A company is considering the purchase of one of its inputs from supplier A. The credit terms are 1.5/10 net 30. What is the effective annual cost of forgoing the discount and paying on day 30?
A) 20.19%
B) 31.76%
C) 73.61%

Question

Quizplus · Accepted Answer

The effective annual cost of forgoing the discount can be calculated using the formula for the cost of not taking the trade discount: $$ \text{Cost} = \left( \frac{\text{Discount \%}}{100\% - \text{Discount \%}} \right) \times \left( \frac{360}{\text{Days in payment period} - \text{Discount period}} \right) $$ Here, the discount is 1.5%, so the discount period is 10 days, and the full payment period is 30 days. Plugging these values into the formula gives: $$ \text{Cost} = \left( \frac{1.5}{100 - 1.5} \right) \times \left( \frac{360}{30 - 10} \right) = \left( \frac{1.5}{98.5} \right) \times 18 = 0.015228 \times 18 = 0.2741 $$ or 27.41% on a per period basis. However, since the period in question is 20 days (from day 10 to day 30), we need to annualize this rate to find the effective annual rate (EAR). The formula for EAR based on a non-annual rate is: $$ \text{EAR} = \left(1 + \text{periodic rate}\right)^{\frac{365}{\text{days in period}}} - 1 $$ Substituting the periodic rate and the days in period gives: $$ \text{EAR} = \left(1 + 0.2741\right)^{\frac{365}{20}} - 1 \approx 31.76\% $$ Therefore, the effective annual cost of forgoing the discount and paying on day 30 is approximately 31.76%.

A Company Is Considering the Purchase of One of Its