A 3-year $1000 face value bond pays an annual coupon of 8% and has a ytm...

A 3-year $1000 face value bond pays an annual coupon of 8% and has a ytm of 4%. What is this bond's price? What is this bond's duration?

Solutions

Expert Solution

Coupon payment = 0.08 * 1000 = 80

Bond price = 80 * [ 1 - 1 / ( 1 + 0.04)³] / 0.04 + 1000 / ( 1 + 0.04)³

Bond price = 80 * 2.775091 + 888.996359

Bond price = $1,111.004

Present value of year 1 cash flow = 80 / ( 1 + 0.04) = 76.9231

Present value of year 2 cash flow = 80 / ( 1 + 0.04)² = 73.9645

Present value of year 3 cash flow = 80 / ( 1 + 0.04)³ = 71.1197

Present value of year 3 face value = 1000 / ( 1 + 0.04)³ = 888.9964

Total year 3 cash flow = 71.1197 + 888.9964 = 960.1161

Total present value = 76.9231 + 73.9645 + 960.1161 = 1,111.0037

Weight of year 1 cash flow = 76.9231 / 1,111.0037 = 0.069237

weight of year 2 cash flow = 73.9645 / 1,111.0037 = 0.066574

Weight of year 3 cash flow = 960.1161 / 1,111.0037 = 0.864188

Period 1 * weight 1 = 1 * 0.069237 = 0.069237

Period 2 * weight 2 = 2 * 0.066574 = 0.133148

Period 3 * weight 3 = 3 * 0.864188 = 2.592564

Duration = 0.069237 + 0.133148 + 2.592564

Duration = 2.79

jeff jeffy answered 1 year ago

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