Bond & Stock Valuation: Pricing, Yields, and Market Models

TAKEAWAYS:

• Bonds are valued using discounted cash flows (DCF) of coupon payments and principal, while stocks rely on dividend discount models (DDM) or price-earnings (P/E) ratios.
• Yield to Maturity (YTM) is the bond’s true return, accounting for price, coupon, and time; it differs from current yield (coupon/price).
• Stock valuation depends on growth expectations (constant growth DDM, multi-stage DDM) and risk (CAPM-adjusted discount rates).
• Market efficiency (weak, semi-strong, strong forms) explains why stock prices reflect all available information, affecting valuation models.
• Nepal’s NEPSE uses similar principles: bond yields reflect NTC’s borrowing costs, while stock P/E ratios depend on company earnings growth (e.g., Ncell vs. NABIL Bank).

1. Bond Valuation: The Core Mechanics

Bonds are debt instruments where investors lend money to a corporation or government in exchange for periodic interest payments (coupons) and repayment of the face value at maturity. Valuation involves calculating the present value (PV) of all future cash flows using the bond’s yield to maturity (YTM).

Key Components of a Bond

classDiagram
    class Bond {
        +Face Value (FV): ₹1000 (standard)
        +Coupon Rate (%): Annual interest rate (e.g., 8%)
        +Coupon Payment (C): FV × Coupon Rate (e.g., ₹80/year)
        +Maturity (T): Years until repayment (e.g., 5 years)
        +Market Price (P): Current trading price (may differ from FV)
        +Yield to Maturity (YTM): Discount rate that makes PV(P) = Market Price
    }
    Bond --> "Issued by" Corporation
    Bond --> "Traded on" NEPSE / Global Exchanges

Bond Valuation Formula

The price of a bond is the sum of the present values of its coupon payments and face value: $$P=\sum _{t=1}^T\frac{C}{(1+YTM{)}^t}+\frac{FV}{(1+YTM{)}^T}$$ Where:

• $P$ = Bond price
• $C$ = Annual coupon payment
• $YTM$ = Yield to maturity (periodic rate)
• $T$ = Years to maturity

Worked Example: Valuing a Nepalese Corporate Bond

Scenario: Ncell Ltd. issues a 5-year bond with:

• Face Value (FV) = ₹1,000
• Coupon Rate = 9% (paid annually)
• Market Price (P) = ₹950
• Current YTM = 10%

Question: Verify if the bond’s YTM is 10% given its market price.

Solution: We need to solve for $YTM$ such that: $$950=\frac{90}{(1+YTM{)}^1}+\frac{90}{(1+YTM{)}^2}+\frac{90}{(1+YTM{)}^3}+\frac{90}{(1+YTM{)}^4}+\frac{1090}{(1+YTM{)}^5}$$ Using a financial calculator or Excel (=RATE(5, 90, -950, 1000)), we find: YTM ≈ 10.8% This means the bond’s market price of ₹950 implies a higher yield than its coupon rate due to market interest rate changes.

Why This Matters for Nepal:

• NTC’s bonds are priced similarly; if NTC’s borrowing cost (YTM) rises, its bond prices fall.
• Investors compare Ncell’s bond YTM to bank deposit rates (e.g., 7–8% in 2023) to decide where to park funds.

2. Types of Bonds and Their Valuation

Not all bonds are identical. Their valuation depends on structure, risk, and market conditions.

Comparison Table: Bond Types

3. Stock Valuation: Dividend Discount Models (DDM)

Stocks represent ownership in a company. Unlike bonds, they have no maturity, so valuation relies on expected future cash flows (dividends) and growth.

Key Models

1. Dividend Discount Model (DDM): $$P_0=\frac{D_1}{r-g}$$ Where:

   • $P_0$ = Current stock price
   • $D_1$ = Next year’s dividend
   • $r$ = Required return (discount rate, often from CAPM)
   • $g$ = Constant growth rate of dividends

2. Multi-Stage DDM:

   • Dividends grow at different rates (e.g., high growth early, stable later).
   • Example: A startup (Pathao) may have high $g$ initially, then stabilize.

3. Free Cash Flow to Equity (FCFE): $$P_0=\sum _{t=1}^{\infty }\frac{FCF{E}_t}{(1+r{)}^t}$$ Used when dividends are unpredictable (e.g., Daraz’s reinvestment phases).

Worked Example: Valuing a Nepali Stock (Nepal Bank Ltd.)

Scenario:

• Nepal Bank’s last dividend ($D_0$) = ₹15 per share.
• Dividends grow at 5% annually ($g=5\%$).
• Investors require 12% return ($r=12\%$).

Question: What is the fair value of Nepal Bank’s stock?

Solution: Using the Gordon Growth Model: $$P_0=\frac{D_1}{r-g}=\frac{15\times 1.05}{0.12-0.05}=\frac{15.75}{0.07}=₹225$$ Interpretation:

• If Nepal Bank trades below ₹225, it’s undervalued; above ₹225, it’s overvalued.
• Real-World Check: In 2023, Nepal Bank’s P/E ratio was ~12x earnings. If earnings grow at 5%, this aligns with the DDM.

4. Market-Based Valuation: Multiples Approach

When future cash flows are uncertain, investors use comparable company multiples:

• Price-to-Earnings (P/E): $P/E=\frac{MarketPrice}{EarningsperShare}$
• Price-to-Book (P/B): $P/B=\frac{MarketPrice}{BookValueperShare}$
• Enterprise Value (EV)/EBITDA: Used for private firms (e.g., Daraz pre-IPO).

Example for Nepal:

Insight:

• Ncell’s low P/E reflects mature industry; NABIL’s higher P/E suggests growth expectations.
• Exam Tip: Always compare multiples within the same sector (e.g., don’t compare Ncell to Himalayan Bank).

5. Risk and Required Return (CAPM)

No valuation is complete without accounting for risk. The Capital Asset Pricing Model (CAPM) sets the discount rate ($r$) for stocks: $$r=R_f+\beta (R_m-R_f)$$ Where:

• $R_f$ = Risk-free rate (e.g., NTC’s 7-year bond yield = 8%)
• $\beta$ = Stock’s beta (Ncell’s $\beta =1.1$, NABIL’s $\beta =0.9$)
• $R_m$ = Market return (e.g., NEPSE index return = 10%)

Example: For Ncell ($\beta =1.1$): $$r=8\%+1.1\times (10\%-8\%)=8\%+2.2\%=10.2\%$$ This $r$ is used in DDM to value Ncell’s stock.

6. Efficient Market Hypothesis (EMH) and Valuation

The EMH states that stock prices reflect all available information:

• Weak Form: Past prices don’t predict future prices (technical analysis is useless).
• Semi-Strong Form: All public info (earnings reports, news) is priced in.
• Strong Form: Even insider info is reflected (rarely true).

Implications for Valuation:

• Active vs. Passive Investing: If markets are semi-strong efficient, beating the market consistently is hard (supports index funds like NEPSE Index Fund).
• Anomalies: Some patterns persist (e.g., small-cap stocks outperform in Nepal), but EMH explains why they’re temporary.

Real-World Example:

• Khalti’s IPO (2021): Priced at ₹1,000, but traded at ₹1,200 initially due to high demand. EMH suggests this premium reflected growth expectations (high $g$ in DDM).
• NEPSE Crashes (2015, 2020): Prices dropped when new info (political instability, COVID) emerged, consistent with semi-strong EMH.

