off at the end of the surrender and renewal than
they were at the start.
For use in conjunction with Michael Blackledge, Introducing Property Valuation. Routledge: London.
© 2009 Michael Blackledge
32 Introducing Property Valuation: Suggested solutions to practical exercises
Alternatively, if the rent under the new lease was fixed in advance at £12,000 p.a. and a premium payable,
the calculation would be as follows.
From tenant’s viewpoint:
Leaseholder’s proposed interest = £58,136 – 2.638x
If x = £12,000 then proposed interest = £26,480
Present interest = £17,477
Therefore, value gained = £9,003 compared to present
From landlord’s viewpoint:
Freehold proposed interest = £147,149 + 3.8896x
If x = £12,000 then proposed interest = £193,781
Present interest = £193,413
Thus virtually same value compared to present interest
Conclusion
Both sides are better off with the proposed deal than at present (freeholder only very marginally) so the
transaction is viable.
The tenant gains more than the landlord (nearly £9,000 more).
If this additional gain is equally split between the two parties, then the premium payable by the tenant will
be say £4,500, payable at the time of surrender and renewal, with the new lease at the agreed initial rent
of £12,000 p.a.
3. Assumptions:
• The recent letting of a similar building provides good evidence of current market ARY at market rent:
£550,000/£6m = 9.16%.
• From comparables, market rent of subject building before refurbishment is £600,000 p.a. (4,000 sq.m.
NIA @ £150 per sq.m.) and after refurbishment will be £720,000 p.a. (4,000 sq.m. @ £180).
• Next rent review on existing lease is 3 years away.
• Full repairing and insuring lease so no outgoings need to be deducted from freeholder’s rental income.
• Under proposed lease the improvement work will be disregarded at the first rent review after 5 years,
thus the rent payable then will be the ‘unimproved’ MR and it will rise to the ‘improved’ MR at the
second review in 10 years’ time
• Leasehold interests are less attractive investments compared to freeholds and command slightly higher
ARYs; thus will use 10.5 per cent as leasehold ARY at market rent.
Existing freehold valuation
Term
Net income
£500,000 p.a.
× YP for 3 yrs @ 8.16%
2.570 £1,284,837
Reversion to market rent
Net income
£600,000 p.a.
× YP perp def 3 yrs @ 9.16%
8.393
£5,035,762
Market value = £6,320,599
SAY = £6,320,000
Existing leasehold valuation
Rent receivable (market rent)
£600,000 p.a.
Less rent payable
£500,000 p.a
Net profit rent
£100,000 p.a.
× YP for 3 yrs @ 10.50%
+ 3.0% & tax @ 30%
1.763 Market value (assignment value) = £176,309
SAY = £176,000
For use in conjunction with Michael Blackledge, Introducing Property Valuation. Routledge: London.
© 2009 Michael Blackledge
33 Introducing Property Valuation: Suggested solutions to practical exercises
Proposed freehold valuation
Term
Net income
× YP for 5 yrs @ 8.16%
Reversion to intermediary rent
Net income
× YP 5 yrs @8.66%
× PV 5 yrs @8.66%
Reversion to market rent
Net income
× YP perp def 10 yrs @ 9.16%
£400,000 p.a.
3.976
= £1,590,372
£600,000 p.a.
3.924
0.660
= £1,554,372
£720,000
4.544
=
Market value =
SAY =
p.a.
£3,271,913
£6,416,657
£6,410,000
Note: differential yields used in term and reversion to reflect proportionally more ‘secure’ or ‘safer’ rental
incomes compared to market rent.
Equivalent yield approach: proposed freehold valuation
Term
Net income
£400,000 p.a.
× YP for 5 yrs @ 9.00%
3.890
= £1,555,861
Reversion to intermediary rent
Net income
£600,000 p.a.
× YP 5 yrs @ 9.00%
3.890 × PV 5 yrs @ 9.00%
0.650
= £1,516,804
Reversion to market rent
Net income
£720,000 p.a.
× YP perp def 10 yrs @ 9.00%
4.693
= £3,379,286
Market value = £6,451,951
SAY = £6,450,000
Nominal equivalent yield = 9%
Note: Equivalent yield based on market evidence of 9.16 per cent and rounded down. This valuation
confirms market value found from ‘differential yield’ approach above.
Proposed leasehold valuation
Term
Rent receivable
Less rent Payable
Net profit rent
× YP for 5 yrs @ 10.50%
+ 3.0% & tax @ 30%
£720,000 p.a.
£400,000 p.a.
£320,000 p.a.
2.673 = £855,437
For use in conjunction with Michael Blackledge, Introducing Property Valuation. Routledge: London.
© 2009 Michael Blackledge
34 Introducing Property Valuation: Suggested solutions to practical exercises
Reversion
Rent receivable
£720,000 p.a.
Less rent payable
£600,000 p.a.
Net profit rent
£120,000 p.a.
