Question

In exchange for a $400 million fixed commitment line of credit, your firm has agreed to do the following:

1. Pay 1.7 percent per quarter on any funds actually borrowed.
2. Maintain a 2 percent compensating balance on any funds actually borrowed.
3. Pay an up-front commitment fee of 0.21 percent of the amount of the line.

Based on this information, answer the following:

a. Ignoring the commitment fee, what is the effective annual interest rate on this line of credit? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
  
Effective annual rate ___ %

b. Suppose your firm immediately uses $219 million of the line and pays it off in one year. What is the effective annual interest rate on this $219 million loan? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
  
Effective annual rate _____ %

Answer 1

a). EAR = [(1 + Interest per period)^(Number of compounding periods in a year)] -1

EAR without compensating balance = (1 + 0.017)⁴ - 1

= 1.0698 - 1 = 0.0698, or 6.98%

This is the cost of 98% balance, as 2% of compensating balance will never be used.

EAR with compensating balance = 0.0698 / 0.98 = 0.0712 or 7.12%

b). Credit drawn = $219,000,000

2% compensating balance = $219,000,000 * 0.02 = $4,380,000

Upfront commitment fee = 0.21% of $219,000,000 = $459,900

Amount availed = $219,000,000 - $4,380,000 - $459,900 = $214,160,100

Interest cost = $219,000,000 x [(1 + 0.017)⁴ - 1] = $219,000,000 x 0.0698 = $15,276,068.08

Effective annual interest rate = $15,276,068.08 / $214,160,100 = 0.0713, or 7.13%