Introductory Corporate Finance: Valuation - Bond Valuation, Face Value Coupon Rate Yield to Maturity Current Yield Bond Pricing Premium vs. Discount Bond Interest Rate Risk Bond Ratings

What This Is

Bond valuation is the process of determining the present value of a bond's future cash flows. This is crucial in corporate finance as it helps investors and creditors assess the value of a bond and make informed investment decisions. For example, consider a $1,000 face value bond with a 5% coupon rate, maturing in 10 years. If the market yield is 6%, the bond's present value would be approximately $844. This means that the bond is trading at a discount to its face value.

Key Formulas & Models

• PV = FV / (1 + r)^n – present value of a future cash flow; used to calculate bond value.
  • PV: present value
  • FV: future value (face value for a bond)
  • r: market yield (discount rate)
  • n: number of periods (years until maturity)
• YTM = (C + (FV - PV) / N) / (FV / PV) – yield to maturity; measures the bond's total return.
  • YTM: yield to maturity
  • C: coupon payment
  • FV: face value
  • PV: present value
  • N: number of periods
• Current Yield = C / PV – current yield; measures the bond's annual return.
  • Current Yield: current yield
  • C: coupon payment
  • PV: present value
• Premium/Discount = (FV - PV) / FV – premium/discount; measures the bond's price relative to its face value.
  • Premium/Discount: premium or discount
  • FV: face value
  • PV: present value
• Interest Rate Risk = ?PV / ?r – interest rate risk; measures the bond's sensitivity to changes in market yield.
  • Interest Rate Risk: interest rate risk
  • ?PV: change in present value
  • ?r: change in market yield
• Bond Rating = (Credit Rating + Market Yield) / 2 – bond rating; measures the bond's creditworthiness.
  • Bond Rating: bond rating
  • Credit Rating: credit rating (e.g., AAA, BBB)
  • Market Yield: market yield
• Credit Spread = Market Yield - Risk-Free Rate – credit spread; measures the bond's credit risk.
  • Credit Spread: credit spread
  • Market Yield: market yield
  • Risk-Free Rate: risk-free rate (e.g., Treasury yield)

Step-by-Step Calculation

1. Determine the bond's face value and coupon rate.
2. Calculate the present value of the bond's future cash flows using the PV formula.
3. Calculate the yield to maturity using the YTM formula.
4. Calculate the current yield using the Current Yield formula.
5. Calculate the premium or discount using the Premium/Discount formula.
6. Calculate the interest rate risk using the Interest Rate Risk formula.

Common Mistakes

• Mistake: Using the wrong discount rate (e.g., using the risk-free rate instead of the market yield).
  • Correction: Use the market yield as the discount rate.
• Mistake: Ignoring flotation costs when calculating the bond's value.
  • Correction: Include flotation costs in the calculation.
• Mistake: Confusing premium and discount bonds.
  • Correction: A premium bond has a price above its face value, while a discount bond has a price below its face value.
• Mistake: Not considering interest rate risk when valuing a bond.
  • Correction: Calculate the interest rate risk using the Interest Rate Risk formula.

Exam / CFA Tips

• Be careful when using the YTM formula, as it assumes the bond's yield remains constant over its life.
• When valuing a bond, consider both the market yield and the credit rating.
• Be able to distinguish between premium and discount bonds.
• Understand the concept of interest rate risk and how it affects bond values.

Quick Practice Problem

A company has a bond with a face value of $1,000, a coupon rate of 5%, and a market yield of 6%. What is the bond's current yield?

Answer: 4.17% Explanation: Current Yield = C / PV = 50 / 1,200 = 4.17%

Last-Minute Cram Sheet

• PV = FV / (1 + r)^n: present value formula
• YTM = (C + (FV - PV) / N) / (FV / PV): yield to maturity formula
• Current Yield = C / PV: current yield formula
• Premium/Discount = (FV - PV) / FV: premium/discount formula
• Interest Rate Risk = ?PV / ?r: interest rate risk formula
• Bond Rating = (Credit Rating + Market Yield) / 2: bond rating formula
• Credit Spread = Market Yield - Risk-Free Rate: credit spread formula
• In M&M Proposition I (no taxes), firm value is independent of capital structure – but with taxes, value increases with debt due to the interest tax shield.
• A premium bond has a price above its face value, while a discount bond has a price below its face value.
• Interest rate risk measures the bond's sensitivity to changes in market yield.