Chapter 9: Valuation of Securities
Security valuation determines the intrinsic or fair value of financial instruments — bonds, preference shares, and equity shares. Understanding valuation is essential for investment decisions, mergers, IPO pricing, and financial analysis. This chapter covers bond valuation, stock valuation models, and yield calculations.
9.1 Bond Valuation
Bond Value = PV of Interest Payments + PV of Par Value at Maturity
V = I × PVIFA(Kd,n) + M × PVIF(Kd,n)
Where: I = annual interest (coupon), M = maturity/par value, Kd = required rate of return, n = years to maturity
Bond Valuation Example
Data: Par value = NPR 1,000, Coupon rate = 12%, Maturity = 5 years, Required return = 10%
Annual coupon = 1,000 × 12% = NPR 120
V = 120 × PVIFA(10%,5) + 1,000 × PVIF(10%,5)
V = 120 × 3.7908 + 1,000 × 0.6209
V = 454.90 + 620.92 = NPR 1,075.82
Since coupon rate (12%) > required return (10%), bond trades at a premium.
Bond Pricing Rules
| Condition | Bond Price | Reason |
|---|---|---|
| Coupon Rate > Required Return | Premium (above par) | Bond offers more than market requires |
| Coupon Rate = Required Return | Par value | Bond offers exactly what market requires |
| Coupon Rate < Required Return | Discount (below par) | Bond offers less than market requires |
Yield to Maturity (YTM)
Approximate YTM = [I + (M-V)/n] / [(M+V)/2]
Example: Par NPR 1,000, Coupon 10%, Market price NPR 900, Maturity 5 years
YTM ≈ [100 + (1000-900)/5] / [(1000+900)/2] = [100+20]/950 = 120/950 = 12.63%
9.2 Preference Share Valuation
Vp = Dp / Kp (perpetuity formula since preference shares typically have no maturity)
Example: Preference dividend = NPR 12/share, Required return = 10%
Vp = 12 / 0.10 = NPR 120
9.3 Equity Share Valuation
Dividend Discount Model (DDM)
| Model | Formula | When to Use |
|---|---|---|
| Zero Growth | P0 = D / Ke | Constant dividend forever |
| Constant Growth (Gordon) | P0 = D1 / (Ke - g) | Dividend grows at constant rate g |
| Variable/Multi-Stage Growth | PV of each dividend individually + PV of terminal value | High growth initially, then stable |
Gordon Growth Model Examples
Constant Growth: D0 = NPR 10, g = 8%, Ke = 14%
D1 = 10 × 1.08 = NPR 10.80
P0 = 10.80 / (0.14 - 0.08) = 10.80 / 0.06 = NPR 180
Two-Stage Growth: D0 = NPR 5, g1 = 20% for 3 years, then g2 = 8% forever. Ke = 15%.
D1 = 5×1.20 = 6.00, D2 = 6×1.20 = 7.20, D3 = 7.20×1.20 = 8.64
D4 = 8.64×1.08 = 9.33 (terminal dividend at stable growth)
Terminal value at year 3 = D4/(Ke-g2) = 9.33/(0.15-0.08) = 133.29
P0 = 6/1.15 + 7.20/1.15² + 8.64/1.15³ + 133.29/1.15³
P0 = 5.22 + 5.45 + 5.68 + 87.65 = NPR 104.00
9.4 P/E Ratio Approach
Share Price = EPS × P/E Ratio
If a company has EPS of NPR 25 and the industry P/E is 12, estimated share price = 25 × 12 = NPR 300.
9.5 Valuation in Nepal (NEPSE)
Nepal's stock market (NEPSE) lists ~230 companies across banking, insurance, hydropower, manufacturing, and other sectors. Key valuation metrics used by Nepali investors: P/E ratio (most popular), book value per share, dividend yield, and market capitalization. NEPSE tends to be sentiment-driven with limited fundamental analysis by retail investors. Understanding intrinsic valuation using DCF/DDM helps BBS graduates make informed investment decisions.
9.6 Semi-Annual Bond Valuation
Many bonds pay interest semi-annually. The valuation formula adjusts: divide annual coupon by 2, divide required return by 2, multiply years by 2.
