ICMA – Nov 2024 – L1 – Q5a – Cost Segregation and Estimation

Determine fixed and variable cost components using regression analysis and estimate total cost for a given production level.

Question

Ebo LTD is planning to determine its variable and fixed cost elements for its planned activity level for the next year. The company has recorded the following costs and production units in the past six months:

Month	Units (X)	Cost (Y)
January	5.8	40.3
February	7.7	47.1
March	8.2	48.7
April	6.1	40.6
May	6.5	44.5
June	7.5	47.1

Required:

i) Construct the least square regression model.
ii) Determine the variable cost per unit of output using the model.
iii) Determine the fixed cost for the month using the model.
iv) Estimate the total cost if the company plans to produce 6,200 units.

Answer

Construction of regression model

Month	X (Units)	Y (Cost)	X²	XY
January	5.8	40.3	33.64	233.74
February	7.7	47.1	59.29	362.67
March	8.2	48.7	67.24	399.34
April	6.1	40.6	37.21	247.66
May	6.5	44.5	42.25	289.25
June	7.5	47.1	56.25	353.25

∑X = 41.8, ∑Y = 268.3, ∑X² = 295.88, ∑XY = 1,885.91

ii) Variable cost per unit (b):

$\frac{n∑XY – ∑X ∑Y}{n∑X² – (∑X)²}$ $\frac{6(1,885.91) – (41.8)(268.3)}{6(295.88) – (41.8)²}$ $\frac{11,315.46 – 11,214.94}{1,775.28 – 1,747.24}$ $\frac{100.52}{28.04} = 3.58$

Variable cost per unit = 3.58 GH¢

iii) Fixed cost (a):

$\frac{∑Y – b∑X}{n}$ $\frac{268.3 – (3.58 \times 41.8)}{6}$ $\frac{268.3 – 149.32}{6}$ $\frac{118.98}{6} = 19.77$

Fixed cost = 19.77 GH¢

iv) Estimated total cost for 6,200 units:

Using the regression model:

$Y = a + b x$ $\times 6,200)$ $Y = 19.77 + 22, 196$ $Y = 22, 215.77 G H ¢$

Total estimated cost = 22,215.77 GH¢

Tags: Cost Estimation, Fixed Cost, Least Squares Method, Regression Analysis, Variable Cost
Level: Level 1

Topic: Cost Segregation and Estimation
Series: Nov 2024

Uploader: Salamat Hamid