Valuation of Bonds & Stocks: Methods, Models & Real Cases

TAKEAWAYS:

• Bonds are valued using discounted cash flows (coupon payments + face value) and YTM (Yield to Maturity) to reflect market interest rates.
• Stocks are valued via dividend discount models (DDM) or free cash flow to equity (FCFE), adjusted for growth and risk.
• Market multiples (P/E, P/B) provide quick but relative valuations, while DCF gives intrinsic value.
• Bond pricing is sensitive to interest rates (inverse relationship), while stock pricing depends on future earnings and dividends.
• Real-world applications: NEPSE uses P/E ratios for stock valuation; banks use bond YTM for loan pricing; Pathao’s valuation relies on FCFE.

1. Bond Valuation: The Core Concept

Bonds are fixed-income securities where an investor lends money to a company/government in exchange for periodic interest payments (coupons) and repayment of the face value at maturity. Their price is determined by:

• Coupon rate (fixed % of face value paid annually/semi-annually).
• Market interest rate (YTM) – the rate investors demand for similar-risk bonds.
• Time to maturity – longer maturities are riskier (higher YTM).

How Bond Pricing Works

The intrinsic value of a bond is the present value (PV) of its future cash flows: $$\text{Bond Price}=\sum _{t=1}^n\frac{\text{Coupon Payment}}{(1+\text{YTM}{)}^t}+\frac{\text{Face Value}}{(1+\text{YTM}{)}^n}$$ Where:

• $n$ = number of periods (years).
• Coupon Payment = Face Value × Coupon Rate.

Key Observations

• If YTM > Coupon Rate, bond trades at a discount (price < face value).
• If **YTM < Coupon Rate**, bond trades at a **premium** (price > face value).
• If YTM = Coupon Rate, bond trades at par (price = face value).

Worked Example: NTC Bond Valuation

Assume Nepal Telecom (NTC) issues a 10-year bond with:

• Face Value (FV) = NPR 1,000
• Coupon Rate = 8% annually (paid at year-end)
• Market YTM = 10%

Step 1: Calculate Annual Coupon Payment $$\text{Coupon Payment}=1,000\times 8\%=\text{NPR 80}$$

Step 2: Discount Cash Flows to Present Value Use the formula or a financial calculator. The bond’s fair value is: $$\text{Bond Price}=\frac{80}{(1.10{)}^1}+\frac{80}{(1.10{)}^2}+\cdots +\frac{80+1,000}{(1.10{)}^{10}}=\text{NPR 856.01}$$ Since **856.01 < 1,000**, the bond trades at a **discount** (YTM > coupon rate).

flowchart TD
    A["Bond Issuer\n(NTC)"] -->|"Issues Bond"| B["Investor\n(Buys at NPR 856.01)"]
    B -->|"Receives Coupons"| C["NPR 80/year"]
    B -->|"Receives Face Value"| D["NPR 1,000 at Maturity"]
    C & D -->|"Discounted at 10%"| E["Present Value = NPR 856.01"]

2. Stock Valuation: Dividend Discount Model (DDM)

Stocks represent ownership in a company. Unlike bonds, they have no maturity and pay dividends (not guaranteed). The intrinsic value of a stock is the present value of all future dividends.

Types of DDM

Where:

• $P_0$ = Current stock price
• $D_1$ = Next year’s dividend
• $r$ = Required return (discount rate, often = cost of equity)
• $g$ = Constant growth rate of dividends
• FCFE = Free Cash Flow to Equity (after debt obligations)

Worked Example: NMB Bank Stock Valuation

Assume NMB Bank pays:

• Last dividend ($D_0$) = NPR 12
• Dividend growth rate ($g$) = 5% (stable)
• Required return ($r$) = 12% (market expectation)

Step 1: Calculate Next Dividend ($D_1$) $$D_1=D_0\times (1+g)=12\times 1.05=\text{NPR 12.60}$$

Step 2: Apply Gordon Growth Model $$P_0=\frac{12.60}{(0.12-0.05)}=\frac{12.60}{0.07}=\text{NPR 180}$$ Interpretation: NMB’s stock should trade at NPR 180 if it grows dividends at 5% and investors demand 12% return.

flowchart TD
    A["NMB Bank"] -->|"Pays Dividend"| B["D0 = NPR 12"]
    B -->|"Grows at 5%"| C["D1 = NPR 12.60"]
    C -->|"Discounted at 12%"| D["PV = NPR 180"]
    D -->|"Market Price"| E["If P0 > 180, Overvalued\nIf P0 < 180, Undervalued"]

