[Verse 1] Corporate bonds trading at discount or premium Face value waits at maturity's end Present value calculations, cash flows discounted back Coupon payments and principal, that's the dividend Market interest rates determine what investors pay Higher rates mean lower prices, that's the game we play [Chorus] PV equals payment over one plus rate to the power n Yield to maturity, IRR that makes NPV zero then Duration measures price sensitivity, modified for the change When interest rates fluctuate, bond values rearrange [Verse 2] Semi-annual coupons compound the mathematics Effective annual rates versus stated face Convexity adjustments when rate changes are dramatic Linear duration estimates lose their accurate place Trading bonds between payment dates, accrued interest due Clean price plus accumulated earnings, dirty price comes through [Chorus] PV equals payment over one plus rate to the power n Yield to maturity, IRR that makes NPV zero then Duration measures price sensitivity, modified for the change When interest rates fluctuate, bond values rearrange [Bridge] Macaulay duration weighted by present value of each cash flow Divided by bond price gives time-weighted average Modified duration equals Macaulay over one plus yield ratio Percentage price change approximated by this leverage Callable bonds and putable features complicate the analysis Yield to call or yield to put, scenarios for paralysis [Verse 3] Credit spreads above treasury benchmarks, default risk premium Investment grade versus junk, ratings matter most Zero coupon bonds, deep discount, no periodic medium Original issue discount, phantom income on your cost Tax implications, capital gains when sold before maturity Book value amortization, straight line or effective entity [Final Chorus] Present value bond equation, discount future payments back Yield to maturity solves for rate where price equals track Duration estimates elasticity, price moves opposite rates Financial instruments behaving as economic mathematics states
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