### Contract Price Adjustment

### Contract Related Risks

**Contract**execution involves some man-hours (

**labour**) and in most cases

**materials**. After a contract has been agreed, the cost of materials or the cost of labour or both may change during the contract period. The contractor must find a way to recover the increased cost to avoid the risk of running at a loss.

One way to recover the cost is for the contractor to submit detail invoices to the customer (or the purchaser) to prove that the prices paid were much higher than the cost showed in the tender document. For simple projects, this method may be possible but it is not practical for majority of contracts.

Other ways of dealing with these price uncertainties include:

- Fixed price which has built-in contingency in the tender price on the basis of experiece of similar past projects
- Using forward-prices in your tender quote
- Freezing salaries of workers during the contract period
- Use retail or consumer price index (RPI/CPI) as a measure of cost inflation

While the methods above are being used successfully by companies, the following risks remain:

- Pricing yourself out of the bid with high contingency or high future prices
- Running at a loss if the actual cost prove to be higher than the tender price
- Renegotiating the price during the contract period
- Reneging on contract if the actual cost prove to be exceesively higher and the purchaser fails to renegotiate
- Low productivity or losing key workers if wages are frozen over long period
- Price mis-match of RPI/CPI with actual material or labour cost variation. CPI measures the cost of living which includes
**food**,**education**,**health**,**housing**,**alcoholic beverages**,**clothing**,**transport**,**restaurants**,**furniture**,**recreation**and other miscellaneous goods. With exception of transport, the components of the CPI have no bearing on the cost of materials for engineering projects.

### Adjustment Formulae

BEAMA indices mitigate contract risks associated with electrical and mechanical projects by tracking the cost of materials and labour in these two industries.
BEAMA also maintain sixteen standard formulae which specify the indices to use for different engineering projects.

The general form of a Contract Price Adjustment (CPA) formula has a material component (\(M\)) and a labour component (\(L\)) which are both variable.

Most CPA formulae also have a non-variable element which is not subject to adjustment. This represents certain overheads and costs which are considered to be fixed over the contract period.

Mathematically, any CPA formula can be represented as:$$\begin{eqnarray*} P_1 &=& \frac{P_0}{100}\left(a + b \frac{M_1}{M_0} +c \frac{L_1}{L_0}\right) \\ 100 &=& a + b +c \end{eqnarray*}$$where

\(P_1\) = Final Contract Price

\(P_0\) = Initial Price

\(M_1\) = Material prices or indices at specified point in time

\(M_0\) = Material prices or indices at base date

\(L_1\) = Labour costs or indices at specified point

\(L_0\) = Labour costs or indices at base date

\(a\) = Percentage proportion of Fixed Costs (non-variable element)

\(b\) = Percentage proportion of Materials

\(c\) = Percentage proportion of Labour

The formula uses the same principle if there are two or more indices for either labour or material. If the formula contains say \(l\) labour indices and \(m\) material indices the formula becomes: $$\begin{eqnarray*} P_1 &=& \frac{P_0}{100} \left[ a + \left(b_1 \frac{M_{11}}{M_{10}} + \ldots +b_m \frac{M_{m1}}{M_{m0}}\right) + \left(c_1 \frac{L_{11}}{L_{10}} +\ldots+c_l \frac{L_{l1}}{L_{l0}}\right) \right] \\ 100 &=& a + \left(b_1+\ldots+b_m\right) +\left(c_1+\ldots+c_l \right) \end{eqnarray*}$$

The general form of a Contract Price Adjustment (CPA) formula has a material component (\(M\)) and a labour component (\(L\)) which are both variable.

Most CPA formulae also have a non-variable element which is not subject to adjustment. This represents certain overheads and costs which are considered to be fixed over the contract period.

Mathematically, any CPA formula can be represented as:$$\begin{eqnarray*} P_1 &=& \frac{P_0}{100}\left(a + b \frac{M_1}{M_0} +c \frac{L_1}{L_0}\right) \\ 100 &=& a + b +c \end{eqnarray*}$$where

\(P_1\) = Final Contract Price

\(P_0\) = Initial Price

\(M_1\) = Material prices or indices at specified point in time

\(M_0\) = Material prices or indices at base date

\(L_1\) = Labour costs or indices at specified point

\(L_0\) = Labour costs or indices at base date

\(a\) = Percentage proportion of Fixed Costs (non-variable element)

\(b\) = Percentage proportion of Materials

\(c\) = Percentage proportion of Labour

The formula uses the same principle if there are two or more indices for either labour or material. If the formula contains say \(l\) labour indices and \(m\) material indices the formula becomes: $$\begin{eqnarray*} P_1 &=& \frac{P_0}{100} \left[ a + \left(b_1 \frac{M_{11}}{M_{10}} + \ldots +b_m \frac{M_{m1}}{M_{m0}}\right) + \left(c_1 \frac{L_{11}}{L_{10}} +\ldots+c_l \frac{L_{l1}}{L_{l0}}\right) \right] \\ 100 &=& a + \left(b_1+\ldots+b_m\right) +\left(c_1+\ldots+c_l \right) \end{eqnarray*}$$