3. Free Cash Flow to Equity (FCFE) Model

Used when dividends are unstable (e.g., tech firms like F1Soft or e-commerce like Daraz Nepal). FCFE is cash available to equity holders after:

1. Operating expenses
2. Capital expenditures (CapEx)
3. Debt repayments

Formula: $$\text{FCFE}=\text{Net Income}+\text{Depreciation}-\text{CapEx}-\Delta \text{Working Capital}+\text{Net Borrowing}$$

Worked Example: Daraz Nepal Valuation

Assume Daraz Nepal has:

• Net Income (2023) = NPR 500 million
• Depreciation = NPR 50 million
• CapEx = NPR 300 million
• ΔWorking Capital = NPR 20 million (increase)
• Net Borrowing = NPR 100 million (new debt)
• Growth Rate (g) = 10%
• Cost of Equity (r) = 15%

Step 1: Calculate FCFE $$\text{FCFE}=500+50-300-20+100=\text{NPR 330 million}$$

Step 2: Apply FCFE Model (Gordon Growth Extension) $$P_0=\frac{{\text{FCFE}}_1}{(r-g)}=\frac{330\times 1.10}{(0.15-0.10)}=\frac{363}{0.05}=\text{NPR 7,260 million}$$ Interpretation: Daraz’s equity value is NPR 7.26 billion (if growth and risk assumptions hold).

4. Market Multiples Approach

Instead of forecasting cash flows, compare similar companies using ratios like:

• P/E (Price-to-Earnings): $\frac{\text{Market Price}}{\text{Earnings per Share (EPS)}}$
• P/B (Price-to-Book): $\frac{\text{Market Price}}{\text{Book Value per Share}}$
• EV/EBITDA: $\frac{\text{Enterprise Value}}{\text{EBITDA}}$

Comparison Table: NEPSE vs. Global Stocks

5. Real-World Applications

📱 eSewa & Khalti: Valuation of Fintech Stocks

• If eSewa were publicly traded (like PayPal), its valuation would use:
  • FCFE Model: High growth in transaction volumes → high FCFE.
  • P/S (Price-to-Sales): Common for unprofitable tech firms (e.g., F1Soft).
• Example: If eSewa’s revenue = NPR 20 billion and P/S ratio = 5x (like global fintechs), its value would be NPR 100 billion.

🚗 Pathao: Ride-Hailing Valuation

• Pathao (like Uber) is valued using:
  • DCF (Discounted Cash Flow): Future cash flows from rides, ads, and commissions.
  • Comparable Company Analysis: Compared to Grab (Southeast Asia) or Ola (India).
• Worked Example:
  • Projected FCFE (next 5 years) = NPR 5 billion/year.
  • Terminal Growth Rate = 3% (long-term).
  • Discount Rate = 18% (high risk).
  • Terminal Value = $\frac{5\times 1.03}{0.18-0.03}=\text{NPR 35.35 billion}$.
  • Present Value of FCFE (Years 1–5) = NPR 12.3 billion (discounted).
  • Total Value = NPR 47.65 billion.

🏦 Banks: Bond YTM for Loan Pricing

• NMB Bank issues 5-year bonds at 9% YTM.
• If a customer wants a 5-year loan, the bank may set the loan interest rate = YTM + risk premium.
• Example: If YTM = 9% and customer risk = 2%, loan rate = 11%.

6. Exam Tip: How to Score Full Marks

1. Show All Steps: Never skip calculations. For bonds, write:

   • Coupon payment formula.
   • Discounting steps (use tables or calculator steps).
   • Final PV with units (NPR).

2. Compare Models: If asked to value a stock, compare DDM and FCFE and justify which is better.

3. Real-World Link: Always relate to NEPSE companies (NMB, NTC, F1Soft) or global firms (Apple, Coca-Cola).

4. Graphs > Words: Draw a DCF timeline for bonds/stocks. Example:

   timeline
     title Bond Cash Flows (NTC Example)
     2024 : Coupon NPR 80
     2025 : Coupon NPR 80
     ...
     2033 : Coupon NPR 80 + Face Value NPR 1,000

5. Common Pitfalls:

   • Forgetting to grow dividends in DDM ($D_1=D_0\times (1+g)$).
   • Misapplying YTM vs. Coupon Rate in bond pricing.
   • Ignoring tax effects (bonds: after-tax YTM; stocks: dividend tax).

Final Note: Master one numerical example per method (bond, DDM, FCFE) and one real-world case (NMB, Pathao, eSewa). Examiners love clear tables, labeled diagrams, and Nepali business examples.