question about high-low method for stepped fixed costs

All types of cost (including Stepped Fixed Cost) and their behavior with changes in volume of activity are explained in Sir John Moffat’s free lectures for FMA/F2. Kindly refer to those lectures to understand cost behavior.

As far as this question is concerned, there must be some mistake in the cost data. The cost of lowest activity cannot be 180,000 because this would result in VC/unit of 0, or the cost of highest activity must be bigger than 195,000. Please recheck the data and correct if there’s anything wrong.

*The highest and lowest activity levels above 5500 units and their associated costs are chosen:

(1) Variable cost per unit = [(54,800 – 50,000) ÷ (7,500 – 6,000)] = $3.20

*You can use either activity level (high or low); it will give the same answer:

(2) Total fixed cost above 5,500 units = [54,800 – (7,500 × 3.20)] = $30,800

*Because the highest and lowest activity levels were above 5500, we can assume that a step up of 10% has already occurred and that our Total fixed cost of $30,800 is actually 110% in value (i.e. 100% + 10% =110%), so to determine the total fixed cost without the extra 10%, we divide the Total fixed cost of $30,800 by 110% to bring it to a value of 1% (i.e. $30,800 ÷ 110 =$280), we then multiply the 1% value by 100 to bring it to 100% value (i.e. $280 x 100 = $28,000):

(3) Total fixed cost below 5,500 units = 30,800/110 × 100 = $28,000

*Now that we’ve determined Total fixed cost at 100%, we can now use it to calculate the total fixed cost at different activity levels:

(4)Total cost for 5,000 units = [(5,000 × 3.20) + 28,000] = $44,000

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