Firm C’s demand for a product is 60 units per month. Its supplier charges an ordering cost of $40 per order and $35 per unit with a 20% discount for orders of 100 units or more. Firm C incurs a 20% annual holding cost. Calculate the economic order quantity without the discount. Then calculate the economic order quantity with the discounted price. What will be the change in Firm C’s annual total cost (purchasing, holding, and ordering) if it decides to take advantage of the quantity discount?

Answer:

$5,107.04

Explanation:

The computation of the change in the annual total cost is shown below;

Without a  discount, the annual total cost is

The computation of the economic order quantity is shown below:

[tex]= \sqrt{\frac{2\times \text{Annual demand}\times \text{Ordering cost}}{\text{Carrying cost}}}[/tex]

[tex]= \sqrt{\frac{2\times \text{720}\times \text{\$40}}{\text{\$7}}}[/tex]

= 91 units

The annual demand is

= 60 × 12 months

= 720

And, the carrying cost is

= $35 × 20%

= $7

Now The computation of the total cost is shown below:

= Purchase cost + ordering cost + carrying cost

where,  

Purchase cost = Annual consumption × Cost per unit

                       = 720 × $35

                       = $25,200

Ordering cost = (Annual demand ÷ EOQ) × Cost to place one order

                       = (720 ÷ 91) × $40

                       = $316.48

Carrying cost = (EOQ ÷ 2) × carrying cost percentage × Cost per unit

                      = (91 ÷ 2) × 7

                      = $318.50

Now put these values to the above formula  

So, the value would equal to

= $25,200 +  $316.48 + $318.50

= $25,834.98

Now if we take the economic order be 101

So, the total cost would be

= Purchase cost + ordering cost + carrying cost

where,  

Purchase cost = Annual consumption × Cost per unit

                       = 720 × $35 × (1 - 0.20)

                       = $20,160

Ordering cost = (Annual demand ÷ EOQ) × Cost to place one order

                       = (720 ÷ 101) × $40

                       = $285.14

Carrying cost = (EOQ ÷ 2) × carrying cost percentage × Cost per unit

                      = (101 ÷ 2) × 7 × (1 - 0.20)

                      = $282.80

Now put these values to the above formula  

So, the value would equal to

= $20,160 +  $285.14 + $282.80

= $20,727.94

Now the change in the annual total cost is

= $25,834.98 - $20,727.94

= $5,107.04

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