Accretion of Discount

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Accretion of Discount

Accretion of discount is the process by which the carrying value of a debt instrument purchased below its face (par) value increases over time, reaching par at maturity. It is an accounting and tax concept used to allocate the capital gain embedded in a discounted bond across its remaining life.

Key points

  • A bond bought at a discount has a purchase price below par. Its value must rise (accrete) to par by maturity.
  • Accretion is the mirror concept to amortization of premium (for bonds purchased above par).
  • Two common methods to account for accretion:
  • Straight-line: spreads the total accretion evenly across periods.
  • Constant-yield (effective interest): increases the basis using the bond’s yield to maturity (YTM); this is the IRS-preferred method for calculating adjusted cost basis.
  • Accretion affects reported basis, taxable income recognition, and portfolio valuation.

How accretion works

All bonds mature at par value. When a bond is bought at a discount, the difference between purchase price and par represents a capital gain that will be realized at maturity. Accretion allocates that gain over the bond’s life, increasing the investor’s adjusted basis each period until it equals par.

Example scenarios:
* Buy at par (no accretion/amortization).
* Buy at premium (amortization of premium — basis decreases toward par).
* Buy at discount (accretion — basis increases toward par).

Accounting methods

  1. Straight-line method
  2. The total discount is divided by the number of periods remaining; the same amount is added to basis each period.

  3. Simpler but less accurate when interest compounds or coupon payments vary.

  4. Constant-yield (effective interest) method

  5. Basis grows each period by the bond’s periodic yield, and the accretion for a period equals the interest income implied by that yield minus any coupon actually received.
  6. Produces increasing accretion amounts as the adjusted basis grows.
  7. Required by the IRS for computing adjusted cost basis for tax purposes.

Formula (periodic accretion, constant-yield)

Accretion for a given period (periodic) = (Beginning adjusted basis) × (periodic YTM) − Coupon payment for that period

If YTM is given as an annual rate and interest compounds more frequently, use the periodic rate (annual YTM divided by accrual periods per year or the appropriate compounding conversion).

Step-by-step example

Assume:
* Par value = $100
Coupon rate = 2% (annual coupon = $2)
 Purchase price = $75
Term = 10 years
 Compounded annually (for simplicity)

  1. Solve for annual YTM r:
    100 = 75 × (1 + r)^10
    (1 + r) = (100/75)^(1/10) ≈ 1.029184 → r ≈ 2.9184%

  2. Year 1 accretion:
    Beginning basis = $75
    Accretion1 = $75 × 2.9184% − $2 ≈ $2.1888 − $2 = $0.1888 ≈ $0.19
    New basis after year 1 = $75 + $0.1888 = $75.1888

  3. Year 2 accretion:
    Accretion2 = $75.1888 × 2.9184% − $2 ≈ $2.1934 − $2 = $0.1934 ≈ $0.19
    New basis after year 2 = $75.1888 + $0.1934 = $75.3822

Repeat until basis reaches $100 at maturity. Note that periodic accretion values gradually increase under the constant-yield method.

Practical considerations

  • For zero-coupon bonds, coupon payments are zero, so accretion equals the periodic yield applied to the adjusted basis; the bond’s imputed interest is taxed as it accrues (depending on jurisdiction and tax rules).
  • The choice of accrual period (annual, semiannual, etc.) affects the periodic rate calculation and accretion schedule.
  • Firms and investors should follow applicable accounting standards and tax regulations when selecting and applying an accretion method.
  • Accretion affects reported yield, adjusted cost basis, and realized gain or loss at sale or maturity.

Conclusion

Accretion of discount systematically allocates the gain on a discounted bond across its life, bringing the bond’s adjusted basis to par at maturity. The constant-yield method is more accurate and typically required for tax reporting, while straight-line is simpler but less precise. Understanding accretion is important for valuation, tax compliance, and assessing true investment return.