Final answer:
The change in monthly profits on a present value basis due to offering credit will be approximately $2,079.21 at a 1% interest rate, and approximately $2,067.98 at a 1.5% interest rate. If only new customers are offered credit at a 1.5% interest rate, the calculation would involve determining the contribution of new customers to the profit and summing it with the current profit from existing customers.
Step-by-step explanation:
To calculate the change in the firm's total monthly profits on a present value basis due to offering credit terms, we need to consider the increase in sales, the cost of goods sold, and the cost of financing these sales for the credit period. Let's first define the additional profit per carton as the price per carton ($100) minus the cost per carton ($65), which is $35 per carton.
With an initial sales increase from 1,050 to 1,110 cartons when credit is offered, the increase in sales volume is 60 cartons. At $35 additional profit per carton, the total additional profit is 60 cartons × $35/carton = $2,100.
For part (a), with a 1% interest rate per month, the present value (PV) of the additional profit is calculated as $2,100 / (1 + 0.01) since the profit will be received one month later. This results in a PV of approximately $2,079.21.
For part (b), with a 1.5% interest rate per month, the PV of the additional profit is $2,100 / (1 + 0.015), which gives us a PV of approximately $2,067.98.
For part (c), assuming only new customers are offered credit and the interest rate is 1.5% per month, let's denote x as the number of new customers. Assuming x cartons sold to new customers, the PV of the additional profit from new customers is x × $35 / (1 + 0.015). The profit from existing customers remains same as they continue to pay cash on delivery. The total PV profit change is the sum of the PV profits from new customers plus the unchanged profit from existing customers.