Question

Thomas s, Ltd., provides nationwide passenger train service on 21,000 miles of routes. Selected operating data for fiscal 2014 are shown below. Fuel Expense Passengers Passenger Train Miles Month (000s) $20,700 $22,897 (000s) Miles (000s) (000s) 2,329 2,398 2,320 2,159 2,132 2,390 2,343499,435 2,316 2,387 2,414 2,698 2,176 October 2013 475,187 465,902 375,339 380,750 3,210 3,259 November 2013 December 2013 3,261 3,210 2,556 3,187 3,288 3,265 3,236 3,219 3,407 3,266 January 2014 $24,538 $22,225 $26,724 $25,853 $25,137 $25,034 $23,666 $25,459 $25,331 February 2014 481,458 March 2014 475,037 April 2014 May 2014 une 2014 uly 2014 August 2014 September 2014 498,117 550,741 579,939 507,644 496,599 The above data provide three possible activity measures that could influence fuel expense. Use the high-low method to develop a cost formula for fuel expense for each of the three measures. (Round unit cost to 2 decimal places, o.g. 12.25 and fixed cost to nearest thousand dollars. If fixed cost is negative using high-low method enter amount with either negative sign preceeding the number, e.g9. -1,225 or parentheses, e.g. (1,225)) Passengers: Fuel expense x passenger Passenger miles: Fuel expense Train Miles: x passenger mile Fuel expense train mile

Answer 1

Thomas Ltd

High-low method to develop a cost formula for fuel expense for each of the three measures:

• Passengers

Computation of Variable fuel cost per passenger:

Highest number of passengers in the month of August, 2014 – 2,698,000

Corresponding fuel expense = $25,459,000

Lowest number of passengers in the month of February 2014 – 2,132,000

Corresponding fuel expense = $22,225,000

Variable Fuel expense per passenger = (25,459,000 – 22,225,000)/(2,698,000 – 2,132,000) = 3,234,000/566,000

Variable Fuel expense per passenger = $5.71

Fixed fuel expense is computed as follows,

At 2,698,000 activity level, $25,459,000 = $5.71 x 2,698,000 + fixed fuel expense

Fixed fuel expense = 25,459,000 – 15,405,580 = $10,053,420

Hence, the cost formula for fuel expense with passengers as activity is as follows,

Fuel expense = $5.71 x passenger + $10,053,420

• Passenger Miles

Computation of Variable fuel cost per passenger mile:

Highest number of passenger miles is in the month of July, 2014 – 579,939,000

Corresponding fuel expense = $23,666,000

Lowest number of passenger miles is in the month of December 2013 – 375,339,000

Corresponding fuel expense = $21,620,000

Variable Fuel expense per passenger mile = (23,666,000 – 21,620,000)/(579,939,000 – 375,339,000)

=$2,046,000/204,600,000

Variable Fuel expense per passenger mile = $0.01

Fixed fuel expense is computed as follows,

At 375,339,000 activity level, $21,620,000 = $0.01 x 375,339,000 + fixed fuel expense

Fixed fuel expense = 21,620,000 – 3,753,390 = $17,866,610

Hence, the cost formula for fuel expense with passenger miles as activity is as follows,

Fuel expense = $0.01 x passenger miles + $17,866,610

Train Miles –

Computation of Variable fuel cost per train mile:

Highest number of train miles is in the month of August, 2014 – 3,407,000 train miles

Corresponding fuel expense = $25,459,000

Lowest number of train miles is in the month of February 2014 – 2,556,000 train miles

Corresponding fuel expense = $22,225,000

Variable Fuel expense per train mile = (25,459,000 – 22,225,000)/(3,407,000 – 2,556,000) = 3,234,000 /851,000

Variable Fuel expense per train mile= $3.80

Fixed fuel expense is computed as follows,

At 2,556,000 activity level, $22,225,000 = $3.80 x 2,556,000 + fixed fuel expense

Fixed fuel expense = 22,225,000 – 9,713,400 = $12,511,600

Hence, the cost formula for fuel expense with train miles as activity is as follows,

Fuel expense = $3.80 x train miles + $12,511,600