Fashion Clothiers Inc.
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.
-Refer to Fashion Clothiers Inc.Now, suppose the manufacturer offers a discount of 0.5 percent for orders of at least 40,000 yards.Should Fashion Clothiers increase its ordering quantity to take the discount?

Question

Quizplus · Accepted Answer

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

Total cost = (1,440,000 yards) x ($2 per yard) + (Total ordering cost) + (Carrying cost)

We know the ordering cost is fixed at $100 per order, but we need to calculate how many orders we would need to place to order 1,440,000 yards.

Let Q be the ordering quantity. Then:

Number of orders = (Annual demand) / (Order quantity) = 1,440,000 / Q

Total ordering cost = (Number of orders) x (Order cost) = (1,440,000 / Q) x $100

The annual carrying cost is 20% of the inventory value, at cost. The inventory value is simply the cost per yard multiplied by the order quantity divided by 2, since we assume the inventory is depleted halfway through the year on average.

Carrying cost = (Annual inventory) x (Carrying cost per unit) = (Q / 2) x ($2 x 0.2)

Putting it all together:

Total cost = (1,440,000 yards) x ($2 per yard) + [(1,440,000 / Q) x $100] + [(Q / 2) x ($2 x 0.2)]

Simplifying:

Total cost = $2,880,000 + ($144,000 / Q) + ($0.20 x Q)

To calculate the optimal ordering quantity, we need to find the value of Q that minimizes total cost. We can do this by taking the derivative of the cost function with respect to Q, setting it equal to zero, and solving for Q:

d(Total cost)/dQ = -($144,000 / Q^2) + $0.20 = 0

Solving for Q:

Q = sqrt($144,000 / $0.20) = 60000

So the optimal ordering quantity without the discount is 60,000 yards, and the total cost is:

Total cost = $2,880,000 + ($144,000 / 60,000) + ($0.20 x 60,000) = $2,979,200

Now, let's consider the discount. A discount of 0.5% on an order of 40,000 yards or more can be written as a price of $1.995 per yard instead of $2.

If we take the discount and order 1,440,000 yards in one order, the total cost would be:

Total cost = (1,440,000 yards) x ($1.995 per yard) + (Total ordering cost) + (Carrying cost)

The ordering cost would simply be $100 for this one order. The optimal ordering quantity doesn't change, since the discount doesn't affect the tradeoff between ordering cost and carrying cost. So the total cost would be:

Total cost = $2,880,100 + $100 + ($0.20 x 60,000) = $2,987,100

The savings from taking the discount would be:

Savings = $2,979,200 - $2,987,100 = -$7,900

So if we take the discount, we would actually lose money compared to not taking it. Therefore, the best choice is not to increase the ordering quantity and not take the discount.

Fashion Clothiers Inc. Assume That Fashion Clothiers Inc. Uses 1,440,000 Yards of Material