Forecasting payments;
If a firm pays its bills with a 30-day delay, what fraction of its purchases will be paid for in the current quarter? In the following quarter? What if its payment delay is 60 days?
To determine the fraction of purchases that will be paid for in the current quarter and the following quarter, you need to consider the payment delay of the firm.
1. Payment delay of 30 days:
- Current quarter: Any purchases made in the current quarter will not be paid for until the next quarter because of the 30-day delay. Therefore, the fraction of purchases paid for in the current quarter is 0.
- Following quarter: Any purchases made in the current quarter will be paid for in the following quarter due to the 30-day payment delay. So the fraction of purchases paid for in the following quarter is 1.
2. Payment delay of 60 days:
- Current quarter: Any purchases made in the current quarter will not be paid for until two quarters later because of the 60-day delay. Therefore, the fraction of purchases paid for in the current quarter is 0.
- Following quarter: Any purchases made in the current quarter will not be paid for until the next quarter due to the 60-day payment delay. So the fraction of purchases paid for in the following quarter is 0.
In summary:
- With a payment delay of 30 days, purchases made in the current quarter will be paid for in the following quarter.
- With a payment delay of 60 days, purchases made in the current quarter will not be paid for until two quarters later.
To forecast the fraction of purchases that will be paid for in a particular quarter, you need to consider the payment delay period given. Let's go through each scenario to calculate the fractions.
Scenario 1: Payment delay of 30 days
In this case, purchases made in a particular quarter will be paid for in the subsequent quarter. To calculate the fraction of purchases paid for in the current quarter, you need to consider the average payment delay and the number of quarters.
Step 1: Calculate the average payment delay period in days:
Average Payment Delay = Payment Delay / Number of Quarters
Average Payment Delay = 30 days / 3 months (assuming the quarter consists of 3 months)
Average Payment Delay = 10 days
Step 2: Calculate the fraction of purchases paid for in the current quarter:
Fraction of Purchases Paid in Current Quarter = Average Payment Delay / (Average Payment Delay + 30 days)
Fraction of Purchases Paid in Current Quarter = 10 days / (10 days + 30 days)
Fraction of Purchases Paid in Current Quarter = 10/40 = 0.25 (or 25%)
Therefore, 25% of purchases will be paid for in the current quarter.
Step 3: Calculate the fraction of purchases paid for in the following quarter:
Fraction of Purchases Paid in Following Quarter = 30 days / (Average Payment Delay + 30 days)
Fraction of Purchases Paid in Following Quarter = 30 days / (10 days + 30 days)
Fraction of Purchases Paid in Following Quarter = 30/40 = 0.75 (or 75%)
Therefore, 75% of purchases will be paid for in the following quarter.
Scenario 2: Payment delay of 60 days
Following the same steps as above:
Step 1: Average Payment Delay = 60 days / 3 months = 20 days
Step 2: Fraction of Purchases Paid in Current Quarter = 20 days / (20 days + 30 days) = 20/50 = 0.4 (or 40%)
Therefore, 40% of purchases will be paid for in the current quarter.
Step 3: Fraction of Purchases Paid in Following Quarter = 30 days / (20 days + 30 days) = 30/50 = 0.6 (or 60%)
Therefore, 60% of purchases will be paid for in the following quarter.
To summarize:
- For a payment delay of 30 days, 25% of purchases will be paid for in the current quarter, and 75% will be paid for in the following quarter.
- For a payment delay of 60 days, 40% of purchases will be paid for in the current quarter, and 60% will be paid for in the following quarter.