Bond Valuation & Yield Measures: Types, Calculations & Market Impact

TAKEAWAYS:

• Bonds are debt instruments with three core cash flows: periodic coupons, face value repayment, and time value of money (TVM) adjustments.
• Yield measures (current yield, YTM, YTC) differ based on whether the bond trades at a premium, discount, or par—visualized via the bond price-yield inverse relationship.
• Zero-coupon bonds and callable bonds introduce unique valuation challenges (e.g., NTC’s zero-coupon treasury bills or Ncell’s callable debt).
• Market forces (interest rates, inflation, credit risk) directly impact bond prices—explained via the bond price-yield curve and duration/convexity.
• Real-world tools: Nepal Rastra Bank’s bond auctions, eSewa’s digital bond purchases, and Daraz’s supplier financing use these concepts daily.
• Exam focus: Calculate YTM/YTC, interpret bond indentures, and distinguish between nominal vs. real yields (critical for inflation-adjusted returns).

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1. What Is a Bond? Core Components and Cash Flows

Bonds are fixed-income securities issued by governments or corporations to raise capital. Unlike stocks, bonds promise periodic interest payments (coupons) and repayment of principal at maturity. Key terms:

How Bonds Generate Cash Flows

Bonds follow a timeline of payments:

Key Idea: The present value (PV) of all future cash flows equals the bond’s market price. If market rates rise, the bond’s PV (and price) falls, and vice versa.

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2. Bond Valuation: The Present Value Formula

Bond valuation uses the discounted cash flow (DCF) model: $$\text{Bond Price}=\sum _{t=1}^n\frac{{\text{Coupon}}_t}{(1+r{)}^t}+\frac{\text{Face Value}}{(1+r{)}^n}$$ Where:

• $r$ = market discount rate (YTM or required return).
• $n$ = years to maturity.

Worked Example: Valuing a Discount Bond

Scenario: A 10-year bond with:

• Par = Rs 1,000
• Coupon rate = 8% (Rs 80/year)
• Market price = Rs 800
• Market interest rate (YTM) = ?

Solution: We solve for $r$ in the PV equation. Using a financial calculator or trial-and-error: $$800=\frac{80}{(1+r{)}^1}+\frac{80}{(1+r{)}^2}+\cdots +\frac{80+1000}{(1+r{)}^{10}}$$ Answer: YTM ≈ 9.5% (higher than coupon rate because the bond sells at a discount).

Why? Investors demand a higher yield to compensate for buying below par.

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3. Yield Measures: Current Yield vs. YTM vs. YTC

Yields measure returns but differ in scope. Visual comparison:

Special Case: Zero-Coupon Bonds

• No periodic coupons; sold at deep discount, mature at par.
• Formula: $\text{Price}=\frac{\text{Face Value}}{(1+r{)}^n}$
• Example: Nepal Rastra Bank’s T-bills (e.g., 90-day zero-coupon security at Rs 950 for Rs 1,000 face value). YTM Calculation: $$950=\frac{1000}{(1+\text{YTM}{)}^{0.25}}⟹\text{YTM}\approx 5.5\%$$

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4. Bond Pricing and the Inverse Relationship with Yields

Core Principle: Bond prices and yields move oppositely. Why?

• If market rates rise, new bonds offer higher yields → existing bonds (with lower coupons) become less attractive → price drops.
• If rates fall, existing bonds’ coupons look attractive → price rises.

Real-World Example: NEPSE Bond Market (2022–2023)

• When NRB raised repo rates to 7.5% (to curb inflation), existing 6% government bonds traded at a discount (e.g., Rs 920 for Rs 1,000 par).
• Investor Impact: Holders of these bonds saw YTM jump to ~9% without coupon changes.

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5. Callable Bonds and Yield to Call (YTC)

Callable bonds allow issuers to repay early (e.g., at Rs 1,160 after 2 years). YTC accounts for this risk.

Worked Example: Ncell’s Callable Bond

• Par: Rs 1,000
• Coupon: 10% (Rs 100/year)
• Call Price: Rs 1,160 after 2 years
• Market Price: Rs 1,050
• Calculate YTC.

Solution: $$1050=\frac{100}{(1+\text{YTC}{)}^1}+\frac{100+1160}{(1+\text{YTC}{)}^2}$$ Answer: YTC ≈ 12.5% (higher than YTM due to call risk).

Why? Investors demand extra yield for the chance the bond may be called early.

