Three tranches of debt are $60 million at 5.25%, $40 million at 6.95%, and $20 million at 8.75%. What is the weighted average interest rate (rounded to one decimal, no percent sign)?

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Multiple Choice

Three tranches of debt are $60 million at 5.25%, $40 million at 6.95%, and $20 million at 8.75%. What is the weighted average interest rate (rounded to one decimal, no percent sign)?

Explanation:
Blend the rates by weight of debt to get the overall cost of borrowing. In other words, multiply each rate by its debt amount to find each tranche’s interest contribution, sum those contributions, and divide by the total debt. Compute: total debt = 60 + 40 + 20 = 120. Interest contributions are 60×5.25% = 3.15, 40×6.95% = 2.78, and 20×8.75% = 1.75. Sum = 7.68. The weighted average rate = 7.68 / 120 = 0.064 = 6.4%. Rounded to one decimal place with no percent sign, the result is 6.4. This value falls between the lowest and highest tranche rates, as expected, and is influenced most by the largest debt portion, which is at the lowest rate.

Blend the rates by weight of debt to get the overall cost of borrowing. In other words, multiply each rate by its debt amount to find each tranche’s interest contribution, sum those contributions, and divide by the total debt.

Compute: total debt = 60 + 40 + 20 = 120. Interest contributions are 60×5.25% = 3.15, 40×6.95% = 2.78, and 20×8.75% = 1.75. Sum = 7.68. The weighted average rate = 7.68 / 120 = 0.064 = 6.4%.

Rounded to one decimal place with no percent sign, the result is 6.4. This value falls between the lowest and highest tranche rates, as expected, and is influenced most by the largest debt portion, which is at the lowest rate.

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