Equated Yield Rate 1n3c46
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Discounted Cash Flow (DCF) ✦ The DCF approach involves discounting all future receipts and expenditures similar to the investment method of valuation, but they can be used allow for inflation, taxation and frequent changes in income. Explicit assumptions are made rather than implicit assumptions contained in the traditional All Risks Yield approach. ✦ for the DCF approach came from the Mallinson Report published by the RICS in 1997: ✦ “Report on the President’s Working Party on Commercial Property Valuations” published by the RICS, March 1994. ✦ “Commercial Investment Property: Valuation Methods”, an Information Paper published by the RICS, May 1997. ✦ Two principal methods of DCF calculations are ✦ the Net Present Value method (NPV) ✦ the Internal Rate of Return Method (IRR) - the rate when gives NPV = 0
Dr K Patel, Department of Land Economy, University of Cambridge
1
Net Present Value Method ✦ In the NPV method the present value of all future receipts from an asset is compared with present value of all outgoings. If the present value of receipts exceed the present value of outgoings, the investment is worthwhile. ✦ The Discount rate: the future receipts and outgoings are discounted at an appropriate discount rate. When calculating the worth of an investment to an investor the discount rate will be the investor’s target rate. When the method is used to determine a general market value a discount rate must be adopted which is best approximates the majority of individual target rate. ✦ The discount rate is commonly arrived at by adopting a risk-free rate and making allowances for the risks associated with the property in question. ✦ The risk-free rate is generally taken as the gross redemption yield on medium-term government gilts (bonds). This has ranged between 7% - 10% over recent years. To this is added a risk , say 2%, to reflect the general risks of investing in property such as illiquidity, location, strength of covenants, depreciation, risks of voids, etc.
Dr K Patel, Department of Land Economy, University of Cambridge
2
✦ The DCF calculation makes specific assumptions as to the rate at which the various elements of the calculation will change in the future. The rates of growth may be different. E.g., it may be assumed that rents will grow faster than building costs.The valuer will often rely on his judgement as to growth rates. ✦ Where the valuer knows the All Risks Yield (ARY) appropriate to a property and also the discount rate, an implied rate of growth of the rental value can be determined. ✦ The All Risks Yield equals the discount rate minus the annual sinking fund to recoup the growth in rental value over the review period at the discount rate. Assume that ARY = 6%, the discount rate is 10%, and there are 5-yearly rent reviews, then 10 = 6 + (SF 5yrs @ 10%) x growth over 5 yrs.)
æ 0.10 ö 6% + ç x growth over 5 yrs. ç (1.1) 5 - 1 è Growth over 5 yrs = (10 - 6)/0.1638 = 24.62% i.e. 4.5% annual growth rate
Dr K Patel, Department of Land Economy, University of Cambridge
3
Freeholds with Annual Rent Review The basic DFC method can be stated as R0 R 0 (1 + g ) R 0 (1 + g ) 2 R 0 (1 + g ) 3 + + + + ... P0 = 2 3 4 1+ r (1 + r ) (1 + r ) (1 + r ) which simplifies to P0 =
R0 r-g
where R0 is the current rental and g is the expected rental growth The current rental yield, k, also referred to as the capitalization rate, is k=
R0 P0
and from above we have k = r - g Dr K Patel, Department of Land Economy, University of Cambridge
4
Calculation of Implied Rental Growth (Baum & Crosby) Example 1: A freehold property has just been let on a 25-year lease with 5-year rent review as a net rent of £200,000 pa and subsequently sold for £4,000,000 £200,000 Capitalization rate k = £4,000,000 = 0.05 or 5%
Suppose that the equated yield, e, (also referred to as the assumed target rate) is 13% Implied annual constant rental growth rate is g. Capital gain:
