Sandy Smith, managing director of the Calgary Consulting Group, is examining how overhead costs behave with changes in monthly professional labour- hours billed to clients. Assume the following historical data:
Total Overhead Costs Professional Labour-Hours 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
1. Compute the linear cost function, relating total overhead cost to professional labour-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 Calgary 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. Smith had a chance to accept a special job that would have boosted professional labour- hours from 4,000 to 5,000 hours. Suppose Smith, 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 actual total contribution margin forgone?