Question

High-Low and Scattergraph Analysis

Sebolt Wire Company heats copper ingots to very high temperatures by placing the ingots in a large heat coil. The heated ingots are then run through a shaping machine that shapes the soft ingot into wire. Due to the long heat-up time, the coil is never turned off. When an ingot is placed in the coil, the temperature is raised to an even higher level, and then the coil is allowed to drop to the “waiting” temperature between ingots. Management needs to know the variable cost of power involved in heating an ingot and the fixed cost of power during “waiting” periods. The following data on ingots processed and power costs are available:

Required:

1. Using the high-low method, estimate a cost formula for power cost. Express the formula in the form Y = a + bX.

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2. Prepare a scattergraph by plotting ingots processed and power cost on a graph. Fit a straight line to the plotted points using a ruler, and estimate a cost formula for power cost using the quick-anddirty method.

 

Answer 1

High-Low Method:

Under High-Low Method difference between the Power Cost at highest and lowest Ingots Processed is divided by the difference between the Ingots processed at the highest and lowest level. The quotient thus obtained gives us the rate of Variable Cost in relation to Ingots processed.

1.

Using the high-low method, estimate a cost formula for power cost.

The highest level of Ingots processed is in the month of May (130 Ingots processed) and the lowest level of Ingots processed is in the month of October (40 Ingots processed). Power Costs during those periods are $6,000 and $2,400 respectively.

The following data on Ingots Processed and Power Costs are provided for Sabot Wire:

We can use the Ingots processed and Power Costs data from those two months to estimate the Variable Cost component as follows:

Variable Cost =

=

= $40 per Ingots processed

Having calculated that the Variable Power Cost is $40 per Ingots processed, we can now calculate the Fixed Power Cost. This can be calculated by subtracting the Variable Power Cost from Total Power Cost.

Fixed Cost Element = Total Power Costs – Variable Power Cost

= $6,000 – ($40 per Ingots processed X 130 Ingots processed)

= $6,000 – $5,200

= $800

Alternatively,

Fixed Cost Element = Total Power Costs – Variable Power Cost

= $2,400 – ($40 per Ingots processed X 40 Ingots processed)

= $2,400 – $1,600

= $800

Having calculated the Fixed Power Cost and Variable Power Cost, the same can be expressed in the form “Y = a + bX”.

where,

Y = Total Power Costs

a = Fixed Power Cost

b = Variable Power Cost

X = Ingots Processed

Hence,

Y = a + bX

Y = $800 + $40X

Hence, equation Y = $800 + $40X.

2. Scatter-Graph Method

While plotting the data on Scatter-Graph, two things should be noted:

(i) The Total Power Cost, which is dependent variable, is plotted on the Vertical Axis(Y). The Amount of Total Power Cost incurred during a period depends on the Ingots Processed.

(ii) The Ingots Processed, which is independent variable, is plotted on the Horizontal Axis(X). It causes the changes in Total Power Cost.

Graph as follows:

It is evident from the scatter-graph, the point lies along a straight line. The straight line, also called “Best-Fit-Line” has been drawn using a ruler through the data points representing 100 Ingots processed and a Power Cost of $5,000.

Quick-and-Dirty Method

The straight line drawn through one of the data points helps make quick-and-dirty estimate of Variable and Fixed costs. The vertical intercept where straight line crosses the Y Axis is an estimate of Fixed Cost, here $1,200.

As we have an estimate of Fixed Cost, we can calculate the Variable Cost by subtracting the Fixed Cost from Total Power Cost at the point lying on the Straight Line.

The Variable Cost per Ingots processed at 100 Ingots processed level will be computed as follows:

Variable Cost Per Ingots processed = $3,800 ÷ 100 Ingots processed

= $38 per Ingots processed

The relation between Power Cost and Ingots processed can be expressed in term of an equation as follows:

Y = $1,200 + $38X

where X is the number of ingots processed.

It is worth to be noted that this is a quick-and-dirty method of estimating Fixed and Variable Cost and not used widely in decision-making.