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03%20bonds%20-%20lecture%20problems%20solutions

03%20bonds%20-%20lecture%20problems%20solutions - Solutions...

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Unformatted text preview: Solutions to lecture problems – bonds What is the value of a bond with a coupon rate of 7.4%, par value of \$1000, 8 years until maturity, and YTM of 8.5% if coupons are paid annually with the next one due in one year? time 1 2 3 4 5 6 7 8 time 1 yr 2 yrs 3 yrs 4 yrs 5 yrs 6 yrs 7 yrs 8 yrs CF cpn cpn cpn cpn cpn cpn cpn cpn + par CF 74 74 74 74 74 74 74 74 + 1000 N = 8 years × 1 coupon per year = 8 I% = YTM ÷ # coupons per year = 8.5% ÷ 1 = 8.5% FV = 1,000 = par PMT = par × coupon rate ÷ # coupons per year = 1000 × 7.4% ÷ 1 = 74 END mode Enter 8 8.5 74 1000 N I% PV PMT FV Solve for-937.97 1 Solutions to lecture problems – bonds What is the current yield of a bond with a coupon rate of 7.4%, par value of \$1000, 8 years until maturity, and YTM of 8.5% if coupons are paid annually with the next one due in one year? The current yield equals the total value of all coupon payments promised by a bond over a year divided by the market value (or present value or price) of the bond. The total annual coupon payments made by a bond equal the coupon rate multiplied by par In this case, the coupon rate = 7.4% and par = \$1,000, so coupons are .074 × \$1,000 = \$74 per year The market value of the bond is \$937.97 Current yield = \$74 / \$937.97 = .0789 = 7.89% 2 Solutions to lecture problems – bonds What is the value of a bond with a coupon rate of 7.2%, par value of \$1000, 12 years until maturity, and YTM of 6.6% if coupons are paid semi-annually with the next one due in six months? time 1 2 3 4 5 … 23 24 time 0y6m 1y0m 1y6m 2y0m 2y6m … 11y6 m 12y0m CF cpn cpn cpn cpn cpn … cpn cpn + par CF 36 36 36 36 36 … 36 36 + 1000 N = 12 years × 2 coupons per year = 24 I% = YTM ÷ # coupons per year = 6.6% ÷ 2 = 3.3% FV = 1,000 = par PMT = par × coupon rate ÷ # coupons per year = 1000 × 7.2% ÷ 2 = 36 END mode Enter 24 3.3 36 1000 N I% PV PMT FV Solve for-1,049.20 3 Solutions to lecture problems – bonds What is the current yield of a bond with a coupon rate of 7.2%, par value of \$1000, 12 years until maturity, and YTM of 6.6% if coupons are paid semi-annually with the next one due in six months? The current yield equals the total value of all coupon payments promised by a bond over a year divided by the market value (or present value or price) of the bond....
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03%20bonds%20-%20lecture%20problems%20solutions - Solutions...

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