📖 长期负债：债券发行与定价

Financial Statement Analysis

I. Lesson Focus

This lesson examines the issuance and subsequent measurement of bonds, the primary form of long-term debt. Candidates must master bond valuation using discounted cash flows, the effective interest method for amortization of discounts and premiums, the relationship between coupon rate and market yield, and the resulting effects on the balance sheet, income statement, and statement of cash flows. The focus is on fixed-rate, interest-bearing bonds under both IFRS and US GAAP.

II. The Problem

A corporation plans to issue a 10-year bond with a face value of $1,000 and a 6% annual coupon rate. At issuance, the market yield is 7%. How should the company determine the issue price? After issuance, how is interest expense recognized each year? Why does recognized interest expense differ from cash interest paid, and how do these differences affect reported liabilities, net income, and cash flows? What happens to the bond’s price if the market yield falls to 5%? This lesson solves these questions through precise present-value calculations, amortization schedules, and financial-statement impacts.

III. Bond Fundamentals and Classification

A bond is a debt security in which the issuer promises to pay periodic interest and repay principal according to a legal contract. For the issuer it is a long-term liability; for the investor it is a debt investment.

Key classifications relevant to CFA Level I: - Coupon vs. zero-coupon bonds - Fixed-rate vs. floating-rate bonds - Callable vs. non-callable bonds - Secured (mortgage) vs. unsecured (debenture) bonds

The curriculum concentrates on fixed-rate, annual or semi-annual coupon bonds.

IV. Bond Pricing Principle

The fair value of a bond equals the present value of its expected future cash flows discounted at the market yield to maturity (YTM).

Cash flows consist of: - Periodic coupon payments = Face value × Coupon rate × Payment frequency - Repayment of face value at maturity

The pricing formula for an annual-pay bond is: $$ PV = \sum_{t=1}^{n} \frac{C}{(1+r)^t} + \frac{F}{(1+r)^n} $$ where $C$ = annual coupon, $r$ = market yield per period, $n$ = number of periods, and $F$ = face value.

• When market yield = coupon rate → bond sells at par.
• When market yield > coupon rate → bond sells at a discount.
• When market yield < coupon rate → bond sells at a premium.

Market yield and bond price move inversely.

V. Issuance and Initial Recognition

Bonds are initially recognized at the issue price (fair value). The difference between proceeds and face value is recorded in a contra or adjunct account (“discount” or “premium” on bonds payable).

Carrying value (book value) = Face value – Unamortized discount (or + Unamortized premium).

VI. Subsequent Measurement: Effective Interest Method

Both IFRS and US GAAP require the effective interest method.

Interest expense each period = Beginning carrying value × Market yield at issuance
Cash interest paid = Face value × Coupon rate
Amortization of discount/premium = Interest expense – Cash interest paid

• For discount bonds, amortization increases the carrying value toward face value.
• For premium bonds, amortization decreases the carrying value toward face value.

Interest expense rises over time for discount bonds and falls for premium bonds.

VII. Impact on the Three Financial Statements

• Balance sheet: Liabilities are reported at amortized cost (carrying value). Discount bonds start below face value; premium bonds start above face value.
• Income statement: Interest expense is recognized at the effective rate and appears in finance costs. Discount bonds produce interest expense > cash paid; premium bonds produce interest expense < cash paid.
• Statement of cash flows: Cash interest paid is typically classified as an operating outflow (IFRS allows policy choice); principal repayment is a financing outflow.

Worked Cases

Case 1: Discount Bond – Basic Calculation

A company issues a 5-year, $1,000,000 face-value bond with a 5% annual coupon on 1 January 2023. The market yield on issuance is 6%. Interest is paid annually.

Step 1: Calculate issue price
Annual coupon $C$ = $1,000,000 × 5% = $50,000
$$ PV = 50,000 \times PVIFA(6\%,5) + 1,000,000 \times PVIF(6\%,5) $$ PVIFA(6%,5) = 4.2124, PVIF(6%,5) = 0.7473
Issue price = $50,000 × 4.2124 + $1,000,000 × 0.7473 = $210,620 + $747,300 = $957,920 (discount of $42,080).

Step 2: Effective-interest amortization (first three years)

Interest expense increases each year while carrying value rises toward $1,000,000.

Case 2: Premium Bond and Financial-Statement Effects

Using the same bond, suppose the market yield at issuance is 4%.

