# 49 Costs of Manufacturing

Learning Objectives

By the end of this section, you should be able to:

**Calculate** the cost of manufacturing based on a few known process costs

## Direct Costs of Manufacturing

Direct Costs of Manufacturing are costs that are directly impacted by the manufacturing rate. To assess the impacts of some of the main elements of the direct costs, we will use multiplication factors based on certain known costs.

Direct manufacturing costs | Symbol or Range of multiplying factors | Avg. factor used |
---|---|---|

1. Raw Materials | [latex]C_{RM}[/latex] | |

2. Utilities | [latex]C_{UT}[/latex] | |

3. Operating Labour | [latex]C_{OL}[/latex] | |

4. Waste Treatment | [latex]C_{WT}[/latex] | |

5. Direct Supervisory and clerical labour | [latex](0.1-0.25)C_{OL}[/latex] | [latex]0.18 C_{OL}[/latex] |

6. Maintenance and repairs | [latex](0.02-0.1)FCI[/latex] | [latex]0.06 FCI[/latex] |

7. Operating supplies | [latex](0.006-0.012)FCI[/latex] | [latex]0.009 FCI[/latex] |

8. Laboratory charges | [latex](0.1-0.2)C_{OL}[/latex] | [latex]0.15 C_{OL}[/latex] |

9. Patents and Royalties | [latex](0-0.06)COM(\text{cost of manufacturing})[/latex] | [latex]0.03COM[/latex] |

Total direct costs of manufacturing |
[latex]C_{RM}+C_{WT}+C_{UT}+1.33C_{OL}+0.03COM +0.069FCI[/latex] |

## Fixed Costs of Manufacturing

Fixed Costs of Manufacturing are costs that are not directly impacted by the manufacturing rate. To assess the impacts of some of the main elements of the fixed costs, we will use multiplication factors based on certain known costs.

Fixed manufacturing costs | Range of multiplication factors | Avg. factor used |
---|---|---|

1. Depreciation – costs associated with buildings and plant equipment. Note that this is not an actual expense, but just accounted for in terms of tax purposes | 0.1 FCI (Note there are a variety of ways depreciation can be calculated, this is a very crude approximation) | [latex]0.1FCI[/latex] |

2. Local taxes and insurance | [latex](0.014-0.05)FCI[/latex] | [latex]0.031FCI[/latex] |

3.Plant overhead costs (referring to the costs related to running the business but not directly related to the process of making the product) | [latex](0.59-0.826)C_{OL}+(0.030-0.42)FCI[/latex] | [latex]0.708C_{OL}+0.036 FCI[/latex] |

Total fixed costs of manufacturing |
[latex]0.708C_{OL}+0.068FCI+depreciation(0.1FCI)[/latex] |

## Depreciation

Governments will not let companies write off all expenses to build a plant immediately. Instead, they are written off over time, in what is known as depreciation.

Depreciation is calculated based on the purchase value of equipment minus the salvage value and evaluated over a number of years specified. This does not include land costs, since land generally retains its value, whereas equipment and buildings tend to lose their value over time.

Straight-line depreciation is the simplest calculation of depreciation:

[latex]\text{Depreciation}=\frac{\text{purchased value } (FCIL)-\text{salvage value}}{\text{life of equipment } (n)}[/latex]

Exercise: Estimate Depreciation Value

The following information is the purchased cost for categories of equipment at a small waste treatment facility.

Equipment categories | Puchased price |
---|---|

pre-treatment | $2,000,000 |

reactors | $5,500,000 |

tanks | $4,000,000 |

pumps and compressors | $3,500,000 |

sensor and control devices | $1,000,000 |

If the life of all of the equipment shown in the table above is 8 years, and the total salvage value of all the equipment is $89,000. Calculate the depreciation per year using the straight-line method.

### Solution

\begin{align*}

Depreciation &=\frac{\text{purchased value } (FCIL)-\text{salvage value}}{\text{life of equipment } (n)}\\

& = \frac{($2,000,000+$5,500,000+$4,000,000+$3,500,000+$1,000,000)-$89,000}{8}\\

& ≈$ 2,000,000

\end{align*}

Exercise: Estimating Depreciation Using FCI

Calculate the yearly straight-line depreciation based on the following information about a hydrodesulphurization plant:

Item | Value (dollars or in units specified) |

Fixed Capital Investment | $87,000,000 |

land cost | $1,000,000 |

salvage value | $3,200,000 |

life of equipment | 12 years |

### Solution

The purchased equipment cost can be calculated using **the Fixed Capital Investment excluding the land cost**:

\begin{align*}

Depreciation &=\frac{\text{purchased value } (FCIL)-\text{salvage value}}{\text{life of equipment } (n)}\\

& = \frac{($87,000,000-$1,000,000)-$3,200,000}{12}\\

& =$6,900,000

\end{align*}

## General Expenses

General expenses are overhead costs related to carrying out business functions. To assess the impacts of some of the main elements of general expenses we will use multiplication factors based on certain known costs.

