a) Use the high-low method to separate the fixed and variable cost elements of the security costs presented above.

The high-low method  involves the following steps:

1. Identify the high and low activity levels and record the cost at each level.
2. Calculate the difference in activity levels and the difference in costs.
3. Divide the cost difference by the difference in activity levels. This gives us the variable cost per room sold (b).
4. Take either the high or the low activity level and input the data including (b) as calculated in step 3 and solve the equation by finding the fixed cost element.

Step 1                                               Activity          Cost

                                        High            280             €20,400

                                        Low             216             €18,480

Step 2                              Difference     64              €1,920           

Step 3      €1,920 ¸ 64 = €30 (the variable cost per unit) 

Step 4    Total cost = fixed costs + (variable cost per unit x number of units sold)

                               y = a + b(x)

                               20,400 = a + 30 (280)

                               20,400 = a + 8,400

                               12,000 = a (the fixed cost amounts to €12,000)

Thus the cost function for the security costs is  Y = 12,000 +30 (x)

b)        As the complex manager plans on increasing opening hours by 10 per cent, re-calculate the costs for the four months presented above, based on the cost function calculated in (a).