📖 长期负债：折价/溢价摊销

Financial Statement Analysis

I. Lesson Focus

This lesson explains the issuance of bonds at a premium or discount, the required effective interest method of amortization, the resulting impact on the balance sheet, income statement, and cash flow statement, and how these amounts affect financial ratios. Mastery of the effective interest method, including construction of amortization schedules for both annual and semi-annual coupon bonds as well as zero-coupon bonds, is essential.

II. The Problem

A company issues a 5-year, CNY 10 million bond with an 8% coupon when the market yield is 6%. The bond sells for a premium of CNY 850,000. Although the company pays CNY 800,000 cash interest each year, should the reported interest expense equal, exceed, or be less than this amount? Conversely, if the market yield is 10%, the bond sells at a CNY 740,000 discount. Must reported interest expense be higher than the cash coupon? How should the premium or discount be systematically amortized over the bond’s life? The answers directly affect reported net income, liability balances, interest coverage, and leverage ratios—core topics in financial statement analysis.

III. Bond Issue Price and the Nature of Premium/Discount

The issue price equals the present value of future cash flows (coupons plus principal) discounted at the market yield prevailing on the issue date.

• Coupon (cash) interest each period = Face value × Coupon rate
• Market yield (effective rate) is the discount rate that equates the PV of cash flows to the proceeds received

If coupon rate > market yield → bond sells at a premium
If coupon rate < market yield → bond sells at a discount
If coupon rate = market yield → bond sells at par

A premium represents interest collected in advance from investors; a discount represents interest that will be paid at maturity. Both must be amortized over the bond’s life so that interest expense each period equals the effective yield times the beginning carrying value.

IV. Amortization Method: Effective Interest Method

CFA Level I requires the effective interest method. The straight-line method is permitted only when the difference is immaterial, but exam questions almost exclusively test the effective interest approach.

Core Calculations: - Interest expense = Beginning carrying value × Market yield (per period) - Cash interest paid = Face value × Coupon rate (per period) - Amortization = Interest expense – Cash interest (negative for premium, positive for discount) - Ending carrying value = Beginning carrying value + Amortization (increases with discount, decreases with premium)

Premium amortization causes interest expense to be less than cash interest and carrying value to decline to face value.
Discount amortization causes interest expense to exceed cash interest and carrying value to rise to face value.

V. Financial Statement Effects

• Balance Sheet: Bonds are reported at amortized cost (carrying value). Premium increases reported liabilities; discount reduces them. Carrying value converges to face value at maturity.
• Income Statement: Interest expense is the effective interest amount, not the cash coupon.
• Cash Flow Statement: Actual cash coupon payments are classified as operating (under IFRS, can be financing) or financing cash flows. Amortization is a non-cash item and does not affect cash flow.
• Ratios: Discount amortization increases reported interest expense, lowering net income and interest coverage. Premium amortization does the opposite.

VI. Zero-Coupon Bonds

Zero-coupon bonds are issued at a deep discount. The entire discount is amortized as interest expense over the life using the effective interest method. There are no periodic cash coupon payments; only the face value is repaid at maturity.

Worked Cases

Case 1: Premium Bond — Full Effective Interest Amortization Schedule

A company issues a CNY 10,000,000, 5-year, 8% annual coupon bond when the market yield is 6%. Proceeds = CNY 10,850,000 (premium of CNY 850,000).

• Cash interest per year = 10,000,000 × 8% = 800,000
• Effective rate per year = 6%

Year 1
Interest expense = 10,850,000 × 6% = 651,000
Amortization = 651,000 – 800,000 = –149,000 (premium reduction)
Ending carrying value = 10,850,000 – 149,000 = 10,701,000

The full schedule (CNY) is:

(*final period adjusted for rounding)

Total interest expense over 5 years = CNY 3,150,000, which is CNY 850,000 less than total cash coupons paid.

Case 2: Discount Bond with Semi-Annual Coupons

A CNY 5,000,000, 4-year, 10% annual coupon bond pays interest semi-annually. Market yield is 12% (6% per semi-annual period). Issue price = CNY 4,650,000 (discount CNY 350,000).

