Finance Chapter: Interest Rates and Bonds

Lecture Note 4: Interest Rates and Bonds

• Interest rates are the price of using money
• Rates are commonly quoted daily, monthly, semi-annually, or annually
• Effective annual rate (EAR) or annual percentage yield (APY) is the total interest earned at the end of one year
• Earning an EAR of 5% for two years is equivalent to earning 10.25% in total interest over the entire period
• Interest rates can be adjusted to different time periods, for example, an annual rate of 5% is equivalent to 2.47% semi-annually
• Computing loan payments involves amortizing loans
• A 30,000carloanwitha6.7530,000 car loan with a 6.75% APR (monthly compounding) for 5 years has a monthly payment of 30,000carloanwitha6.75590.50
• Computing outstanding loan balances uses the present value (PV) of remaining payments
• Interest rates are determined by market forces based on the relative supply and demand of funds Factors include inflation, current economic activity, expectations future growth
• Nominal interest rates are the rate at which your money will grow when invested for a particular period
• Real interest rate is the rate of growth of your purchasing power, after adjusting for inflation
• Real rate ≈ Nominal rate – Inflation rate
• Investment and interest rates influence individual's propensity to save and firms' incentive to raise capital and invest.
• Central banks use interest rates to guide the economy, stimulating investment during slowdowns and reducing it during overheating.
• The yield curve displays the relationship between the investment term and the interest rate
• The yield curve is crucial for computing present values and future values of risk-free cash flows.
• Risk-free rate is the rate at which money can be borrowed or lent without risk.
• Understanding the opportunity cost of capital is determining the best available expected return offered in the market
• This relates to the return forgone when an investor decides to invest in a new project, and sets the minimum required return for similar risk-term investments
• Bond pricing changes due to the passage of time and changes in interest rates
• Bond prices converge to their face value as maturity approaches
• A bond's market price reflects the current market interest rates which affect its yield to maturity

Bond Valuation

• Bond Terminology:
  • Bond certificate: stipulates bond terms, payment amounts, and dates
  • Face value, par value, or principal amount: the notional amount
  • Maturity date: the final payment date for the bond
  • Term: time remaining until the final repayment
  • Coupons: periodic interest payments

Zero-Coupon Bonds

• Zero-coupon bonds do not pay coupons during their life
• Zero-coupon bonds have only two cash flows: the purchase price and the face value at maturity
• Determining the fair price of a zero-coupon bond involves calculating the present value of the future face value, using the market interest rate as the discount rate

Coupon Bonds

• Coupon bonds make regular coupon interest payments and pay the face value at maturity
• The value of a coupon bond is the sum of the present values of all future coupon payments and the face value

Corporate Bonds

• Credit risk is the possibility of default by the issuer of a bond
• Corporate bonds have credit risk because corporations may fail to pay promised cash flows
• Rating agencies assess creditworthiness
• Corporate bonds with higher credit risk (default risk) need to pay higher coupons to attract investors.
• Bond ratings help investors evaluate credit worthiness
• Investment-grade bonds have low default risk.
• Speculative/high-yield bonds have higher default risk