Issue price:
PVIFA(4%,5) = 4.4518, PVIF(4%,5) = 0.8219
Price = $50,000 × 4.4518 + $1,000,000 × 0.8219 = $1,044,490 (premium of $44,490).

Year 1:
Interest expense = $1,044,490 × 4% ≈ $41,780
Cash paid = $50,000
Premium amortization = $41,780 – $50,000 = –$8,220
Ending carrying value = $1,044,490 – $8,220 = $1,036,270.

Financial-statement impact:
- Income statement reports only $41,780 finance cost (less than cash outflow).
- Balance sheet shows long-term liability of $1,036,270.
- Cash-flow statement shows $50,000 operating cash outflow for interest.

Case 3: Semi-Annual Coupon Bond

A $1,000 face-value bond pays 8% annual coupon semi-annually (3-year maturity). Market yield at issuance is 10% (5% per semi-annual period).

Semi-annual coupon = $1,000 × 8% × 0.5 = $40
Number of periods = 6.

$$ PV = 40 \times PVIFA(5\%,6) + 1,000 \times PVIF(5\%,6) $$ PVIFA(5%,6) = 5.0757, PVIF(5%,6) = 0.7462
Issue price = $40 × 5.0757 + $1,000 × 0.7462 = $949.23 (discount).

First period:
Interest expense = $949.23 × 5% ≈ $47.46
Amortization = $47.46 – $40 = $7.46
Ending carrying value = $949.23 + $7.46 = $956.69.

This example demonstrates that semi-annual payments require halving both the yield and doubling the number of periods.

Traps

Key Formulas

• Bond price = $\sum \frac{\text{Coupon}}{(1+r)^t} + \frac{\text{Face}}{(1+r)^n}$
• Interest expense = Beginning carrying value × Effective (market) rate
• Amortization = Interest expense – Cash coupon payment
• Ending carrying value = Beginning carrying value + Amortization (positive for discount, negative for premium)
• Market rate > coupon rate → discount → interest expense > cash paid
• Market rate < coupon rate → premium → interest expense < cash paid
• Bond price and market yield have an inverse relationship

Practice Questions

Q1. If the market yield is higher than the coupon rate, the bond will be issued at:
A. Par
B. A premium
C. A discount
D. Cannot be determined

Q2. A 5-year bond with face value $1,000, 6% coupon paid annually, is issued when the market yield is 5%. The issue price is most likely:
A. Below $1,000
B. Equal to $1,000
C. Above $1,000
D. Cannot be calculated

Q3. Under the effective interest method, interest expense on a discount bond:
A. Remains constant
B. Decreases each period
C. Increases each period
D. Increases then decreases

Q4. Amortization of a bond premium:
A. Increases interest expense on the income statement
B. Decreases interest expense on the income statement
C. Has no effect on the income statement
D. Increases liabilities on the balance sheet

Q5. A bond is issued at $920 (face $1,000). First-year interest expense is $55 and cash coupon paid is $40. The carrying value at the end of year 2 is closest to:
A. $935
B. $945
C. $965
D. $980

Q6. Which statement is correct regarding zero-coupon bonds?
A. Issued at face value with no discount
B. Periodic interest expense equals the coupon payment
C. Carrying value increases over time to face value
D. Large cash interest outflows appear each year on the cash-flow statement

Q7. After issuance, if market interest rates decline, the bond’s amortized cost on the issuer’s balance sheet:
A. Increases immediately
B. Decreases immediately
C. Remains unchanged (except for normal amortization)
D. Depends on whether the issuer resets the coupon

Q8. When pricing a semi-annual coupon bond, the correct procedure is to:
A. Use the annual market rate and annual periods
B. Use the semi-annual market rate and semi-annual periods
C. Use the annual market rate and semi-annual periods
D. Use the semi-annual market rate and annual periods

Answers

Takeaways

• Bond fair value is the present value of future coupons and principal discounted at the market yield; price and yield move inversely.
• Under the effective interest method, interest expense equals beginning carrying value multiplied by the original market yield.
• Discount bonds generate interest expense greater than cash coupons; premium bonds generate lower expense; carrying value converges to face value by maturity.
• Balance sheet reports amortized cost, income statement reports effective interest expense, and cash-flow statement reports actual cash paid.
• Semi-annual bonds require halving the periodic rate and doubling the number of periods in all calculations.
• Zero-coupon bonds accrue interest expense throughout their life even though no cash is paid until maturity.