Mazzio's Italian Eatery network - pastas, fast-casual hot toasted sandwiches
The Correct Answer and Explanation is:
$232,222.22
To determine the total monthly redemption cost for Mazzio’s coupons for the most recent month, we must calculate and sum three separate cost components derived from the provided text: the face value of properly redeemed coupons, the processing fees paid to franchises for these coupons, and the cost associated with misredemptions.
First, we calculate the cost from the face value of the actual coupons that were redeemed. The report states that for the most recent month, the “actual number of coupon redemptions at Mazzio’s restaurants was 200,000.” Each of these coupons has a face value of $1.00. Therefore, the total cost from the face value discount is calculated by multiplying the number of redeemed coupons by their value: 200,000 coupons multiplied by $1.00 per coupon equals $200,000.
Second, we calculate the cost of the franchise processing fees. The text specifies that “Mazzio’s also pays each of their 165 franchises a $.05 processing fee for each coupon redemption.” This fee applies to the 200,000 coupons that were physically redeemed. The total cost for these fees is 200,000 redemptions multiplied by $0.05 per redemption, which amounts to $10,000.
The third and most complex component is the cost of misredemptions. The report indicates that misredemptions, where a $1.00 discount is given without a coupon, are “projected to be 10% of all total redemptions.” This implies that the 200,000 actual coupon redemptions represent the remaining 90% of total redemption activity. To find the total number of redemptions (both proper and improper), we can set up the calculation: 200,000 divided by 0.90, which equals approximately 222,222.22 total redemptions. The number of misredemptions is the difference, which is 22,222.22. Each of these cost Mazzio’s $1.00, resulting in a misredemption cost of $22,222.22. It is important to note that the $0.05 processing fee does not apply to misredemptions because no physical coupon was presented for processing.
Finally, to find the total monthly redemption cost, we sum these three figures:
$200,000 (Face Value) + $10,000 (Processing Fees) + $22,222.22 (Misredemptions) = $232,222.22.
