What it means
The situation it addresses is a bond bought for something other than its face value. Buy a $100,000 bond for $92,000 and the $8,000 difference is part of the return, but it arrives only at maturity, so it has to be spread across the years in between.
The straight line alternative simply divides the discount by the number of years. That is easy, and wrong in the same way that ignoring compound interest is wrong, because it recognises the same dollar amount on a small balance early on and a large balance later.
The constant yield approach fixes that by working from the yield to maturity. Each period's income is the opening carrying value multiplied by that yield, and the part not paid out as coupon is added to the carrying value, which is why the amounts recognised rise over time on a discount bond.
For taxable investors the method matters because it creates income before cash. Holders of original issue discount bonds are taxed each year on accreted income they have not yet received, an effect commonly described as phantom income, which makes such bonds better suited to tax sheltered accounts.
The same mechanics run in reverse on a bond bought at a premium. The carrying value is written down each period, the amortised premium reduces reported interest income, and the balance arrives at face value on the maturity date.
In practice
Real-world examples.
Example
An investor holds a corporate bond issued at a discount in a taxable brokerage account. Each year the accreted amount is reported as taxable interest income even though no cash has been received, so tax is paid from other funds until the bond matures.
Example
A company issues $10,000,000 of five year notes at 96 to make a below market coupon attractive. Its accountants amortise the $400,000 discount by the constant yield method, so reported interest expense rises modestly each year rather than staying flat.
Example
A bond fund buys a portfolio of premium priced municipal bonds. The premium is amortised on a constant yield basis, which reduces the reported income each year and prevents the fund from distributing a yield it is not really earning.
Formula
Calculation
Period accretion = (adjusted basis at the start of the period x yield to maturity) - coupon received
Adjusted basis at the end of the period = adjusted basis at the start + accretion
Take a zero coupon bond with a face value of $100,000 maturing in three years, bought to yield 10%. Since 1.10 x 1.10 x 1.10 = 1.331, the price is $100,000 / 1.331 = $75,131.48, and the total discount is $100,000 - $75,131.48 = $24,868.52. With no coupon, the entire return comes through accretion.
Year one accretion is $75,131.48 x 10% = $7,513.15, lifting the basis to $82,644.63. Year two is $82,644.63 x 10% = $8,264.46, taking the basis to $90,909.09. Year three is $90,909.09 x 10% = $9,090.91, which brings the basis to exactly $100,000.00, the amount repaid at maturity.
Straight line accretion would have reported $24,868.52 / 3 = $8,289.51 in every one of the three years. The constant yield method reports less than that in year one and more in year three, which reflects the simple fact that a larger balance is invested as time goes on.Case study
Seen in the real world.
Here is an illustrative and entirely fictional example. Harrow Bay Capital, an invented family office, bought $2,000,000 of face value zero coupon bonds maturing in three years at a 10% yield. It paid $2,000,000 / 1.331 = $1,502,629.60 and expected to record nothing until maturity.
Its accountant explained that the constant yield method required income each year. Year one accretion was $1,502,629.60 x 10% = $150,262.96, and because the office was a taxable entity, tax was payable on income no one had actually received. Over the three years the reported accretion totalled $2,000,000.00 - $1,502,629.60 = $497,370.40.
The fictional office moved its remaining zero coupon holdings into a tax deferred structure and kept coupon paying bonds in the taxable accounts. The underlying return had not changed at all; only the timing of the tax it triggered had.
Watch out
Common mistakes.
- Using straight line accretion because it is simpler, which misstates income in every period and is not accepted for most tax and reporting purposes.
- Assuming no tax is due on a zero coupon bond until it matures, when accreted income is normally taxable every year along the way.
- Forgetting to adjust the cost basis for accretion already reported, which produces a phantom capital gain when the bond is sold or redeemed.
Questions
People also ask.
Is the constant yield method the same as the effective interest method?
Yes, they describe the same calculation, with the first name more common in tax discussions and the second in accounting standards.
Does the method apply to bonds bought at a premium too?
Yes, the mechanics simply run in reverse, writing the carrying value down each period and reducing reported interest income as the premium is amortised.
What yield should be used once the bond has been bought?
The yield to maturity locked in at the purchase price, which stays fixed for the holder even as market yields move afterwards.
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