Bond Valuation & Cost of Capital: Bonds, YTM, WACC, Debt Cost

Core Concepts

1. What is a Bond?

A bond is a debt instrument issued by a company or government to raise capital. Investors lend money to the issuer in exchange for periodic interest payments (coupons) and repayment of the face value (par value) at maturity.

Key Terms

---

2. Types of Bonds

A. Coupon Bonds

• Pay fixed periodic interest (coupons) + face value at maturity.
• Example: A 10-year bond with a 12% coupon rate and Rs 1,000 face value pays Rs 120/year (Rs 10/month) + Rs 1,000 at maturity.

B. Zero-Coupon Bonds

• No periodic interest payments; sold at a discount and redeemed at face value.
• Example: A zero-coupon bond with Rs 1,000 face value, 10-year maturity, and Rs 500 market price implies an implicit return of ~14.87% per year.

C. Perpetual Bonds

• No maturity date; pay forever (rare, but used in some sovereign bonds).
• Example: A perpetual bond with a 15% coupon rate and Rs 1,000 face value pays Rs 150/year indefinitely.

Comparison Table

---

3. Bond Valuation

Bond prices are determined by discounting future cash flows (coupons + face value) to present value using the required rate of return (YTM).

Formula for Bond Price

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

• $P$ = Market price
• $C$ = Annual coupon payment
• $F$ = Face value
• $r$ = Yield to maturity (YTM)
• $n$ = Years to maturity

Worked Example: Ncell’s Bond Valuation

Given:

• Face Value (F) = Rs 1,000
• Coupon Rate = 10% → Annual Coupon (C) = Rs 100
• Maturity (n) = 5 years
• Market Price (P) = Rs 950
• Find: Yield to Maturity (YTM)

Solution: We solve for $r$ in: $$950=\frac{100}{(1+r{)}^1}+\frac{100}{(1+r{)}^2}+\frac{100}{(1+r{)}^3}+\frac{100}{(1+r{)}^4}+\frac{100+1000}{(1+r{)}^5}$$ *(This requires trial-and-error or financial calculator → YTM ≈ 11.25%)*

Mermaid Diagram: Bond Cash Flows

---

4. Cost of Debt (Pre- and After-Tax)

The cost of debt is the YTM of the company’s bonds, adjusted for taxes (since interest is tax-deductible).

Formula

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

Worked Example: Garudnahani Company (Exam Question)

Given:

• Zero-coupon bond, 10-year maturity, selling at Rs 500, face value Rs 1,000, tax rate = 40%.
• Find: After-tax cost of debt.

Solution:

1. Calculate YTM (Pre-tax Cost of Debt): $$500=\frac{1000}{(1+r{)}^{10}}⟹r=7.18\%\text{ (YTM)}$$
2. After-tax Cost: $$7.18\%\times (1-0.40)=4.31\%$$

Why?

• Ncell issues bonds at a discount to attract investors → higher YTM.
• Nepal Rastra Bank (NRB) bonds are low-risk, so their YTM is closer to government bond rates (~8-10%).

---

5. Weighted Average Cost of Capital (WACC)

WACC is the average cost a company pays to finance its operations, weighted by the proportion of debt and equity.

Formula

$$WACC=\left(\frac{E}{V}\times Re\right)+\left(\frac{D}{V}\times Rd\times (1-T)\right)$$

• $E$ = Market value of equity
• $D$ = Market value of debt
• $V=E+D$ = Total capital
• $Re$ = Cost of equity (from CAPM or dividend growth model)
• $Rd$ = Cost of debt (after-tax)
• $T$ = Tax rate

Worked Example: Kathmandu Retail Shop

Given:

• Debt (D) = Rs 5,000,000 (10-year bond, 12% coupon, YTM = 11%)
• Equity (E) = Rs 10,000,000 (cost of equity = 15%)
• Tax Rate (T) = 25%

Solution:

1. After-tax Cost of Debt: $$Rd=11\%\times (1-0.25)=8.25\%$$
2. WACC Calculation: $$WACC=\left(\frac{10M}{15M}\times 15\%\right)+\left(\frac{5M}{15M}\times 8.25\%\right)=13.13\%$$

Mermaid Diagram: WACC Components

---

## In the Real World

1. Ncell’s Bond Issuance

   • Ncell issues corporate bonds to raise capital for expansion.
   • Zero-coupon bonds are used when the company wants to avoid periodic interest payments (common in telecom sectors).
   • YTM calculation helps investors decide if the bond is undervalued or overvalued.

2. Nepal Rastra Bank (NRB) Bonds

   • NRB issues government bonds with fixed coupon rates (e.g., 9-12%).
   • WACC is used by NRB to determine optimal funding mix (debt vs. equity).

3. NEPSE-Listed Companies (e.g., Himalayan Bank, Global IME)

   • Companies like Himalayan Bank use WACC to evaluate new projects (e.g., expanding ATMs in Pokhara).
   • Cost of debt affects loan interest rates (e.g., Nabil Bank’s SME loans at ~12-14%).

---

## Exam Tip

✅ For YTM calculations:

• Use financial calculators (or Excel’s RATE function).
• Zero-coupon bonds simplify to: $$P=\frac{F}{(1+r{)}^n}⟹r={\left(\frac{F}{P}\right)}^{1/n}-1$$

✅ For WACC:

• Always adjust debt for taxes (since interest is tax-deductible).
• Memorize the formula and practice numericals (exams often test this).

✅ Common Mistakes to Avoid:

• Ignoring tax adjustments in cost of debt.
• Mixing nominal and real rates (unless inflation is given).
• Forgetting to annualize (if payments are semi-annual, adjust periods).

---

Final Note: Bond valuation and WACC are core to financial decision-making—whether it’s Ncell expanding 4G networks or a Kathmandu shop taking a bank loan. Master these, and you’ll ace the exam and impress future employers! 🚀