ACCA MA · Guided practice (Show me how)
Chapter 18: Semi-Variable Costs
Splitting a semi-variable cost - high-low, then regression
A semi-variable cost is part fixed and part variable, so a single monthly figure tells you nothing on its own. Both techniques below end with the same kind of answer: a cost equation y = a + bx, where a is the fixed cost for the period and b is the variable cost per unit.
Part (a). Electricity costs for the first six months of the year were as follows.
| Units produced | Cost ($) | |
|---|---|---|
| January | 340 | 2,260 |
| February | 300 | 2,160 |
| March | 380 | 2,320 |
| April | 420 | 2,400 |
| May | 400 | 2,300 |
| June | 360 | 2,266 |
Part (b). A different set of records, this time for seven months, shows the number of units produced each month and the total cost incurred.
| Units | Cost ($000) | |
|---|---|---|
| January | 100 | 40 |
| February | 400 | 65 |
| March | 200 | 45 |
| April | 700 | 80 |
| May | 600 | 70 |
| June | 500 | 70 |
| July | 300 | 50 |
Work in hundreds of units for x (so January is x = 1) and $000 for y, exactly as the printed answer does. The formulae are given to you in the examination:
b = (n.SUMxy - SUMx.SUMy) / (n.SUMx2 - (SUMx)2) a = ybar - b.xbar
r = (n.SUMxy - SUMx.SUMy) / SQRT( (n.SUMx2 - (SUMx)2) x (n.SUMy2 - (SUMy)2) )
(a) High-low method
Calculate the fixed cost per month and the variable cost per unit of electricity, using the high-low method on the figures for January to June.
(b) Regression and correlation
Calculate, for the seven months January to July, the regression line y = a + bx, the correlation coefficient r and the coefficient of determination r squared.
Opening this exercise…