## Variable Costs

Variable costs are associated with the operation of a machine and occur only when the machine is used. The term operating costs frequently is used to describe variable costs. Variable costs are usually figured on an hourly basis, but they can be figured using acres, bales or any other appropriate unit. The common variable costs are:

1. Repairs and maintenance (RM%): The costs of repair and maintenance are related to the type of machine, the purchase price and the hours of use. The repair and maintenance costs can be estimated using the following equation.

V1000/

where Crm = accumulated repair and maintenance cost (\$); RF1 & RF2 = repair and maintenance factors (Appendix IV); P = machine price in current dollars, multiply original price by (1 + i )n where i is the average inflation rate and n is the age of the machine to adjust for inflation; h = accumulated use of machine (h).

Problem: Estimate the accumulated repair and maintenance costs for a self-propelled combine that was purchased 4 years ago for a price of \$90,000.00. The machine has 1,200 hr of use and the average inflation has been 6.5%.

Solution: The first step is to adjust the price of the machine for inflation.

\$ = \$90,000.00 x (1 + i)n = \$90,000.00 x (1 + 0.065)4 = \$90,000.00 x 1.286... = 115781.9... or \$120, 000

Next the repair and maintenance costs can be estimated:

000 J

2. Fuel (F): The fuel consumption for an engine is influenced by the size of the engine and the percent of load. Average annual consumption can be estimated using the procedures printed in ASABE Standard D497.4 FEB03.

Qavg = 0.0305 x Ppto where Qavg = average gasoline consumption, L/hr; Ppto = maximum PTO power, kW or

Qavg = 0.06 x Ppto where Qavg = average gasoline consumption, gal/hr; Ppto = maximum PTO power, hp.

These equations must be multiplied by 0.73 for diesel and by 1.20 for liquefied petroleum gas (LPG) tractors.

Problems: Estimate the annual fuel consumption for a 125 PTO Hp diesel tractor that will be used for 850 hr per year.

Solution: The first step is to use the equation to determine the hourly use.

The second step is the multiply the hourly use by the hours per year:

gal gal hr gal

Ë— = 5.5 — x 850 — = 4,675 or 4,700 — yr hr yr yr

Estimating the fuel consumption for a specific operation requires determining the total tractor power for that operation. ASABE standard D497.4 provides a method for estimating fuel consumption for a specific operation.

3. Oil (O): The oil cost in dollars per hour will be the product of the oil consumption (gal/hr or L/hr) during operation and oil changes, and the oil price (\$/qt or \$/L). The total oil used (gal/hr) on a per hour basis can be estimated assuming manufacturer's recommended change interval by:

Gasoline (0.00011 x P) + 0.00657 Diesel (0.00021 x P) + 0.00573 LPG (0.00008 x P) + 0.00755

The total oil used (L/hr) on a per hour bases can be estimated by:

Gasoline (0.000566 x P) + 0.02487 Diesel (0.00059 x P) + 0.02169 LPG (0.00041 x P) + 0.02

Problem: Determine the amount of oil that will be used by a 120 PTO horsepower diesel tractor.

Solution:

— = (0.00021 x 120) + 0.00573 = 0.03093 or 0.031 — hr hr

4. Labor (L): The hourly wage for labor to operate the equipment in dollars per hour.

5. Consumables (C): Some machines, such as balers, have twine, netting or other materials that are consumed as a part of the machine operation.

Thus, the total hourly operating cost (THOC), in dollars per hour, of a machine is the sum of items 1, 2, 3,4 and 5 above.

Problem: Determine the total costs for a \$35,000.00 grain drill that is used 120 hr per year. It has an expected life of 10 years and a salvage value of \$1,000.00. It is pulled by a 98 horsepower diesel tractor. Assume an interest rate of 8%.

Solution: The total annual cost is the sum of the annual fixed costs and the annual variable costs. The fixed costs can be determined by calculating each individual cost, or by using the ownership cost equation to determine the ownership cost percentage. For this example the ownership cost equation will be used.

Fixed costs: the ownership cost equation requires salvage value expressed as a percentage.

Salvage value factor:

Total fixed cost percent:

((1 - 0.028 \ (1 + 0.028 \ = 100 X M-10-) + ( ^^-X 0.08 j + 0.02

= 100 x (0.0972 + 0.04112 + 0.02) = 100 x 0.15832 = 15.832 or 16% Total fixed costs:

yr yr yr

Variable costs: Annual variable costs=repair and maintenance+Fuel+Oil+Labor Repair and maintenance:

1000/

Fuel: The fuel cost for the grain drill is determined by the power and fuel efficiency of the tractor. Estimating tractor fuel costs for specific operation is not included in this text. See ASABE D496 for this information. Average fuel consumption based on the fuel type and power of the tractor can be estimated using the information from ASABE EP496.2 FEB03. The fuel use (gal/hr) is:

The fuel cost is: (assuming fuel is 2.25 \$/gal)

yr hr gal yr

Oil costs:

Assuming an oil cost of 2.00 \$/qt:

yr qt gal hr yr

Labor: Labor costs are determined by multiplying the annual use by the tractor operator cost in \$/hr.

yr yr hr yr

The total cost of owning and using the grain drill 120 hr per year is:

Total annual cost = Annual fixed costs + Annual variable costs

\$ / \$ \$ \$ \$ = 5,600.00 — + 130.00 — + 1,200.00 — + 25.00 — + 1,200.00 —

yr yr yr yr yr

yr yr

Machinery costs in dollars per year are useful for the owner/operator of a machine, but for custom work the operator needs to know the costs in terms of dollars/acre, dollars/hour, dollars/bale etc. The cost of a machine on a unit volume basis is influenced by the annual use because as the annual use increases, the fixed costs are spread out over more units. This makes the fixed costs per unit less. To illustrate this point Figure 10.1 shows the costs per acre for the grain drill in the previous problem for an annual use ranging from 100 to 1200 hr per year.

Note that the dollars per hour costs decrease until about 700 hr and then they start back up. This is because the equation used by ASABE to estimate repair and maintenance costs is designed to increase repair costs as the machine uses increases. FIGURE 10.1. Total costs per hour of use.