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Bond Valuation: Pricing Coupon Bonds

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Textbook ELI8 Excel User Guide

Navigating Coupon Bond Pricing: A Practical Insight

Let's dive into the nuts and bolts of pricing coupon bonds without drowning in complex formulas. In plain language, we're going to explore how the bond prices are calculated in two real-life scenarios.

Example 1:

Consider a $1,000 face value coupon bond with a 5% annual coupon rate, an 8% required rate of return, and a 5-year maturity.

Step 1: Compute Present Value of Each Cash Flow

  • First-year cash flow: $50 / (1 + 0.08)^1 ≈ $46.30
  • Second-year cash flow: $50 / (1 + 0.08)^2 ≈ $42.87
  • Third-year cash flow: $50 / (1 + 0.08)^3 ≈ $39.65
  • Fourth-year cash flow: $50 / (1 + 0.08)^4 ≈ $36.63
  • Fifth-year cash flow: $50 / (1 + 0.08)^5 ≈ $33.80
  • Maturity cash flow: $1,000 / (1 + 0.08)^5 ≈ $620.92

Step 2: Sum Up Present Values Add up all these present values to find the total bond price: $46.30 + $42.87 + $39.65 + $36.63 + $33.80 + $620.92 ≈ $819.17

Therefore, the price of this coupon bond would be approximately $819.17.

Example 2

Consider a different coupon bond with the following characteristics:

  • Face value (F) = $10,000
  • Coupon rate = 6% (annual coupon payment rate)
  • Coupon payment (C) = $600 (6% of $10,000)
  • Required rate of return (r) = 4.5%
  • Maturity (n) = 10 years

Step 1: Compute Present Value of Each Cash Flow

  • First-year cash flow: $600 / (1 + 0.045)^1
  • Second-year cash flow: $600 / (1 + 0.045)^2
  • Third-year cash flow: $600 / (1 + 0.045)^3
  • Fourth-year cash flow: $600 / (1 + 0.045)^4
  • Fifth-year cash flow: $600 / (1 + 0.045)^5
  • Sixth-year cash flow: $600 / (1 + 0.045)^6
  • Seventh-year cash flow: $600 / (1 + 0.045)^7
  • Eighth-year cash flow: $600 / (1 + 0.045)^8
  • Ninth-year cash flow: $600 / (1 + 0.045)^9
  • Tenth-year cash flow: $600 / (1 + 0.045)^10
  • Maturity cash flow: $10,000 / (1 + 0.045)^10

Step 2: Sum Up Present Values

Add up all these present values to find the total bond price:

Bond Price ≈ $5,392.55

Therefore, the price of this coupon bond would be approximately $5,392.55.

Conclusion

Pricing coupon bonds involves determining the present value of future coupon payments and the principal payment at maturity. By discounting these cash flows using a required rate of return, investors can determine the fair price of a coupon bond. Understanding the pricing process allows market participants to assess the attractiveness of bond investments, evaluate yields, and make informed decisions regarding buying, selling, or holding coupon bonds in debt and money markets.

This article takes inspiration from a lesson found in FIN 4243 at the University of Florida.