28 Sep Amortization

Bond Premiums

When purchasing a bond with a coupon rate above the market rate, investors must pay a premium to entice the seller to part with the high coupon. The amount of premium paid is a function of time to maturity, the bond’s coupon rate, and the yield at which the bond is purchased. An Example Consider the following example. On May 20, 2016, an investor purchases $100,000 par value of a bond with a coupon of 8.125% and a maturity of May 20, 2019. At a yield to maturity of 2.87%, the investor pays a premium price of $115, meaning the total cost of the purchase is $115,000.

If the investor holds the bond until it matures, the cashflow from the investment will be six coupon payments of $4,062.50 insemi-annual installments from the time of purchase along with the return of the $100,000 par value of the bond at maturity. While investors may like the high coupon payments, they are less happy about the disappearing premium, as they paid $115,000 at the time of purchase and only receive back $100,000 at maturity.

Amortization of Premium

In the above example, the investor buys a bond whose coupon, 8.125%, far exceeds the market rate of 2.87%. To better understand the true economic impact of the investment, the investor must adjust the semi-annual coupon cashflow received by amortizing a portion of the $15,000 premium paid. The amortization amounts to $5,000 per year ($15,000/3 years to maturity), or $2,500 semi-annually. The semi-annual amortization has two effects, as illustrated in Table 1. First, the amount of premium amortized can be viewed as an offset to the coupon payment, reducing the economic impact to the investor to $1,562.50 ($4,062.50—$2,500). Second, the negative impact to income is offset by a reduction in the cost basis of the bond by the amount of the amortization.

Date	Coupon Payment	Amortization	Adjusted Cost
November 16	$4,062.50	$2,500.00	$112,500.00
May 17	$4,062.50	$2,500.00	$110,000.00
November 17	$4,062.50	$2,500.00	$107,500.00
May 18	$4,062.50	$2,500.00	$105,000.00
November 18	$4,062.50	$2,500.00	$102,500.00
May 19	$4,062.50	$2,500.00	$100,000.00