Short-Term Decision-Making

Alta Production, Inc., reported the following production costs for the 12 months January through December. (These are the same data presented in Note 5.17 "Review Problem 5.3".)

1. Using the information, perform the five steps of the scattergraph method to estimate costs and state your results in cost equation form Y = f + vX.
2. Assume Alta Production, Inc., will produce 400 units next month. Calculate total production costs for the month.
3. When is this approach likely to yield more accurate results than the high-low method?

Solution to Review Problem 5.4

1. The five steps are as follows:

    

   Step 1. Plot the data points for each period on a graph.

   
   

    

   Step 2. Visually fit a line to the data points, and be sure the line touches one data point.

    

   Step 3. Estimate the total fixed costs (f).

   The y-intercept represents total fixed costs. This is where the line meets the y-axis. Total fixed costs in the graph appear to be approximately $5,000. You will likely get a different answer because the answer depends on the line that you visually fit to the data points. Remember you must draw the line through one data point. The line intersects the data point for March ($480,000 production costs; 330 units produced). This will be used in step 4.

    

   Step 4. Calculate the variable cost per unit (v).

   After completing step 3, the equation to describe the line is partially complete and stated as Y = $5,000 + vX. The goal of this step is to calculate a value for variable cost per unit (v). Use the data point the line intersects (for March, 330 units produced and $480,000 total costs), and fill in the data to solve for v (variable cost per unit)
   
   \(Y = f +  \upsilon X\)
   $480,000 - $5,000 = \( (\upsilon \times 330)\)
   $475,000 =  \( (\upsilon \times 330)\)
   \( \upsilon\) = $475,000 \(\div\) 330
   \( \upsilon\) = $1,439.39 (rounded)
   
   Step 5. State the results in equation form \(Y = f + vX\).
   
   We know from step 3 that the total fixed costs are $5,000, and from step 4 that variable cost per unit is $1,439.39. Thus the equation used to estimate total production costs is stated as:
   \(Y = $5,000+  $1,439.39X\)
   It is evident from this information that this company has very little in fixed costs and relatively high variable costs. This is indicative of a company that uses a high level of labor and materials (both variable costs) and a low level of machinery (typically a fixed cost through depreciation or lease costs).
   

2. Using the equation, simply substitute 400 units for X, as follows:
   
   \(Y\) = $5,000+  $1,439.39 \(\times\) 400 units
   \(Y\) = $5,000+  $575,756
   \(Y\) = $580,756
   
   Thus total production costs are expected to be $580,756 for next month.

3. This approach is likely to yield more accurate results than the high-low method when the high and low points are not representative of the entire set of data. Notice that fixed costs are much lower using the scattergraph method ($5,000) than the high-low method ($25,000).