### A1. BEAMA

BEAMA is a trade body for Electrical Manufactureres in UK. This is a micro-site for companies who subscribe to the BEAMA indices.

For information about BEAMA please visit the main BEAMA website http://www.beama.org.uk .

### A2. Contract Risk

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.

### A3. BEAMA Contract Price Advisory Service

BEAMA indices mitigate contract risks associated with electrical and mechanical projects by tracking the cost of materials and labour in these two industries (see section A4 ). BEAMA also maintain sixteen standard formulae which specify the indices to use for different engineering projects (see section A6 ).

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: $$\begin{eqnarray} \label{eqn_32} P_1 &=& \frac{P_0}{100} \left[ a + \left(b_1 \frac{M_{11}}{M_{10}} + \ldots +b_m \frac{M_{m1}}{M_{m0}}\right) + \left(c_1 \frac{L_{11}}{L_{10}} +\ldots+c_l \frac{L_{l1}}{L_{l0}}\right) \right] \\ 100 &=& a + \left(b_1+\ldots+b_m\right) +\left(c_1+\ldots+c_l \right) \end{eqnarray}$$

### A4. BEAMA Indices

#### Labour Indices

• BEAMA Electrical Labour Cost Index (BEL)
• BEAMA Mechanical Labour Cost Index (BML)

#### Material Indices

• BEAMA Basic Electrical Equipment Cost Index (BEE)
• BEAMA Mechanical Engineering Cost Index (BMI)
• BEAMA Factory Built Assemblies Cost Index(BFB)
• BEAMA Distribution Transformer Cost Index (BTD)
• BEAMA Industrial Electronic Cost Index(BIE)
• BEAMA Large Power Transformer Index(BLT)
• BEAMA Basic Iron & Steel Cost Index(BIS)
• BEAMA Composite Index (BCI)
• BEAMA Basic Iron & Steel Producers Cost Index(BIP)

### A5. BEAMA Standard Formula Notations

• $$P_0$$   Initial Contract Price (FOB price for export contracts
• $$P_n$$   Final Contract Price (FOB price for export contracts
• $$I_0$$   Index value last published before date of Tender
• $$I_n$$   Index value last published before the completion date
• $$I_{mth:0}$$   Index (or Price) of $$I$$ published in month in which Tender date falls
• $$I_{mth:x}$$   Index (or Price) of $$I$$ published $$x$$ months after the date of Tender
• $$I_{day:0}$$   Index (or Price) published on the same day as the date of Tender
• $$I_{day:x}$$   Index (or Price) published $$x$$ days after the date of Tender
• $$I_{avg|t:x\rightarrow y}$$   Average of Index (or Price) $$I$$, published between $$x\%$$ and $$y\%$$ of the contract period
• $$I_{avg|mth:x,y,z}$$   Average of Index (or Price) $$I$$, published for months of $$x ,y$$ and $$z$$ after the contract start date
• $$I_{avg|mth:n-x,n-y,n-z}$$  Average of index $$I$$ published for months of $$x ,y$$ and $$z$$ before the completion date
• $$I_{date:agreed}$$   Index (or Price) of $$I$$ published on the $$date$$ specified in advance by the Purchaser and $$agreed$$ by the Contractor
• $$I_{date:order}$$   Index (or Price) of $$I$$ published on the $$date$$ the Contractor places the $$order$$ with the supplier

### A6. BEAMA Standard Formulae

The equations below are the list of existing BEAMA Standard Formulae using the abbreviations in section A4 and notations in section A5 .

1. #### Electrical Machinery

$$P_n = \frac{P_0}{100} \left(5 + 47.5\times \frac{{BEE}_{avg|t:40\rightarrow 80}}{{BEE}_0} +47.5\times \frac{{BEL}_{avg|t:33\rightarrow 100}}{{BEL}_0}\right)$$

2. #### Mechanical Plant

$$P_n = \frac{P_0}{100}\left(5 + 47.5\times \frac{BMM_{avg|t:40\rightarrow 80}}{BMM_0} +47.5\times \frac{BML_{avg|t:33\rightarrow 100}}{BML_0}\right)$$

3. #### Industrial Electronic Equipment

$$P_n = \frac{P_0}{100}\left(5 + 32\times \frac{BIE_{avg|t:40\rightarrow 80}}{BIE_0} +63\times \frac{BML_{avg|t:33\rightarrow 100}}{BML_0}\right)$$

4. #### Rotating Electrical Machinery

$$P_n = \frac{P_0}{100}\left(5 + 40\times \frac{BEE_{avg|t:58\rightarrow 75}}{BEE_0} +55\times \frac{BEL_{avg|t:58\rightarrow 100}}{BEL_0}\right)$$

5. #### Distribution Transformers $$<$$ 10 MVA

$$P_n = \frac{P_0}{100}\left(5 +35\times \frac{BEL_{mth:n-1}}{BEL_{mth:0}} + x\times \frac{BLT_{mth:n-2}}{BLT_{mth:0}}+ y\times \frac{{LMEcu}_{date:agreed}}{{LMEcu}_{day:0}}\right)$$
$$x+y=60$$
$$y$$ is the proportion of the contract price at the date of tender wholly related to copper (i.e. the weight of copper multiplied by the cost per kilo of copper at tender date, expressed as proportion of the contract price at date of tender. This proportion should be scaled down by $$60\%$$ to preserve the material proportion of the formula.

