Bonds & Stocks Valuation: Types, Pricing, Risk & Real-World Applications

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Core Concepts: Bonds and Stocks Valuation

1. Bonds: The Foundation of Fixed-Income Investments

Bonds are debt instruments issued by governments or corporations to raise capital. Investors lend money to the issuer in exchange for periodic interest payments (coupons) and the return of the principal at maturity.

Key Components of a Bond

How Bonds Work: A Nepali Example

Scenario: Kathmandu Retail Pvt. Ltd. issues a Rs 1,000 par value, 10% coupon bond with 7 years to maturity, paying interest semiannually. An investor requires a 12% annual return (6% semiannual).

Step-by-Step Valuation:

1. Coupon Payment (Semiannual): $\text{Coupon}=\frac{10\%\times 1000}{2}=\text{Rs 50 per period}$.

2. Number of Periods: $7\text{ years}\times 2=14\text{ periods}$.

3. Present Value of Coupons (Annuity): $$P{V}_{\text{coupons}}=50\times \left[\frac{1-(1+0.06{)}^{-14}}{0.06}\right]=50\times 9.1826=\text{Rs 459.13}$$

4. Present Value of Principal: $$P{V}_{\text{principal}}=\frac{1000}{(1+0.06{)}^{14}}=\text{Rs 455.59}$$

5. Total Bond Value: $$\text{Bond Price}=459.13+455.59=\text{Rs 914.72}$$ Interpretation: Since Rs 914.72 < Rs 1,000 (par), this is a discount bond.

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(Shows par value, coupon rate, maturity date, and interest payment schedule.)

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2. Types of Bonds and Their Valuation

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Why Bonds Trade at Premium/Discount?

• Premium: Market interest rates fall after issuance (investors pay more for higher coupons).
• Discount: Market interest rates rise after issuance (investors accept lower coupons for future gains).

(Shows a downward-sloping curve: as YTM ↑, bond price ↓.)

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3. Stock Valuation: Dividend Discount Models (DDM)

Stocks represent ownership in a company. Their value depends on future dividends and growth.

Key Models

1. Dividend Growth Model (Gordon Model): $$P_0=\frac{D_1}{r-g}$$

   • $P_0$: Current stock price
   • $D_1$: Next year’s dividend
   • $r$: Required return
   • $g$: Constant growth rate

2. Non-Growing Stock (Zero Growth): $$P_0=\frac{D}{r}$$ (Used for preferred stocks or mature firms like NTC.)

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Example: Sagarmatha Company

• Current price ($P_0$) = Rs 360
• Last dividend ($D_0$) = Rs 24
• Growth rate ($g$) = 5%
• Required return ($r$) = 12%

Step 1: Calculate $D_1$: $$D_1=D_0\times (1+g)=24\times 1.05=\text{Rs 25.20}$$

Step 2: Apply Gordon Model: $$P_0=\frac{25.20}{0.12-0.05}=\frac{25.20}{0.07}=\text{Rs 360}$$ Verification: Matches given price → correct valuation.

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(Horizontal line with arrows: $D_0\to D_1\to D_2$, each increasing by 5%.)

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4. Real-World Applications in Nepal

1. eSewa and Khalti: Zero-Coupon Bonds Analogy

• How it works: When you buy a digital voucher (e.g., Rs 1,000 for Rs 950), you’re effectively getting a discount for early payment—similar to a zero-coupon bond where the "interest" is the discount.
• Key Idea: Time value of money (TVM) applies to digital transactions too. The platform earns the "coupon" (Rs 50) upfront.

2. NEPSE Stock Market: Dividend Growth in Companies

• Example: Nabil Bank consistently pays dividends. If an investor buys shares at Rs 500 expecting 8% return and 3% growth: $$P_0=\frac{D_1}{0.08-0.03}=\frac{500\times 1.03\times 0.10}{0.05}=\text{Rs 526}$$ (Here, $D_1=500\times 1.03\times 0.10=\text{Rs 51.50}$, assuming 10% payout ratio.)
• Why it matters: Investors use DDM to decide if a stock is over/undervalued.

3. Pathao’s Loan Interest: Bond-Like Structure

• When Pathao offers installment loans (e.g., Rs 10,000 repaid in 6 months with 2% monthly interest), it’s like issuing a short-term bond:
  • Par Value: Rs 10,000
  • Coupon: 2% of Rs 10,000 = Rs 200/month
  • YTM: $(1.02{)}^6-1\approx 12.6\%$ annualized.
• Risk: If inflation rises, Pathao’s cost of capital (like a bond’s YTM) increases.

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(Line graph with dividend payouts marked as vertical bars.)

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5. Risk vs. Return: Bonds vs. Stocks

Why Stocks Are Riskier:

• No legal obligation to pay dividends (unlike bond coupons).
• Market volatility: Stocks react to news (e.g., NEPSE crashes during political instability).
• Example: In 2020, NEPSE dropped 30% due to COVID-19, while NTC bonds remained stable.

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(Scatter plot with bonds clustered near origin, stocks spread upward-right.)

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6. The Accounting Cycle for Bonds (T-Accounts)

When a company issues bonds, it records:

1. Cash inflow (debit to Cash)
2. Liability created (credit to Bonds Payable)
3. Interest expense (credit to Interest Payable)

Example: Kathmandu Retail issues Rs 1,000 bond at Rs 950 (discount)

At Maturity:

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(Table with columns: Date | Account | Dr | Cr | Narration.)

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Exam Tip: How to Score Full Marks

1. Memorize Formulas:

   • Bond valuation: $P=\sum \frac{C}{(1+r{)}^t}+\frac{F}{(1+r{)}^n}$
   • Stock valuation: $P_0=\frac{D_1}{r-g}$
   • Always show steps—examiners deduct for missing intermediate calculations.

2. Watch for Units:

   • Convert annual rates to periodic (e.g., 10% annual → 5% semiannual).
   • Ensure coupon payments match periods (annual vs. semiannual).

3. Real-World Links:

   • Relate Nepal Rastra Bank bonds to zero-coupon bonds.
   • Compare NEPSE stocks to dividend growth models.
   • Use eSewa/Khalti discounts to explain present value.

4. Common Pitfalls:

   • Ignoring growth rate ($g$) in DDM → leads to incorrect $P_0$.
   • Miscounting periods (e.g., 7 years = 14 semiannual periods).
   • Premium/discount confusion: If $r<$ coupon rate → premium bond.

5. Diagrams Save Marks:

   • Draw a timeline for dividends (for DDM).
   • Sketch a bond price-YTM graph (for premium/discount questions).
   • Use T-accounts for bond transactions.

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Past Exam Question Solved: Q: A preferred stock pays Rs 15 dividend. Investor’s required return is 12%. What’s its value? A: $$P_0=\frac{D}{r}=\frac{15}{0.12}=\text{Rs 125}$$ (No growth → use zero-growth model.)