Bonds & Interest Rates: Types, Valuation, YTM, Cost of Debt

TAKEAWAYS:

• Bonds are fixed-income securities issued by governments/corporations to raise debt capital, with par value, coupon rates, and maturity dates defining their structure.
• Interest rates (nominal, real, effective) determine bond prices via inverse relationship: when rates rise, bond prices fall (and vice versa).
• Yield to Maturity (YTM) is the true return on a bond if held to maturity, calculated using IRR on cash flows (coupons + principal).
• Zero-coupon bonds sell at a discount and mature at par, while perpetual bonds pay forever with no maturity.
• Cost of debt (after-tax) is critical for WACC calculations and reflects a company’s borrowing expense.
• Real-world applications include Nepal’s NTC bonds (government debt), bank loans (corporate bonds), and Khalti’s interest-bearing digital wallets.

1. What is a Bond?

A bond is a debt instrument issued by a borrower (government/corporation) to raise capital. Investors lend money in exchange for:

• Periodic interest payments (coupons).
• Repayment of principal (par value) at maturity.

Key Bond Features

classDiagram
  class Bond {
      +Par Value: Rs 1,000 (standard)
      +Coupon Rate: 8% (annual)
      +Maturity: 5–30 years
      +Issuer: Govt/Corporation
      +Market Price: Fluctuates
      +YTM: Market Interest Rate
  }
  class ZeroCouponBond {
      +No Coupons
      +Sold at Discount
      +Matures at Par
      +Price = Par / (1 + YTM)^n
  }
  class PerpetualBond {
      +No Maturity
      +Pays Coupons Forever
      +Price = Coupon / YTM
  }
  Bond <|-- ZeroCouponBond
  Bond <|-- PerpetualBond
  classDiagram {
      class Bond {
          +Par Value: Rs 1,000
          +Coupon Rate: 8%
          +Maturity: 5–30 years
          +Issuer: Govt/Corporation
          +Market Price: Fluctuates
          +YTM: Market Interest Rate
      }
      class ZeroCouponBond {
          +No Coupons
          +Sold at Discount
          +Matures at Par
          +Price = Par / (1 + YTM)^n
      }
      class PerpetualBond {
          +No Maturity
          +Pays Coupons Forever
          +Price = Coupon / YTM
      }
      Bond <|-- ZeroCouponBond
      Bond <|-- PerpetualBond
  }

A physical bond certificate (e.g., Nepal Rastra Bank bond) showing par value, coupon rate, and maturity. (Image: Public domain, via Wikimedia Commons)

2. Bond Pricing Mechanics

Bond prices are present value (PV) of future cash flows (coupons + principal), discounted at the market interest rate (YTM).

Formula: Bond Price = PV of Coupons + PV of Par Value

$$P=\sum _{t=1}^n\frac{C}{(1+r{)}^t}+\frac{F}{(1+r{)}^n}$$

• $P$ = Market price
• $C$ = Coupon payment ($=\text{Par}\times \text{Coupon Rate}$)
• $r$ = Market interest rate (YTM)
• $F$ = Par value
• $n$ = Years to maturity

Example: Kathmandu Retail Shop Bond

A shop issues a 5-year bond with:

• Par value = Rs 1,000
• Coupon rate = 10% (annual, paid yearly)
• Market YTM = 12%

Calculate the bond’s market price.

Total Bond Price = Rs 89.29 + 79.72 + 71.18 + 63.55 + 624.14 = Rs 927.88

Key Insight: The bond sells at a discount (Rs 927.88 < Rs 1,000)** because the **market rate (12%) > coupon rate (10%).

3. Types of Bonds

4. Interest Rates: Nominal vs. Real vs. Effective

Worked Example: Chaurikhola Credit Card

• APR = 19.5%, compounded daily.
• Calculate EAR.

$$\text{EAR}={\left(1+\frac{0.195}{365}\right)}^{365}-1=21.4\%$$

Why it matters: Banks (e.g., NMB, Global IME) use EAR to disclose true borrowing costs under Nepal’s Banking Act.

5. Yield to Maturity (YTM) and Yield to Call (YTC)

• YTM: Internal Rate of Return (IRR) if bond is held to maturity.
• YTC: IRR if bond is called early (issuer buys back before maturity).

