Math Problem Statement

Which of the following changes would result in the largest increase in Total Net Leverage? Assume the initial values are Gross Total Debt = $500m, Cash & Equivalents = $50m, EBITDA = $100m, EBITDA Margin =20%

Your answer: An increase in Gross Senior Debt of $75m A decrease in Cash of $50m A decrease in EBITDA of $10m A decrease in EBITDA margin of 5 percentage points

Solution

Definitions:

Total Net Leverage is typically calculated as:

Total Net Leverage=Gross Total DebtCash & EquivalentsEBITDA\text{Total Net Leverage} = \frac{\text{Gross Total Debt} - \text{Cash \& Equivalents}}{\text{EBITDA}}

  • Gross Total Debt: $500m
  • Cash & Equivalents: $50m
  • EBITDA: $100m
  • EBITDA Margin: 20% (though not directly used, this can help interpret changes in EBITDA).

Let's calculate how each of the four proposed changes would impact Total Net Leverage:


1. An increase in Gross Senior Debt of $75m

  • New Gross Total Debt = $500m + $75m = $575m
  • Cash remains unchanged at $50m
  • EBITDA remains unchanged at $100m

New Net Leverage=575m50m100m=525m100m=5.25\text{New Net Leverage} = \frac{575m - 50m}{100m} = \frac{525m}{100m} = 5.25

The original Net Leverage is:

Original Net Leverage=500m50m100m=450m100m=4.5\text{Original Net Leverage} = \frac{500m - 50m}{100m} = \frac{450m}{100m} = 4.5

Change in Net Leverage: 5.25 - 4.5 = +0.75


2. A decrease in Cash of $50m

  • Gross Total Debt remains $500m
  • New Cash & Equivalents = $50m - $50m = $0
  • EBITDA remains $100m

New Net Leverage=500m0m100m=500m100m=5.0\text{New Net Leverage} = \frac{500m - 0m}{100m} = \frac{500m}{100m} = 5.0

Change in Net Leverage: 5.0 - 4.5 = +0.5


3. A decrease in EBITDA of $10m

  • Gross Total Debt remains $500m
  • Cash remains $50m
  • New EBITDA = $100m - $10m = $90m

New Net Leverage=500m50m90m=450m90m=5.0\text{New Net Leverage} = \frac{500m - 50m}{90m} = \frac{450m}{90m} = 5.0

Change in Net Leverage: 5.0 - 4.5 = +0.5


4. A decrease in EBITDA margin of 5 percentage points

  • The EBITDA margin decreases from 20% to 15%, but the question does not directly provide a revenue figure. To interpret this, assume that the revenue remains unchanged and focus on the relative decrease in EBITDA.
  • Assumption: EBITDA margin decreases by 5%, which is a proportional decrease in EBITDA.

New EBITDA=100m×(1520)=75m\text{New EBITDA} = 100m \times \left(\frac{15}{20}\right) = 75m

  • Gross Total Debt remains $500m
  • Cash remains $50m

New Net Leverage=500m50m75m=450m75m=6.0\text{New Net Leverage} = \frac{500m - 50m}{75m} = \frac{450m}{75m} = 6.0

Change in Net Leverage: 6.0 - 4.5 = +1.5


Conclusion:

The largest increase in Total Net Leverage occurs with the decrease in EBITDA margin by 5 percentage points, which increases Net Leverage by +1.5.

Would you like more details or have any questions?


5 Related Questions:

  1. How does an increase in Gross Senior Debt affect the balance sheet ratios?
  2. What are the implications of decreasing EBITDA for debt servicing?
  3. How is EBITDA margin connected to overall profitability metrics?
  4. What other financial ratios are impacted by changes in cash levels?
  5. How would issuing new equity impact leverage?

Tip: Always monitor both debt and EBITDA changes in tandem, as leverage is sensitive to shifts in both.

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Math Problem Analysis

Mathematical Concepts

Leverage
Debt Management
Financial Ratios

Formulas

Total Net Leverage = (Gross Total Debt - Cash & Equivalents) / EBITDA

Theorems

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Suitable Grade Level

University/Finance