Question: Rahimafrooz is a leading producer of automobile batteries. It turns out $1,500$ batteries a day at a cost of $6.2$ per battery for materials and labor. It takes the firm $22$ days to convert raw materials into the battery. It allows its customers $40$ days in which to pay for the batteries and the firm generally pays its suppliers in $30$ days.
Required:
(i) What is the length of the cash conversion cycle?
(ii) If the firm always produces and sales $1,250$ batteries a day, what amount of working capital must it finance?
1. **State the problem:**
We need to find (i) the length of the cash conversion cycle (CCC) and (ii) the amount of working capital the firm must finance given daily production and costs.
2. **Formula for Cash Conversion Cycle:**
$$\text{CCC} = \text{Inventory Conversion Period} + \text{Receivables Collection Period} - \text{Payables Deferral Period}$$
3. **Given data:**
- Inventory Conversion Period = $22$ days
- Receivables Collection Period = $40$ days
- Payables Deferral Period = $30$ days
4. **Calculate CCC:**
$$\text{CCC} = 22 + 40 - 30 = 32 \text{ days}$$
5. **Working capital calculation:**
- Daily production = $1,250$ batteries
- Cost per battery = $6.2$
- Daily cost = $1,250 \times 6.2 = 7,750$
6. **Working capital needed to finance the CCC period:**
$$\text{Working Capital} = \text{Daily Cost} \times \text{CCC} = 7,750 \times 32 = 248,000$$
7. **Summary:**
- The cash conversion cycle is $32$ days.
- The firm must finance $248,000$ in working capital to cover the cash conversion cycle period.
This means the firm needs to have $248,000$ available to fund operations during the $32$ days before cash inflows from customers are received.