6. #### Distribution Transformers $$\geq$$ 10 MVA

$$P_n = \frac{P_0}{100}\left(5 +47.5\times \frac{BEL_{mth:n-1}}{BEL_{mth:0}} + x\times \frac{BLT_{mth:n-2}}{BLT_{mth:0}}+ y\times \frac{{LMEcu}_{date:agreed}}{{LMEcu}_{day:0}} + z\times \frac{{TDEoil}_n}{{TDEoil}_0} \right)$$
$$x+y+z=47.5$$
$$y$$ is the proportion of the contract price at the date of tender wholly related to copper (the weight of copper multiplied by the cost per kilo of copper at tender date, expressed as proportion of the contract price at date of tender
$$z$$ is the proportion of the contract price at date of tender which is wholly related to insulating oil (i.e. the quantity of insulating oil multiplied by the cost per litre of insulating oil at tender date, expressed as a proportion of the contract price at date of tender

7. #### Large Power Transformers

$$P_n = \frac{P_0}{100}\Bigl( 5 +25\times \frac{BEL_{mth:n-1}}{BEL_{mth:0}} + 20\times \frac{BLT_{mth:n-2}}{BLT_0} +10\times \frac{BIS_{mth:n-2}}{BIS_0} + 15\times \frac{LMEcu_{ order|day:1} }{ LMEcu_{ day:0} } + 5\times \frac{ TDEoil_{n-2} }{ TDEoil_{mth:0-1} } + 20\times \frac{TDEgoes_{n-2}}{TDEgoes_{mth:0-1}} \Bigl)$$

8. #### Turbo Generating & Allied Plant

$$P_n = \frac{P_0}{100}\left(5 +47.5\times \frac{BEL_{avg|t:33\rightarrow 100}}{BEL_0} + 33.25\times \frac{BIS_{avg|t:40\rightarrow 80}}{BIS_0} + 14.25\times \frac{BMM_{avg|t:40\rightarrow 80}}{BMM_0} \right)$$

9. #### Distribution Feeder Pillars

$$P_n = \frac{P_0}{100} \left(5 + 56\times \frac{{BEL}_{mth:n-1}}{{BEL}_{mth:0-1}} + 39\times \frac{{BEE}_{mth:n-1}}{{BEE}_{mth:0-1}} \right)$$

10. #### Switchgear $$\leq 36 kV$$

$$P_n = \frac{P_0}{100}\left(5 + 45\times \frac{{BEL}_{mth:n-1}}{{BEL}_{mth:0}} +50\times \frac{{BEE}_{mth:n-1}}{{BEE}_{mth:0-1}}\right)$$

11. #### Switchgear $$> 36 kV$$

$$P_n = \frac{P_0}{100}\left(5 + 45\times \frac{{BEL}_{avg|mth:n-3,n-2,n-1}}{{BEL}_{mth:0}} +50\times \frac{{BEE}_{avg|mth:n-4,n-3}}{{BEE}_{mth:0}}\right)$$

12. #### Factory Built Assemblies for Control Equipment

$$P_n = \frac{P_0}{100}\left(5 +47.5\times \frac{{BEL}_{mth:n-1}}{{BEL}_{mth:0}} + 47.5\times \frac{BFB_{mth:n-1}}{BFB_{mth:0}} \right)$$

13. #### Factory Built Assemblies for Low Voltage Switchgear

$$P_n = \frac{P_0}{100}\left(5 +47.5\times \frac{{BEL}_{mth:n-1}}{{BEL}_{mth:0}} + 47.5\times \frac{BEE_{mth:n-1}}{BEE_{mth:0}} \right)$$

14. #### Service and Maintenance (Electrical)

$$P_n = \frac{P_0}{100}\left(5 + x\times \frac{{BEL}_{mth:n-1}}{{BEL}_{mth:0}} +y\times \frac{BEE_{mth:n-1}}{BEE_{mth:0}}\right)$$
$$x + y = 95$$

