Question

Finance - CFIN 6th Edition Chapter 14, Problem 12 Solution

I am not able to come up with the same solution posted in the Chegg Study Textbook solution for this question beginning with step 4 of 7. The issue has to do with computing the EAR. I followed the textbook solution, but the response does not make sense for the EAR. Please help.

Chapter 14 Problem 12

Montana Allied Products (MAP) must borrow $1.7 million to finance its working capital requirements. The bank has offered a 45-day simple interest loan with a quoted interest rate of 8 percent. Calculate the loan’s APR and assuming there is (a) no compensating balance requirement and (b) a 15 percent compensating balance requirement, which MAP must satisfy from the loan proceeds. (c) How much does MAP have to borrow so that it has $1.7 million to pay its bills if the loan requires a 15 percent compensating balance?

The formula and the solution provided does not match up

(1+8/360)^8-1

Answer 1

Annual Effective Interest Rate =8%

45 day interest =R

Number of 45 days period in a year =360/45=8

Future value of 1$ after one year at interest rate of R per 45 days =(1+R)^8

Future value of $1 after one year at  Annual interest rate =8%=1+0.08

(1+R)^8=1+0.08=1.08

1+R=1.08^(1/8)=1.009667

45 days interest rate =R=0.009667=0.9667%

APR (Annual Percentage Rate )=0.9667*8=0.077332

APR=7.7332%

(b) 15% compensating Balance :

For loan of $1.7 , Compensating balance =15%=0.15

Loan amount received in hand =(1-0.15)*1.7 million=$1,445,000

Compensating Balance =1700000-1445000=$255,000

Amount to be returned after 45 days =$1.7 million *1.009667=$1,716,433

Less: Compensating Balance available =$255,000

Amount returned =1716433-255000=$1,461,433

Effective interest rate for 45 day period =(1461433/1445000)-1=0.011372

Annual Percentage Rate (APR)=0.011372*8=0.090979=9.0979%

(c)

Amount of Loan Needed =$1,700,000

Amount to be borrowed =X

Amount of compensating Balance =0.15X

Amount in hand =(1-0.15)X=0.85X

0.85X=$1,700,000

Amount to be borrowed =X=1700000/0.85=$2,000,000