Answer :
Sure, let's break down the steps to solve the question:
We have the following information:
- Period Covered: 365 days
- Average period of credit allowed by suppliers: 16 days
- Average Total of Debtors Outstanding: 4,800
- Raw Material Consumption: 44,000
- Total Production Cost: 100,000
- Total Cost of Sales: 101,000
- Sales for the Year: 16,000
- Value of Average Stock maintained:
- Raw Materials: 3,200
- Work-in-Progress: 3,500
- Finished Goods: 2,000
We need to calculate the following:
(i) Raw materials held in stock (in days)
(ii) Work-in-progress (in days)
(iii) Finished goods held in stock (in days)
(iv) Average period allowed to Debtors (in days)
(v) Total operating cycle period (in days)
(vi) Number of operating cycles in a year
### Step-by-Step Solution:
#### (i) Raw materials held in stock (in days)
To find the number of days that raw materials are held in stock, use the formula:
[tex]\[ \text{Raw materials held in stock (in days)} = \left(\frac{\text{Value of raw materials}}{\text{Raw material consumption per year}}\right) \times \text{Period covered in days} \][/tex]
[tex]\[ \text{Raw materials held in stock} = \left(\frac{3200}{44000}\right) \times 365 \approx 26.55 \text{ days} \][/tex]
#### (ii) Work-in-progress (in days)
To find the duration in days for work-in-progress, use the formula:
[tex]\[ \text{Work-in-progress (in days)} = \left(\frac{\text{Value of work-in-progress}}{\text{Total production cost}}\right) \times \text{Period covered in days} \][/tex]
[tex]\[ \text{Work-in-progress} = \left(\frac{3500}{100000}\right) \times 365 \approx 12.78 \text{ days} \][/tex]
#### (iii) Finished goods held in stock (in days)
To find the number of days that finished goods are held in stock, use the formula:
[tex]\[ \text{Finished goods held in stock (in days)} = \left(\frac{\text{Value of finished goods}}{\text{Total cost of sales}}\right) \times \text{Period covered in days} \][/tex]
[tex]\[ \text{Finished goods held in stock} = \left(\frac{2000}{101000}\right) \times 365 \approx 7.23 \text{ days} \][/tex]
#### (iv) Average period allowed to Debtors (in days)
To calculate the average duration that debts are outstanding, use the formula:
[tex]\[ \text{Average period allowed to Debtors (in days)} = \left(\frac{\text{Average total of debtors outstanding}}{\text{Sales for the year}}\right) \times \text{Period covered in days} \][/tex]
[tex]\[ \text{Average period allowed to Debtors} = \left(\frac{4800}{16000}\right) \times 365 \approx 109.5 \text{ days} \][/tex]
#### (v) Total operating cycle period (in days)
The total operating cycle period is the sum of raw materials held in stock, work-in-progress, finished goods held in stock, and the average period allowed to debtors.
