Episode 38: Bond Pricing From Scratch

Hey! I'd love to hear your thoughts, send me a voice note.Episode Summary Why do bond prices fall when interest rates rise, even when the underlying company is perfectly healthy and paying on time? The answer lies in the fundamental concept of present value—the reality that a dollar today is worth more than a dollar in the future. This episode breaks down the unglamorous but load-bearing math of present value, shows how to calculate a bond's price by hand, and builds the mathematical intuition behind discounts, premiums, and why the final principal payment dominates a bond's value.Key ConceptsThe Time Value of Money: A dollar in the future is worth less than a dollar today because of inflation and opportunity cost—namely, what that dollar could have earned in the meantime.Discounting & The Discount Rate: "Discounting" is the arithmetic of running growth backwards to find what a future sum is worth today. The "discount rate" is the return available elsewhere on something of comparable risk. When market interest rates change, the discount rate changes because the alternative has changed.Bond Price as a Sum of Parts: A bond is simply a schedule of future cash flows. Its current market price is the exact sum of the present values of every single coupon and principal payment it will make.Calculating a Bond's Price by Hand To see the arithmetic in action, consider a three-year, $1,000 face value bond with a 5% annual coupon ($50/year) when the market demands a 6% required return:Year 1 Coupon ($50): Discounted one year at 6% ($50 / 1.06) = $47.17.Year 2 Coupon ($50): Discounted two years at 6% ($50 / 1.06²) = $44.50.Year 3 Coupon & Principal ($1,050): Discounted three years at 6% ($1,050 / 1.06³) = $881.60.Total Present Value (The Price): Adding these three values together gives $973.27.Because this bond pays only 5% while the market demands 6%, the bond's price must fall below par ($1,000) to a discount so the total return becomes competitive. Conversely, if the market only demanded 4%, the price would rise to a premium of $1,027.75.The Dominant Number In our $973.27 bond, the final principal repayment in year three represents over 90% of the bond's total value ($881.60). This illustrates why the final repayment dominates the pricing structure and why longer-term bonds are far more sensitive to interest rate shifts.Complications & NuancesSemi-Annual Conventions: Most real-world bonds pay semi-annually, meaning you discount twice as many cash flows using half of the annual required rate.Risk & The Yield Curve: In reality, different cash flows may be discounted at different rates depending on maturity (the yield curve), and the discount rate must continuously adjust to reflect the issuer's specific default risk.Embedded Options: Bonds with callable or convertible features can have their cash flows altered early at the issuer's option, requiring more complex valuation models.Disclaimer This show provides educational content and does not constitute financial advice. Speakers are not registered to advise you on securities; please consult a licensed professional for your personal situation.