The price spike from $10 to $15 per unit cannot be solely attributed to the 20% increase in raw material costs, as this explanation is inconsistent with the data. Here's a step-by-step analysis:

• Selling price (SP₁) = $10
• Profit margin per unit = $2
• Cost price per unit (CP₁) = SP₁ - Profit margin = $10 - $2 = $8
  This cost includes raw materials (RM₁) and other costs (OC₁):
  RM₁ + OC₁ = $8

After Raw Material Cost Increase:

• Raw material cost increases by 20%: RM₂ = 1.2 × RM₁
• New selling price (SP₂) = $15
• New profit margin per unit = $5
• New cost price (CP₂) = SP₂ - New profit margin = $15 - $5 = $10
  This new cost includes RM₂ and other costs (OC₂):
  RM₂ + OC₂ = $10

Key Observations:

1. Total cost increased by $2 (from $8 to $10).

   • If this increase were only due to raw materials, then:
     Increase in raw material cost = RM₂ - RM₁ = 0.2 × RM₁
     This should equal the total cost increase:
     2 × RM₁ = $2
     → RM₁ = $10
   • However, from the original cost equation:
     RM₁ + OC₁ = $8
     If RM₁ = $10, then OC₁ = $8 - $10 = -$2 (negative cost, which is impossible).

2. Maximum possible raw material cost increase:

   • In the original scenario, RM₁ ≤ $8 (since OC₁ ≥ 0).
   • Maximum raw material cost increase = 20% of $8 = $1.60.
   • But the actual cost increase is $2, which is $0.40 more than the maximum raw material cost increase.

Conclusion:

• The 20% rise in raw material costs cannot fully explain the $2 cost increase (max $1.60 vs. actual $2).
• The remaining $0.40 cost increase must come from other factors, such as:
  • An increase in other costs (e.g., labor, overhead).
  • Or, the company intentionally raised prices beyond cost increases to boost profits (profit margin rose from $2 to $5, a $3 increase).
• The company’s claim that the spike is solely due to raw materials is invalid. The analyst’s suspicion is correct: other factors (e.g., higher other costs or profit-driven pricing) contributed to the price spike.

Why This Matters:

• The raw material cost increase (≤ $1.60) is insufficient to cover the total cost rise ($2), and the extra $0.40 (or more) suggests either hidden cost increases or opportunistic pricing.
• This could indicate inaccurate cost reporting or exploitative pricing by the company. Further investigation into other cost components or profit motives is warranted.