The SYX Sdn. Bhd. factors all of its receivables immediately at a discount rate of 1.1 percent. The average collection period is 37.4 days and default are unlikely. What is the effective cost of borrowing?

a.
10.24 percent

b.
15.82 percent

c.
13.97 percent

d.
11.40 percent

To determine the effective cost of borrowing, we need to calculate the annualized discount rate based on the given terms. Here’s the step-by-step solution:

1. **Discount rate**: 1.1% for 37.4 days.

2. **Annualizing the rate**:
   Since the discount is given for 37.4 days, we need to find out how many such periods fit into a year (assuming 365 days in a year).

   \[
   \text{Number of periods in a year} = \frac{365}{37.4} \approx 9.76
   \]

3. **Effective annual rate (EAR)**:
   The effective annual rate can be found using the formula for compound interest, which in this context is:
   
   \[
   \text{EAR} = (1 + \text{periodic rate})^n - 1
   \]

   Here, the periodic rate is 1.1%, or 0.011, and \( n \) is the number of periods in a year.

   \[
   \text{EAR} = (1 + 0.011)^{9.76} - 1
   \]

4. **Calculating the EAR**:

   \[
   \text{EAR} = (1 + 0.011)^{9.76} - 1 \approx 0.1140 \text{ or } 11.40\%
   \]

Therefore, the effective cost of borrowing is 11.40 percent.

The correct answer is:

d. 11.40 percent

Would you like more details or have any questions? 

Here are 5 questions you might want to ask:

1. How is the effective annual rate (EAR) different from the nominal annual rate?
2. Can you explain the impact of the collection period on the effective borrowing cost?
3. What assumptions are we making in this calculation?
4. How would the effective borrowing cost change if the discount rate was higher?
5. Can you show a comparison of effective borrowing costs with different collection periods?

Tip: Always ensure to annualize periodic rates correctly by considering the frequency of the period within a year to get an accurate effective rate.

Learn how to calculate the effective cost of borrowing with a step-by-step solution. This problem involves discounting receivables at a given rate, calculating the annualized rate, and determining the effective annual rate (EAR). Explore detailed calculations and understand the impact of discount rates on borrowing costs.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation