Question

3. Jetboats Ltd uses the high-low method to estimate the cost function. Jetboat operates jet boat rides on Sydney Harbour. The number of hours the engines are run in each month is provided below along with the labour costs for maintaining the jet boats for 2018. 3 3 Month Machine (engine) HoursLabour costs $4,300 $2,510 $3,040 $2,780 $1,750 $1,200 $1,500 $2,470 S3.480 $3,590 $3,800 $3,950 180 110 January February March April May June 120 August September October November December 110 155 160 170 175 Required a) What is the cost function? b) What is the estimate of Jetboats's labour costs when: 2 i) 130 machine hours are used? ii) 220 machine hours are used?

Answer 1

This is the method of separating fixed and variable portion within a total cost.

The highest and lowest machine hours should be chosen for their respective costs; this is required for calculating variable cost per hour. The highest hour is in the month of January (180 hours), when the cost is $4,300; the lowest hour is in the month of June (50 hours), when the cost is $1,200.

Variable cost per hour = (Cost in the highest machine hour – Cost in the lowest machine hour) / (Highest machine hour – Lowest machine hour)

                                    = ($4,300 - $1,200) / (180 – 50)

                                    = $3,100 / 130

                                    = $23.846

Fixed cost = Total cost for 180 hours – (Variable cost per hour × 180 hours)

                  = 4,300 – (23.846 × 180)

                  = 4,300 – 4292.28

                  = 7.7

In order of checking the above calculation, fixed cost could be founded in 50 hours

Fixed cost = Total cost for 50 hours – (Variable cost per hour × 50 hours)

                  = 1,200 – (23.846 × 50)

                  = 1,200 – 1,192.3

                  = 7.7 (tally)

a.

Required cost function (TC) should be as below:

TC = {Variable cost per unit × Machine hours (H)} + Fixed cost

TC = (23.846 × H) + 7.7

TC = 23.846H + 7.7 [Answer]

b.

In case of 130 machine hours:

TC = 23.846H + 7.7

      = (23.846 × 130) + 7.7

      = 3,099.98 + 7.7

      = 3,107.68 (Answer)

In case of 220 machine hours:

TC = 23.846H + 7.7

      = (23.846 × 220) + 7.7

      = 5246.12 + 7.7

      = 5,253.82 (Answer)