1/8. PRINCIPLES OF COST CONTROL
Page 1-2-3-4-5-6-7-8
1.1 Introduction
1.2 Basic Classification of Costs
1.3 Total Cost and Unit-Cost Formulas
1.4 Breakeven Analysis
1.5 Minimum Cost Analyses
1.1 Introduction
Cost is important to all industry. Costs can be
divided into two general classes; absolute costs and relative costs. Absolute
cost measures the loss in value of assets. Relative cost involves a comparison
between the chosen course of action and the course of action that was rejected.
This cost of the alternative action - the action not taken - is often called
the "opportunity cost".
The accountant is primarily concerned with the
absolute cost. However, the forest engineer, the planner, the manager needs to
be concerned with the alternative cost - the cost of the lost opportunity.
Management has to be able to make comparisons between the policy that should be
chosen and the policy that should be rejected. Such comparisons require the
ability to predict costs, rather than merely record costs.
Cost data are, of course, essential to the
technique of cost prediction. However, the form in which much cost data are
recorded limits accurate cost prediction to the field of comparable situations
only. This limitation of accurate cost prediction may not be serious in
industries where the production environment changes little from month to month
or year to year. In harvesting, however, identical production situations are
the exception rather than the rule. Unless the cost data are broken down and
recorded as unit costs, and correlated with the factors that control their
values, they are of little use in deciding between alternative procedures.
Here, the approach to the problem of useful cost data is that of
identification, isolation, and control of the factors affecting cost.
1.2 Basic Classification of Costs
Costs are divided into two types: variable
costs, and fixed costs. Variable costs vary per unit of production. For
example, they may be the cost per cubic meter of wood yarded, per cubic meter
of dirt excavated, etc. Fixed costs, on the other hand, are incurred only once
and as additional units of production are produced, the unit costs fall.
Examples of fixed costs would be equipment move-in costs and road access costs.
1.3 Total Cost and Unit-Cost Formulas
As harvesting operations become more complicated
and involve both fixed and variable costs, there usually is more than one way
to accomplish a given task. It may be possible to change the quantity of one or
both types of cost, and thus to arrive at a minimum total cost. Mathematically,
the relationship existing between volume of production and costs can be
expressed by the following equations:
Total cost = fixed cost
+ variable cost × output
In symbols using the first letters of the cost
elements and N for the output or number of units of production, these simple
formulas are
C = F + NV
UC = F/N + V
1.4 Breakeven Analysis
A breakeven analysis determines the point at
which one method becomes superior to another method of accomplishing some task
or objective. Breakeven analysis is a common and important part of cost
control.
One illustration of a breakeven analysis would
be to compare two methods of road construction for a road that involves a
limited amount of cut-and-fill earthwork. It would be possible to do the
earthwork by hand or by bulldozer. If the manual method were adopted, the fixed
costs would be low or non-existent. Payment would be done on a daily basis and
would call for direct supervision by a foreman. The cost would be calculated by
estimating the time required and multiplying this time by the average wages of the
men employed. The men could also be paid on a piece-work basis. Alternatively,
this work could be done by a bulldozer which would have to be moved in from
another site. Let us assume that the cost of the hand labor would be $0.60 per
cubic meter and the bulldozer would cost $0.40 per cubic meter and would
require $100 to move in from another site. The move-in cost for the bulldozer
is a fixed cost, and is independent of the quantity of the earthwork handled.
If the bulldozer is used, no economy will result unless the amount of earthwork
is sufficient to carry the fixed cost plus the direct cost of the bulldozer
operation.
Figure 1.1 Breakeven
Examples for Excavation.
If, on a set of coordinates, cost
in dollars is plotted on the vertical axis and units of production on the
horizontal axis, we can indicate fixed cost for any process by a horizontal
line parallel to the x-axis. If variable cost per unit output is constant, then
the total cost for any number of units of production will be the sum of the
fixed cost and the variable cost multiplied by the number of units of
production, or F + NV. If the cost data for two processes or methods, one of
which has a higher variable cost, but lower fixed cost than the other are
plotted on the same graph, the total cost lines will intersect at some point.
