# Capital Intensity Ratio Calculation for Island Angler Fishing Team ## Key Information - **Current Operating Capacity:** 90% - **Increase to Full Capacity:** 100% - **Projected Sales Growth:** 20% - **Costs, Assets (except net fixed assets and current liabilities):** Proportional to sales - **Long-term Debt & Equity:** Not proportional ## Definitions - **Capital Intensity Ratio (CIR):** \( \text{CIR} = \frac{\text{Total Assets}}{\text{Sales}} \) Measures the amount of assets needed to generate \$1 of sales. ## Steps to Calculate CIR at Full Capacity ### 1. **Understand Current Situation** - At 90% capacity, current sales = \( S \) - Current total assets = \( A \) - Current CIR = \( \frac{A}{S} \) ### 2. **Calculate Full Capacity Sales** - At 100% capacity, sales would be: \( S_{\text{full}} = \frac{S}{0.9} \) ### 3. **Projected Sales** - Projected sales after 20% growth (based on current sales): \( S_{\text{new}} = S \times 1.2 \) ### 4. **Determine Asset Requirement for Projected Sales** - Since assets (other than net fixed assets and current liabilities) are proportional to sales, but we adjust for full capacity. #### **a. Find Asset Utilization at Full Capacity** - At full capacity, existing assets can support sales up to \( S_{\text{full}} \). - If \( S_{\text{new}} \leq S_{\text{full}} \): No new assets needed. - If \( S_{\text{new}} > S_{\text{full}} \): Need new assets for the excess sales. #### **b. Projected Sales vs. Full Capacity Sales** - Compare \( S_{\text{new}} \) and \( S_{\text{full}} \): - If 20% growth keeps you below 100% capacity, no new assets needed. - If above, calculate additional assets. ### 5. **Calculate New Capital Intensity Ratio** - At full capacity, \( \text{CIR}_{\text{full}} = \frac{A}{S_{\text{full}}} \) - For projected sales, \( \text{CIR}_{\text{projected}} = \frac{\text{Total Assets needed}}{S_{\text{new}}} \) ### 6. **Formula Derivation** #### **If sales after growth are still within full capacity:** - No new assets needed, CIR decreases: \[ \text{CIR}_{\text{projected}} = \frac{A}{S_{\text{new}}} \] But since \( S_{\text{new}} < S_{\text{full}} \), assets are "spread" over higher sales. #### **If sales after growth exceed full capacity:** - Additional assets needed for sales above full capacity: - Let \( S_{\text{excess}} = S_{\text{new}} - S_{\text{full}} \) - Additional assets needed: \( A_{\text{excess}} = \text{CIR}_{\text{current}} \times S_{\text{excess}} \) - Total assets needed: \( A_{\text{new}} = A + A_{\text{excess}} \) - New CIR: \( \text{CIR}_{\text{projected}} = \frac{A_{\text{new}}}{S_{\text{new}}} \) ## **Summary Table** | Scenario | Sales (\( S_{\text{new}} \)) | Total Assets Needed | Capital Intensity Ratio | |----------|------------------------------|---------------------|------------------------| | Growth ≤ Full Capacity | \( S \times 1.2 \leq \frac{S}{0.9} \) | \( A \) | \( \frac{A}{S \times 1.2} \) | | Growth > Full Capacity | \( S \times 1.2 > \frac{S}{0.9} \) | \( A + \text{CIR}_{\text{current}} \times (S_{\text{new}} - S_{\text{full}}) \) | \( \frac{A_{\text{new}}}{S_{\text{new}}} \) | ## **Conclusion** - **If 20% growth keeps sales within current asset capacity, the capital intensity ratio falls.** - **If sales surpass full capacity, calculate additional asset needs for the excess, and recompute the CIR.** --- **If you provide actual numbers for sales and assets, the ratio can be calculated numerically.**