"""Create an educational video to explain the CFA Level 1 knowledge: PV calculation (fixed-income/equity) 🎓 Content Requirements: Start with a clear, beginner-friendly definition of the concept Explain the core components and logic step by step Include simple numerical examples or visual analogies Add a short summary or key takeaways at the end Ensure the structure follows a logical teaching flow from concept to application 🎨 Visual and Layout Requirements: Full-screen visuals with centered, readable content Use smooth animations to transition between steps or sections Highlight important terms, formulas, and keywords with bright accent colors (e.g., yellow, red, blue) Avoid text crowding or overlap; leave clear visual spacing Use animated icons, graphs, or diagrams where appropriate (e.g., timelines, flowcharts, charts) Minimize blank space; keep each screen visually rich and balanced 🗣️ Tone and Style: Friendly, clear, and professional Focus on making the topic accessible for first-time learners Avoid excessive jargon; use plain language wherever possible Maintain alignment with CFA curriculum terminology and scope"""

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Welcome to Present Value calculation, a fundamental concept in CFA Level 1. Present Value, or PV, represents the current worth of future money given a specific rate of return. It's essential for bond pricing, stock valuation, and investment decisions. The core principle is that money today is worth more than the same amount in the future due to earning potential. Our basic formula is PV equals Future Value divided by one plus the discount rate, raised to the power of time periods. Now let's examine the three core components of Present Value calculation. First, Future Cash Flow represents the amount we expect to receive, such as bond coupons or stock dividends. Second, the Discount Rate reflects our required rate of return or opportunity cost. Third, Time Period indicates how long we must wait for the payment. Our formula shows how these elements work together. The timeline illustrates a typical bond with annual coupon payments and final principal repayment. Let's apply PV calculation to a fixed income security. Consider a 3-year bond with $1,000 face value, paying $80 annual coupons, requiring 10% return. We calculate the present value of each cash flow separately. Year 1 coupon: $80 divided by 1.10 equals $72.73. Year 2 coupon: $80 divided by 1.10 squared equals $66.12. Year 3 final payment of $1,080 divided by 1.10 cubed equals $811.42. The bond's fair value is the sum: $950.27. Now let's examine equity valuation using the Dividend Discount Model. Consider ABC stock expected to pay a $5 dividend in 2 years, with a 12% required return. Using our PV formula, we calculate $5 divided by 1.12 squared, which equals $5 divided by 1.2544, giving us $3.99. This means the stock's fair value today is $3.99 based solely on this future dividend payment. This single-period example forms the foundation for more complex multi-period dividend models used in equity analysis. Let's summarize the key takeaways for Present Value in CFA Level 1. PV converts future cash flows to today's equivalent value using a discount rate and time period. Remember: higher discount rates and longer time periods both result in lower present values. PV is fundamental to bond pricing, stock valuation through dividend discount models, and capital budgeting decisions. For CFA Level 1 success, master the basic formula, understand time value of money concepts, and practice applying PV to both fixed income and equity securities. Work through multiple examples to build strong intuition.