A company issued an annual-pay bond with a face value of $135,662, maturity of 4 years, and 7% coupon, while the market interest rates are 8%.
What is the present value of the interest payments on the date when the bonds are issued?
Present value of the interest payments on the date of issue is $31,453 = [I/Y = 8.00%; N = 4; PMT = $9,496.34 ($135,662 × 0.07); FV = $0; CPT → PV].
What is the unamortized discount on the date when the bonds are issued?
The unamortized discount rate at the time bonds are issued will be $4,493.
Face value of bonds = $135,662. Proceeds from bond sale = $131,168.70 [I/Y = 8.00%; N = 4; PMT = $9,496.34 ($135,662 × 0.07 ); FV = $135,662; CPT → PV]. Unamortized discount = $4,493 = ($135,662 ? $131,169).
What is the unamortized discount at the end of the first year?
The unamortized discount will decrease by $998 at the end of first year and will be $3,495.
Interest expense = ($131,169)(0.08) = $10,493.52, or $10,494. Coupon payment = ($135,662)(0.07) = $9,496. Change in discount = ($10,494 ? $9,496) = $998. Discount at the end of first year = $4,493 ? $998 = $3,495.
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