The previous article on this subject suggested that growth-implicit methods of valuation were dependent on a number of additional variables:
The equivalent yield, e
The growth rate, g
The review period, t
The inflation-risk-free yield, i.
Equivalent yield
The equivalent yield is the inflation-prone target yield required by the investor, in effect the internal rate of return, traditionally found by reference to the yield on undated securities plus a margin to allow for the essential differences between property and gilts, this is commonly taken to be about + 2%.
Growth rate
In practice the valuer would have to derive the growth rate from the available evidence. It is sometimes argued that this is the weakness of growth-explicit methods of valuation, but, as this is just one of the elements of the all-risk yield, it is also a weakness inherent in the conventional approach. At least now, with a growth-explicit method, the valuer is making his assumptions clear.
Every all-risks yield contains an implicit assumption about growth; this is why the 6% yield adopted in valuation 1 appears to be low. If the target rate or equivalent yield is known, it is possible to calculate the rate of growth implied by the all-risk yield using the following formula:
The rate of growth implied by a yield of 6% where the equated yield is 13% is therefore as follows:
Inflation-risk-free yield
The inflation-risk-free yield is the yield on a totally inflation-proof income, being the real return on such an investment. It assumes that the rent can be reviewed to a new rent which cancels out the effect of inflation, thus producing a static real value profile. This is the basis for the real value model.
The inflation-risk-free yield can be found by the formula:
Now that the average rate of growth implied by the yield of 6% and the equated yield of 13% have been found, the inflation-proof yield can be calculated:
Once the average annual growth rate has been computed the investment can be valued using normal DCF methods as well as variants of the “real value” method. The variables are as follows:
The equivalent yield, e = 0.13
The growth rate, g = 0.07768
The review period, t = 5 years
The inflation-risk-free yield, i = 0.04855
The capitalisation rate, k = 0.06
It will be recalled from example one, where the conventional term and reversion approach was used to value a shop let two years ago on a lease with a five-year review pattern and the rent fixed under the lease was £8,000 and the FRV £10,000, that the valuation based on an all-risk yield of 6% produced a capital value of £161,284.
The same valuation can now be undertaken utilising discounted cash flow (Valuation 2) and a variant of the real value approach (Valuation 3), which has been described as “a real value/equated yield hybrid”(*)
Valuation (2) discounted cash flow
This is a valuation based on the assumption of an income flow which will grow at 7.768% pa. For convenience of layout it is assumed that the investment is sold after 18 years. (See table.)
DCF by formula
The term is valued by capitalising the current rental value by the YP for the remaining term at the equivalent yield — a return which fully acknowledges the inflation-prone nature of the income during the term period.
The reversion is the full rental value, increased by the growth rate capitalised in perpetuity at the capitalisation rate which reflects future growth at the average rate of 7.768%, implied by the relationship between the all-risk and equivalent yields, but deferred at the equated yield again allowing for the effects of inflation over the three-year waiting period.
Each tranche of the reversion takes the full rental value, suitably increased to take account of growth multiplied by the YP for the review period at the equivalent yield suitably deferred at the equivalent yield. The reversion part of the formula is derived from a full-blown DCF calculation, which is of course a geometric progression and can therefore be reduced to a single expression.
If the two discounted cash flow calculations are compared it can be seen that they provide similar but not identical solutions. The difference in capital value of £33 arises as a result of the early cut-off point (18 years) in the conventionally tabulated DCF. This is necessary purely as a matter of presentation. For the calculation to proceed on the assumption that the investment is held in perpetuity would require an infinite amount of paper!
Valuation (3) Real Value Method
Alternatively the valuation can be carried out using a real value method, and although this is derived from a DCF approach the valuation can again be undertaken using a familiar valuation format:
As with the discounted cash flow in Valuation 2, the term is capitalised at the appropriate equivalent yield, 13%, a higher rate which recognises the inflation-prone nature of the three-year fixed-income flow. The reversion income is capitalised at the all-risk yield, reflecting the growth which will take place between reviews, but this is deferred at the inflation-risk-proof yield, thus assuming the constant real static income flow resulting from the balancing out of the effects of growth and inflation which is characteristic of real value models.
The three valuations compared
Valuation (1) Term and reversion £161,284
Valuation (2) DCF by formula £163,463
Valuation (3) Real value £163,460
Valuations 2 and 3 are in fact identical, the small difference resulting from rounding errors. This is because they are broadly the same. The term is valued in the same way in each case, recognising the important fact that during the term period the income flow will be totally inflation-prone.
That these two valuations are fairly close to the term and reversion solution (Valuation 1) is, of course, no coincidence. This arises because the assumed growth rate was derived directly from the relationship between the all-risks yield of 6% and the equated yield of 13%. However, there is one major difference; the term in valuation 1 is clearly overvalued by the application of a yield which assumes growth to the capitalisation of an income which, by definition, will not grow.
Conclusion
Given a yield drawn from evidence provided by investment markets generally, and an explicit assumption about future income growth, it should be possible to formulate a method of valuation which more logically reflects reality rather than a convenience contrived out of the habit of conventional methods. It is submitted that valuations can be based on reasoned and explicit assumptions and a model of income flows which is directly related to reality using yields that can be compared with other investment opportunities and yet which should command the attention and understanding of valuers by utilising recognisable valuation formats.
Conventional approaches to investment valuation are neither rational nor logical, worse still, they are limited in their application. Where market evidence is short, the use of the method will lead to inaccuracy. Valuers using any method of valuation should fully understand the model upon which it is based if it is not to be misapplied. Better still, they should be prepared to adopt a more explicit approach reflecting the present economic realities of the real world in which investment actually takes place. This is a world which changes, and as change takes place so should the valuer be prepared to be genuinely flexible in the methods adopted.
Note
The earlier article which dealt with Valuation 1 implied that the initial return on the shop investment was 6% when of course it was actually nearer 5% being the initial income divided by the capital value;
(*) Baum A and Crosby N, Property Investment Appraisal, Routledge 1988.
