Question

In exchange for a $500 million fixed commitment line of credit, your firm has agreed to do the following:

1.	Pay 2 percent per quarter on any funds actually borrowed.
2.	Maintain a 4 percent compensating balance on any funds actually borrowed.
3.	Pay an up-front commitment fee of .2 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. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Effective annual interest rate

%

b.	Suppose your firm immediately uses $200 million of the line and pays it off in one year. What is the effective annual interest rate on this $200 million loan? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Effective annual interest rate

%

Answer 1

Exchange Requirement a For every dollar borrowed, you pay interest of: Interest = $1[(1 +.020)^4 - 1] Interest = $.082 You also must maintain a compensating balance of 4 percent of the funds borrowed, so for each dollar borrowed, you will only receive: Amount received = $1(1-04) Amount received = $.96 We can adjust the EAR equation we have been using to account for the compensating balance by dividing the EAR by one minus the compensating balance, so: EAR = [(1.020) -4 -1)/(1-04) EAR = .0858, or 8.58% Another way to calculate the EAR is using the FVIF (or PVIF). For each dollar borrowed, we must repay: Amount owed = $1(1.020) 44 Amount owed = $1.08243 At the end of the year the compensating balance will be returned, so your net cash flow at the end of the year will be: End of year cash flow = $1.0824 - .04 End of year cash flow = $1.0424 The present value of the end of year cash flow is the amount you receive at the beginning of the year, so the EAR is: FV = PV(1 +R) $1.0424 = $.96(1+R) R=$1.0424/$.96-1 EAR = .0858, or 8.58% Requirement b The EAR is the amount of interest paid on the loan divided by the amount received when the loan is originated. The amount of interest you will pay on the loan is the amount of the loan times the effective annual interest rate, so: Interest = $200,000,000[(1.020)^4 - 1] Interest = $16,486,432 For whatever loan amount you take, you will only receive 96 percent of that amount since you must maintain a 4 percent compensating balance on the portion of the credit line used. The credit line also has a fee of.2 percent, so you will only get to use: Amount received =.96($200,000,000) - .002($500,000,000) Amount received = $191,000,000 So, the EAR of the loan is: EAR = $16,486,432/$191,000,000 EAR = .0863, or 8.63%