Valuation Mathematics - Part Two - Capitalisation and other dastardly computations

Still no jokes but here is the skinny on Capitalisation (

Know the difference between income flows and capital sums. Law, in his book Oxford Dictionary of Business and Management defines the former as "any sum that a person or organisation receives either as a reward for effort (Earned income as the tax office defines it) or as a return on investments including land and property (unearned in the eyes of the tax office).

Whereas capital expenditure (costs, investments) is the expenditure by an organisation of a significant amount for the purchase or improvement of a fixed asset. Parsons, The Glossary of Property Terms defines capital value as the value of an asset as distinct from its annual or periodic (rental) value. Capital sums are payments of a one-off basis as to purchase or acquire an investment, good or chattel.

E.G.
An investor buys a property for £1 million and then lets the property out at £80,000 per annum. The tenant has the right to occupy and use the premises in return for the rental payments and these provide the owner with an income of £80,000 per annum in return for the capital sum expended of £1 million

Capitalisation of income is achieved by multiplying the annual income flow by a multiplier, known as the years purchase (YP).

Years purchase (YP) in perpetuity (perp)
This is the present value of £1 per annum forever, thus at 5 per cent the YP perp is 20, which is the sum total of all the PVs from year 1 to infinity and the equation is commonly shown as:

YP perp = 1/i
Where i = interest rate, or yield, expressed as a decimal rate

or

the calculation may be easier to undertake as 100 / Yield
The YP perp at 8% can be found from 100/8 = 12.5

The multiplier is used to capitalise the income flow from a freehold property investment, where the current income is already the full market rent (MR) and thus in present values can't be any higher.

E.G. Where the freehold interest in a business property on the open market was sold for £10 million, a blue-chip company leases it for a long-term period at £550,000 annum. On analysis, the ARY is 5.5% (550,000 x 100 / 10 000 000). But if the purchasers had decided to gain a return of 5.5% on their investment, the price they would be prepared to pay to acquire it would be YP perp at 5.5% x market rent income.

YP perp @ 5.5% = 1/0.055 or 100/5.5 = 18.1818
18.1818 x £550,000 p.a. = £9,999,999.99
that is to SAY £10,000,000.

Get out your Parry's and remember where these five valuation tables are in the book:

Amount of £1 to calculate the future amount of a fixed sum benefitting from compound interest:

(1 + i) n

Present Value of £1 to calculate the present value of a sum expected in the future, given that compound interest could have been earned on it during the period before it is received.

1 / (1 + i) n

Amount of £1 per annum to calculate the future amount of a regular annual investment benefitting from compound interest.

{(1 + i) n - 1} / 1

Annual Sinking Fund to calculate the annual amount required to be invested, at a given rate of compound interest, to grow to a desired future sum.

i / {(1 + i) n - 1}

Years Purchase (or Present Value of £1 per annum) to calculate the present value of an annual amount receivable for a period into the future.

{1 - (1 + i) -n} / 1