## What Is the Constant Yield Method?

The constant yield method is a way to calculate the accrued discount of a bond that trades in the secondary market.

It is an alternative to the ratable accrual method, and although it usually results in a lesser accrual of a discount than the latter method, it requires a more complex calculation.

## Understanding the Constant Yield Method

For tax purposes, either the ratable accrual method or the constant yield method can be used to calculate the yield on a discount bond or zero-coupon bond.

The ratable accrual method calculates the amount of income or expenses accrued rather than the amount paid. It results in a greater accrual of a discount than the constant yield method.

The ratable accrual method is calculated by dividing the market discount of the bond by the number of days from the bond's maturity date less the purchase date, multiplied by the number of days the investor actually held the bond.

The constant yield calculation is more complex. The constant yield amount is calculated by multiplying the adjusted basis by the yield at issuance and then subtracting the coupon interest.

This method is also known as the effective or scientific method of amortization.

### How Zero-Coupon Bonds Work

A zero-coupon bond pays no interest or coupon over the life of the bond. Instead, the bonds are issued at a discount to their face values, and bond investors are repaid the face values at maturity. The difference between the price paid and the amount repaid is the investor's profit.

### Key Takeaways

- Zero-coupon bonds don't pay coupons but the IRS requires that their owners report the imputed interest as income.
- Either the constant yield method or the ratable accrual method can be used.
- The constant yield method calculates the value of a zero-coupon bond at a given point of time before its maturity.

For example, a zero-coupon bond with a face value of $100 might be purchased for $75. On the maturity date, the bondholder is repaid the full $100 face value of the bond.

Even though these bonds don’t pay coupons, the Internal Revenue Service (IRS) requires that zero-coupon bondholders still report the imputed interest earned on the bond as income for tax purposes. Using the constant yield method, the bond owner can determine how much can be deducted each year.

### How to Calculate Constant Yield

The constant yield method is a method of accretion of bond discounts, which translates to a gradual increase over time, given that the value of a discount bond increases over time until it equals the face value.

The first step in the constant yield method is determining the yield to maturity (YTM). This is the yield that will be earned on a bond if it is held until maturity. For example, a zero-coupon bond is issued for $75 with a 10-year maturity date. The yield to maturity depends on how frequently the yield is compounded.

The IRS allows the taxpayer some flexibility in determining which accrual period to use for computing yield. For simplicity's sake, let’s assume it is compounded annually. For this example, the YTM can be calculated as:

$100 par value = $75 x (1 + r)^{10}

$100/$75 = (1 + r)^{10}

1.3333 = (1 + r)^{10}

r = 2.92%

Let’s assume the coupon rate on this bond is 2% (assuming that similar interest-paying bonds pay 2%). After one year (remember we’re compounding annually), the accrual on the bond will be:

Accrual_{period1} = ($75 x 2.92%) – Coupon interest

*Since coupon interest = 2% x $100 = $2*

Accrual_{ period1} = $2.19 – $2

Accrual_{ period1} = $0.19

The purchase price of $75 represents the bond’s basis at issuance. However, in subsequent periods, the basis becomes the purchase price plus accrued interest. For example, after year 2, the accrual can be calculated as:

Accrual_{ period2} = [($75 + $0.19) x 2.92%] - $2

Accrual_{ period2} = $0.20

Periods 3 to 10 can be calculated in a similar manner, using the former period’s accrual to calculate the current period’s basis.

Intuitively, a discount bond has a positive accrual. In other words, the basis accretes.

### Calculating Interest in a Premium Bond

Similarly, interest in a premium bond can also be determined using the constant yield method. A premium bond is issued at a price higher than the par value of the bond. The value of the bond decreases over time until it reaches par at maturity.

The imputable interest on a premium bond is negative and the constant yield method amortizes (as opposed to accretes) the bond premiums.

A premium bond will, thus, have a negative accrual.

The decision to use either the constant yield method or ratable accrual method must be made at the time the bond is purchased. This decision is irreversible and is similar to the method the IRS prescribes to computer-taxable original issue discount (OID) as outlined in IRS Publication 1212.