Question

In exchange for a $400 million fixed commitment line of credit, your firm has agreed to do the following: Pay 1.84 percent per quarter on any funds actually borrowed. Maintain a 2 percent compensating balance on any funds actually borrowed. Pay an up-front commitment fee of 0.29 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 $214 million of the line and pays it off in one year. What is the effective annual interest rate on this $214 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). Assumed all funds borrowed & There are two solutions of the question:

---- If Effective Rate of Interest is compounded:

Annual Rate of Interest= (1+r)ⁿ-1

= (1+0.0184)⁴ -1

= 0.0757

=7.57%

Effective Rate of Interest of LOC = R/ 1-c

= 7.57/ 1-0.02

= 7.72%

----- If Effective Rate of Interest is not compounded:

Annual Rate of Interest= 4 x 1.84

= 7.36%

Effective Rate of Interest of LOC = R/ 1-c

= 7.36/1-0.02

= 7.51%

b). Two possible answers:

---- Compounded Rate of Interest

Effective Rate of Interest as calculated in Part (a). = 7.72%

Interest & Compensation fee = $214 m x 7.72% = $ 16.5208 m

Upfront Fee= $400 m x 0.29% = $ 1.16 m

Total = $ (16.5208 +1.16) m

= $ 17.6808m

Effective annual rate of interest = $(17.6808/214) m

= 8.26%

-------Normal Rate of Interest

Effective Rate of Interest as calculated in Part (a). = 7.51%

Interest & Compensation fee = $214 m x 7.51% = $ 16.0714 m

Upfront Fee= $400 m x 0.29% = $ 1.16 m

Total = $ (16.0714 +1.16) m

= $ 17.2314 m

Effective annual rate of interest = $(17.2314 /214) m

= 8.05 %