Fizzy Animators, Inc. currently makes all sales on credit and offers no cash discount. The firm is considering a $2$ percent cash discount for payment within $10$ days. The firm's current average collection period is $90$ days, sales are $400$ films per year, selling price is $$25,000$ per film, variable cost per film is $$15,000($note the variable cost $\%$ is $60\%).$ The firm expects that the change in credit terms will result in an increase in sales of $20$ films per year, that $80$ percent of the sales will take the discount, and the average collection period will drop to $30$ days. The firm's required return on equal$-$risk investments is $10$ percent. $($Assume a $360-$day year.$)$

What is the firm's marginal contribution margin from sales under the proposed plan of initiating the cash discount?

Group of answer choices

$$200,000$

$$100,000$

$$62,500$

$$500,000$