P t - P0 = P 0 (1 + g) t P0 Pt = P 0 (1 + g) t - 1 P0
If the original capital sum is £1 the the capital gain is (1+g)t - 1
Dr K Patel, Department of Land Economy, University of Cambridge
5
The implied constant rental growth rate can be worked out as follows. The equated yield, e, is made up of the capitalization rate, k, plus the annual sinking fund to replace the capital gain at the equated yield over the rent review period:
e = k + Rearranging,
k = e -
e (1 + e) t - 1 e (1 + e) t - 1
x [(1 + g ) t - 1]
x [(1 + g) t - 1]
1 1 1 - (1 + e) t t = + (1 + g) x k e k(1 + e) t
(1 + g )
t
YP perp. @ k - YP t yrs. @ e = YP @ perp. @ k x PV t yrs. @ e
Dr K Patel, Department of Land Economy, University of Cambridge
6
As in the previous example suppose that t = 5 years, k = 5%, e = 13% then g can be calculated as follows
(1 + g ) t =
=
YP perp. @ 5% − YP t yrs. @ 13% YP @ perp. @ 5% x PV t yrs. @ 13%
20 − 3.5172 16.4828 = = 1.5185 20 x 0.5427 10.855
g = (1.5185) 1/5 − 1 = 0.0871
or 8.71% pa
Dr K Patel, Department of Land Economy, University of Cambridge
7
Example 2: Value the freehold interest in a shop to be let on a 25-year lease with 5-year reviews at its current net rental value of £100,000 pa. Assuming a holding period of 30 rears, equated yield 13%, implied growth rate 8.712%, and market capitalization 5%. Capital value = ERV/k = £100,000/0.05 = £2,000,000 Rental £807,160 £531,580 £350,090 £230,560 £151,840 £100,000
5
10
15 Years
20
Dr K Patel, Department of Land Economy, University of Cambridge
25
Perp 8
Valuation assuming a holding period of 30 years: Years 0-5 6-10 11-15 16-20 21-25 26-30 30
Current g @ 8.712% ERV £ pa 100,000 1.0000 100,000 1.5184 100,000 2.3056 100,000 3.5009 100,000 5.3156 100,000 8.0716 100,000 12.2562
Forecasted Income 100,000 151,840 230,560 350,090 531,580 807,160 1,225,620
YP 5 yrs @ 13% 3.5172 3.1572 3.1572 3.1572 3.1572 3.1572 20.000*
PV @ 13% 1.000 0.5428 0.2946 0.1599 0.0868 0.0471 0.0256
Present Value £ 351,720 289,870 238,890 196,880 162,260 133,720 626,660 2,000,000
* YP in perpetuity @ 5% to establish the exit value
Dr K Patel, Department of Land Economy, University of Cambridge
9
Example 3: Value the freehold interest in a shop which was recently let for 20 years at £20,000pa with 5-yearly reviews. All risks yield is 6%. Conventional Method Rent reserved and full rental value £2,000 YP in perp. @ 6% 16.667 Capital value £333,334 DCF Method discount rate is 10%, growth rate 4.5% pa Years Cash flow YP@10% PV@10% 1-5 £20,000 3.7908 6-10 £24,884 3.7908 0.6209 11-15 £30,961 3.7908 0.3855 16-20 £38,522 3.7908 0.2394 20 to perp. £47,929 16.6667* 0.1486 Net Present Value
Capital value £75,816 £58,570 £45,249 £34,959 £118,704 £333,294
*YP in perpetuity @ 6% to establish exit value. Dr K Patel, Department of Land Economy, University of Cambridge
10
Example 4: In Example 3 assume that on expiry of the lease the freehold owner will need to spend £80,000 at current prices and building costs are expected to rise at 3% pa. It is expected to take 3-month rent free period to relet and a 3-month rent freeperiod is likely. The rental value will be unchanged by the work. Years Cash flow 1-20 as before 21 (146,400) 22 £49,547 Net Present Value
YP@10%
PV@10% 0.1452 0.1385
Dr K Patel, Department of Land Economy, University of Cambridge
Capital value £214,594 (21,257) £114,373 £307,710
11
Example 5: In Example 3 assume that the property was let 12 years ago, the current ing rent fixed two years ago is £17,000 pa., and the lease is 8 years unexpired. Conventional Method Term Rent reserved £17,000 YP 3 yrs @ 6% 2.6730 £45,441 Reversion Full Rental value £20,000 YP perp. Def. 3 yrs @ 6% 13.9937 £279,874 Capital value £325,315 DCF Method Years 1-3 4-8 8 to perpetuity Net Present Value
Cash flow £17,000 £22,824 £28,397
YP@10% 2.4869 3.7908 16.6667
PV@10% 0.7513 0.4665
Dr K Patel, Department of Land Economy, University of Cambridge
Capital value £42,277 £65,003 £220,787 £328,067 12
