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The issuance costs for a zero-coupon bond are no less or more than for any other bond.
The interest expense that is amortized each period must be shown as interest expense by the issuer.
In a zero-coupon bond the bond is sold at a discount from its face amount. During the life of the bond, no interest is paid, but at the maturity date the face amount of the Bond is repaid to the buyer. So, there is no annual interest payment for a zero-coupon bond.
Each period the amount of the discount at the sale of the bond needs to be amortized so even though there is no cash payment, there is an interest calculation each period.