Question

SHATTA MOVEMENT Ltd produces a single product. The company’s directors want to explore new markets, and they require an accurate analysis of the firm’s cost structure for both forecasting and pricing purposes. An attempt to provide this analysis from the aggregation of individual costs has produced a poor correspondence between actual and predicted costs. You are an accountant employed by SHATTA MOVEMENT Ltd, and you have been asked to provide a statistical approach to the problem. The financial director has given you the following data:

Period

July August September October 1November December

Output (units)

9,000 14,000 11,000 8,000 6,000 12,000

Average unit cost (GHS)

12.8

13

11.4 12 13 11.7

You obtain the following further information:

 The costs from which the averages have been computed consist of the firm’s entire costs for the relevant month.

 Fixed costs can be assumed to be unaffected by seasonal factors except for harmattan heating. In July and August a supplementary heating system was employed; this cost GHS 10,000 per month to operate.

Required:

Estimate SHATTA MOVEMENT Ltd.’s normal fixed and variable cost of production using linear regression.

Answer 1

Month	Units (a)	Avg Unit Cost (b)	Total Cost (a*b)	Heating System Cost	Total Cost excluding Heating cost
July	9000	12.8	1,15,200.00	10,000.00	1,05,200.00
August	14000	13	1,82,000.00	10,000.00	1,72,000.00
September	11000	11.4	1,25,400.00	-	1,25,400.00
October	8000	12	96,000.00	-	96,000.00
November	6000	13	78,000.00	-	78,000.00
December	12000	11.7	1,40,400.00	-	1,40,400.00
Cost may be represented in the form of following equation:
y = a + bx where,
y = total cost
a = total fixed cost
b = variable cost per unit
x = units
?=?⅀b=n⅀xy - (⅀x)(⅀y)/n⅀x2 - (⅀x)2
?= ⅀a= ⅀y - b⅀x/n
Least-Square Regression Calculator
	x	y	x2	xy
1	9000	1,05,200.00	8,10,00,000.00	94,68,00,000.00
2	14000	1,72,000.00	19,60,00,000.00	2,40,80,00,000.00
3	11000	1,25,400.00	12,10,00,000.00	1,37,94,00,000.00
4	8000	96,000.00	6,40,00,000.00	76,80,00,000.00
5	6000	78,000.00	3,60,00,000.00	46,80,00,000.00
6	12000	1,40,400.00	14,40,00,000.00	1,68,48,00,000.00
Total	60000	7,17,000.00	64,20,00,000.00	7,65,50,00,000.00
?=?⅀b=n⅀xy - (⅀x)(⅀y)/n⅀x2 - (⅀x)2
2,91,00,00,000.00
25,20,00,000.00
11.54761905
Variable Cost per unit = 11.55 approx
?= ⅀a= ⅀y - b⅀x/n
24,142.86
6
4,023.81
Fixed cost exluding heating system = 4024 approx