Question

Question:10-24 Linear cost approximation. Terry Lawler, managing director of the Memphis Consulting Group, is

examining how overhead costs behave with changes in monthly professional labor-hours billed to clients.

Assume the following historical data:

Professional Labor-Hours

Total Overhead Costs Billed to Clients

$340,000 3,000

400,000 4,000

435,000 5,000

477,000 6,000

529,000 7,000

587,000 8,000

required:

1. Compute the linear cost function, relating total overhead cost to professional labor-hours, using the representative

observations of 4,000 and 7,000 hours. Plot the linear cost function. Does the constant component

of the cost function represent the fixed overhead costs of the Memphis Consulting Group? Why?

2. What would be the predicted total overhead costs for (a) 5,000 hours and (b) 8,000 hours using the cost

function estimated in requirement 1? Plot the predicted costs and actual costs for 5,000 and 8,000 hours.

3. Lawler had a chance to accept a special job that would have boosted professional labor-hours from

4,000 to 5,000 hours. Suppose Lawler, guided by the linear cost function, rejected this job because it

would have brought a total increase in contribution margin of $38,000, before deducting the predicted

increase in total overhead cost, $43,000. What is the total contribution margin actually forgone?

Please provide correct answer. Attend only you are sure about the answer.

Answer 1

1. Let y be the fixed overhead component and x be the variable component of the overheads. So, for 4000 and 7000 hrs we get below two equations:

4000x + y = 400,000 (Eq1)

7000x + y = 529,000 (Eq 2)

Subtracting Eq1 from Eq2, we get

3000x = 129,000 i.e. x = $43

Substituting x = 43 in Eq 1 or Eq 2, we get , y = $228,000.

Therefore, we get the variable overhead rate at $43/ hr and fixed overhead is equal to $228,000.

The linear cost function using representative observations of 4000 and 7000 labour hours is given by:

Overhead Cost (OC) = 228,000 + 43h, where h= no. of labour hours. This can be plotted on a graph as follows:

Refer Graph 1 in image.

The constant component here represents fixed overhead costs because it remains same irrespective of number of labour hours. It means that $228k of costs will need to be borne irrespective of level of activity.

2. a) For 5000 hours, From part 1 answer, we know that our overhead cost function is given by:

OC = 228,000 + 43h, Substituting h = 5000 in this equation we get

OC = $443,000. Therefore, predicted cost at 5000 hours is equal to $443,000

b) For 8000 hours,

OC = 228,000 + 43h, Substituting h = 8000,

OC = $572,000. Therefore, predicted cost at 8000 hours is equal to $572,000.

The predicted and actual costs are plotted on graph as follows:

Refer Graph 2 in image

५१ph1 cost 600,000 Overhead Cose 500,000 400,00 300.000 200000 2000 4000 6000 8000 Hours Groot Graph II I cost Actual overheads Predicted Overheads book Hock Book took 2K 4K 6K 8 Hours

3. From the information given in the question, we know that actual costs at 4000 hours = $400,000 and actual costs for 5000 hours = $435,000. Therefore for additional 1000 increase in labour hours, the cost would have increased by $35,000 (435000-400000).

The poposed order would have brought additional contribution of $38,000.

Hence, contribution margin actually foregone = Increased contribution - Increased costs i.e. $38,000 - $35,000 = $3,000