Question

Below are the processing costs of Darnell Products observed over the last 10 months:

Month	Units Produced	Processing Cost
1	7,500	$44,000
2	11,000	60,000
3	12,500	54,000
4	5,500	20,000
5	9,000	47,000
6	8,500	52,000
7	4,500	22,000
8	7,000	41,000
9	11,500	52,000
10	6,000	41,000

1. 1. Use the high low method to determine the variable cost per unit and fixed cost per month. Express your results in the form of a linear equation y = a + bx.                                                                                                                                                                               (6 marks)
2. 2. Predict the total processing cost if 22,000 units are produced.                      (4 mark

Answer 1

Part 1 :

As per high low method, Variable cost per unit =

(Highest Activity Cost - Lowest Activity Cost) / (Highest Activity Units - Lowest Activity Units)

Highest Activity Level = Month 3 (because highest number of units are produced in month 3)

Highest Activity Cost = $54,000

Highest Activity Units = 12,500 Units

Lowest Activity Level = Month 7 (because lowest number of units are produced in month 7)

Lowest Activity Cost = $22,000

Lowest Activity Units = 4,500 units

Variable cost per unit = (Highest Activity Cost - Lowest Activity Cost) / (Highest Activity Units - Lowest Activity Units)

= ($54,000 - $22,000) / (12,500 - 4,500)

= $32,000 / 8,000

= $4 / unit

Total Processing Cost in month 3 = Fixed Cost per month + (Variable cost per unit * Number of Units produced in month 3)

$54,000 = Fixed Cost per month + ( $4 * 12,500)

$54,000 = Fixed Cost per month + $50,000

Fixed Cost per month = $54,000 - $50,000

= $4,000

NOTE : We can calculate the fixed cost by using the processing cost of month 7 (lowest activity level) as well.

Total Processing Cost in month 7 = Fixed Cost per month + (Variable cost per unit * Number of Units produced in month 7)

$22,000 = Fixed Cost per month + ( $4 * 4,500)

$22,000 = Fixed Cost per month + $18,000

Fixed Cost per month = $22,000 - $18,000

= $4,000

y = a + bx

In the above equation : y is the total cost , a is the fixed cost per month , b is the variable cost per unit and x is the number of units of the activity.

In Highest Activity Level : y = $54,000 , a = $4,000 , b = $4/unit , x = 12,500 units

y = a + bx

y = $4,000 + ($4 * 12,500)

y = $4,000 + $50,000

y = $54,000

Hence , the equation is verified.

In Lowest Activity Level : y = $22,000 , a = $4,000 , b = $4/unit , x = 4,500 units

y = a + bx

y = $4,000 + ($4 * 4,500)

y = $4,000 + $18,000

y = $22,000

Hence , the equation is verified.

Part 2 :

Total processing cost when 22,000 units are produced (y) = a + bx

y = $4,000 + ($4 * 22,000)

y = $4,000 + $88,000

y = $92,000

Therefore, total processing cost when 22,000 units are produced = $92,000

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