Chapter 3 Study Notes: Valuing Bonds

Companies often require substantial investment for new plant and equipment, typically funded through:
- Retained Earnings: Accumulated funds from profits.
- Borrowing: When retaining earnings is insufficient, companies might choose to issue bonds, which are long-term loans.
- Issuing Stock: While additional equity can be issued, firms may prefer debt to avoid diluting ownership.

Government bonds have lower interest rates compared to corporate bonds as they generally carry less risk due to government backing.
- Example: In early 2018, $14.8 trillion of U.S. government securities were held by investors.
Market Characteristics:
- Large and sophisticated markets with professional traders making frequent trades often based on small price discrepancies.
- Managers must understand key concepts including spot rates, yields, and interest rate risk.

Complex Securities: More complex than government bonds due to higher default risk.
Liquidity: Corporate bonds tend to have lower liquidity than government bonds, making them harder to buy/sell quickly.
The risk of default on corporate bonds affects their pricing and yields compared to similar maturity government bonds.

When holding a bond, investors are entitled to fixed cash payoffs:
- Interest Payments (Coupons): Regular payments till maturity.
- Final Payment: The principal (face value) is returned at maturity.

Example: Valuing a Government Bond (French OAT)

Bond Details: €100 face value, 6.00% interest rate, matures in 2025.
- Annual interest payment: €6.00.
- Cash flows: €6 annually for 8 years, total €106.00 at maturity in 2025.
- Opportunity cost of capital: 0.3% based on returns from similar government bonds.
- Bond Pricing: Quoted at 144.99% of face value, indicating market premium due to lower alternative yields.

Defined as the interest rate that equals the present value of future cash flows to its price.
For the above bond, the YTM is 0.3% due to its premium pricing over face value.
- YTM Comparison to Current Yield: Current yield is calculated as
  $rac{Coupon Payment}{Bond Price} = rac{6}{144.99} <br>ightarrow 4.14\%$
Premium Bonds: Bonds priced above face value tend to have lower YTM than their coupon rates, indicating capital loss at maturity.
Discount Bonds: Priced below face value with higher YTM reflecting anticipated capital gains to maturity.

YTM is typically calculated through trial and error or using software tools; functions in Excel provide convenient calculations.

U.S. Treasury bonds are issued with face values typically at $1,000, and generally, interest is paid semiannually.
For example, an 8.00% Treasury bond maturing in 2021:
- Provides a coupon payment of 4% every six months.
- Trading and Pricing: Not traded on stock exchanges, prices provided by dealers are displayed in financial press.
- Example Pricing Quote: If asked price is 123.41, it costs $1,234.10 for a bond worth $1,000.

Cash flows include semiannual coupon payments and final principal repayment. When yields rise, prices re-adjust downward reflecting inversely related relationship.
- YTM Impact: If market demand shifts, YTM calculations will adjust to reflect the new market conditions, requiring recalculation of price at new YTM.

Concept of Interest Rate Sensitivity: Bond prices move inversely with interest rates. When interest rates increase, bond prices drop.
Price Adjustment Examples: Higher YTMs lead to lower bond prices, which is crucial for risk assessment in bond portfolio management.
Duration measures the expected change in bond price due to interest rate fluctuations, explaining why long-term bonds have greater sensitivity for rates changes than short-term bonds.

Definition of Duration: The average time until cash flows are received, weighted by present value.
Modified Duration: Provides a percentage measure of price volatility in reaction to interest shifts.
- Formula: $ext{Modified Duration} = rac{ ext{Duration}}{1 + ext{YTM}}$

Bonds represent long-term loans with set coupon payments and repayment of principal at maturity.
The value of bonds reflects discounted future cash flows based on spot rates, while YTM provides a single return measure summary across cash flows.
Understanding duration is essential for assessing interest rate risks and price volatility for investment decisions.
The term structure of interest rates illustrates different yields across maturity dates which may rise or fall due to economic conditions and inflation expectations.