Introduction
Having valued zero-coupon bonds in the previous lesson, Luna is now ready to tackle more complex bond types.
In this lesson, she will learn to value fixed-rate bonds by discounting their regular coupon payments and face value.
Additionally, Luna will explore floating-rate bonds, which feature variable interest rates tied to benchmarks.
This lesson builds on her DCF knowledge, enabling her to accurately assess a wider range of bonds and enhance her investment strategy.
Fixed-Rate Bond Valuation Basics
Fixed-rate bonds offer regular coupon payments at a set interest rate, plus the repayment of face value at maturity.
Valuing such bonds requires discounting each coupon payment and the face value separately back to their present values.
This is because each payment occurs at different times in the future.
The total bond price is the sum of the present values of all expected cash flows.
Understanding this process is essential for determining whether a fixed-rate bond is a worthwhile investment.
Calculating Present Value of Coupon Payments
Coupon payments from fixed-rate bonds can be treated as an annuity, a series of equal payments made at regular intervals.
The present value of these payments is calculated using the formula:
PV of Annuity = C × [1 - (1 + r)ⁿ] / r, where “C” is the coupon payment, “r” is the discount rate, and “n” is the number of periods.
Accurate discounting of each payment period is crucial, as it ensures the bond's valuation reflects the true worth of the expected income stream over time.
Present Value of Face Value at Maturity
The face value, or principal, of the bond is repaid in a lump sum at maturity.
To find its present value, the formula is: PV = Face Value / (1 + r)ⁿ, where “r” is the discount rate and “n” is the number of periods until maturity.
This calculation discounts the future lump-sum payment back to today's dollars.
Combining this present value with that of the coupon payments gives the total bond valuation, essential for determining if the bond is priced appropriately in the market.
Luna Values a Fixed-Rate Bond
Luna now evaluates a fixed-rate corporate bond with a face value of $1,000, a 5% annual coupon rate, and five years to maturity.
Using her discount rate of 6.5%, she calculates the present value of the $50 annual coupons: PV = $50 × [1 - (1 + 0.065)⁵] / 0.065 ≈ $209.05.
She then computes the present value of the $1,000 face value: PV = $1,000 / (1 + 0.065)⁵ ≈ $730.69.
Summing these up, the bond's total value is $209.05 + $730.69 = $939.74. Seeing the market price is $940, Luna notes the bond is fairly valued.