Example: Par = NPR 1,000, Coupon = 12% (semi-annual payments), Maturity = 4 years, Required return = 10%
Semi-annual coupon = 1,000 × 12%/2 = NPR 60
Semi-annual required return = 10%/2 = 5%
Number of periods = 4 × 2 = 8
V = 60 × PVIFA(5%,8) + 1,000 × PVIF(5%,8)
V = 60 × 6.4632 + 1,000 × 0.6768
V = 387.79 + 676.84 = NPR 1,064.63
9.7 Relationship Between Bond Price and Interest Rate
| Required Return | Bond Price (12% coupon, 5yr) | Relationship |
|---|---|---|
| 8% | NPR 1,159.71 | Premium (coupon > required) |
| 10% | NPR 1,075.82 | Premium |
| 12% | NPR 1,000.00 | Par (coupon = required) |
| 14% | NPR 931.34 | Discount |
| 16% | NPR 869.17 | Discount (coupon < required) |
Key Observations: (1) Bond prices move inversely to interest rates. (2) As maturity approaches, bond price converges to par value. (3) Longer maturity bonds are more sensitive to rate changes. (4) This is crucial for Nepal's government bond market — when NRB raises rates, existing bond prices fall.
9.8 Free Cash Flow Valuation Model
For companies that don't pay dividends (or pay irregular dividends), the Free Cash Flow to Equity (FCFE) model is used:
V = Σ [FCFE_t / (1+Ke)^t] + Terminal Value / (1+Ke)^n
Where FCFE = Net Income - Net Capital Expenditure - Change in Working Capital + New Debt - Debt Repayment
Example: Valuing a Nepali Hydropower Company
FCFE projections: Year 1 = NPR 5 crore, Year 2 = 7 crore, Year 3 = 10 crore. After Year 3, stable growth at 5%. Ke = 14%.
Terminal Value at Year 3 = FCFE4 / (Ke-g) = (10 × 1.05) / (0.14-0.05) = 10.5/0.09 = NPR 116.67 crore
V = 5/1.14 + 7/1.14² + 10/1.14³ + 116.67/1.14³
V = 4.39 + 5.39 + 6.75 + 78.74 = NPR 95.27 crore
If company has 1 crore shares, intrinsic value = 95.27/1 = NPR 95.27 per share
If market price is NPR 80: Undervalued — buy signal
9.9 Practical Valuation Issues in NEPSE
| Issue | Description | Impact on Valuation |
|---|---|---|
| Limited Market Efficiency | NEPSE is semi-efficient at best; information asymmetry exists | Market prices may not reflect intrinsic value; fundamental analysis valuable |
| Bonus Share Obsession | Investors overvalue bonus shares (which don't change total value) | Companies issuing bonus shares see price jumps despite no value creation |
| Low Floating Shares | Promoters hold 51%+; limited shares trade | Low liquidity causes price volatility |
| Herd Behavior | Investors follow trends rather than fundamentals | Bubbles and crashes more likely |
| Limited Information | Many companies provide minimal financial disclosure | Valuation models require assumptions; increases uncertainty |
9.10 Valuation Ratios for NEPSE Analysis
Example: Comparing Two NEPSE-Listed Banks
| Metric | Bank A | Bank B | Better |
|---|---|---|---|
| Market Price | NPR 500 | NPR 300 | — |
| EPS | NPR 35 | NPR 30 | A |
| P/E Ratio | 14.3x | 10.0x | B (cheaper) |
| Book Value | NPR 250 | NPR 200 | A |
| P/B Ratio | 2.0x | 1.5x | B (cheaper) |
| DPS | NPR 15 | NPR 20 | B |
| Dividend Yield | 3.0% | 6.7% | B |
| ROE | 14% | 15% | B |
Analysis: Bank B appears more attractive — lower P/E, lower P/B, higher dividend yield, and higher ROE. It offers more value per rupee invested. However, Bank A may command a premium due to larger size, better brand, or growth prospects. Always look beyond numbers at qualitative factors.
Practice Questions
Short Answer:
1. How is a bond valued? State the formula.
2. What determines whether a bond trades at premium or discount?
3. Calculate YTM approximation for a bond.
4. State Gordon's Growth Model and its assumptions.
5. How is the P/E ratio used for valuation?
Long Answer:
6. Bond: Par NPR 1,000, coupon 14%, maturity 6 years, required return 12%. Calculate bond value. What if required return rises to 16%? (15 marks)
7. D0=NPR 8, growth 15% for 3 years then 6% forever, Ke=13%. Calculate intrinsic value using two-stage DDM. (15 marks)
8. Compare bond valuation and equity valuation methods. Why is equity valuation more complex? (15 marks)
9. Current market price of a share is NPR 500. D0=NPR 20, g=10%, Ke=15%. Is the stock overvalued or undervalued? Should you buy? (15 marks)
10. Discuss the valuation methods used by investors in NEPSE. What improvements are needed in Nepal's stock market valuation practices? (15 marks)
Exam Tips: ✓ Bond valuation using PVIFA and PVIF is always asked ✓ Gordon model is the most important equity valuation formula ✓ Two-stage growth model is a common long question ✓ YTM approximation formula must be memorized ✓ Know premium/discount/par rules for bonds