A company has approached their bank to negotiate a line of credit agreement. The company would like a total line of $50 M. The bank quotes a rate of Libor + 2.25%, with a 75 bp commitment fee on the unused portion of the line. If the company uses (on average) $30 M of this over the course of the year, what will their effective annual interest rate be? (Assume LIBOR = 3.5% over the life of the loan)

Question

BlackTom AI · Accepted Answer

Here is the step-by-step analysis of each option and the underlying calculation.

Option 1: 3.25% — If you assume only the drawn funds incur interest at LIBOR+2.25% (5.75%), and you ignore the commitment fee, you'd get an average cost far below the total annual charge when the unused portion isn’t costed. But in reality, there is a cost associated with keeping the line available, even if not drawn, so this undervalues the true cost.

Option 2: 6.25% — This value can arise if you compute the total annual cost of the facility and then divide by the actual amount drawn (not by the full 50M). Here’s the breakdown: the interest on drawn funds is 30M × (LIBOR + 2.25%) = 30M × 5.75% = 1.725M. The commitment fee on the unused portion is 20M × 0.75% = 0.15M. The total annual cost is 1.725M + 0.15M = 1.875M. If you then allocate that total cost over the actual usage of 30M, the effective rate becomes 1.875M / 30M = 6.25%. This reflects the cost of maintaining the facility relative to the amount actually utilized.

Option 3: 1.25% — This is far too low for the financed amount once you include the drawn interest at 5.75% on 30M and the 0.75% commitment fee on the unused portion. Even if you incorrectly prorated differently, getting down to 1.25% would require substantial undercounting of either the drawn interest or the commitment fee, which isn’t consistent with the given figures.

Option 4: 2.25% — This equals the spread over LIBOR (the stated additional cost) but ignores the drawn amount’s interest and the commitment fee’s impact on the total annual cost. Framing the cost solely as the spread misses the fact that LIBOR+2.25% applies to drawn balances and there’s a separate fee on unused capacity, so this option does not capture the full annual burden.

A concise way to see the correct approach is to separate two components: the interest on actual usage and the commitment fee on the unused portion, then compare the total annual cost to the actual funds used. The numbers are: interest = 30M × 5.75% = 1.725M, commitment fee = 20M × 0.75% = 0.15M, total = 1.875M. Dividing by the 30M actually drawn yields 1.875M / 30M = 0.0625, i.e., 6.25%. The key conceptual point is that the effective rate often uses the cost per dollar actually drawn, not the entire facility size, for facilities with commitment fees.

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