Let's go through the solution step-by-step:
### a. Determine the accounts receivable turnover for 20Y9 and 20Y8
1. Accounts Receivable Turnover Formula:
[tex]\[
\text{Accounts Receivable Turnover} = \frac{\text{Sales}}{\text{Average Accounts Receivable}}
\][/tex]
2. Calculate the Average Accounts Receivable for each year:
- For 20Y8:
[tex]\[
\text{Average Accounts Receivable} = \frac{\text{Beginning of Year Accounts Receivable} + \text{End of Year Accounts Receivable}}{2}
\][/tex]
[tex]\[
\text{Average Accounts Receivable (20Y8)} = \frac{\$530,000 + \$610,000}{2} = \$570,000
\][/tex]
- For 20Y9:
[tex]\[
\text{Average Accounts Receivable} = \frac{\text{Beginning of Year Accounts Receivable} + \text{End of Year Accounts Receivable}}{2}
\][/tex]
[tex]\[
\text{Average Accounts Receivable (20Y9)} = \frac{\$610,000 + \$600,000}{2} = \$605,000
\][/tex]
3. Calculate the Accounts Receivable Turnover for each year:
- For 20Y8:
[tex]\[
\text{Accounts Receivable Turnover (20Y8)} = \frac{\$6,612,000}{\$570,000} = 11.6
\][/tex]
- For 20Y9:
[tex]\[
\text{Accounts Receivable Turnover (20Y9)} = \frac{\$8,107,000}{\$605,000} = 13.4
\][/tex]
So the answers for a. would be:
- 20Y8: 11.6
- 20Y9: 13.4
### b. Determine the days' sales in receivables for 20Y9 and 20Y8.
1. Days' Sales in Receivables Formula:
[tex]\[
\text{Days' Sales in Receivables} = \frac{365}{\text{Accounts Receivable Turnover}}
\][/tex]
2. Calculate the Days' Sales in Receivables for each year:
- For 20Y8:
[tex]\[
\text{Days' Sales in Receivables (20Y8)} = \frac{365}{11.6} = 31.5 \text{ days}
\][/tex]
- For 20Y9:
[tex]\[
\text{Days' Sales in Receivables (20Y9)} = \frac{365}{13.4} = 27.2 \text{ days}
\][/tex]
So the answers for b. would be:
- 20Y8: 31.5 days
- 20Y9: 27.2 days
### c. Are the changes in the accounts receivable turnover and days' sales in receivables from 20Y8 to 20Y9 favorable or unfavorable?
- A higher Accounts Receivable Turnover is favorable because it indicates that the company is collecting its receivables more frequently.
- A lower Days' Sales in Receivables is also favorable because it indicates that the company is collecting its receivables faster.
From 20Y8 to 20Y9:
- Accounts Receivable Turnover increased from 11.6 to 13.4 (favorable)
- Days' Sales in Receivables decreased from 31.5 days to 27.2 days (favorable)
Thus, the changes are favorable.
So the answer for c. would be:
- Favorable ✔
To summarize:
[tex]\[
\begin{aligned}
& \text{a. Accounts Receivable Turnover} \\
& \text{20Y8:} \quad 11.6 \\
& \text{20Y9:} \quad 13.4 \\
& \text{b. Days' Sales in Receivables} \\
& \text{20Y8:} \quad 31.5 \text{ days} \\
& \text{20Y9:} \quad 27.2 \text{ days} \\
& \text{c. Changes:} \\
& \text{Favorable} \checkmark \\
\end{aligned}
\][/tex]
