The Stephens Leadership Center provides training seminars in personal development and time management. The company is relatively new and management is seeking information regarding the Center's cost structure. The following information has been gathered since the inception of the business in January of the current year: Required:
a. Using the high-low method, estimate the variable cost per seminar and the total fixed cost per month.
b. Using the least-squares method, estimate the variable cost per seminar and the total fixed cost per month.

Question

The Stephens Leadership Center provides training seminars in personal development and time management. The company is relatively new and management is seeking information regarding the Center's cost structure. The following information has been gathered since the inception of the business in January of the current year:  Required:
a. Using the high-low method, estimate the variable cost per seminar and the total fixed cost per month.
b. Using the least-squares method, estimate the variable cost per seminar and the total fixed cost per month.

Quizplus · Accepted Answer

The Answer is a. High-Low Method:

a. High-Low Method: Variable cost = Change in Cost/Change in activity = $6,762/8 seminars = $845.25 per seminar Fixed cost element = Total cost - Variable cost element = $23,762 - ($845.25 per seminar × 18 seminars) = $8,547.50 Cost formula for seminar costs: $8,547.50 per month plus $845.25 per seminar held b. Least-Squares Method: n = 6 sumX = 84 sumY = 121,662 sumXY = 1,737,816 sumX^2 = 1,218 b = [n(sumXY) - (sumX)(sumY)]/[n(sumX^2) - (sumX)^2] = [6(1,737,816) - (84)(121,662)]/[6(1,218) - (84)^2] = $822.57 (rounded to the nearest whole cent) a = [(sumY) - b(sumX)]/n = [(121,662) - 822.57(84)]/6 = $8,761 (rounded to the nearest whole dollar) The cost formula is $8,761 per month plus $822.57 per seminar. A similar answer can be obtained using Microsoft Excel.

Variable cost = Change in Cost/Change in activity = $6,762/8 seminars = $845.25 per seminar
Fixed cost element = Total cost - Variable cost element
= $23,762 - ($845.25 per seminar × 18 seminars) = $8,547.50
Cost formula for seminar costs: $8,547.50 per month plus $845.25 per seminar held
b. Least-Squares Method:
n = 6
sumX = 84
sumY = 121,662
sumXY = 1,737,816
sumX^2 = 1,218
b = [n(sumXY) - (sumX)(sumY)]/[n(sumX^2) - (sumX)^2]
= [6(1,737,816) - (84)(121,662)]/[6(1,218) - (84)^2]
= $822.57 (rounded to the nearest whole cent)
a = [(sumY) - b(sumX)]/n
= [(121,662) - 822.57(84)]/6
= $8,761 (rounded to the nearest whole dollar)
The cost formula is $8,761 per month plus $822.57 per seminar. A similar answer can be obtained using Microsoft Excel.

The Stephens Leadership Center Provides Training Seminars in Personal Development