28.2 Discount & Premium Bonds

For a premium bond, interest expense is

less than the coupon payment (yield < coupon rate). The difference between interest expense and the coupon payment is the amortization of the premium. The premium amortization is subtracted each period from the bond liability on the balance sheet. Thus, interest expense will decrease over time as the bond liability decreases.

Zero-coupon bonds

make no periodic interest payments. A zero-coupon bond, also known as a pure-discount bond, is issued at a discount from its par value and its annual interest expense is implied, but not explicitly paid. The actual interest payment is included in the face value that is paid at maturity. The effects of zero-coupon bonds on the financial statements are qualitatively the same as any discount bond, but the impact is larger because the discount is larger.

The purposes of amortizing the discount are to

(1) increase the book value of the bond liability over time, and (2) increase interest expense so that the coupon payment plus discount amortization is approximately equal to the interest expense that would have prevailed had the bond been issued at par. Conversely, amortizing a premium decreases the book value of the bond liability over time and decreases interest expense.

On December 31, 20X2, a company issued a 3-year, 10% annual coupon bond with a face value of $100,000. Calculate the book value of the bond at year-end 20X2, 20X3, and 20X4, and the interest expense for 20X3, 20X4, and 20X5, assuming the bond was issued at a market rate of interest of (a) 10%, (b) 9%, and (c) 11%.

(a) Bond issued at par. If the market rate of interest at issuance is 10%, the book value of the bonds will always be $100,000, and the interest expense will always be $10,000, which is equal to the coupon payment of 0.10 × $100,000. There is no discount or premium to amortize. (b) Premium bond. If the market rate of interest is 9%, the present value of the cash payments (a 3-year annuity of $10,000 and a payment in three years of $100,000) is $102,531: N = 3; PMT = 10,000; FV = 100,000; I/Y = 9; CPT → PV = −$102,531 (c) Discount bond. If the market rate of interest is 11%, the present value of the cash payments (a 3-year annuity of $10,000 and a payment in three years of $100,000) is $97,556. N = 3; PMT = 10,000; FV = 100,000; I/Y = 11; CPT → PV = $97,556

On December 31, 20X0, Vine Corp. issues a three-year, zero-coupon bond with a par value of $1,000 when the market interest rate is 12%. Using the effective interest method and an annual periodicity, calculate interest expense and the book value of the bond liability at the end of 20X1, 20X2, and 20X3.

Cash received at issuance—and the initial book value of the bond liability—is $711.78:N = 3; I/Y = 12; PMT = 0; FV = 1,000; CPT → PV = -711.78

The effective interest rate method of amortizing a discount or premium is required under

IFRS

While coupon interest is paid in cash, amortization is

a noncash item.

Firms that follow IFRS can report cash interest paid as

either an operating or financing cash flow.

or a discount bond, interest expense is

greater than the coupon payment (yield > coupon rate). The difference between interest expense and the coupon payment is the amortization of the discount. The amortization of the discount each period is added to the bond liability on the balance sheet. Therefore, interest expense will increase over time as the bond liability increases.

When presenting the cash flow statement using the indirect method

net income must be adjusted to remove the effects of any amortization of a discount or premium in order to calculate cash flow from operations.

For a bond issued at a premium or discount, interest expense and coupon interest payments are

not equal. Interest expense includes amortization of any discount or premium.

Firms that follow U.S. GAAP must report cash interest paid in the cash flow statement as an

operating cash flow

Under U.S. GAAP, the effective interest rate method is preferred, but

straight-line method is allowed if the results are not materially different. The straight-line method is similar to straight-line depreciation in that the total discount or premium at issuance is amortized by equal amounts each period over the life of the bond.

Using the effective interest rate method, interest expense is equal to

the book value of the bond liability at the beginning of the period, multiplied by the bond's yield at issuance.

In the case of a discount bond, the coupon is

too low relative to the required rate of return of the market.