FMF9
Syllabus C. Working Capital Management C2c. Management of inventories

EOQ with Discounts 2 / 4

EOQ with discounts

Bulk buying discounts may be available if the order quantity is above a certain size.

To calculate the best order quantity then we need to:

  1. Calculate EOQ in normal way (and the costs)

  2. Calculate costs at the lower level of each discount above the EOQ

  3. Then choose the lowest cost option!

Illustration

Demand is 100 units per month. Purchase cost per unit £10. Order cost £20
Holding cost 10% p.a. of stock value.

  • Required
    Calculate the minimum total cost with a discount of 2% given on orders of 350 and over

Solution

Calculate EOQ in normal way (and the costs)
Calculate costs at the lower level of each discount above the 

EOQ
Sq root 2 x 20 x 1200 / 1 = 219

  • Ordering Costs
    = Order cost per unit x (Annual Demand / Order amount) 
    = 20 x 1200 / 219
    = 110

  • Holding Costs
    = Holding Cost per unit x (Order amount / 2)
    = 1 x 219 / 2
    = 110
    = 220

  • At discount level 350

    Ordering Costs
    = Order cost per unit x (Annual Demand / Order amount) 
    = 20 x 1200 / 350 = 69

  • Holding Costs
    = Holding Cost per unit x (Order amount / 2)
    = 0.98 x 350 / 2 = 171.5
    = 240.5

    240.5 is higher than 220 (it would be as EOQ is the best level)

    However we now need to take into account the 2% price discount

    Discount = 2% x 1200 x 10 = 240

    Clearly with the discount being offered the company should take the discount and order at 350