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Sagot :
To determine the post-reward program customer lifetime value, we need to calculate several components: annual spending per customer, the related costs (cost of goods and cost of the reward program), the annual profit per customer, and then extend these values over the assumed relationship duration of 30 years.
Here is the step-by-step solution:
1. Annual Spending Per Customer Post-Reward Program:
- Spending per visit: \$5
- Frequency of visits per week: 6
- Number of weeks in a year: 52
- Calculation: \( \[tex]$5 \times 6 \, \text{times/week} \times 52 \, \text{weeks/year} = \$[/tex]1560 \, \text{per year} \)
2. Annual Cost of Goods Post-Reward Program:
- Annual spending per customer: \$1560
- Cost of goods: 25%
- Calculation: \( 25\% \times \[tex]$1560 = 0.25 \times \$[/tex]1560 = \$390 \)
3. Annual Cost of Reward Program:
- Annual spending per customer: \$1560
- Cost of reward program: 5% (including 4.5% discount + 0.5% reward operation cost)
- Calculation: \( 5\% \times \[tex]$1560 = 0.05 \times \$[/tex]1560 = \$78 \)
4. Annual Profit Per Customer Post-Reward Program:
- Annual spending per customer: \$1560
- Subtracting the cost of goods and the cost of the reward program:
- Cost of goods: \$390
- Cost of reward program: \$78
- Calculation: \( \[tex]$1560 - (\$[/tex]390 + \[tex]$78) = \$[/tex]1560 - \[tex]$468 = \$[/tex]1092 \)
5. Customer Lifetime Value Post-Reward Program:
- Annual profit per customer: \$1092
- Customer relationship duration: 30 years
- Calculation: \( \[tex]$1092 \times 30 \, \text{years} = \$[/tex]32760 \)
Therefore, the post-reward program customer lifetime value is:
[tex]\[ \$32760 \][/tex]
Comparing the given choices:
- \$26,595
- \$28,655
- \$27,955
- \$33,345
The correct choice based on our calculations is:
[tex]\[ \$32760 \][/tex]
However, given the nature of the question and the provided answer options, it appears there's a discrepancy. Yet, based on the mathematical solution provided, \[tex]$32760 is the correct answer for the customer lifetime value post-reward program. Among the given choices, none match exactly, indicating a possible error in the provided choices or calculations. The correct mathematical result is \(\$[/tex]32760\).
Here is the step-by-step solution:
1. Annual Spending Per Customer Post-Reward Program:
- Spending per visit: \$5
- Frequency of visits per week: 6
- Number of weeks in a year: 52
- Calculation: \( \[tex]$5 \times 6 \, \text{times/week} \times 52 \, \text{weeks/year} = \$[/tex]1560 \, \text{per year} \)
2. Annual Cost of Goods Post-Reward Program:
- Annual spending per customer: \$1560
- Cost of goods: 25%
- Calculation: \( 25\% \times \[tex]$1560 = 0.25 \times \$[/tex]1560 = \$390 \)
3. Annual Cost of Reward Program:
- Annual spending per customer: \$1560
- Cost of reward program: 5% (including 4.5% discount + 0.5% reward operation cost)
- Calculation: \( 5\% \times \[tex]$1560 = 0.05 \times \$[/tex]1560 = \$78 \)
4. Annual Profit Per Customer Post-Reward Program:
- Annual spending per customer: \$1560
- Subtracting the cost of goods and the cost of the reward program:
- Cost of goods: \$390
- Cost of reward program: \$78
- Calculation: \( \[tex]$1560 - (\$[/tex]390 + \[tex]$78) = \$[/tex]1560 - \[tex]$468 = \$[/tex]1092 \)
5. Customer Lifetime Value Post-Reward Program:
- Annual profit per customer: \$1092
- Customer relationship duration: 30 years
- Calculation: \( \[tex]$1092 \times 30 \, \text{years} = \$[/tex]32760 \)
Therefore, the post-reward program customer lifetime value is:
[tex]\[ \$32760 \][/tex]
Comparing the given choices:
- \$26,595
- \$28,655
- \$27,955
- \$33,345
The correct choice based on our calculations is:
[tex]\[ \$32760 \][/tex]
However, given the nature of the question and the provided answer options, it appears there's a discrepancy. Yet, based on the mathematical solution provided, \[tex]$32760 is the correct answer for the customer lifetime value post-reward program. Among the given choices, none match exactly, indicating a possible error in the provided choices or calculations. The correct mathematical result is \(\$[/tex]32760\).
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