Question

On January 1, 2021, Water Wonderland issues $20 million of 5% bonds, due in nine years, with interest payable semiannually on June 30 and December 31 each year. Use Table 2 and Table 4. 1. If the market rate is 4%, will the bonds issue at face amount, a discount, or a premium? Calculate the issue price. (Round "PV Factor" to 5 decimal places. Round other intermediate calculations and final answer to the nearest dollar amount. Enter your answer in dollars, not in millions.) The bonds issue at and the issue price is 2. If the market rate is 5%, will the bonds issue at face amount, a discount, or a premium? Calculate the issue price. (Round "PV Factor" to 5 decimal places. Round other intermediate calculations and final answer to the nearest dollar amount. Enter your answer in dollars, not in millions.) The bonds issue at and the issue price is 3. If the market rate is 6%, will the bonds issue at face amount, a discount, or a premium? Calculate the issue price. (Round "PV Factor" to 5 decimal places. Round other intermediate calculations and final answer to the nearest dollar amount. Enter your answer in dollars, not in millions.) The bonds issue at and the issue price is

Answer 1

Solution: Calculation of Issue Price of Bond at Different rates: Face Value of Bonds = $20,000,000 Annual Coupon Rate = 5.00% Semiannual Coupon Rate = 2.50% Semiannual Coupon = 2.50% * $20,000,000 Semiannual Coupon = $500,000 Maturity Period = 9 years Semiannual = 18 Requiremnt 1: Calculation of Issue Price at market rate 4% Annual Market Interest Rate = 4.00% Semiannual Market Interest Rate = 2.00% The bonds issued at premium. Issue Price of Bonds = $500,000 * PVA of $1 (2.00%, 18) + $20,000,000 * PV of $1 (2.00%, 18) Issue Price of Bonds = $500,000 * 14.99203 + $20,000,000 * 0.70016 Issue Price of Bonds = $ 2,14,99,215 Requiremnt 2: Calculation of Issue Price at market rate 5% Annual Market Interest Rate = 5.00% Semiannual Market Interest Rate = 2.50% The bonds issued at par. Issue Price of Bonds = $500,000 * PVA of $1 (2.50%, 18) + $20,000,000 * PV of $1 (2.50%, 18) Issue Price of Bonds = $500,000 * 14.35336 + $20,000,000 * 0.64117 Issue Price of Bonds = $ 2,00,00,080 Issue Price Approx = 20000000 Requiremnt 3: Calculation of Issue Price at market rate 6% Annual Market Interest Rate = 6.00% Semiannual Market Interest Rate = 3.00% The bonds issued at discount. Issue Price of Bonds = $500,000 * PVA of $1 (3.00%, 18) + $20,000,000 * PV of $1 (3.00%, 18) Issue Price of Bonds = $500,000 * 13.75351 + $20,000,000 * 0.58739 Issue Price of Bonds = $ 1,86,24,555 * Kindly Comment down for any clarifications/ queries and please upvote.