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--- en:grundlagenhandbuch:kostenkalkulation [2026/02/09 21:03] – [Calculation of the Machine Hour Rate] neelest
+++ en:grundlagenhandbuch:kostenkalkulation [2026/05/28 10:01] (aktuell) – deppe2
@@ Zeile 15: / Zeile 15: @@
 The machine dependent costs are determined by the following equation:
-$$K_{Maschine} = K_{Ab} + K_R + K_I + K_Z + K_E$$
+$$K_{Maschine} = K_{Ab} + K_R + K_I + K_Z + K_E \tag{1}$$
 The parameters of the equation will we explained below.
 ==== Depreciation ====
+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:
-Depreciation costs $K_{Ab}$                    $$K_{Ab} = \frac{W_{Wb}}{t_N}$$
+^ Depreciation costs $K_{Ab}$ ^ $K_{Ab} = \frac{W_{Wb}}{t_N}$ ^
+| Current replacement cost $W_{Wb}$ | $W_{Wb} = K_{Ask} \cdot I_p$ |
+| Acquisition cost $K_{Ask}$ | tbd  |
+| Price index $I_p$ | 1,21 |
+| Machine life $t_N$ | - |
-Current replacement cost $W_{Wb}$               $$W_{Wb} = K_{Ask} \cdot I_p$$
-^ Acquisition cost | $K_{Ask}$ |
-^ Price index | $I_p$ | 1,21 |
-^ Machine life | $t_N$ | 7 |
-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.
 ==== Occupancy Costs ====
@@ Zeile 37: / Zeile 36: @@
 To calculate the occupancy costs the following parameters are needed:
-Occupancy costs $K_R$                          $$K_R = B_R \cdot P_{Fl} \cdot 12$$
-^ Required space | $B_R$ | 20 m² |
+^ Occupancy costs $K_R$ ^ $K_R = B_R \cdot P_{Fl} \cdot 12$ ^
-^ Price per m² | $P_{Fl}$ | 9 € |
+| Required space $B_R$ | 20 m² |
+| Price per m² per month $P_{Fl}$ | 9 € |
 The occupancy costs results when the required space is multiplyed by the price per m².
@@ Zeile 48: / Zeile 48: @@
 The addition of the wear costs and the maintenance costs are total maintenance costs.
-^ Wear costs | $K_V$ |
+^ Total Maintenance Costs $K_I$ ^ $K_I = K_V + K_W$ ^
-^ Maintenance costs | $K_W$ |
+| Wear costs | $K_V$ |
-^ Sum | $K_I$ | $$K_I = K_V + K_W$$ |
+| Servicing costs | $K_W$ |
 ==== Imputed Interest Expense ====
 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 $K_Z$                  $$K_Z = \left(\frac{K_{Ask}}{2}\right) \cdot Z_s$$
+^ Imputed interest expense ^ $K_Z = \left(\frac{K_{Ask}}{2}\right) \cdot Z_s$ ^
+| Interest rate $Z_s$ | 8 % |
-^ Interest rate | $Z_s$ | 8 % |
 ==== Energy Costs ====
@@ Zeile 64: / Zeile 62: @@
 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:
-$$e_{eff} = \frac{e}{\eta_G \cdot \eta_M}$$
+$$e_{eff} = \frac{e}{\eta_G \cdot \eta_M} \tag{2}$$
 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:
-$$\frac{\dot{Q}_H}{\dot{m}}$$
+$$\frac{\dot{Q}_H}{\dot{m}} \tag{3}$$
 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:
-$$\frac{\dot{Q}_C}{c_{pw} \cdot \rho_w \cdot \Delta T}$$
+$$\frac{\dot{Q}_C}{c_{pw} \cdot \rho_w \cdot \Delta T} \tag{4}$$
 $\dot{Q}_C$ 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.
@@ Zeile 80: / Zeile 78: @@
 The amount of operating hours is determined by the following equation:
-$$t_{Bs} = t_C - t_M - t_R - t_A$$
+$$t_{Bs} = t_C - t_M - t_R - t_A \tag{5}$$
 With
@@ Zeile 93: / Zeile 91: @@
 To calculate the machine hour rate, the machines cost must be divided by the operating hours.
-$$M_{SS} = \frac{(K_{Ab} + K_R + K_I + K_Z + K_E)}{t_{Bs}}$$
+$$M_{SS} = \frac{(K_{Ab} + K_R + K_I + K_Z + K_E)}{t_{Bs}} \tag{6}$$
 ===== Full Cost Calculation =====
@@ Zeile 113: / Zeile 111: @@
 The material costs can be calculated with the following equation:
-$$\left(\sum_{i=1}^n \dot{m} \cdot K_M \cdot A_m\right) \frac{t_{eff}}{t_{Bs}}$$
+$$\left(\sum_{i=1}^n \dot{m} \cdot K_M \cdot A_m\right) \frac{t_{eff}}{t_{Bs}} \tag{7}$$
-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:
+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.
-$$\frac{t_{eff}}{t_{Bs}} \leq 1$$
+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:
-$$GK_M = EK_M \cdot P_M$$
+$$GK_M = EK_M \cdot P_M \tag{8}$$
   * The residual production is calculated pro rata from the manufacturing costs. It applies:
-$$GK_F = L_F \cdot P_F$$
+$$GK_F = L_F \cdot P_F \tag{9}$$
   * The overhead costs of administration and sales are calculated pro rata from the production costs. It applies:
-$$GK_{VW} = K_{Herst} \cdot P_{VW}$$ and $$GK_{VT} = K_{Herst} \cdot P_{VT}$$
+$$GK_{VW} = K_{Herst} \cdot P_{VW} \tag{10}$$ and $$GK_{VT} = K_{Herst} \cdot P_{VT} \tag{11}$$
 The prime costs are calculated with the following equation:
-$$K_S = K_{Herst} + GK_{VW} + GK_{VT}$$
+$$K_S = K_{Herst} + GK_{VW} + GK_{VT} \tag{12}$$
 ===== Symbols =====