**MDCL: High low technique series** for AAT Professional Diploma students

**How do you decide between two suppliers of services that are paid for per unit, but which also incur a fixed fee, when both suppliers offer a bulk discount for purchases over a given quantity? **

In previous articles we have looked at the high low technique, which separates a total semi-variable cost into its variable and fixed elements. We have also considered how, at professional level, we are expected to adjust the basic technique to accommodate situations where the fixed element also includes stepped fixed costs (article on this aspect coming soon).

In this article, we’re going to focus on using the high-low technique when a bulk discount has been applied to the total semi-variable cost. Quantity discounts complicate the variable element of the total cost because they only apply after a certain quantity. Often the discount is stepped, for example 2% after 1,000 units which is 98p per unit, or 5% after 3,000 units which is 95p per unit. The general idea of bulk discounts is economies of scale, in other words, the more you buy in one go, the cheaper it is!

Sounds great, doesn’t it? So what’s the problem?

Well, if the discount is applied to the whole purchase then there isn’t an issue because it just reduces the variable cost per unit and the high low technique can be applied as normal. However, the stepped nature of quantity discounts can complicate the calculations because the discount only applies after a certain level.

## Tackling quantity discounts as a cost accountant

Let’s assume we’re the cost accountant for a manufacturing organisation and we’re forecasting costs for the next quarter. Two suppliers have been asked to tender for the contract of a service which is charged per unit but also incurs a fixed fee. Both have submitted quotes that include bulk discounts.

We have information about previous purchases from both suppliers and know that the discounts have been incorporated into the total cost figures and that the fixed costs do not include any steps in cost. The following quarter will require 5,500 units so we need to calculate how much that will cost from each supplier, then decide which will be awarded the contract. Let’s start with supplier X whose quote shows:

Notice that only one of the previous purchases was for a quantity that would qualify for the discount. Therefore, the simplest solution to forecasting the future cost, is to use the information we have and remove the effect of the discount from the quantity to which it has been applied.

That way, the two previous sets of information become comparable. The high low technique can then be applied in the normal way to calculate the variable cost per unit and the fixed element. Finally, the discount can be reapplied to forecast the cost of 5,500 units.

**Step 1 – remove the effect of the discount**

Due to the terms of the discount, it will only have been applied to the previous order of 5,000 units.

Therefore, the total cost for 1,500 units is £2.50 per unit more that total cost for 5,000 units. In order to accurately use the high low technique, we need to make the total cost figures comparable by increasing the cost of 5,000 units by £12,500 (5,000 x £2.50) to £135,000 (£122,500 + £12,500) because that would have been the cost if the purchase hadn’t been discounted.

**Step 2 – high low technique**

Now the total costs are comparable we can use the high low technique as usual:

The variable cost per unit is the difference in the adjusted total costs (£135,000 – £47,500 = £87,500) divided by the difference in the quantities: £87,500 ÷ (5,000 – 1,500) = £25 variable cost per unit.

The value of the variable element for 1,500 units is therefore £37,500 and is £125,000 for 5,000 units: The fixed element is calculated by deducting the variable element from the total cost at both levels and ensuring the figures reconcile:

**Step 3 – forecast**

Now we have established the variable cost per unit and fixed cost, we can apply the discount and calculate the forecast cost of purchasing 5,500 units, all of which qualify for the discount:

- Variable element is £123,750 (5,500 units x (£25 – £2.50) per unit)
- The fixed element is £10,000

Therefore the cost will be £133,750 if the materials are purchased from supplier X.

What about the second supplier’s quote? The terms of the bulk discount from supplier Y are couched in slightly different terms but the solution for accurately forecasting the purchase cost is similar. Here are the details from supplier’s Y quote:

Notice that neither of the previous purchases were for quantities that would qualify for the discount. This means that we do not have to remove the effect of the discount before we use the high low method, just adjust the variable cost per unit by the discount, before we forecast the purchase cost of 5,500 units.

Have a go and then decide which supplier you would place the order with, if the decision is purely based on cost.

Click here to check your answers against mine.

Head over to part 2 now, where we look at using the High Low Technique with stepped fixed costs.

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**
Gill Myers is a self-employed accounts consultant. She has taught AAT qualifications since 2005 and written numerous articles and e-learning resources.
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