Fixed costs are independent of machine use, and occur whether or not the machine is used. They are referred to as the cost of ownership. Each fixed cost is estimated on a calendar year or an annual basis. The common fixed costs are:

1. Depreciation: Depreciation is the loss in value of a machine with the passage of time, whether or not it is used. Depreciation can be regarded as the amount of money that should be saved each year as a machine is used so that, at the end of its useful life, this money along with the remaining value of the machine (salvage value) could be used to replace it. Several choices exist in the way by which depreciation can be figured for cost and/or tax purposes. All depreciation methods require an estimation of the machine service life. The simplest method is straight line depreciation:

$ _ P - SV yr yr where $/yr = Annual depreciation; P = Purchase price; SV = Salvage value; yr = Years of service.

Problem: Determine the annual depreciation for a machine with a purchase price of $15,400, a salvage value of $800.00 and an expected life of 8 years.

Solution:

yr yr

The annual straight line depreciation is $1,825.00 per year.

2. Interest on investment: An interest cost should be used because the money tied up in purchasing a machine could have been used for another purpose or invested. When money is owed on a machine the annual interest charges added to the depreciation can be used to estimate yearly costs of ownership. A method that includes the yearly costs of ownership and the time value of money is called capital recovery factor, CRF. CFR can be calculated by:

Si i where R = one of a series of equal payments due at the end of each compounding period, q times per year; P = principal amount; i = interest rate as compounded q times per year; n = life of the investment in years; S = salvage value, $.

Problem: Determine the capital recovery factor for a machine that cost $125,000.00 at purchase, has a salvage value of $3,000.00. A 10-year loan is used with an interest rate of 10.5% per year.

Solution:

10x1

The CRF for this machine is $20,600.00 per year.

3. Taxes: Any property and sales taxes paid on the equipment must be included as a fixed cost. An estimate of the annual taxes for agricultural machinery is 1% of remaining value.

Problem: What is the annual tax during the 2 year of ownership for a $55,000.00 machine when the expected life is 12 years? The salvage value is $500.00.

Solution: The first step is to determine the value of the machine at the beginning of the second year. The value at the beginning of the second year is determined by the amount of depreciation that occurred during the first year. Assuming straight nq i i

10 1

line method:

yr 12 yr

The value of the machine at the beginning of the second year is:

$ = $55,000.00 - $4,540.00 = $50,460.00 The annual taxes are:

yr yr yr

4. Shelter: A cost of shelter should be assigned to machinery. If a shelter is used, the cost can be determined and assigned over the life of the machine. If the machine is not sheltered, a cost still should still be assigned for shelter because the resale value of the machine will be less than that of a sheltered machine. An estimate for the annual cost of shelter is 0.75% of the value of the machine at the beginning of the year.

Problem: What is the annual cost of shelter during the fourth year for a $4,500.00 machine when the expected life is 5 years and the salvage value is $1,500.00?

Solution: The first step is to determine the value of the machine at the beginning of the fourth year. Assuming straight line depreciation the annual depreciation is:

The value of the machine at the beginning of the fourth year is:

= $4,500.00 - $1,800.00 = $2,700.00 The cost of the shelter during the fourth year is:

yr yr yr

A shelter cost of $20.25 should be used during the fourth year for this machine.

5. Insurance: Any liability or replacement insurance carried on the machine should be included. An estimate for the annual cost of insurance is 0.25% of the remaining value at the beginning of the year.

Problem: Determine the lifetime insurance cost for a $125,500.00 machine when the expected life is 15 years and the salvage value is $10,000.00.

Solution: The annual insurance cost for a machine is determined by multiplying the insurance factor time the value of the machine at the beginning of the year. The lifetime insurance cost for a machine is determined by summing the annual insurance costs. Because of depreciation the value of the machine declines each year and therefore the annual insurance cost declines each year. This problem

Purchase price |
$125,500.00 | |

Insurance factor |
0.0025 | |

Annual depreciation |
$7,700.00 | |

Year |
Value |
Insurance cost |

1 |
$125,500.00 |
$313.75 |

2 |
$117,800.00 |
$294.50 |

3 |
$110,100.00 |
$275.25 |

4 |
$102,400.00 |
$256.00 |

5 |
$94,700.00 |
$236.75 |

6 |
$87,000.00 |
$217.50 |

7 |
$79,300.00 |
$198.25 |

8 |
$71,600.00 |
$179.00 |

9 |
$63,900.00 |
$159.75 |

10 |
$56,200.00 |
$140.50 |

11 |
$48,500.00 |
$121.25 |

12 |
$40,800.00 |
$102.00 |

13 |
$33,100.00 |
$82.75 |

14 |
$25,400.00 |
$63.50 |

15 |
$17,700.00 |
$44.25 |

Sum |
$2,685.00 |

The total cost of insurance over the lifetime of the machine is $2,685.00.

The total cost of insurance over the lifetime of the machine is $2,685.00.

can be solved by using a complex equation or using the same method as the previous examples, but it is also an example of a problem that can be solved using a spreadsheet, Table 10.1. Assuming straight line depreciation, the life time cost of insurance is $2, 685.00.

The annual cost of owning a piece of equipment, then, is the sum of the fixed costs listed above. Notice that at this point no mention has been made of machine use.

With accurate records, the annual cost of a machine can be determined by figuring the cost in dollars per year for each of the five fixed costs. Another approach is to combine the five items into an annual fixed cost percentage (FC%). Cost analysis of data indicates that the FC% times the purchase price of the machine is an acceptable estimate for the annual ownership costs of a machine.

Annual owinership cost (AOC) = FC% x P

An ownership cost percentage can be estimated by:

where Co = ownership cost percentage; Sv = salvage value factor (percent of salvage value compared to the purchase price) of machine at end of machine life (year L), decimal; L = machine life, yr; l = annual interest rate; K2 = ownership cost for taxes, housing, and insurance, decimal.

Problem: What is the ownership cost percentage for a machine that as an expected life of 10 years, cost $23,000, a cost for taxes, housing and insurance of 2% and has a salvage value of $3,400.00?

Solution: The ownership cost percentage is determined using the previous equation. This equation requires the salvage factor as a percent. To determine the percent divide the purchase price by the salvage value and multiply times 100. The salvage factor is:

The fixed cost percent is: Co = 100 x

Problem: What is the annual ownership cost for a $150,000.00 combine when the fixed cost percentage is 18%?

Solution:

AOC ( — = FC% x P = 0.18 x $150,000.00 = 27,000.00 — yr yr

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