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:

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

The parameters of the equation will we explained below.

To calculate the depreciation cost the following parameters are needed:

Depreciation costs $K_{Ab}$ $$K_{Ab} = \frac{W_{Wb}}{t_N}$$

Current replacement cost $W_{Wb}$ $$W_{Wb} = K_{Ask} \cdot I_p$$

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 occupancy costs the following parameters are needed:

Occupancy costs $K_R$ $$K_R = B_R \cdot P_{Fl} \cdot 12$$

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.

Imputed interest expense $K_Z$ $$K_Z = \left(\frac{K_{Ask}}{2}\right) \cdot Z_s$$

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:

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

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:

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

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:

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

$\dot{Q}_C$ 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:

$$t_{Bs} = t_C - t_M - t_R - t_A$$

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.

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