Internal Rate of Return: Equated Yield Rate ✦ The NPV method assesses an investment by discounting the future receipts and outgoings at a selected discount rate. The selected discount rate may produce the result that NPV < 0, NPV = 0 or NPV > 0. ✦ The IRR method determines the value of the discount rate by trial and error such that NPV = 0. ✦ The expression equated yield has been given different definitions. The equated yield is in fact the IRR: the discount rate which needs to be applied to the projected income (allowing for growth) so that the summation of all the incomes discounted at this equated yield rate, equates with the capital outlay. It may be estimated by using the following formula:
ù é NPV1 R1 + (R 2 - R1)ê ë NPV1 + NPV2 where NPV1 is caluculated using the lower discount rate R1 and NPV2 is calculated using the higher discount rate R2. Dr K Patel, Department of Land Economy, University of Cambridge
13
In Example 3 assuming the offered sale capital value of the shop is £300,000, the IRR can be caluculated as follows: Assuming that estimated growth is 4.5% and discount rate of 10% the capital value is found to be £333,294. The difference between £333,294 and the offered sale price £300,000 is £33,294. Try 12%. Years Cash flow 1-5 £20,000 6-10 £24,884 11-15 £30,961 16-20 £38,522 20 to perp. £47,929 Net Present Value
YP@12% 3.6048 3.6048 3.6048 3.6048 16.6667*
PV@12% 0.5674 0.3220 0.1827 0.1037
Capital value £72,096 £50,897 £39,308 £25,370 £82,837 £270,508
At 12% the NPV is £270,508. It is £29,492 below the offered sale price of £300,000.
Dr K Patel, Department of Land Economy, University of Cambridge
14
The IRR can be now estimated using the two values of R1 = 10% and R2 = 12% and NPV1 = £33,294 and NPV2 = £29,492
ù é NPV1 R1 + (R 2 - R1)ê ú NPV NPV + 1 2 ë
é ù 33,294 10% + (12% - 10%)ê êë 33,294 + 29,492 = 11.06% In fact at 11% the NPV is £2,388 below the offered price £300,000.
Dr K Patel, Department of Land Economy, University of Cambridge
15
Dr K Patel, Department of Land Economy, University of Cambridge
1
Net Present Value Method ✦ In the NPV method the present value of all future receipts from an asset is compared with present value of all outgoings. If the present value of receipts exceed the present value of outgoings, the investment is worthwhile. ✦ The Discount rate: the future receipts and outgoings are discounted at an appropriate discount rate. When calculating the worth of an investment to an investor the discount rate will be the investor’s target rate. When the method is used to determine a general market value a discount rate must be adopted which is best approximates the majority of individual target rate. ✦ The discount rate is commonly arrived at by adopting a risk-free rate and making allowances for the risks associated with the property in question. ✦ The risk-free rate is generally taken as the gross redemption yield on medium-term government gilts (bonds). This has ranged between 7% - 10% over recent years. To this is added a risk , say 2%, to reflect the general risks of investing in property such as illiquidity, location, strength of covenants, depreciation, risks of voids, etc.
Dr K Patel, Department of Land Economy, University of Cambridge
2
✦ The DCF calculation makes specific assumptions as to the rate at which the various elements of the calculation will change in the future. The rates of growth may be different. E.g., it may be assumed that rents will grow faster than building costs.The valuer will often rely on his judgement as to growth rates. ✦ Where the valuer knows the All Risks Yield (ARY) appropriate to a property and also the discount rate, an implied rate of growth of the rental value can be determined. ✦ The All Risks Yield equals the discount rate minus the annual sinking fund to recoup the growth in rental value over the review period at the discount rate. Assume that ARY = 6%, the discount rate is 10%, and there are 5-yearly rent reviews, then 10 = 6 + (SF 5yrs @ 10%) x growth over 5 yrs.)