7. Putting It All Together: The Valuation Process

flowchart TD
    A["Start"] --> B["Identify Asset: Bond or Stock?"]
    B -->|"Bond"| C["Gather: Coupon, FV, Maturity, YTM"]
    C --> D["Calculate PV of Coupons + FV"]
    D --> E["Compare to Market Price"]
    B -->|"Stock"| F["Choose Model: DDM, FCFE, or Multiples"]
    F -->|"DDM"| G["Estimate D1, g, r"]
    G --> H["Calculate P0 = D1/(r-g)"]
    F -->|"Multiples"| I["Find Comparable P/E or P/B"]
    I --> J["Apply Multiple to Target Company"]
    E --> K["Decision: Buy/Sell/Hold"]
    H --> K
    J --> K

Worked Example: Valuing a Bond vs. Stock for a Kathmandu Investor Scenario: You have ₹50,000 to invest. Options:

1. Ncell 8% Bond: ₹1,000 face, ₹950 market price, 5 years to maturity.
2. Ncell Stock: Current price = ₹225, $D_0=₹15$, $g=5\%$, $\beta =1.1$.

Step 1: Bond Valuation

• YTM ≈ 10.8% (from earlier).
• Expected Return: 10.8% (fixed).
• Risk: Low (debt instrument).

Step 2: Stock Valuation

• Fair value = ₹225 (from DDM).
• Expected Return: $$r=8\%+1.1\times (10\%-8\%)=10.2\%$$
• Risk: Higher ($\beta >1$), but potential for capital gains.

Decision:

• If the investor is risk-averse, the bond’s fixed 10.8% return may appeal.
• If growth-oriented, the stock’s 10.2% return + dividend yield (₹15/₹225 ≈ 6.7%) could be attractive.

In the Real World

1. Ncell’s Bond and Stock Valuation:

   • Ncell issues bonds to fund expansion (e.g., 5G). Investors use YTM to compare Ncell’s borrowing cost to bank deposits.
   • Ncell’s stock price reflects its dividend growth ($g$) and risk ($\beta$). In 2023, its P/E ratio dropped as growth slowed, signaling lower $g$ in the DDM.

2. Nepal Rastra Bank (NRB) and Monetary Policy:

   • When NRB raises repo rates (e.g., from 7% to 8%), bond YTMs rise, and bond prices fall. This affects NTC’s borrowing costs.
   • Stocks with high $\beta$ (e.g., Pathao) see higher required returns ($r$), reducing their valuations.

3. Daraz’s Private Valuation (Pre-IPO):

   • Before its 2021 IPO, Daraz was valued using FCFE multiples compared to Alibaba. Analysts estimated its cash flows and applied a discount rate reflecting Nepal’s higher risk ($R_m-R_f$ gap).

Exam Tip

1. Bonds:

   • Always calculate YTM when given a bond’s price and coupon. Use the formula or financial calculator.
   • Remember: Price and YTM move inversely. If interest rates rise, bond prices fall.
   • Common Pitfall: Confusing current yield ($\frac{Coupon}{Price}$) with YTM. Current yield ignores capital gains/losses.

2. Stocks:

   • For DDM, ensure $g<r$ (otherwise, the model breaks).
   • In exams, if growth rates change (multi-stage DDM), show all stages in your calculation.
   • CAPM is critical: Never skip calculating $r$ for stocks. Use NTC’s bond yield for $R_f$ and NEPSE index return for $R_m$.

3. Numerical Questions:

   • Always show work: Partial credit is given for correct formulas, even if numbers are wrong.
   • Units matter: Label all answers in ₹ or % (e.g., “YTM = 10.8%”).
   • Real-World Tie: If the question mentions Ncell or NABIL, assume:
     • Ncell: $\beta =1.1$, $g=5\%$
     • NABIL: $\beta =0.9$, $g=4\%$

4. Short Answer/True-False:

   • Key Terms to Know:
     • YTM vs. Current Yield
     • DDM Assumptions (constant growth, infinite horizon)
     • EMH Forms (weak, semi-strong, strong)
   • Example Question: “A bond trading at a premium has a coupon rate higher than its YTM.” → True (premium bonds have coupon > YTM).

5. Case Studies:

   • Expect questions like: “Nepal Bank’s stock is priced at ₹200 with D0 = ₹12 and g = 6%. What’s the required return if the stock is fairly valued?” Solution: Rearrange DDM to find $r$: $$200=\frac{12\times 1.06}{r-0.06}⟹r=12.6\%$$