Question

Hand-to-Mouth (H2M) is currently​ cash-constrained, and must make a decision about whether to delay paying one of its​ suppliers, or take out a loan. They owe the supplier $ 12 comma 500 with terms of 2.4​/10 Net​ 40, so the supplier will give them a 2.4 % discount if they pay by today​ (when the discount period​ expires). ​ Alternatively, they can pay the full $ 12,500 in one month when the invoice is due. H2M 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 needed to pay its supplier today from Bank​ A, which has offered a​ one-month loan at an APR of 12.4 %. The bank will require a​ (no-interest) compensating balance of 4.6 % of the face value of the loan and will charge a $ 90 loan origination fee. Because H2M has no​ cash, it will need to borrow the funds to cover these additional amounts as well.

Alternative​ C: Borrow the money needed to pay its supplier today from Bank​ B, which has offered a​ one-month loan at an APR of 14.9 %. The loan has a 1.3 % loan origination​ fee, which again H2M will need to borrow to cover.

Answer 1

Alternative A:

Discount, D = 2.4%

Interest rate for n = 40 - 10 = 30 days will be = r = D / (1 - D) = 2.4% / (1 - 2.4%) =  0.02459

Hence, effective annual rate = (1 + r)^365/n - 1 = (1 +  0.02459)^{(365 / 30)} - 1 = 34.39%

Alternative B:

Disbursement required = (amount to be paid to the party + loan origination fees) / (1 - Compensating balance factor) = [(12,500 x (1 - 2.4%) + 90] / (1 - 4.6%) =  12,882.60

Amount actually available in hand = 12,500 x (1 - 2.4%) =  12,200

Interest = 12,882.60 x 12.4% / 12 =  133.12

Hence, effective interest cost for a month = (interest + loan origination fees) / Net proceeds in hands = (133.12 + 90) / 12,200 =  0.0183

Hence, effective annual rate = (1 +  0.0183)¹² - 1 = 0.2429 = 24.29%

Alternative C

Amount that needs to be disbursed = amount to be paid to the party / (1 - loan origination fees) = 12,200 / (1 - 1.3%) =  12,361

Interest for a month = 12,361 x 14.9% / 12 =  153.58

Interest rate for 1 month = (interest + loan origination fees) / Net proceeds = (153.58 + 12,361 - 12,200) / 12,200 = 0.025759878

Hence, effective annual rate = (1 + 0.025759878)¹² - 1= 0.356902044 = 35.69%

Since alternative B has the least effective annual rate, hence Hand-to-Mouth (H2M) should choose alternative B.