# FRA: Bonds (Issuer's Perspective)

Hi guys. I hope someone can assist me in some subtleties here. When computing for ending book values (beginning BV + interest expense - coupon payments), what’s the logic behind adding back the interest expense instead of subtracting it? I mean, it’s an expense. right? It’s an easy computation but I’m looking for the reasoning behind that.

Thanks

Think of the beginning balance + interest as the balance owing to the lender. It’s your coupon payment plus the payment of the face amount on the maturity date that actually reduce your balance owing.

interest expense = coupon payments + amortization of premium/discount

If interest expense > coupon payments, we’re amortizing a discount, so ending BV of (net) bonds payable is greater than beginning BV. Interest expense − coupon payments > 0, and

ending BV = beginning BV + interest expense − coupon payments

If interest expense < coupon payments, we’re amortizing a premium, so ending BV of (net) bonds payable is less than beginning BV. Interest expense − coupon payments < 0, and

ending BV = beginning BV + interest expense − coupon payments

It’s because only the proportion of the coupon payments excluding the interest payment reduces(increases) the principle value(ending BV).

So think of it as

Beginning Balance - (coupon payment - interest payment),

which becomes

Beginning Balance + interest payment - coupon payment = Ending Balance

Wish it helps