15. #### Service and Maintenance (Mechanical)

$$P_n = \frac{P_0}{100}\left(5 + x\times \frac{{BML}_{mth:n-1}}{{BML}_{mth:0}} +y\times \frac{BMM_{mth:n-1}}{BMM_{mth:0}}\right)$$
$$x + y = 95$$

16. #### Electrical / Mechanical Contracts

$$P_n = \frac{P_0}{100} \left(5 + 23.75\times \frac{{BEE}_{avg|t:40\rightarrow 80}}{{BEE}_0} +23.75\times \frac{{BEL}_{avg|t:33\rightarrow 100}}{{BEL}_0} + 23.75\times \frac{BMM_{avg|t:40\rightarrow 80}}{BMM_0} +23.75\times \frac{BML_{avg|t:33\rightarrow 100}}{BML_0}\right)$$

### A7. Worked Example: Electrical Machinery

#### Formula

If the cost to the Contractor of performing his obligations under the Contract shall be increased or reduced by reason of any rise or fall in labour costs or in the cost of material the amount of such increase or reduction shall be added to or deducted from the Contract Price as the case may be. Provided that no account shall be taken of any amount by which any cost incurred by the Contractor has been increased by the default or negligence of the Contractor.

Variations in the cost of materials and labour shall be calculated in accordance with the following Formula:

$$P_n = \frac{P_0}{100} \left(5 + 47.5\times \frac{{BEE}_{avg|t:40\rightarrow80}}{{BEE}_0} +47.5\times \frac{{BEL}_{avg|t:33\rightarrow100}}{{BEL}_0}\right)$$where
$$P_0$$ = Contract Price at Date of Tender

$$P_1$$ = Final Contract Price

$${BEE}_0$$ = BEAMA Electrical Equipment index figure last published before the date of tender

$${BEE}_{avg|t:40\rightarrow80}$$ = Average of BEAMA Electrical Equipment index last published at $$\frac{2}{5}$$ point of the Contract Period and ending with the Index last published before the $$\frac{4}{5}$$ point of the Contract Period.

$${BEL}_0$$ = BEAMA Labour Cost index figure for Electrical Engineering published for the month in which the tender date falls.

$${BEL}_{avg|t:33\rightarrow100}$$ = Average of the BEAMA Labour Cost index figures for Electrical Engineering published for the last $$\frac{2}{3}$$ of the Contract Period

#### Data

• A - Contract Price,   $$P_0$$ = £20,000
• B - Date of Tender,   $$T_0$$ = 20TH JAN 2005
• C - Date of Order,   $$T_1$$ = 14TH FEB 2005
• D - Completion Date,  $$T_2$$ = 12TH AUG 2008

#### Calculation

##### Contract Days
• E - Contract days between C and D , $$\Delta T = T_2 - T_1 = 1275$$

##### Electrical Material Indices (2000=100)
• F - Date at two-fifths of Contract Period, $$T_{40\%} = T_1+\frac{2}5\Delta T = T_1 + 510(days)$$ = (09/Jul/06)
• G - Date at four-fifths of Contract Period, $$T_{80\%} = T_1+\frac{4}{5}\Delta T = T_1 + 1020(days)$$ = (01/Dec/07)
• H - Average of indices published between F and G , $${BEE}_{avg|t:40\rightarrow80} =$$ average(issue$$_{441}$$ to issue$$_{459}$$) = 135.87
• I - Index last published before the date of tender B , $${BEE}_0$$ = issue$$_{425}$$ = 113.3

##### Electrical Labour Indices (Jan 1980=100)
• J - Date at one-third of Contract Period, $$T_{33\%} = T_1+\frac{1}{3}\Delta T = T_1 + 425(days)$$ = (15/Apr/06)
• K - Completion date, $$T_{100\%} = T_2 =$$ (12/Aug/08)
• L - Average of indices published between J and K , $${BEL}_{avg|t:33\rightarrow100} =$$ average(issue$$_{439}$$ to issue$$_{467}$$ ) = 702.06
• M - Index published for the month in which the tender date falls B , $${BEL}_0$$ = issue$$_{424}$$ = 640.2

##### Final Contract Price
$$\begin{eqnarray} P_n &=& \frac{P_0}{100} \left(5 + 47.5\times \frac{{BEE}_{avg|t:40\rightarrow80}}{{BEE}_0} +47.5\times \frac{{BEL}_{avg|t:33\rightarrow100}}{{BEL}_0}\right)\\ &=& \frac{20000}{100} \left[5+47.5\times \frac{135.87}{113.30}+47.5\times \frac{702.06}{640.20} \right] \\ &=& 22,810.00 \end{eqnarray}$$
$$\begin{eqnarray} \Delta P &=& P_n - P_0 \\ &=& 22,810.00 - 20,000.00\\ &=& 2,810.00 \end{eqnarray}$$