æ 0.10 ö 6% + ç x growth over 5 yrs. ç (1.1) 5 - 1 è Growth over 5 yrs = (10 - 6)/0.1638 = 24.62% i.e. 4.5% annual growth rate
Dr K Patel, Department of Land Economy, University of Cambridge
3
Freeholds with Annual Rent Review The basic DFC method can be stated as R0 R 0 (1 + g ) R 0 (1 + g ) 2 R 0 (1 + g ) 3 + + + + ... P0 = 2 3 4 1+ r (1 + r ) (1 + r ) (1 + r ) which simplifies to P0 =
R0 r-g
where R0 is the current rental and g is the expected rental growth The current rental yield, k, also referred to as the capitalization rate, is k=
R0 P0
and from above we have k = r - g Dr K Patel, Department of Land Economy, University of Cambridge
4
Calculation of Implied Rental Growth (Baum & Crosby) Example 1: A freehold property has just been let on a 25-year lease with 5-year rent review as a net rent of £200,000 pa and subsequently sold for £4,000,000 £200,000 Capitalization rate k = £4,000,000 = 0.05 or 5%
Suppose that the equated yield, e, (also referred to as the assumed target rate) is 13% Implied annual constant rental growth rate is g. Capital gain:
P t - P0 = P 0 (1 + g) t P0 Pt = P 0 (1 + g) t - 1 P0
If the original capital sum is £1 the the capital gain is (1+g)t - 1
Dr K Patel, Department of Land Economy, University of Cambridge
5
The implied constant rental growth rate can be worked out as follows. The equated yield, e, is made up of the capitalization rate, k, plus the annual sinking fund to replace the capital gain at the equated yield over the rent review period:
e = k + Rearranging,
k = e -
e (1 + e) t - 1 e (1 + e) t - 1
x [(1 + g ) t - 1]
x [(1 + g) t - 1]
1 1 1 - (1 + e) t t = + (1 + g) x k e k(1 + e) t
(1 + g )
t
YP perp. @ k - YP t yrs. @ e = YP @ perp. @ k x PV t yrs. @ e
Dr K Patel, Department of Land Economy, University of Cambridge
6
As in the previous example suppose that t = 5 years, k = 5%, e = 13% then g can be calculated as follows
(1 + g ) t =
=
YP perp. @ 5% − YP t yrs. @ 13% YP @ perp. @ 5% x PV t yrs. @ 13%
20 − 3.5172 16.4828 = = 1.5185 20 x 0.5427 10.855
g = (1.5185) 1/5 − 1 = 0.0871
or 8.71% pa
Dr K Patel, Department of Land Economy, University of Cambridge
7
Example 2: Value the freehold interest in a shop to be let on a 25-year lease with 5-year reviews at its current net rental value of £100,000 pa. Assuming a holding period of 30 rears, equated yield 13%, implied growth rate 8.712%, and market capitalization 5%. Capital value = ERV/k = £100,000/0.05 = £2,000,000 Rental £807,160 £531,580 £350,090 £230,560 £151,840 £100,000
5
10
15 Years
20
Dr K Patel, Department of Land Economy, University of Cambridge
25
Perp 8
Valuation assuming a holding period of 30 years: Years 0-5 6-10 11-15 16-20 21-25 26-30 30
Current g @ 8.712% ERV £ pa 100,000 1.0000 100,000 1.5184 100,000 2.3056 100,000 3.5009 100,000 5.3156 100,000 8.0716 100,000 12.2562
Forecasted Income 100,000 151,840 230,560 350,090 531,580 807,160 1,225,620
YP 5 yrs @ 13% 3.5172 3.1572 3.1572 3.1572 3.1572 3.1572 20.000*
PV @ 13% 1.000 0.5428 0.2946 0.1599 0.0868 0.0471 0.0256
Present Value £ 351,720 289,870 238,890 196,880 162,260 133,720 626,660 2,000,000
* YP in perpetuity @ 5% to establish the exit value
Dr K Patel, Department of Land Economy, University of Cambridge
9
Example 3: Value the freehold interest in a shop which was recently let for 20 years at £20,000pa with 5-yearly reviews. All risks yield is 6%. Conventional Method Rent reserved and full rental value £2,000 YP in perp. @ 6% 16.667 Capital value £333,334 DCF Method discount rate is 10%, growth rate 4.5% pa Years Cash flow YP@10% PV@10% 1-5 £20,000 3.7908 6-10 £24,884 3.7908 0.6209 11-15 £30,961 3.7908 0.3855 16-20 £38,522 3.7908 0.2394 20 to perp. £47,929 16.6667* 0.1486 Net Present Value
