## Ch. 7: Interest Rates and Bond Valuation

Bond Basics

• Typically, a bond is an interest-only loan, but the debt contract can be customized to meet the needs of the company issuing the security.
• Three required pieces:
• Face (par) value - the principal amount of a bond
• Coupon rate - the stated interest rate of a bond
• Maturity - the specified date on which the principal is repaid

Valuing a Bond

• You already know how to value a bond. Simply price the pieces and add them together.
• The lump sum repayment of the principal
• An annuity consisting of the coupon payments
• Bond Pricing Formula: $Bond \ Value = C[\frac{1-\frac{1}{(1+r)^t}}{r}]+\frac{FV}{(1+r)^t}$
• Note: $r$ is the required rate of return on the bond, not the coupon rate. This rate is often called the yield to maturity (YTM).

Example

• 5 yr bond
• 14% yield
• 6% coupon
• $1000 par Bond Relationships • Value relative to par • If the coupon rate and the discount rate are equal, then the bond value will equal par. • If coupon rate < discount rate, then the bond will sell at a discount to par. • If coupon rate > discount rate, then the bond will sell at a premium to par. • Price and discount rate are inversely related. Interest Rate Risk • As a bondholder, you face interest rate risk to the value of your bond as interest rates change in the market. • Interest rate risk increases with maturity. • Interest rate risk decrease with coupon rate. • See Figure 7.2 Bond Features • Indenture - written agreement between the corporation and the lender detailing the terms of the debt issue • Collateral - any asset pledged against a debt • Seniority - preference in position over other lenders • Call provision - agreement giving the corporation the option to repurchase a bond at a specified price prior to maturity • Convertibility - a provision granting the bondholder the option to exchange the bond for a fixed number of shares of stock anytime before maturity • Convenant - a provision limiting certain issuer actions Types of Bonds • Government vs. Corporate Bonds • Zero Coupon Bonds • Floating-Rate Bonds Real vs. Nominal Interest Rates • Nominal rate - rate that has not been adjusted for inflation (decrease in purchasing power) • Real rate - rate that has been adjusted for inflation • Fisher Effect:$R = (1+r)(1+h)–1\$
• R is the nominal rate
• r is the real rate
• h is expected inflation rate
• If we require a 10% real return and we expect inflation to be 8%, what is the nominal rate?

Term Structure

• The term structure of interest rates is the relationship between maturity and yields.
• Since it is important to hold everything else constant, we usually associate government bonds with the term structure.
• No default risk
• No coupons
• Yield Curve - a graphical representation of the term structure of interest rates
• See Figure 7.6

Other Risks