Example $(8$A$)$: Fixed, Variable, and Semivariable Distinction

Review the chapter text for the distinction between fixed, variable, and semivariable costs. Pay particular attention to the accompanying Figures $81,82,83,84,$ and $85.$

This Practice Exercise is a mini$-$lesson that and example that will prepare you for this week's homework.

Practice Exercise $81$: Analyzing Mixed Costs

The Metropolis Health System has a system$-$wide training course for nurse aides. The course requires a packet of materials that MHS calls the training pack. Due to turnover and because the course is system$-$wide, there is a monthly demand for new packs. In addition the local community college also obtains the training packs used in their credit courses from MHS$.$

The Education Coordinator needs to know how much of the cost is fixed and how much of the cost is variable for these training packs. She decides to use the high$-$low method of computation.

Example: Using the monthly utilization information presented below, find the fixed and variable portion of costs through the high$-$low method.

Number of

Month Training Packs Cost

January $1,000$ $$6,200$

February $2001,820$

March $2502,350$

April $4003,440$

May $7004,900$

June $3002,730$

July $1501,470$

August $1001,010$

September $1,1007,150$

October $3002,850$

November $2502,300$

December $1001,010$

Solution to Practice Exercise $81$

Step $1.$ Find the highest volume of $1,100$ packs at a cost of $$7,150$ in September and the lowest volume of $100$ packs at a cost of $$1,010$ in August.

Step $2.$ Compute the variable rate per pack as:

Training

# of Packs Pack Cost

Highest volume $1,100$ $$7,150$

Lowest volume $1001,010$

$\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

Difference $1,000$ $$6,140$

Step $3.$ Divide the difference in cost $($$$6,140)$ by the difference in # of packs $(1,000)$ to arrive at the variable cost rate:

$$6,140$ divided by $1,000$ meals $=$ $$6\mathrm{.}14$ per pack.

Step $4.$ Compute the fixed overhead rates as follows:

At the highest level:

Total cost $$7,150$

Less: Variable portion

$[1,100$ packs $\backslash$times $$6\mathrm{.}14$ @$](6,754)$

$\_\_\_\_\_\_$

Fixed Portion of Cost $$396$

At the lowest level:

Total cost $$1,010$

Less: Variable portion

$[100$ packs $\backslash$times $$6\mathrm{.}14$ @$](614)$

$\_\_\_\_\_\_$

Fixed Portion of Cost $$396$

Proof totals: $$396$ fixed portion at both levels.

Now it's Your Turn! Assignment Exercise $81$: Analyzing Mixed Costs

The Education Coordinator decides that the Community College packs may be unduly influencing the high$-$low computation. She decides to re$-$run the results omitting the Community College volume.

Required

$1.$ Using the monthly utilization information presented below, and omitting the Community College training packs, find the fixed and variable portion of costs through the high$-$low method. Note that the college only acquires packs in three months of the year: January, May, and September. These dates coincide with the start dates of their semesters and summer school.

$2.$ The reason the Education Coordinator needs to know how much of the cost is fixed is because she is supposed to collect the appropriate variable cost from the Community College for their packs. For her purposes, which computation do you believe is better? Why?

Month

Total Number of

Training Packs

Total

Cost

Community College

Number Packs

Community College

Cost

January

$1,000$

$$6,200$

$200$

$$1,240$

February

$200$

$1,820$

March

$250$

$2,350$

April

$400$

$3,$