• Semi-annual cash interest = 5,000,000 × 5% = 250,000
• Semi-annual effective rate = 6%

Period 1
Interest expense = 4,650,000 × 6% = 279,000
Amortization = 279,000 – 250,000 = +29,000
Ending carrying value = 4,650,000 + 29,000 = 4,679,000

Carrying value rises each period until it reaches CNY 5,000,000 after 8 semi-annual periods. Total interest expense over life = CNY 4,350,000 (cash coupons CNY 4,000,000 + discount amortized CNY 350,000).

Case 3: Zero-Coupon Bond Amortization

A CNY 1,000,000, 5-year zero-coupon bond is issued at CNY 680,583 when the market yield is 8% (deep discount of CNY 319,417). No periodic cash interest.

Year 1
Interest expense = 680,583 × 8% = 54,447
Ending carrying value = 680,583 + 54,447 = 735,030

Year 2
Interest expense = 735,030 × 8% = 58,802 → CV = 793,832

Year 3
Interest expense = 793,832 × 8% = 63,507 → CV = 857,339

Year 4
Interest expense = 857,339 × 8% = 68,587 → CV = 925,926

Year 5
Interest expense = 925,926 × 8% = 74,074 → CV = 1,000,000

Total interest expense equals the entire discount of CNY 319,417, recognized gradually using the effective interest method.

Traps

Key Formulas

• Bond issue price = $\sum_{t=1}^{n} \frac{C}{(1+r)^t} + \frac{F}{(1+r)^n}$
• Interest expense = Beginning carrying value × Market yield (per period)
• Amortization = Interest expense – Cash coupon (negative for premium)
• Ending carrying value = Beginning carrying value + Amortization (discount positive, premium negative)
• Total lifetime interest expense (premium bond) = Total cash coupons – Premium
• Total lifetime interest expense (discount bond) = Total cash coupons + Discount
• Zero-coupon interest expense = Beginning CV × Market yield (no cash outflow)

Practice Questions

Q1. When using the effective interest method, amortization of a bond premium:
A. Increases interest expense
B. Decreases interest expense
C. Has no effect on interest expense
D. Affects only the cash flow statement

Q2. A bond with face value CNY 1,000,000, 6% coupon, and market yield of 8% is issued at a discount for 3 years with annual payments. First-year interest expense is:
A. Exactly CNY 60,000
B. Greater than CNY 60,000
C. Less than CNY 60,000
D. Equal to issue price × 8% but size cannot be determined

Q3. Interest expense on a zero-coupon bond is:
A. Recognized only at maturity
B. Calculated each year using the coupon rate
C. Recognized each year as beginning carrying value × market yield
D. Never recognized

Q4. Under the effective interest method, the periodic interest expense on a discount bond:
A. Decreases each period
B. Increases each period
C. Remains constant
D. Increases then decreases

Q5. A company issues a premium bond. In year 1, interest expense is CNY 650,000 and cash interest paid is CNY 800,000. The carrying value at the end of year 1 will:
A. Increase by CNY 150,000
B. Decrease by CNY 150,000
C. Remain unchanged
D. Increase by CNY 650,000

Q6. The primary reason the effective interest method is preferred to straight-line is that it:
A. Is computationally simpler
B. Reflects the actual economic cost of the liability each period
C. Produces higher operating cash flow
D. Reduces income tax expense

Q7. Compared with par issuance, issuing a bond at a discount will initially cause the interest coverage ratio (EBIT/Interest) to:
A. Increase
B. Decrease
C. Remain unchanged
D. Depend on the level of EBIT

Q8. A 5-year zero-coupon bond with face value CNY 1,000,000 is issued for CNY 783,500 at a market rate of approximately 5%. First-year interest expense is closest to:
A. CNY 39,200
B. CNY 50,000
C. CNY 45,000
D. CNY 216,500

Answers

Takeaways

• Under the effective interest method, interest expense always equals beginning carrying value multiplied by the market yield at issuance—this is the fundamental rule.
• Premium amortization reduces reported interest expense below cash coupons; discount amortization increases it above cash coupons.
• Carrying value of any bond converges to face value at maturity: premium declines, discount accretes.
• The entire discount on a zero-coupon bond is recognized as interest expense over its life using the effective interest method.
• Amortization affects net income and balance-sheet debt but has no direct cash-flow impact.
• When analyzing true borrowing cost, focus on the market (effective) rate rather than the stated coupon rate.