Question

In: Accounting

SHATTA MOVEMENT Ltd produces a single product. The company’s directors want to explore new markets, and...

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.

Solutions

Expert Solution

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

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