× YP for 5 yrs @ 10.50%
+ 3.0% & tax @ 30%
2.673 × PV 5 yrs @ 10.50%
0.607
= £194,719
Less costs of improvements (£750,000)
Market value (assignment value) = £300,155
SAY = £300,000
Proposed leasehold valuation eliminating ‘double sinking fund error’
Annual sinking fund for 10 yrs @ 3.00% =0.08723051
× gross tax factor @ 30% =
1.42857143
Annual sinking fund multiplier=
0.12461501
Term
Net profit rent
£320,000 p.a.
Less annual sinking fund
£134,263 p.a.
£185,737 p.a.
× YP for 5 yrs @ 10.16%
3.775
= £701,219
Reversion
Net profit rent
£120,000 p.a.
Less annual sinking fund
£134,263 p.a.
(£14,263) p.a.
× YP for 5 yrs @ 10.16%
3.775 × PV 5 yrs @ 10.16%
0.616
= (£33,194)
Capital replaced at end of lease
by sinking fund =
£1,077,426 × Present value @ ARY of 10.16% =
0.380
= £409,400
£1,077,426
Less costs of improvements today = (£750,000)
Market value (assignment value) = £327,426
SAY = £ 327,000
Summary and conclusion
• Freeholder better off by £90,000 or more.
• Tenant better off by at least £124,000 and maybe as much as £151,000.
• Could argue no premium payable, as both better off than now and especially as tenant will pay for
improvements.
• Alternatively, tenant pays premium of £34,000/2 = £17,000 or up to maximum of £61,000/2 = £30,500.
4. Valuation of tenant’s present interest
Rent receivable =
Less rent payable =
Net profit rent =
× YP 8yrs @ 8%+3% (tax 21%)
Capital value =
SAY =
£25,000
£10,000
£15,000
4.497
£67,461
£67,500
For use in conjunction with Michael Blackledge, Introducing Property Valuation. Routledge: London.
© 2009 Michael Blackledge
35 Introducing Property Valuation: Suggested solutions to practical exercises
Valuation of present freehold interest
Term
Net income
=
× YP 8yrs @ 6%
Reversion
Net income
=
× YP perp def 8yrs @ 7%
£10,000
6.21
= £ 62,100
£25,000
8.314
= £207,850
Value = £269,950
SAY = £270,000
Note: term yield reduced by 1 per cent as term income a lot lower than reversionary income and so much
more ‘secure’.
Valuation of proposed freehold interest
Net income =
× YP perp @ 7%
=
SAY =
£25,000
14.286
£357,150
£357,000
Marriage value = Proposed freehold minus (Present leasehold + Present freehold) = £357,000 – (£67,500
+ £270,000) = £19,500
If parties agree to split marriage value 50/50 then price to be paid by tenant to buy out the landlord and
acquire the freehold interest will be:
Present freehold value + 50% of marriage value = £270,000 + £9,750
= £279,750 to be paid by tenant to purchase the freehold
5. Can use ‘rule of thumb’ or Jack Rose’s ‘Constant Rent’ formula.
Rule of thumb = 7 – 5 yrs = +2
× 1% (as low growth rate) = +2%
£60,000 plus 2% = £61,200 per annum
Constant rent:
k=
(1 + 0.1)7 − (1 = 0.25)7
(1 + 0.1)5 − 1
×
(1 = 0.1)7 − 1
(1 = 0.1)5 − (1 + 0.25)5
k = 1.0208
£60,000 × 1.0208 = £61,248 per annum
6. Leasehold valuation
Rent receivable (market rent)
Less rent payable
Net profit rent
× YP for 65 yrs @ 8.50%
+ 3.0% & tax @ 30%
Market value (assignment price) =
SAY =
£300,000 p.a.
£20,000 p.a.
£280,000 p.a.
10.828 £3,031,906
£3,030,000
Alternatives: discounted cash flow, conventional dual rate but no tax or single rate no tax as per freehold
but at higher ARY:
Net profit rent =
× YP 65 yrs @ 9.2%
Market value =
SAY =
£280,000 p.a.
10.8339414
£3,033,503
£3,030,000
For use in conjunction with Michael Blackledge, Introducing Property Valuation. Routledge: London.
© 2009 Michael Blackledge
36 Introducing Property Valuation: Suggested solutions to practical exercises
7. Analysis period needs to be decided. Could look to analyse both deals either over the next 5 years or
the next 15 years. It may be each would give a different conclusion and it would depend on the client’s
requirements as to whether they are more interested in the shorter or longer-term investment strategy.
Possible analyses over next 5 years
Offer A
Rent received
£60,000
YP 1.5 yrs @ 7%
1.379
Rent received
£75,000
YP 1.5 yrs @ 7.5%
1.371
× PV 1.5 yrs @ 7.5%
0.8971
Rent received
£100,000
YP 2 yrs @ 8%
1.783
× PV 3 yrs @ 8%
0.7938
Less reverse premium
Value =
Offer B
Rent received
£105,000
Less service charge
@ say 15%
(£15,750)
Net rent received
£89,250
YP 5 yrs @ 8%
3.993
Less legal costs
Value =
Note: legal costs assumed at 7 per cent of rental.
p.a.
£82,740
p.a.
£92,254
p.a.
