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{ "quality": "incomplete", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Term of Analysis", "Real Interest Rate" ], "new_concepts": [ "Net Present Value", "Cost Increase Analysis" ], "current_concepts": [ "Term of Analysis", "Real Interest Rate", "Net Present Value", "Cost Increase Analysis" ] } ## Identify the missing parameters from the context $$ \begin{aligned} &\text{Term of Analysis } (N) = 10 \text{ years}\ &\text{Real Interest Rate } (i) = 2.91\% = 0.0291\ &\text{Annual Cost of Salt-Brine} = \$15,000\ &\text{Annual Cost of Beet Juice} = \$25,000\ &\text{Annual Cost Increase } (A) = \$25,000 - \$15,000 = \$10,000 \end{aligned} $$ ## Calculate the Present Value of the Annuity $$ \begin{aligned} &PV = A \times \frac{1 - (1 + i)^{-N}}{i}\ &PV = 10000 \times \frac{1 - (1 + 0.0291)^{-10}}{0.0291}\ &PV = 10000 \times \frac{1 - (1.0291)^{-10}}{0.0291}\ &PV \approx 10000 \times \frac{1 - 0.750614}{0.0291}\ &PV \approx 10000 \times \frac{0.249386}{0.0291}\ &PV \approx 10000 \times 8.56996\ &PV \approx 85,699.60 \end{aligned} $$ Step 3: In this analysis, we are only concerned with the cost increase in going from Salt-Brine to Beet Juice. What is the Net Present Value of the cost increase (that is, the difference between the annual costs), over the term of analysis? 85,699.60 { "subject": "Business", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Business", "Finance", "Net Present Value" ] }

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Identify the missing parameters from the context

Calculate the Present Value of the Annuity

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