Order Quantities And Projected Profits For SuperFun Toys

Order quantities and projected profits for SuperFun Toys demand scenarios

The primary focus of this analysis is to compute the projected profit for different suggested order quantities of Weather Teddy units—namely 15,000; 18,000; 24,000; and 28,000 units—under three sales demand scenarios: pessimistic (10,000 units), most likely (20,000 units), and optimistic (30,000 units). This evaluation aids in understanding potential revenue outcomes and guides managerial decision-making regarding optimal inventory levels.

To accurately forecast profits, it is essential to incorporate the costs, expected sales price, salvage value of unsold units, and the demand-supply relationship. The purchase cost per unit is established at $16, and sales revenue per unit is $24 when sold during the holiday season. Unsold units can be liquidated at a salvage value of $5 per unit after the holiday season. This profit structure influences the total revenue and profit calculations based on actual sales volumes relative to the ordered quantities.

Methodology for Profit Calculation

The calculation process involves assessing the sales revenue from units sold during the holiday period, accounting for the number of units ordered versus the actual demand in each scenario. When demand exceeds supply, all units are sold at $24 per unit, generating maximum revenue. Conversely, if demand is lower than the order quantity, surplus units are sold at salvage value of $5, reducing overall profit. When demand is between these two extremes, profit is computed proportionally, integrating both sales revenue and salvage value accordingly.

Using this framework, the profit for each scenario and order quantity is calculated as follows:

• Sales Revenue: Determined by the minimum of demand and order quantity times the selling price ($24).
• Cost of Goods Sold: Order quantity times unit purchase cost ($16).
• Remaining Inventory: When demand is less than order quantity, remaining units are sold at salvage value ($5).
• Total Profit: Sum of revenue from sold units plus salvage sales minus total purchase cost.

Profit Projections under Different Demand Scenarios

Pessimistic Scenario (Demand = 10,000 units)

For the pessimistic case, where demand is 10,000 units, the profit calculations are as follows:

• Order Quantity: 15,000; 18,000; 24,000; 28,000 units.
• Revenue is capped at demand multiplied by $24, as demand cannot exceed 10,000 units.
• Remaining units (if any) are sold at salvage value of $5 per unit.

For example, with a 15,000-unit order:

Units sold: 10,000 units at $24 = $240,000

Remaining units: 5,000 units sold at $5 = $25,000

Total revenue: $240,000 + $25,000 = $265,000

Total cost: 15,000 units × $16 = $240,000

Profit: $265,000 - $240,000 = $25,000

The profit for larger order quantities (18,000; 24,000; 28,000) remains the same: revenue maximizes at 10,000 units sold, with surplus units being liquidated at salvage value, resulting in similar profit figures. Increased order size does not improve profit under low demand in this scenario, as excess stock is sold at salvage value.

Most Likely Scenario (Demand = 20,000 units)

In the most probable case of demand at 20,000 units:

• Order quantity of 15,000 units yields maximum sales revenue of 15,000 × $24 = $360,000
• Remaining demand (5,000 units) cannot be fulfilled due to supply limits, resulting in lost sales and potential lost profits.
• However, for higher order quantities, the sales are constrained by actual demand, and surplus units are sold at salvage value.

For 24,000 units ordered:

Units sold: 20,000 units at $24 = $480,000

Remaining units: 4,000 units sold at $5 = $20,000

Total revenue: $480,000 + $20,000 = $500,000

Total cost: 24,000 × $16 = $384,000

Profit: $500,000 - $384,000 = $116,000

Optimistic Scenario (Demand = 30,000 units)

In the optimistic demand case of 30,000 units, the profit calculations for each order quantity are as follows:

• For 15,000 units ordered:
• Sold at demand: 15,000 units at $24 = $360,000
• Remaining demand unmet: 15,000 units, leading to potential loss, but since only 15,000 units are ordered, no surplus inventory is liquidated at salvage value.
• The profit here is constrained by order quantity; any additional demand beyond the order quantity cannot be fulfilled, leading to lost sales.

Order quantities exceeding 15,000 units display similar profit patterns, with higher potential sales constrained by the order size. For instance, ordering 24,000 units permits selling 24,000 units at $24, totaling $576,000, minus purchase costs. The profit increases substantially with larger orders under this demand, provided that actual demand matches or exceeds these levels.

Analysis Summary and Recommendations

Overall, the profit projections reveal that increasing order quantities generally boosts profit potential, especially under higher demand scenarios. However, excessive ordering beyond anticipated demand levels might lead to surplus inventory, which must be liquidated at salvage value, potentially eroding profit margins.

Considering the scenarios and the balance between risk and reward, the optimal order quantity appears to be aligned with the most probable demand (20,000 units). Ordering 24,000 units offers a favorable compromise, providing sufficient stock to meet most demand levels while maintaining manageable surplus and associated costs.

Implications of the 70% Stock-Out Policy

The manager advocating for a policy that aims for a 70% chance of meeting demand and a 30% chance of stock-outs suggests a different approach to order quantity. This policy prioritizes matching demand, potentially reducing leftover stock and associated liquidation costs but increasing the risk of stock-outs and missed sales opportunities.

To implement this policy, the ordered quantity should be set based on the demand level corresponding to a 70% service level within the forecasted demand distribution. Given the demand follows a normal distribution with a mean of 20,000 units and a standard deviation derived via the Empirical Rule (assuming a 95% confidence interval from 10,000 to 30,000 units), the z-score for 70% service level is approximately -0.52 (from standard normal tables).

Calculating the order quantity for a 70% service level:

• Order quantity = mean + (z-score × standard deviation)
• Standard deviation estimate: (Range/4) = (30,000 – 10,000) / 4 = 5,000 units
• Order quantity = 20,000 + (-0.52 × 5,000) ≈ 20,000 - 2,600 = 17,400 units

The closest order quantity is approximately 17,400 units. Under this policy, projected profits would resemble those at this stock level across the three demand scenarios, with the benefits of balancing inventory risk and customer service levels.

Conclusion

This analysis underscores the importance of aligning order quantities with demand forecasts, risk appetite, and profit objectives. The recommended approach involves selecting an order quantity around 24,000 units based on the expected demand and profit maximization, with a strategic consideration of service level alternatives such as the 70% stock-out policy. Such decisions should also incorporate sensitivity analyses to adjust for actual market conditions and demand variability, ensuring that managerial choices optimize profitability while managing risk effectively.

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