At this point the levels of production and total cost are the same. This point
is known as the "breakeven" point, since at this level one method is
as economical as the other. Referring to Figure 1.1 the breakeven point at
which quantity the bulldozer alternative and the manual labor alternative
become equal is at 500 cubic meters. We could have found this same result
algebraically by writing F + NV = F' + NV' where F and V are the fixed and
variable costs for the manual method, and F' and V' are the corresponding
values for the bulldozer method. Since all values are known except N, we can
solve for N using the formula
N = (F' - F) / (V - V')
1.5 Minimum Cost Analyses
A similar, but different problem is the
determination of the point of minimum total cost. Instead of balancing two
methods with different fixed and variable costs, the aim is to bring the sum of
two costs to a minimum. We will assume a clearing crew of 20 men is clearing
road right-of-way and the following facts are available:
1. Men are paid at the rate of $0.40 per hour.
2. Time is measured from the time of leaving camp to the time of return.
3. Total walking time per man is increasing at the rate of 15 minutes per day.
4. The cost to move the camp is $50.
2. Time is measured from the time of leaving camp to the time of return.
3. Total walking time per man is increasing at the rate of 15 minutes per day.
4. The cost to move the camp is $50.
If the camp is moved each day, no time is lost
walking, but the camp cost is $50 per day. If the camp is not moved, on the
second day 15 crew-minutes are lost or $2.00. On the third day, the total
walking time has increased 30 minutes, the fourth day, 45 minutes, and so on.
How often should the camp be moved assuming all other things are equal? We
could derive an algebraic expression using the sum of an arithmetic series if
we wanted to solve this problem a number of times, but for demonstration
purposes we can simply calculate the average total camp cost. The average total
camp cost is the sum of the average daily cost of walking time plus the average
daily cost of moving camp. If we moved camp each day, then average daily cost
of walking time would be zero and the cost of moving camp would be $50.00. If
we moved the camp every other day, the cost of walking time is $2.00 lost the
second day, or an average of $1.00 per day. The average daily cost of moving
camp is $50 divided by 2 or $25.00. The average total camp cost is then $26.00.
If we continued this process for various numbers of days the camp remains in
location, we would obtain the results in Table 1.1.
TABLE 1.1 Average daily total camp cost as the
sum of the cost of walking time plus the cost of moving camp.
Days camp remained in location
|
Average daily cost of walking time
|
Average daily cost of moving camp
|
Average total camp cost
|
1
|
0.00
|
50.00
|
50.00
|
2
|
1.00
|
25.00
|
26.00
|
3
|
2.00
|
16.67
|
18.67
|
4
|
3.00
|
12.50
|
15.50
|
5
|
4.00
|
10.00
|
14.00
|
6
|
5.00
|
8.33
|
13.33
|
7
|
6.00
|
7.14
|
13.14
|
8
|
7.00
|
6.25
|
13.25
|
9
|
8.00
|
5.56
|
13.56
|
10
|
9.00
|
5.00
|
14.00
|
We see the average daily cost of
walking time increasing linearly and the average cost of moving camp decreasing
as the number of days the camp remains in one location increases. The minimum
cost is obtained for leaving the camp in location 7 days (Figure 1.2). This
minimum cost point should only be used as a guideline as all other things are
rarely equal. An important output of the analysis is the sensitivity of the
total cost to deviations from the minimum cost point. In this example, the
total cost changes slowly between 5 and 10 days. Often, other considerations
which may be difficult to quantify will affect the decision. In Section 2, we
discuss balancing road costs against skidding costs. Sometimes roads are spaced
more closely together than that indicated by the point of minimum total cost if
excess road construction capacity is available. In this case the goal may be to
reduce the risk of disrupting skidding production because of poor weather or
equipment availability. Alternatively, we may choose to space roads farther
apart to reduce environmental impacts. Due to the usually flat nature of the
total cost curve, the increase in total cost is often small over a wide range
of road spacings.
Figure 1.2 Costs for Camp Location Example
Figure 1.2 Costs for Camp Location Example
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