Question

Hand-to-Mouth is currently cash-constrained and must make a decision about whether to delay paying one of its suppliers or taking out a loan. They owe the supplier $12,500, but the supplier will give them a 2% discount if they pay by today (when the discount period expires). That is, they can either pay $12,225 today, or $12,000 in one month when the net invoice is due. Because Hand-to-Mouth does not have the $12,250 in cash right now, it is considering three options:

Alternative A: Forgo the discount on its trade credit agreement, wait and pay the full $12,500 in one month.

Alternative B: Borrow the money from Bank A, which has offered to lend the firm $12,250 for one month at an APR (compounded monthly) of 11.6%. The bank will require a (no-interest) compensating balance of 5% of the face value of the loan and will charge a $90 loan origination fee, which means Hand-to-Mouth must borrow even more than the $12,250.

Alternative C: Borrow the money from Bank B, which has offered to lend the firm $12,250 for one month at an APR of 15.5% (compounded monthly). The loan has a 1.4% loan origination fee.

1. What is the effective annual cost under Alternative A?

2. What is the effective annual rate under Alternative B?

2. What is the effective annual rate under Alternative C?

Answer 1

ALTERNATIVE - A

Interest rate for the period of additional 30 days = 2/98 = 2.04%

Effective annual cost = (1.0204)^(365/30) -1 = 27.85%

ALTERNATIVE - B (Borrowing from Bank A):

Loan amount = 12250

Compensating baance = 5%of 12500 = 612.5

Oigination fee = 90

Receipt (net loan amount)= Loan amount - Compensating balance - Origination fee=12250-612.5-90=11547.5

interest for a month = 12250*11.6%*30/365 = 116.8

rate for 30 days = (Loan amount -Compensating balance + interest)/net loan amount -1 =

(12250-612.5+116.8)/11547.5 -1 = 1.77% = 0.018

Effective annual rate = (1+0.018)^(365/30) -1=24.24%

ALTERNATIVE - C (Borrowing from Bank B):

Loan amount = 12250

Oigination fee = 1.4% of 12250 = 171.5

Receipt (net loan amount)= Loan amount - Origination fee=12250-171.5=12078.5

interest for a month = 12250*15.5%*30/365 = 156.06

rate for 30 days = (Loan amount -Compensating balance + interest)/net loan amount -1 =

(12250+156.06)/12078.5-1 = 1.77% = 0.027

Effective annual rate = (1+0.027)^(365/30) -1=38.28%

Go for Aternative B (bank A) as cost is lower