Capital value £75,816 £58,570 £45,249 £34,959 £118,704 £333,294
*YP in perpetuity @ 6% to establish exit value. Dr K Patel, Department of Land Economy, University of Cambridge
10
Example 4: In Example 3 assume that on expiry of the lease the freehold owner will need to spend £80,000 at current prices and building costs are expected to rise at 3% pa. It is expected to take 3-month rent free period to relet and a 3-month rent freeperiod is likely. The rental value will be unchanged by the work. Years Cash flow 1-20 as before 21 (146,400) 22 £49,547 Net Present Value
YP@10%
PV@10% 0.1452 0.1385
Dr K Patel, Department of Land Economy, University of Cambridge
Capital value £214,594 (21,257) £114,373 £307,710
11
Example 5: In Example 3 assume that the property was let 12 years ago, the current ing rent fixed two years ago is £17,000 pa., and the lease is 8 years unexpired. Conventional Method Term Rent reserved £17,000 YP 3 yrs @ 6% 2.6730 £45,441 Reversion Full Rental value £20,000 YP perp. Def. 3 yrs @ 6% 13.9937 £279,874 Capital value £325,315 DCF Method Years 1-3 4-8 8 to perpetuity Net Present Value
Cash flow £17,000 £22,824 £28,397
YP@10% 2.4869 3.7908 16.6667
PV@10% 0.7513 0.4665
Dr K Patel, Department of Land Economy, University of Cambridge
Capital value £42,277 £65,003 £220,787 £328,067 12
Internal Rate of Return: Equated Yield Rate ✦ The NPV method assesses an investment by discounting the future receipts and outgoings at a selected discount rate. The selected discount rate may produce the result that NPV < 0, NPV = 0 or NPV > 0. ✦ The IRR method determines the value of the discount rate by trial and error such that NPV = 0. ✦ The expression equated yield has been given different definitions. The equated yield is in fact the IRR: the discount rate which needs to be applied to the projected income (allowing for growth) so that the summation of all the incomes discounted at this equated yield rate, equates with the capital outlay. It may be estimated by using the following formula:
ù é NPV1 R1 + (R 2 - R1)ê ë NPV1 + NPV2 where NPV1 is caluculated using the lower discount rate R1 and NPV2 is calculated using the higher discount rate R2. Dr K Patel, Department of Land Economy, University of Cambridge
13
In Example 3 assuming the offered sale capital value of the shop is £300,000, the IRR can be caluculated as follows: Assuming that estimated growth is 4.5% and discount rate of 10% the capital value is found to be £333,294. The difference between £333,294 and the offered sale price £300,000 is £33,294. Try 12%. Years Cash flow 1-5 £20,000 6-10 £24,884 11-15 £30,961 16-20 £38,522 20 to perp. £47,929 Net Present Value
YP@12% 3.6048 3.6048 3.6048 3.6048 16.6667*
PV@12% 0.5674 0.3220 0.1827 0.1037
Capital value £72,096 £50,897 £39,308 £25,370 £82,837 £270,508
At 12% the NPV is £270,508. It is £29,492 below the offered sale price of £300,000.
Dr K Patel, Department of Land Economy, University of Cambridge
14
The IRR can be now estimated using the two values of R1 = 10% and R2 = 12% and NPV1 = £33,294 and NPV2 = £29,492
ù é NPV1 R1 + (R 2 - R1)ê ú NPV NPV + 1 2 ë
é ù 33,294 10% + (12% - 10%)ê êë 33,294 + 29,492 = 11.06% In fact at 11% the NPV is £2,388 below the offered price £300,000.
Dr K Patel, Department of Land Economy, University of Cambridge
15
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