Face Value of Bonds = $50,000,000
Issue Value of Bonds = $43,768,920
Discount on Bonds = Face Value of Bonds - Issue Value of
Bonds
Discount on Bonds = $50,000,000 - $43,768,920
Discount on Bonds = $6,231,080
Annual Coupon Rate = 8%
Semiannual Coupon Rate = 4%
Semiannual Coupon = 4% * $50,000,000
Semiannual Coupon = $2,000,000
Time to Maturity = 10 years
Semiannual Period = 20
Semiannual Amortization of Discount = Discount on Bonds /
Semiannual Period
Semiannual Amortization of Discount = $6,231,080 / 20
Semiannual Amortization of Discount = $311,554
Semiannual Interest Expense = Semiannual Coupon + Semiannual
Amortization of Discount
Semiannual Interest Expense = $2,000,000 + $311,554
Semiannual Interest Expense = $2,311,554
Answer 1 and 2.
Answer 3.
Interest Expense for Year 1 = $2,311,554
Answer 4.
Yes. Proceed from issue of bonds will always be less than the face amount when the contract rate is less than the market rate of interest.
Answer 5.
Annual Interest Rate = 10%
Semiannual Interest Rate = 5%
Present Value of Face Amount = $50,000,000 * PV of $1 (5%,
20)
Present Value of Face Amount = $50,000,000 * 0.37689
Present Value of Face Amount = $18,844,500
Present Value of Semiannual Interest Payments = $2,000,000 * PVA
of $1 (5%, 20)
Present Value of Semiannual Interest Payments = $2,000,000 *
12.46221
Present Value of Semiannual Interest Payments = $24,924,420
Price Received for the Bonds = Present Value of Face Amount +
Present Value of Semiannual Interest Payments
Price Received for the Bonds = $18,844,500 + $24,924,420
Price Received for the Bonds = $43,768,920
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