Gild Company has been offered credit terms of 3/10, net 30. Using a 365-day year, what is the nominal cost of not taking advantage of the discount if the firm pays on the 35th day after the purchase?
14.2%
32.2%
37.6%
45.2%
The correct answer and explanation is :
To calculate the nominal cost of not taking advantage of the discount, we use the following formula:
[
\text{Cost of Trade Credit} = \frac{\text{Discount %}}{1 – \text{Discount %}} \times \frac{365}{\text{Days beyond discount period}}
]
Step 1: Identify Given Information
- Credit Terms: 3/10, net 30 → This means a 3% discount is available if paid within 10 days, otherwise, the full amount is due in 30 days.
- Payment Date: The firm pays on day 35, which is 25 days after the discount period (35 – 10 = 25 days).
- Discount = 3% or 0.03.
- Days beyond discount period = 25 days.
Step 2: Apply the Formula
[
\text{Cost of Trade Credit} = \frac{0.03}{1 – 0.03} \times \frac{365}{25}
]
[
= \frac{0.03}{0.97} \times 14.6
]
[
= 0.03093 \times 14.6
]
[
= 0.4516 \text{ or } 45.2\%
]
Conclusion
The nominal cost of not taking the discount is 45.2%, which is the correct answer. This means the firm is effectively paying an annualized interest rate of 45.2% by delaying payment instead of taking advantage of the 3% discount. This is a high cost, so if the firm has the cash available, it should take the discount and pay early.