Question

The following data were obtained from the accounting information system of Attawfik Corporation:

                       Units           Total Cost                                       

Month         Produced                                       

January              60       SAR1,533.4                    

February            50               1,300                       

March                80               2,000                       

April                  30                  833.5                    

a.   Use the data for February and March and the two - point method to determine a cost function.

b.   Use the high - low method to determine a cost function.

C. How do you think that a cost function may provide poor estimates of future costs?

 

Answer 1

Ans a. Let Input function be Units Produced = x

Let Output function be Total Cost = C

For the month of feb (x,c) = (50,1300)

For the month of march (x,c) = (80,2000)

Cost function formula is: F(x)= mx+b

Where F(x)= cost function

m= slope = ▲output/▲input= constant rate of change

b = vertical intercept = initial amount

Calculating m using the above formula, we get :

m= (2000-1300)/(80-50)

=700/30

=23.33

Here, C= mx+b

applying the values for the month of feb we get ,

1300= 23.33(50)+b

b= 1300 - 1166.50

b= 133.50

Hence Cost function is :

C= 23.33x+133.50

Ans b) The following four steps are required to achieve cost function by high - low method:

1. Identify high - low activities from the data provided

2. Calculate the variable cost per unit (v)

3. Calculate the total fixed cost (f)

4. Form the equation Y= f+vX

In the given data set Highest activity was recorded in the month of march (80 units produced at the cost of 2000) and the lowest activity was recorded in the month of April (30 units produced at the cost of 833.50)

Calculating the variable cost(v):

v= (Highest cost - lowest cost)/(Highest units - lowest units)

v= (2000-833.50)/(80-30)

v= 1166.50/50

v= 23.33

Calculating the fixed cost (f) using the lowest activity:

Y = f+vx

833.50 = f +(23.33 * 30)

f= 833.50 - 699.90

f= 133.60

Hence Cost function is :

Y = 133.60 + 23.33X

Ans C) Cost function provides only estimates based on the Highest and lowest data readings of 2 points. This can lead to poor estimates of future costs where future costs can have high variance as compared to the estimates calculated based on cost function.