Formula: YTM (for Annual Coupons)

$$P=\sum _{t=1}^n\frac{C}{(1+\text{YTM}{)}^t}+\frac{F}{(1+\text{YTM}{)}^n}$$ Solve for YTM using financial calculators or Excel’s RATE function.

Example: Zero-Coupon Bond (NTC Treasury Bill)

• Price = Rs 400
• Par = Rs 1,000
• Maturity = 8 years
• Calculate YTM.

$$400=\frac{1000}{(1+\text{YTM}{)}^8}$$ $$\text{YTM}={\left(\frac{1000}{400}\right)}^{1/8}-1=11.09\%$$

Real-World Tie: NTC issues zero-coupon bonds to fund infrastructure. Investors earn 11.09% annualized return if held to maturity.

6. Cost of Debt (After-Tax)

Companies use after-tax cost of debt in WACC calculations.

Formula

$$\text{After-Tax Cost of Debt}=\text{YTM}\times (1-\text{Tax Rate})$$

Example: Garudnahani Company (Exam Question)

• Zero-coupon bond: Rs 500 price, Rs 1,000 par, 10-year maturity.
• Tax rate = 40%
• Calculate after-tax cost of debt.

1. Find YTM (as above): $$500=\frac{1000}{(1+\text{YTM}{)}^{10}}⟹\text{YTM}=7.18\%$$
2. After-tax cost: $$7.18\%\times (1-0.40)=4.31\%$$

Why it matters: Garudnahani uses this 4.31% in WACC to evaluate new projects (e.g., expanding a Kathmandu factory).

7. Bond Price vs. Interest Rate Relationship

Key Insight:

• If YTM > Coupon Rate → Bond sells at discount.
• If YTM = Coupon Rate → Bond sells at par.
• If YTM < Coupon Rate → Bond sells at premium.

Real-World Example: When the Nepal Rastra Bank raises policy rates, existing bonds (e.g., NMB’s 8% bonds) lose value because their coupons become less attractive.

8. Bonds in Nepal’s Financial Markets

In the Real World

1. NTC Bonds (National Transmission & Distribution Company)

   • Idea Used: Fixed-rate corporate bonds to fund power projects.
   • How: NTC issues 10-year bonds at 12% coupon to raise Rs 50 billion. Investors (banks, insurance firms) earn fixed income while NTC expands the grid.

2. Khalti’s Interest-Bearing Wallets

   • Idea Used: Floating-rate savings instruments (e.g., 6% annualized, compounded monthly).
   • How: Khalti offers higher yields than bank deposits to attract users, using funds to lend to merchants (e.g., Daraz sellers) at higher rates.

3. Nepal Investment Bank’s Loan Pricing

   • Idea Used: Effective Annual Rate (EAR) for transparency.
   • How: A 15% APR loan compounded monthly becomes 16.08% EAR. Banks must disclose EAR under Financial Institutions Act, 2019.

4. Daraz’s Supplier Financing

   • Idea Used: Zero-coupon commercial paper for short-term cash flow.
   • How: Daraz issues 90-day zero-coupon notes at 95% of face value to suppliers. At maturity, suppliers get Rs 100 for every Rs 95 paid upfront (10% discount = 43.6% annualized yield).

Exam Tip

1. Memorize the Inverse Relationship: Bond prices and interest rates move opposite. If YTM rises, bond price falls (and vice versa).
2. Zero-Coupon Bonds: Always sell at a discount. Use the formula: $$P=\frac{F}{(1+\text{YTM}{)}^n}$$
3. YTM vs. Coupon Rate:
   • YTM > Coupon Rate → Bond sells at discount.
   • YTM = Coupon Rate → Bond sells at par.
   • YTM < Coupon Rate → Bond sells at premium.
4. After-Tax Cost of Debt: Always multiply YTM by (1 – Tax Rate) for WACC calculations.
5. Perpetual Bonds: Price = $\frac{\text{Coupon}}{\text{YTM}}$. No maturity date!
6. Real-World Applications: Exams often test Nepal-specific examples (e.g., NTC bonds, Khalti wallets). Relate theory to Nepal’s financial markets.

Final Visual Summary