[tex]\[ \text{Total operating cycle period} = \text{Raw materials held in stock} + \text{Work-in-progress} + \text{Finished goods held in stock} + \text{Average period allowed to Debtors} \][/tex]
[tex]\[ \text{Total operating cycle period} = 26.55 + 12.78 + 7.23 + 109.5 \approx 156.05 \text{ days} \][/tex]
#### (vi) Number of operating cycles in a year
To find the number of operating cycles in a year, use the formula:
[tex]\[ \text{Number of operating cycles in a year} = \frac{\text{Period covered in days}}{\text{Total operating cycle period}} \][/tex]
[tex]\[ \text{Number of operating cycles in a year} = \frac{365}{156.05} \approx 2.34 \text{ cycles per year} \][/tex]
### Summary of Results:
- Raw materials held in stock: 26.55 days
- Work-in-progress: 12.78 days
- Finished goods held in stock: 7.23 days
- Average period allowed to Debtors: 109.5 days
- Total operating cycle period: 156.05 days
- Number of operating cycles in a year: 2.34 cycles per year
We have the following information:
- Period Covered: 365 days
- Average period of credit allowed by suppliers: 16 days
- Average Total of Debtors Outstanding: 4,800
- Raw Material Consumption: 44,000
- Total Production Cost: 100,000
- Total Cost of Sales: 101,000
- Sales for the Year: 16,000
- Value of Average Stock maintained:
- Raw Materials: 3,200
- Work-in-Progress: 3,500
- Finished Goods: 2,000
We need to calculate the following:
(i) Raw materials held in stock (in days)
(ii) Work-in-progress (in days)
(iii) Finished goods held in stock (in days)
(iv) Average period allowed to Debtors (in days)
(v) Total operating cycle period (in days)
(vi) Number of operating cycles in a year
### Step-by-Step Solution:
#### (i) Raw materials held in stock (in days)
To find the number of days that raw materials are held in stock, use the formula:
[tex]\[ \text{Raw materials held in stock (in days)} = \left(\frac{\text{Value of raw materials}}{\text{Raw material consumption per year}}\right) \times \text{Period covered in days} \][/tex]
[tex]\[ \text{Raw materials held in stock} = \left(\frac{3200}{44000}\right) \times 365 \approx 26.55 \text{ days} \][/tex]
#### (ii) Work-in-progress (in days)
To find the duration in days for work-in-progress, use the formula:
[tex]\[ \text{Work-in-progress (in days)} = \left(\frac{\text{Value of work-in-progress}}{\text{Total production cost}}\right) \times \text{Period covered in days} \][/tex]
[tex]\[ \text{Work-in-progress} = \left(\frac{3500}{100000}\right) \times 365 \approx 12.78 \text{ days} \][/tex]
#### (iii) Finished goods held in stock (in days)
To find the number of days that finished goods are held in stock, use the formula:
[tex]\[ \text{Finished goods held in stock (in days)} = \left(\frac{\text{Value of finished goods}}{\text{Total cost of sales}}\right) \times \text{Period covered in days} \][/tex]
[tex]\[ \text{Finished goods held in stock} = \left(\frac{2000}{101000}\right) \times 365 \approx 7.23 \text{ days} \][/tex]
#### (iv) Average period allowed to Debtors (in days)
To calculate the average duration that debts are outstanding, use the formula:
[tex]\[ \text{Average period allowed to Debtors (in days)} = \left(\frac{\text{Average total of debtors outstanding}}{\text{Sales for the year}}\right) \times \text{Period covered in days} \][/tex]
[tex]\[ \text{Average period allowed to Debtors} = \left(\frac{4800}{16000}\right) \times 365 \approx 109.5 \text{ days} \][/tex]
#### (v) Total operating cycle period (in days)
The total operating cycle period is the sum of raw materials held in stock, work-in-progress, finished goods held in stock, and the average period allowed to debtors.
[tex]\[ \text{Total operating cycle period} = \text{Raw materials held in stock} + \text{Work-in-progress} + \text{Finished goods held in stock} + \text{Average period allowed to Debtors} \][/tex]
[tex]\[ \text{Total operating cycle period} = 26.55 + 12.78 + 7.23 + 109.5 \approx 156.05 \text{ days} \][/tex]
#### (vi) Number of operating cycles in a year
To find the number of operating cycles in a year, use the formula:
[tex]\[ \text{Number of operating cycles in a year} = \frac{\text{Period covered in days}}{\text{Total operating cycle period}} \][/tex]
[tex]\[ \text{Number of operating cycles in a year} = \frac{365}{156.05} \approx 2.34 \text{ cycles per year} \][/tex]
### Summary of Results:
- Raw materials held in stock: 26.55 days
- Work-in-progress: 12.78 days
- Finished goods held in stock: 7.23 days
- Average period allowed to Debtors: 109.5 days
- Total operating cycle period: 156.05 days
- Number of operating cycles in a year: 2.34 cycles per year
