Question

Boston Railroad decided to use the high-low method and operating data from the past six months to estimate the fixed and variable components of transportation costs. The activity base used by Boston Railroad is a measure of railroad operating activity, termed "gross-ton miles," which is the total number of tons multiplied by the miles moved.

	Transportation Costs		Gross-Ton Miles
January	$542,300		217,000
February	604,600		242,000
March	427,300		157,000
April	579,700		235,000
May	486,200		189,000
June	623,300		255,000

Determine the variable cost per gross-ton mile and the total fixed cost.

Variable cost (Round to two decimal places.)	$ per gross-ton mile
Total fixed cost	$

Answer 1

Answer-1)- Variable cost = $2 per gross-ton mile.
2) Total fixed costs =$113300.

Explanation:-

High-Low Method:-

Variable Cost per Unit

Variable cost per unit (b) is calculated using the following formula:

Variable cost per unit = (Y2-Y1)/(X2-X1)

Where,
y2 is the total cost at highest level of activity;
y1 is the total cost at lowest level of activity;
x2 are the number of units/miles/ labor ,machine hours etc. at highest level of activity; and
x1 are the number of units/miles/ labor, machine hours etc. at lowest level of activity

The variable cost per unit is equal to the slope of the cost volume line (i.e. change in total cost ÷ change in number of machine hours).

Total Fixed Cost

Total fixed cost (a) is calculated by subtracting total variable cost from total cost, thus:

Total Fixed Cost = (y2 – b)*x2 = (y1 – b*x1)

We have,
at highest activity: x₂ = 255000 Gross-Ton miles; y₂ = $623300
at lowest activity: x₁ = 157000 Gross-Ton miles; y₁ = $427300

1)-Variable Cost per gross-ton mile = ($623300− $427300) /(255000 gross-ton miles −157000 gross-ton miles)  

= $196000/98000 gross-ton miles

= $2 per gross-ton mile
Total Fixed Cost = $623300 − ($2 per gross-ton mile*255000 gross-ton miles)

= $623300 – $510000

=$113300