Bonds Issued at Discount and Premium — The Effective Interest Method

A bond's price is determined by the present value of all its future cash flows, discounted at the current market rate. When the coupon rate differs from the market rate, the present value calculation produces a number other than face value:

The effective interest method is built on one principle: interest expense each period = carrying value at the start of the period × the market rate locked in at issuance. The amortization amount is the difference between this interest expense and the cash coupon paid:

1. Step 1 — Calculate interest expense: Carrying value (beginning of period) × Market rate × Time fraction. For the amortization table above: Year 1, Carrying value $920 × 8% = $73.60 interest expense.
2. Step 2 — Calculate cash coupon paid: Face value × Coupon rate × Time fraction. $1,000 × 6% = $60.00 cash every year.
3. Step 3 — Discount amortization: Interest expense − Cash paid = $73.60 − $60.00 = $13.60. This amount reduces the discount (or reduces the premium for premium bonds).
4. Step 4 — New carrying value: Prior carrying value + Amortization = $920 + $13.60 = $933.60. The carrying value rises each period for discount bonds (moving toward $1,000) and falls each period for premium bonds (also moving toward $1,000).
5. By final period: The remaining discount or premium is fully amortized, and carrying value = face value = $1,000. The last period's interest expense is calculated so that the final carrying value lands exactly at par.

From the investor's perspective, buying a bond at a discount means paying less than $1,000 but receiving $1,000 at maturity — the difference is additional return on top of the coupon. The effective yield (yield to maturity) captures this total return. From the issuer's perspective, the effective interest method ensures that the interest expense reflects the true economic cost of borrowing at the original market rate:

• Discount bond: issuer reports MORE interest expense than cash paid each period. This is economically correct — the issuer received less than $1,000 in cash but must repay $1,000 at maturity. The extra amortization expense recognizes this additional cost over the bond's life, not as a lump sum at maturity.
• Premium bond: issuer reports LESS interest expense than cash paid each period. This is economically correct — the issuer received more than $1,000 in cash upfront. The excess coupon payments are partially a return of that premium, not all interest. Amortization reduces reported interest expense below the cash outflow.
• Why not the straight-line method? The straight-line method amortizes an equal discount or premium amount each period. GAAP prohibits it when the effective interest method produces a materially different result (which it almost always does). The effective method is required because it produces a constant effective interest rate — the straight-line method produces a varying effective rate, which misrepresents the economics.
• Financial statement impact: discount amortization increases interest expense above the coupon cash payment, reducing net income relative to the cash paid. Premium amortization reduces interest expense below the coupon cash, increasing net income relative to the cash paid. Analysts should always look at the cash paid (coupon), not just the reported interest expense, when evaluating debt burden.