General expenses | Range of multiplication factors | Avg. factor used |
---|---|---|

1. Administrative costs | [latex](0.147-0.207)C_{OL}+(0.0075-0.0105)FCI[/latex] | [latex]0.177C_{OL}+0.009FCI[/latex] |

2. Product distribution and selling costs | [latex](0.02-0.2)COM[/latex] | [latex]0.11COM[/latex] |

3. Research and development | [latex]0.05COM[/latex] | [latex]0.05COM[/latex] |

Total general expenses |
[latex]0.177C_{OL}+0.009FCI+0.16COM[/latex] |

## Overall Manufacturing Costs

Summing together the Direct Costs of Manufacturing, Fixed Costs of Manufacturing, and General Expenses, we can get a general formula to estimate the total cost of manufacturing.

Direct Cost of Manufacturing: [latex]C_{RM}+C_{WT}+C_{UT}+1.33C_{OL}+0.03COM +0.069FCI[/latex]

Fixed Cost of Manufacturing: [latex]0.708C_{OL}+0.068FCI+depreciation(0.1FCI)[/latex]

General Expenses: [latex]0.177C_{OL}+0.009FCI+0.16COM[/latex]

Cost of Manufacturing: [latex]0.180FCI+1.23(C_{RM}+C_{WT}+C_{UT})+2.73C_{OL}+\text{depreciation}(0.1FCI)[/latex]

Depreciation is not included in most of the calculations we perform – depreciation is not a real cost that we need to pay, but it is part of the money we lose for tax purposes.

Exercise: Estimating the Cost of Manufacturing

Suppose the following information is obtained from a plant producing 100,000 tonnes of ethylene oxide annually.

Item | Value (dollars) |

Fixed Capital Investment | $46,000,000 |

Raw Material Cost | $27,600,000 |

Waste Treatment Cost | $5,000,000 |

Utility Cost | $800,000 |

Direct Labour Cost | $840,000 |

a. What is the cost of manufacturing?

b. Calculate the percentage of each element (Direct Cost of Manufacturing, Fixed Cost of Manufacturing, and General Expenses) as a portion of the Cost of Manufacturing.

Do not include depreciation in the calculations above.

### Solution

**a. Cost of Manufacturing (COM):**

\begin{align*}

&\;\;\;\;0.180FCI+1.23(C_{RM}+C_{WT}+C_{UT})+2.73C_{OL}\\

& = 0.180×46,000,000+1.23×(27,600,000+5,000,000+800,000)+2.73×840,000\\

& ≈ 51,700,000

\end{align*}

**b. **

**Direct Cost of Manufacturing **

\begin{align*}

& \;\;\;\;C_{RM}+C_{WT}+C_{UT}+1.33C_{OL}+0.03COM +0.069FCI\\

& =27,600,000+5,000,000+800,000+1.33×840,000+0.03×51,700,000+0.069×46,000,000\\

& ≈ 39,200,000

\end{align*}

\begin{align*}

\frac{\text{Direct Cost of Manufacturing}}{\text{Cost of Manufacturing}}×100\text{%}&=\frac{39,200,000}{51,700,000}×100\text{%}\\

&≈75.8\text{%}

\end{align*}

**Fixed Cost of Manufacturing **

\begin{align*}

& \;\;\;\;0.708C_{OL}+0.068FCI\\

& =0.708×840,000+0.068×46,000,000\\

& ≈ 3,700,000

\end{align*}

\begin{align*}

\frac{\text{Fixed Cost of Manufacturing}}{\text{Cost of Manufacturing}}×100\text{%}&=\frac{3,700,000}{51,700,000}×100\text{%}\\

&≈7.2\text{%}

\end{align*}

**General Expenses **

\begin{align*}

&\;\;\;\; 0.177C_{OL}+0.009FCI+0.16COM\\

& =0.177×840,000+0.009×46,000,000+0.16×51,700,000\\

& ≈ 8,800,000

\end{align*}

\begin{align*}

\frac{\text{General Expenses}}{\text{Cost of Manufacturing}}×100\text{%}&=\frac{8,800,000}{51,700,000}×100\text{%}\\

&≈17.0\text{%}

\end{align*}

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