Question: Another approach to identifying fixed and variable costs for cost estimation purposes is the high$-$low method A method of cost analysis that uses the high and low activity data points to estimate fixed and variable costs. $.$ Accountants who use this approach are looking for a quick and easy way to estimate costs, and will follow up their analysis with other more accurate techniques. How is the high$-$low method used to estimate fixed and variable costs?

Answer: The high$-$low method uses historical information from several reporting periods to estimate costs. Assume Susan Wesley obtains monthly production cost information from the financial accounting department for the last $12$ months. This information appears in Table $2\mathrm{.}4$Monthly Production Costs for Bikes Unlimited$.$

Table $2\mathrm{.}4$ Monthly Production Costs for Bikes Unlimited

Reporting Period $($Month$)$Total Production CostsLevel of Activity $($Units Produced$)$July$$230,0003,500$August$250,0003,750$September$260,0003,800$October$220,0003,400$November$340,0005,800$December$330,0005,500$January$200,0002,900$February$210,0003,300$March$240,0003,600$April$380,0005,900$May$350,0005,600$June$290,0005,000$

Step $1.$ Identify the high and low activity levels from the data set.

Step $2.$ Calculate the variable cost per unit $($ v $).$

Step $3.$ Calculate the total fixed cost $($ f $).$

Step $4.$ State the results in equation form Y $=$ f $+$ v X$.$

Question: How are the four steps of the high$-$low method used to estimate total fixed costs and per unit variable cost?

Answer: Each of the four steps is described next.

Step $1.$ Identify the high and low activity levels from the data set.

The highest level of activity $($level of production$)$ occurred in the month of April $(5,900$ units; $$380,000$ production costs$),$ and the lowest level of activity occurred in the month of January $(2,900$ units; $$200,000$ production costs$).$ Note that we are identifying the high and low activity levels rather than the high and low dollar levels$$choosing the high and low dollar levels can result in incorrect high and low points.

Step $2.$ Calculate the variable cost per unit $($ v $).$

The calculation of the variable cost per unit for Bikes Unlimited is shown as follows:

Unit$$variable$$cost$($v$)=$Cost$$at$$highest$$level$$Cost$$at$$lowest$$level$$Highest$$activity$$level$$Lowest$$activity$$level$=$$$380,000$$$200,0005,900$units$2,900$units$=$$$180,0003,000$units$=$$$60$

Step $3.$ Calculate the total fixed cost $($ f $).$

After completing step $2,$ the equation to describe the line is partially complete and stated as Y $=$ f $+$ $$60$X$.$ The goal of step $3$ is to calculate a value for total fixed cost $($f$).$ Simply select either the high or low activity level, and fill in the data to solve for f $($total fixed costs$),$ as shown.

Using the low activity level of $2,900$ units and $$200,000,$

Y$=$f$+$vX$$200,000=$f$+($$$602,900$units$)$f$=$$$200,000($$$602,900$units$)$f$=$$$200,000$$$174,000$f$=$$$26,000$

Thus total fixed costs total $$26,000.($Try this using the high activity level of $5,900$ units and $$380,000.$ You will get the same result as long as the per unit variable cost is not rounded.$)$