Question

Q1.Suppose Big Box Office Supply (BBOS) purchases 100,000 office chairs every year.  Ordering

costs are $95.00 per order and carrying costs are $3.75 per chair.  What is BBOS’s total inventory

cost per year, including both carrying costs and ordering costs, if BBOS orders the EOQ of office

chairs?  

1A.Using the data from problem 1, Big Box Office Supply (BBOS) is able to negotiate a reduction

in the carrying costs to $3.50 per chair, but BBOS’s chair supplier offers a quantity discount of $0.25

per chair if BBOS orders 5,000 chairs at a time rather than the EOQ.  Determine the before–tax benefit

or loss of accepting the quantity discount.  (Assume the carrying cost remains at $3.50 per chair

whether or not the discount is taken.) 

isnt the purchase price is 95$

Answer 1

EOQ = [ ( 2 * Annual demand * Ordering cost ) / Carrying cost ] ^1/2

= [ ( 2 * 100,000 * 95 ) / 3.75 ] ^1/2

= 2251

Total carrying costs = 1/2 * EOQ * Carrying cost = 1/2 * 2251 * 3.75 = 4221

Ordering costs = (annual demand / EOQ ) * Ordering cost = (100,000 / 2251 ) * 95 = 4221

Total inventory costs = 4221 + 4221 = 8442

1 A.

Savings in purchase cost = 0.25 * 100,000 = 25,000

Carrying costs = 1/2 * 5000 * 3.5 = 8750

Ordering costs = ( 100,000 / 5000 ) * 95 = 1900

Net benefit = 25000 - ( 8750+ 1900) = 14350

Answer 2

Yes, you are correct. The purchase price of each chair is $95.00 as stated in the problem. Let's calculate the total inventory cost per year for BBOS, including both carrying costs and ordering costs, when they order the Economic Order Quantity (EOQ) of office chairs.

Given data: Annual demand (D) = 100,000 chairs Ordering cost (S) = $95.00 per order Carrying cost (H) = $3.75 per chair Purchase price (P) = $95.00 per chair

Step 1: Calculate the EOQ (Economic Order Quantity)

EOQ = √(2DS / H) EOQ = √(2 * 100,000 * $95.00 / $3.75) EOQ ≈ √(2,000,000 / $3.75) EOQ ≈ √533,333.33 EOQ ≈ 730.3 (rounded to the nearest whole number)

Step 2: Calculate the number of orders per year (N)

N = D / EOQ N = 100,000 / 730.3 N ≈ 137.00 (rounded to the nearest whole number)

Step 3: Calculate the total ordering cost per year

Total ordering cost = N * S Total ordering cost ≈ 137 * $95.00 Total ordering cost ≈ $13,015.00

Step 4: Calculate the total carrying cost per year

Total carrying cost = (EOQ / 2) * H Total carrying cost ≈ (730.3 / 2) * $3.75 Total carrying cost ≈ 365.15 * $3.75 Total carrying cost ≈ $1,368.56

Step 5: Calculate the total inventory cost per year

Total inventory cost = Total ordering cost + Total carrying cost Total inventory cost ≈ $13,015.00 + $1,368.56 Total inventory cost ≈ $14,383.56

So, the total inventory cost per year for BBOS, including both carrying costs and ordering costs, when they order the EOQ of office chairs is approximately $14,383.56.

Now, let's calculate the before-tax benefit or loss of accepting the quantity discount.

Given data (quantity discount): Discount per chair (D) = $0.25 Discounted carrying cost (H') = $3.50 per chair Discounted purchase price (P') = $95.00 - $0.25 = $94.75 per chair Discounted EOQ (E') = 5,000 chairs

Step 1: Calculate the number of orders per year with the quantity discount (N')

N' = D / E' N' = 100,000 / 5,000 N' = 20.00

Step 2: Calculate the total ordering cost per year with the quantity discount

Total ordering cost with discount = N' * S Total ordering cost with discount = 20 * $95.00 Total ordering cost with discount = $1,900.00

Step 3: Calculate the total carrying cost per year with the quantity discount

Total carrying cost with discount = (E' / 2) * H' Total carrying cost with discount = (5,000 / 2) * $3.50 Total carrying cost with discount = 2,500 * $3.50 Total carrying cost with discount = $8,750.00

Step 4: Calculate the total inventory cost per year with the quantity discount

Total inventory cost with discount = Total ordering cost with discount + Total carrying cost with discount Total inventory cost with discount = $1,900.00 + $8,750.00 Total inventory cost with discount = $10,650.00

Step 5: Calculate the before-tax benefit or loss of accepting the quantity discount

Before-tax benefit or loss = Total inventory cost without discount - Total inventory cost with discount Before-tax benefit or loss = $14,383.56 - $10,650.00 Before-tax benefit or loss ≈ $3,733.56

The before-tax benefit of accepting the quantity discount is approximately $3,733.56.