In SIGMA are two methods of cost accounting, the full cost calculation and the machine hour rate calculation. The calculation of the machine hour rate sums up all machine dependent costs, for example energy and occupancy costs. This calculation is useful to compare two machines with different screw diameters on cost basis. The full cost calculation method includes all costs of one period, so that the user can see all costs which incur in a period. In the following section, both calculation methods will be explained.

The machine hour rate calculation is a cost accounting method. Cost accounting is used to support corporate decisions. The aim of the machine-hour rate calculation is to determine the machine dependent costs which incur per hour run time. Machine dependent costs are costs which relates to the extruder like energy costs, occupancy costs, wear costs etc. Variable costs like material costs are not considered.

The machine hour rate calculation in SIGMA proceeds in the following steps:

1. Determination of productive machine time $t_{Bs}$. Cleaning time, servicing time, changing and batch time are not considered.
2. Determination of machine costs $K_{Maschine}$. Therefore only the indirect labor costs as occupancy costs, maintenance costs and energy costs are considered. Variable costs like for example material costs are not considered
3. Calculation of the machine hour rate with $M_{SS} = \frac{K_{Maschine}}{t_{Bs}}$.

The machine dependent costs are determined by the following equation:

$$K_{Maschine} = K_{Ab} + K_R + K_I + K_Z + K_E \tag{1}$$

The parameters of the equation will we explained below.

The current replacement costs are calculated by multiplying the acquisition costs with the price index. To get the deprecation costs the current replacement costs are divided by the machine life time. In SIGMA, the user only needs to enter the acquisition cost.

To calculate the depreciation cost the following parameters are needed:

To calculate the occupancy costs the following parameters are needed:

The occupancy costs results when the required space is multiplyed by the price per m².

The addition of the wear costs and the maintenance costs are total maintenance costs.

The calculation of the average interest rate is based on the assumption that after the machine life time the declining balance is zero. The interest rate is defined with 8 percent in SIGMA but can be adjusted if it is needed.

The energy costs are the sum of driving costs, heating costs and water costs. The drive power is calculated with SIGMA and divided by the efficiency factor of the engine $\eta_M$ and the gear $\eta_G$. This results in the following equation:

$$e_{eff} = \frac{e}{\eta_G \cdot \eta_M} \tag{2}$$

The heating capacity $\dot{Q}_H$ is the sum of all positive heat flows along the screw. $\dot{Q}_H$ is divided by the throughput, so that the heating capacity in kWh/kg can be calculated. The equation is:

$$\frac{\dot{Q}_H}{\dot{m}} \tag{3}$$

Cooling costs are estimated of water consumption. For this purpose a contact cooling is adopted and the following formula is used to calculate the volume flow:

$$\frac{\dot{Q}_C}{c_{pw} \cdot \rho_w \cdot \Delta T} \tag{4}$$

$\dot{Q}_C$ is the sum of all negative heat flows along the screw. $c_{pw}$ is the specific heat capacity and $\rho_w$ the density of water. The temperature difference of the contact cooling is assumed with 5 Kelvin.

If the user has a different cooling system or another water gerenating system he can modify the calculation by changing the water price.

The amount of operating hours is determined by the following equation:

$$t_{Bs} = t_C - t_M - t_R - t_A \tag{5}$$

With

Servicing-, cleaning- and maintenance time have been determined on basis of assumptions and empirical estimators and can be varied by the user.

To calculate the machine hour rate, the machines cost must be divided by the operating hours.

$$M_{SS} = \frac{(K_{Ab} + K_R + K_I + K_Z + K_E)}{t_{Bs}} \tag{6}$$

The aim of the full cost calculation method is the determination of the actually incurred costs of the product in one period. With these supplied information the economics of the process can be controlled. The procedure of the calculation is shown in the following table.

The material costs can be calculated with the following equation:

$$\left(\sum_{i=1}^n \dot{m} \cdot K_M \cdot A_m\right) \frac{t_{eff}}{t_{Bs}} \tag{7}$$

This equation multiplies the amount of material with the respective material price and its fraction $A_m$. It applies $\sum_{i=1}^n A_m = 1$. Then the sum is multiplied by the ratio $\frac{t_{eff}}{t_{Bs}}$. This ratio indicates the proportion of the effective machine running time to the operation hours and takes the degraded material into account. For $\frac{t_{eff}}{t_{Bs}}$ applies:

$\frac{t_{eff}}{t_{Bs}} \leq 1 $

The overhead rates are expressed as percentages and considered as follows:

• The overhead costs of supplies are calculated pro rata from the material costs. It applies:

$$GK_M = EK_M \cdot P_M \tag{9}$$

• The residual production is calculated pro rata from the manufacturing costs. It applies:

$$GK_F = L_F \cdot P_F \tag{10}$$

• The overhead costs of administration and sales are calculated pro rata from the production costs. It applies:

$$GK_{VW} = K_{Herst} \cdot P_{VW} \tag{11}$$ and $$GK_{VT} = K_{Herst} \cdot P_{VT} \tag{12}$$

The prime costs are calculated with the following equation:

$$K_S = K_{Herst} + GK_{VW} + GK_{VT} \tag{13}$$

Table sorted by Meaning.