£141,540
(£20,000)
£296,534
p.a.
p.a.
p.a.
£356,375
(£7,350)
£349,025
Offer B provides the significantly higher value, but offer A has better long-term security and the contribution
to the fitting-out may result in a better-presented property. The decision will depend on the requirements,
preferences and circumstances of the client, but as mentioned above, additional analysis may help them
reach a decision.
Possible analyses over next 15 years
Offer A
Rent received
£60,000
YP 1.5 yrs @ 7%
1.379
Rent received
£75,000
YP 1.5 yrs @ 7.5%
1.371
× PV 1.5 yrs @ 7.5%
0.8971
Rent received
£100,000
YP 2 yrs @ 8%
1.783
× PV 3 yrs @ 8%
0.7938
Rent received (MR)
£95,000
YP 10 yrs @ 8%
6.71
× PV 5 yrs @ 8%
0.6806
Less reverse premium
Value =
p.a.
£82,740
p.a.
£92,254
p.a.
£141,540
p.a.
£433,848
(£20,000)
£730,383
For use in conjunction with Michael Blackledge, Introducing Property Valuation. Routledge: London.
© 2009 Michael Blackledge
37 Introducing Property Valuation: Suggested solutions to practical exercises
Offer B
Rent received
£105,000
Less service charge
@ say 15%
(£15,750)
Net rent received
£89,250
YP 5 yrs @ 8%
3.993
Relet at MR
£95,000
YP 9.5 yrs @ 8%
6.483
× PV 5.5 yrs @ 8%
0.6549
Less legal costs now
Less legal/agents costs on relet
Value =
p.a.
p.a.
£356,375
p.a.
£403,338
(£7,350)
(£14,250)
£738,113
Notes: legals/estate agents fees on relet assumed @ 15% of MR. Assumed rental void of 6 months at end of
next 5 years to allow time for reletting.
Again, offer B provides the better overall value, but this time only slightly higher. It now becomes a much
harder choice between the two offers. To try to reach a final decision, a DCF analysis may help as shown
in the tables below
Offer A
Years
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Rental
incl
growth @
3%
£60,000
Costs
£20,000
£67,500
£75,000
£60,000
£75,000
£100,000
£100,000
£100,000
£110,131
£110,131
£110,131
£110,131
£110,131
£110,131
£110,131
£110,131
£110,131
£110,131
£127,672
£127,672
£127,672
£127,672
£127,672
£127,672
£127,672
£148,007
(£20,000)
£67,500
£100,000
£127,672
Net cash
flow
£127,672
£22,201
£127,672
YP/PV @
10.000%
DCF
1
(£20,000)
0.8264
£55,785
0.9091
0.7513
0.6830
0.6209
0.5645
0.5132
0.4665
0.4241
0.3855
0.3505
0.3186
0.2897
0.2633
0.2394
2.1763
NPV =
Cumulative
DCF
£54,545
£56,349
£68,301
£62,092
£62,166
£56,515
£277,073
(after 5 yrs)
£51,377
£46,706
£42,460
£44,748
£40,680
£36,982
£33,620
£30,564
£299,905
£1,022,796
For use in conjunction with Michael Blackledge, Introducing Property Valuation. Routledge: London.
© 2009 Michael Blackledge
£712,891
(after 15yrs)
38 Introducing Property Valuation: Suggested solutions to practical exercises
Offer B
Years
0
1
2
3
4
Rental incl
growth @ 3%
£89,250
7
£110,131
9
10
11
12
13
14
15
16
£89,250
£14,250
£110,131
£40,816
£110,131
£110,131
£110,131
£110,131
£127,672
£127,672
£127,672
£127,672
£127,672
£127,672
£127,672
£148,007
£89,250
£110,131
£110,131
£127,672
£89,250
£89,250
£89,250
£55,066
(£7,350)
£89,250
£89,250
£89,250
8
£7,350
£89,250
5
6
Costs Net cash flow
£127,672
£22,201
£127,672
YP/PV @
10.000%
DCF Cumulative DCF
1
(£7,350)
0.8264
£73,760
0.9091
0.7513
0.6830
0.6209
0.5645
0.5132
0.4665
0.4241
0.3855
0.3505
0.3186
0.2897
0.2633
0.2394
2.1763
NPV =
£81,136
£67,055
£60,959
£55,417
£23,039
£56,515
£330,978
(after 5 yrs)
£51,377
£46,706
£42,460
£44,748
£40,680
£36,982
£33,620
£30,564
£299,905
£1,037,575
£737,669
(after 15yrs)
Assumption made that, at end of 15 years, investment sold and agents/legal fees incurred. These DCF
analyses again show offer B to provide the higher NPV after 5 years (substantially) and 15 or 16 years
(marginally). Thus from a purely financial viewpoint, offer B is the best, but other considerations may lead
client to choose offer A (i.e. better presented property, initial extra security of income, removal of need to
relet building in 5 years’ time). Need to present the ‘fors’ and ‘againsts’ and leave client to make the final
choice.
For use in conjunction with Michael Blackledge, Introducing Property Valuation. Routledge: London.
© 2009 Michael Blackledge