# Emden Formula, Hudsen Formula, Eichleay Formula

One of the principal elements of a claim for loss and expense or costs due to the prolongation of the works is a claim for the costs of head office overheads. Such claims are made under two quite distinct bases, either an actual cost approach or a lost opportunity approach.

The lost opportunity approach is made on the premise that because of the delay the contractor’s organization is unable to move on to another project and earn the combined profit and head office overheads of which it is reasonably capable, i.e. the opportunity to earn elsewhere is lost.

The actual cost approach is simply the identification and cost of the head office overheads affected by the delay. The lost opportunity approach is by far the most popular with contractors, for two reasons. Firstly, because the actual costs are so difficult to identify and prove, and secondly, because the lost opportunity approach uses a formula for its calculation. Contractors love to use a formula to calculate head office overhead costs and it is easy to see why. A formula calculation is simple, cheap, quick and produces a reasonable sum of money for very little effort.

There are two formulae commonly used for such calculations, the Hudson’s formula and the Emden formula. Hudson’s formula was first produced by Mr. Duncan Wallace (purportedly upon the advice of a quantity surveyor) and published in Hudson’s Building and Engineering Contracts.

Basically there are three quantity surveying formulas which are used to calculate the head office overhead.

### Hudson’s formula

Hudson’s formula is Head Office Contract overhead Percentage 1 x Sum x Period of 100 Contract Delay Period. The Head Office Overhead percentage in the Contract and it has received judicial support in a number of cases.

The formula is criticised by many principally because it adopts the head office overhead percentage from the contract as the factor for calculating the costs, and this may bear little or no relation to the actual head office costs of the contractor. In an attempt to improve upon the Hudson’s formula an alternative was published in Emden’s Building Contracts and Practice.

### Emden’s formula

Head office o/h delay in Project = total over hesd cost(profit)*100
total turnover

Emden’s formula is Head Office Contract Overhead Percentage2 x Sum x Period of 100 Contract Delay Period

The HO/Profit percentage is head office percentage, arrived at by dividing the total overhead cost and profit of the Contractor’s organization as a whole by the total turnover. This formula has the advantage of using the contractor’s actual head office/ profit percentage rather than the one contained in the contract and has received judicial support in a number of cases.

These two formulae were used for many years until the use of formula, and indeed the opportunity costs approach in general fell out of favour following the (non construction) case of Tate & Lyle

Where the court would not accept a calculation of head office overheads based upon a simple percentage, and stated that it was necessary to prove actual additional costs incurred rather than a hypothetical loss of opportunity approach. Many felt that this case sounded the death knell for head office overhead claims based upon the loss of opportunity approach and in particular by the use of simple formula. However, the difficulties of proving the actual additional costs incurred in respect of head office overheads (and possibly of judges in assessing them) have recently led to the courts taking a more relaxed view of the degree of proof necessary to prove that the delay had caused the contractor to lose the opportunity to fully earn its head office overheads elsewhere, and in a number of cases claims using the loss of opportunity approach and a formula are re-appearing.

So there seems to be a swing back to accepting the use of Hudson’s or Emden’s formulae for the assessment of head office overheads, provided of course the contractor can prove that due to the delay he has in some way lost the opportunity to fully earn the head office overheads on other projects. Where the loss of opportunity cannot be proven, and an actual cost approach is necessary there is however a formula that may be appropriate. This formula is the American Eichleay formula and it is one, which I have personally found very useful recently. This formula is calculated by comparing the value of work carried out in the contract period for the project with the value of work carried out by the contractor as a whole for the contract period. A share of head office overheads for the contractor can then be allocated in the same ratio and expressed as a lump sum to the particular contract. The amount of head office overhead allocated to the particular contract is then expressed as a weekly amount by dividing it by the contract period. Theperiod of delay can then be multiplied by the weekly amount to give a total sum claimed.

### Eichleay formula

Eichleay formula is thus Value of work during Total Head Office Contract Period x Overhead during Total value of work during contract For Company as a whole Period During Contract period

= Total Head Office Overheads during contract Period

Head Office Overhead Allocated to the Contract x Period of Delay Contract period

= Amount Claimed

The formula looks complicated, but is not and was recently used (but not named) in the case of this complexity.

So the use of formula to calculate head office overheads is not dead, Hudson’s or probably better Emden’s formula can be used where the contractor can prove some lost opportunity to recover contributions to head office overheads from other projects, and Eichleay can be used where a claim based on actual costs is more appropriate.