Bond Valuation & Fixed Income Securities: Types, Valuation, Yields & Risks

Key Concepts & Definitions

What Are Fixed Income Securities?

Fixed income securities are debt instruments that pay a fixed periodic income (coupon payments) to investors until maturity, when the principal is repaid. Unlike stocks, they do not represent ownership but a loan to the issuer (government, corporation, or financial institution).

classDiagram
    class FixedIncomeSecurity {
        +Issuer: Government/Corporation
        +Face Value (Par Value): Rs. 1,000 (standard)
        +Coupon Rate: Fixed % of face value
        +Maturity: Years until repayment
        +Payment Frequency: Annual/Semi-annual
    }
    class Bond {
        +Secured by assets/collateral
    }
    class Debenture {
        +Unsecured, backed by issuer's credit
    }
    class TreasuryBill {
        +Short-term (<1 year), no coupon
    }
    FixedIncomeSecurity <|-- Bond
    FixedIncomeSecurity <|-- Debenture
    FixedIncomeSecurity <|-- TreasuryBill

Types of Fixed Income Securities in Nepal

Real-World Example:

• Nepal Rastra Bank (NRB) Bonds: When NRB issues 10-year bonds at 8% coupon, retail investors (via banks like NMB or SBI) buy them for fixed income. The bond’s price fluctuates with market interest rates, but the coupon remains fixed.
• NMB Bank’s Corporate Bonds: Listed on NEPSE, these bonds pay semi-annual coupons and are traded like stocks but with lower volatility.

How Bonds Are Valued: The Present Value Approach

Bonds are valued using the time value of money principle. Their price depends on:

1. Face Value (Par Value): Rs. 1,000 (standard in Nepal).
2. Coupon Rate: Fixed % of face value (e.g., 8% = Rs. 80/year).
3. Market Interest Rate (YTM): Current rate demanded by investors.
4. Maturity: Years until repayment.

Bond Valuation Formula

The price of a bond is the present value (PV) of all future cash flows (coupons + principal): $$P=\sum _{t=1}^n\frac{C}{(1+r{)}^t}+\frac{F}{(1+r{)}^n}$$ Where:

• $P$ = Bond price
• $C$ = Coupon payment (e.g., Rs. 80 for 8% coupon on Rs. 1,000)
• $r$ = Market interest rate (YTM)
• $F$ = Face value (Rs. 1,000)
• $n$ = Years to maturity

Worked Example: Valuing a Corporate Bond

Problem: A bond issued by Pokhara Foods has:

• Face value = Rs. 1,000
• Coupon rate = 8% (paid semi-annually)
• Maturity = 10 years
• Current market interest rate (YTM) = 10% Find: The bond’s price.

Solution:

1. Adjust for semi-annual payments:

   • Coupon per period = $\frac{8\%\times 1000}{2}=Rs.40$
   • YTM per period = $\frac{10\%}{2}=5\%$
   • Total periods = $10\times 2=20$

2. Calculate PV of coupons: $$P{V}_{\text{coupons}}=40\times \left(\frac{1-(1+0.05{)}^{-20}}{0.05}\right)=40\times 12.462=Rs.498.48$$

3. Calculate PV of face value: $$P{V}_{\text{face}}=\frac{1000}{(1.05{)}^{20}}=Rs.376.89$$

4. Total bond price: $$P=498.48+376.89=Rs.875.37$$

Interpretation: The bond trades at a **discount (Rs. 875.37 < Rs. 1,000)** because the market rate (10%) > coupon rate (8%). Investors demand a lower price to achieve the higher yield.

Key Yield Measures for Bonds

Real-World Tie-In:

• NMB Bank’s 7% Bond (2025): If trading at Rs. 980, its current yield is $\frac{70}{980}=7.14\%$. But its YTM might be higher if market rates rise before maturity.
• NRB’s 91-Day T-Bill: Sold at Rs. 980 for Rs. 1,000 face value. Its yield is $\frac{1000-980}{980}\times \frac{365}{91}=8.73\%$.

Factors Affecting Bond Prices

flowchart TD
    A["Market Interest Rates ↑"] --> B["Bond Prices ↓"]
    A --> C["Inverse Relationship"]
    D["Credit Risk ↑"] --> E["Bond Prices ↓"]
    F["Time to Maturity ↑"] --> G["Price Sensitivity ↑"]
    H["Inflation ↑"] --> I["Real Yield ↓"]
    J["Liquidity ↓"] --> K["Yield Spread ↑"]

Risks in Fixed Income Investments

Real-World Example:

• 2015 Nepal Financial Crisis: Many corporate bonds (e.g., Everest Bank’s) saw credit risk spike, causing prices to crash. Investors demanded higher yields to compensate.

In the Real World

1. eSewa & Khalti’s Treasury Bill Investments:

   • Both platforms allow retail investors to buy NRB’s 91-day T-Bills via their apps. The yield (e.g., 8-9%) is higher than savings accounts, and the short term makes it low-risk. The discount pricing mechanism (buying at Rs. 980 for Rs. 1,000) directly applies the bond valuation formula.

2. NMB Bank’s Corporate Bond Portfolio:

   • NMB Bank sells its own 7-10 year bonds to retail investors (via NEPSE) to raise capital. The bank uses the proceeds for lending (e.g., home loans at 10-12%), while investors earn fixed coupons. The yield to maturity helps NMB price these bonds competitively against NRB securities.

3. Pathao’s Debt Financing:

   • Pathao (ride-hailing app) issued convertible debentures in 2022 to raise Rs. 500 million. These paid 9% coupons but could be converted to equity at Rs. 50/share. The conversion value (5 shares × Rs. 50 = Rs. 250 per debenture) was tied to Pathao’s stock price, showing how fixed income can morph into equity.

Comparing Bonds to Other Investments

Exam Tip: How This Unit Is Tested

1. Calculations (40% weight):

   • Must know: How to compute current yield, YTM, and bond price using PV formulas.
   • Past exam trick: Always check if payments are annual or semi-annual (adjust periods and rates accordingly).
   • Example: For a bond with semi-annual coupons, divide the annual coupon by 2 and the YTM by 2 before plugging into the formula.

2. Conceptual Questions (30% weight):

   • Define fixed income securities, coupon rate, and credit risk.
   • Explain why a bond trades at a premium (price > face value) or discount (price < face value).
   • Compare government bonds vs corporate bonds in terms of risk and return.

3. Real-World Applications (20% weight):

   • Relate bond valuation to Nepal’s financial instruments (e.g., NRB bonds, corporate debentures).
   • Discuss how interest rate hikes by NRB affect bond prices (inverse relationship).
   • Explain why Treasury Bills are considered risk-free but offer lower yields than corporate bonds.

4. Shortcomings (10% weight):

   • Identify risks like inflation risk, credit risk, and liquidity risk.
   • Critique fixed income as an investment (e.g., "Bonds are safe but offer lower returns than stocks in high-growth economies like Nepal’s").

Pro Tip:

• Memorize the bond valuation formula and practice with semi-annual vs annual coupon scenarios.
• Use a financial calculator (or Excel’s PV function) for YTM calculations—examiners expect precise answers.
• Link theory to Nepal: Always tie examples to NRB, NEPSE, or local banks (e.g., "NMB’s bonds are riskier than NRB’s due to credit risk").