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6. Risk Factors Affecting Bond Valuation

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7. Bond Indentures: The Legal Contract

A bond indenture is the legal agreement between issuer and investor, specifying:

• Covenants (e.g., "issuer cannot pay dividends > Rs 500M without bondholder approval").
• Collateral (e.g., NTC’s bonds backed by tax revenue).
• Call provisions (e.g., "can be called after Year 5 at Rs 1,050").

Example from Nepal:

• Nepal Government Securities (NGS): Indenture states coupons are tax-free and backed by the federal budget.
• Corporate Bonds (e.g., NMB Bank): May require minimum net worth ratios to avoid default.

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## In the Real World

1. eSewa’s Digital Bond Purchases

   • Concept: Yield to Maturity (YTM).
   • How? When NRB auctions T-bills (e.g., 364-day zero-coupon at 6.5% YTM), eSewa users buy them via the app. The discount from par (e.g., Rs 935 for Rs 1,000) reflects the market’s required return.

2. Ncell’s Supplier Financing Bonds

   • Concept: Callable Bonds + Yield to Call (YTC).
   • How? Ncell issues 5-year bonds at 9% coupon but includes a call option after Year 3 at Rs 1,075. Suppliers (e.g., Huawei) demand YTC > 10% to compensate for call risk.

3. NTC’s Zero-Coupon Treasury Bills

   • Concept: Zero-Coupon Valuation.
   • How? NTC sells 91-day T-bills at Rs 990 for Rs 1,000 face value. The YTM ≈ 4% is used by traders to hedge against short-term rate changes.

4. Nepal Rastra Bank’s Open Market Operations (OMO)

   • Concept: Bond Price-Yield Inverse Relationship.
   • How? When NRB buys bonds (injecting liquidity), bond prices rise and yields fall → stimulating the economy. Conversely, selling bonds raises yields to curb inflation.

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## Exam Tip: How to Score Full Marks

1. Memorize the YTM Formula Structure

   • Always write: $$\text{Price}=\sum \frac{\text{Cash Flows}}{(1+\text{YTM}{)}^t}$$
   • Partial credit tip: If stuck, list all cash flows explicitly (e.g., Year 1: Rs 80, Year 2: Rs 80, etc.).

2. Distinguish Between YTM and Current Yield

   • Current Yield = Annual Coupon / Market Price (quick but ignores capital gains).
   • YTM = Full-term return (includes price changes). Always preferred in exams.

3. Zero-Coupon Bonds

   • Shortcut: Use the formula $\text{Price}=\frac{\text{Face Value}}{(1+\text{YTM}{)}^n}$.
   • Example: For a 1-year zero-coupon bond at Rs 950 (par Rs 1,000): $$950=\frac{1000}{1+\text{YTM}}⟹\text{YTM}=5.26\%$$

4. Callable Bonds

   • Key Point: YTC is always higher than YTM because investors demand compensation for early repayment risk.
   • Exam Trap: If a bond is called, ignore cash flows after the call date.

5. Real-World Applications

   • NTC/Ncell Bonds: Assume coupons are paid annually unless stated otherwise.
   • Government Securities: Often tax-free—mention this in explanations for bonus marks.

6. Graphs Are Your Friend

   • Draw the inverse relationship between bond prices and yields in exams. Label axes clearly:
     • X-axis: Yield (%)
     • Y-axis: Bond Price (Rs)
     • Curve: Downward-sloping (steeper for longer maturities).

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## Practice Questions (Exam-Style)

1. Calculate YTM: A bond has a par of Rs 1,000, 5 years to maturity, 7% coupon (paid annually), and trades at Rs 950. What is its YTM? (Answer: ~8.5%)

2. YTC Scenario: A bond with Rs 1,000 par, 6% coupon, and 3 years to maturity is callable at Rs 1,030 in Year 2. If it trades at Rs 1,010, calculate YTC. (Answer: ~7.5%)

3. Zero-Coupon Bond: A 2-year zero-coupon bond sells for Rs 920 with Rs 1,000 par. What is its YTM? (Answer: ~9.0%)

4. Current Yield vs. YTM: A bond with 8% coupon trades at:

   • Rs 1,000 (par) → Current Yield = 8%, YTM = 8%.
   • Rs 900 (discount) → Current Yield = 8.89%, YTM > 8.89%. Explain why YTM > Current Yield in the second case. (Answer: Capital gain from price appreciation.)