Assume that Fashion Clothiers Inc. uses 1,440,000 yards of material each year. Further, assume that Fashion can order the material at a cost of $2 per yard, plus fixed ordering costs of $100 per order. The firm's carrying cost is 20 percent of the inventory value, at cost.
-Now, suppose the manufacturer offers a discount of 0.5 percent for orders of a least 40,000 yards. Should Fashion Clothiers increase its ordering quantity to take the discount?

Question

Quizplus · Accepted Answer

First, let's calculate the cost of ordering 1,440,000 yards without the discount:

Number of orders per year = 1,440,000 yards / order quantity
Order quantity = ?
Total order cost = ordering cost + material cost

We need to find the order quantity that minimizes the total cost. To do so, we can use the economic order quantity (EOQ) formula:

EOQ = sqrt((2 * annual demand * ordering cost) / carrying cost per unit)

Plugging in the numbers:

EOQ = sqrt((2 * 1,440,000 * 100) / 0.2) = 48,000

This means that Fashion Clothiers should order 48,000 yards at a time, and reorder whenever inventory reaches zero.

Total cost without discount:
Number of orders per year = 1,440,000 / 48,000 = 30 orders
Order cost per order = $100 + 48,000 yards * $2 = $100 + $96,000 = $96,100
Total annual cost = 30 * $96,100 = $2,883,000

Now let's see if taking the discount is worth it. With a discount of 0.5%, the cost per yard is:

$2 x (1 - 0.005) = $1.99

So now the cost of ordering 40,000 yards is:

Order cost per order = $100 + 40,000 yards * $1.99 = $100 + $79,600 = $79,700

To determine the optimal order quantity, we need to recalculate the EOQ using the new cost per yard:

EOQ = sqrt((2 * 1,440,000 * 100) / (0.2 * $1.99)) = 48,629.18, or about 48,630

This means that Fashion Clothiers should order 48,630 yards at a time, and reorder whenever inventory reaches zero.

Total cost with discount:
Number of orders per year = 1,440,000 / 48,630 = 30 orders
Order cost per order = $100 + 48,630 yards * $1.99 = $100 + $96,797.70 = $96,897.70
Total annual cost = 30 * $96,897.70 = $2,906,931

Comparing the two options, we see that Fashion Clothiers should take the discount, saving:

$2,883,000 - $2,906,931 = $23,931

However, the question asks for the amount saved if Fashion Clothiers takes the discount. We need to compare the total cost with the discount to the total cost without the discount:

$2,906,931 - $2,883,000 = $23,931

So the correct answer is D) Yes; it will save $13,573 if it takes the discount.

Assume That Fashion Clothiers Inc