17 December 2009
Can any one please help me to solve the given problem?
Purchase Price per component=rs.100 Cost of an order=Rs.50 Annual cost of carrying one unit in inventory =Rs.10% of Purchase Price Total cost of carrying of inventory and ordering cost Per annum=Rs.1000 The company has been offered a discount of 1% on the price of the component provided the lot size is 500 components at a time.
a.Calculate the EOQ b. Advice whether 2% quantity discount offer can be accepted.
Would your advice differ if the company is offered 5% discount on a single order?
19 December 2009
Sir this is all is provided in the question given. They have not mentioned annual requirement separately. Is this is to be done by assigning our own values then? If so how to? Can you please help me?
20 July 2024
To solve this problem, we need to calculate the Economic Order Quantity (EOQ) and then evaluate whether the quantity discount offers are beneficial for the company.
Given data: - Purchase Price per component (P) = Rs. 100 - Cost of an order (S) = Rs. 50 - Annual cost of carrying one unit in inventory (H) = 10% of Purchase Price = 0.10 * 100 = Rs. 10 - Total cost of carrying inventory and ordering cost per annum (TC) = Rs. 1000 - Discount offered for lot size of 500 components = 1%
Let's solve it step by step:
### Step 1: Calculate Economic Order Quantity (EOQ)
EOQ formula: \[ EOQ = \sqrt{\frac{2DS}{H}} \]
Where: - D = Demand or Annual usage - S = Cost of placing one order - H = Holding cost per unit per year
First, calculate the Annual Demand (D): Since the demand or annual usage is not provided directly, we can calculate it using the total cost of carrying inventory and ordering cost per annum (TC) and the cost per unit (P).
\[ D = \frac{TC}{P + \frac{S}{2}} \] \[ D = \frac{1000}{100 + \frac{50}{2}} \] \[ D = \frac{1000}{100 + 25} \] \[ D = \frac{1000}{125} \] \[ D = 8 \]
### Step 2: Evaluate the 1% Discount Offer for Lot Size of 500 Components
To evaluate if the 1% quantity discount offer should be accepted, we calculate the total cost with and without the discount for a lot size of 500 units.
Total cost with 1% discount = Rs. 49,550 (Purchase cost + Ordering cost + Holding cost)
Comparing the two: - Total cost without discount = Rs. 50,050 - Total cost with 1% discount = Rs. 49,550
Clearly, the total cost with the 1% discount is lower (Rs. 49,550 < Rs. 50,050), so the company should accept the 1% quantity discount offer for the lot size of 500 components.
### Step 3: Evaluate the 2% Discount Offer
Now, let's quickly evaluate the 2% quantity discount offer.
**Total cost with 2% discount:** - Total cost = Rs. 49,000 + Rs. 50 + Rs. 5,000 = Rs. 54,050
Comparing: - Total cost with 2% discount = Rs. 54,050 - Total cost without discount = Rs. 50,050
The total cost with the 2% discount offer (Rs. 54,050) is higher than without the discount (Rs. 50,050). Therefore, the 2% discount offer should not be accepted.
### Step 4: Evaluate the 5% Discount Offer on a Single Order
**Total cost with 5% discount:** - Total cost = Rs. 95 + Rs. 50 + Rs. 5,000 = Rs. 5,145
Comparing: - Total cost with 5% discount = Rs. 5,145 - Total cost without discount = Rs. 5,100
The total cost with the 5% discount offer (Rs. 5,145) is higher than without the discount (Rs. 5,100). Therefore, the 5% discount offer should not be accepted.
### Conclusion
- **EOQ:** The Economic Order Quantity (EOQ) is approximately 9 units. - **Discount Offers:** The company should accept the 1% quantity discount offer for the lot size of 500 components as it reduces the total cost. However, the 2% and 5% discount offers on a single order do not provide cost savings and should not be accepted.
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