Question

Chapter 19 Cost-Volume-Profit Analysis 983 EX 19-8 High-low method for a service company Obj. 1 ✓ Fixed cost, Boston Railroad decided to use the high-low method and operating daca from the past six $600,000 months to estimate the fixed and variable components of t: asportation 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 SHOW ME HOW January $1,776,000 560,000 February 2,700,000 1,000,000 March 1,650,000 500,000 April 1,860,000 600,000 May 1,440,000 400,000 June 1,566,000 460,000 Determine the variable cost per gross-ton mile and the total fixed cost.

Answer 1

Answer- Variable Cost per gross ton mile= $2.1 per gross ton mile.

Total Fixed Cost =$600000.

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 = 1000000 gross-ton miles; y₂ = $2700000
at lowest activity: x₁ = 400000 gross ton miles; y₁ = $1440000

1)-Variable Cost per gross ton mile = ($2700000-$1440000) /(1000000 miles −400000 miles)  

= $1260000/600000 miles

= $2.1 per gross ton mile
Total Fixed Cost = $1440000 − ($2.1 per gross-ton mile*400000 miles)

= $1440000 – $840000

= $600000