Hand to mouth is currently cash-constrained and must take decision about whether
ID: 2733032 • Letter: H
Question
Hand to mouth is currently cash-constrained and must take decision about whether to delay paying one of its suppliers, or taking out a loan.They owe the supplier $13,000,but the supplier will give them a 1.6% discount if they pay by today (when the discount period expires). That is, they can either pay $12,792 today, or $13,000 in one month when the net invoice is due.Because Hand-to-Mouth does not have the $12,792 in cash right now,it is considering three options: Alternative A: Forgo the discount on its trade credit agreement, wait and pay the full $13,000 in one month. Alternative B: Borrow the money from Bank A,which has offered to lend the firm $12,792 for one month at an APR (compounded monthly) of 11.7%.The bank will require a (no-interest) compensating balance of 4.9% of the face value of the loan and will charge a $110 loan origination fee,which means Hand-to-Mouth must borrow even more than the $12,792. Alternative C:Borrow the money from Bank B,which has offered to lend the firm $12,792 for one month at an APR of 15.4% (compounded monthly).The loan has a 0.6% loan origination fee. Question: Alternative A (a)The effective annual cost is ------%(Round to two decimal places). Alternative B: (b)The effective annual rate is ------%(Round to two decimal places). Alternative C: (c)The effective annual rate is ------%(Round to two decimal places).Note question A ask for the annual cost.The expert had answer these type of question 3 times with wrong answers.
Explanation / Answer
a) Alternative A: Effective annual cost = (208/12792) = 1.63% per month
Effective rate = (1.0163)^12 - 1 = 1.2141 - 1 = 21.41%
b) Alternative B:
Effective Loan amount = 12792 - 627 (compensating balance) - 110 = 12,055
Repayment = 12792*(1 + 0.117/12) = 12917
Amount to be paid = 12917 - 627 = 12290
Rate of interest = (12290/12055) - 1 = 1.95% per month
Effective annual rate = 1.0195^12 - 1 = 1.2608 -1 = 26.08%
c) Alternative C:
Effective Loan = 12792 - 77 = 12715
Amount to be repaid = 12792*(1 + 0.154/12) = 12,956
Interest rate for one month = (12956/12715) - 1 = 1.90%
Effective annual cost = 1.019^12 - 1 = 1.2534 -1 = 25.34%
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