Overview
This lecture explains how to calculate yield to maturity (YTM) for bonds, including step-by-step examples with annual and semi-annual coupon payments.
Yield to Maturity Basics
- Yield to maturity (YTM) is the rate of return earned if a bond is held until maturity.
- YTM is the discount rate at which the present value (PV) of all future cash flows equals the bond’s current market price.
- YTM is also called the required rate of return for a bond.
YTM Calculation with Annual Coupons (Example 1)
- Given: ANZ bond, 4 years to maturity, $1,000 face value, $1,018.24 price, 4.3% annual coupon.
- Number of periods (N) = 4; annual coupon payment (C) = 4.3% of $1,000 = $43.
- Rearrange bond price formula to solve for YTM (R), which requires trial and error, a financial calculator, or Excel.
- In Excel, use the RATE function with N = 4, PMT = $43, PV = -$1,018.24, FV = $1,000.
- Calculated YTM = 3.8% per year.
YTM Calculation with Semi-Annual Coupons (Example 2)
- Given: CBA bond, 8 years to maturity, $1,000 face value, $1,181.61 price, 4.3% coupon (semi-annual).
- Number of periods (N) = 8 × 2 = 16; semi-annual coupon payment (C) = (4.3% × $1,000) / 2 = $21.50.
- Use the RATE function in Excel with N = 16, PMT = $21.50, PV = -$1,181.61, FV = $1,000.
- The result (0.0092376) is the yield per period (half-year).
- Annualize the YTM using the formula: Effective annual rate = (1 + semi-annual yield)^2 – 1.
- Calculated annual YTM ≈ 1.86%.
Key Terms & Definitions
- Yield to Maturity (YTM) — The total return anticipated if the bond is held to maturity.
- Present Value (PV) — Current worth of future cash flows discounted at YTM.
- Coupon Payment (C) — Periodic interest paid by the bond, calculated as coupon rate × face value / number of payments per year.
- Face Value (FV) — The bond’s value at maturity, typically $1,000.
- N — Number of periods until maturity.
- RATE Function (Excel) — Calculates interest rate per period given N, PMT, PV, and FV.
- Effective Annual Rate — Converts periodic (e.g., semi-annual) yields into an annual yield.
Action Items / Next Steps
- Practice YTM calculations using both trial-and-error and Excel’s RATE function.
- Review the bond price formula and how to input values for different payment frequencies.
- Try annualizing periodic yields using the effective interest rate formula.