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You intend to purchase a 1-year, $1,000 face value bond. Coupon rate of this bond is...

You intend to purchase a 1-year, $1,000 face value bond. Coupon rate of this bond is 18%. Market interest rate is 24 percent. Coupon payments are semiannual, what is the duration of the bond? (Answer is rounded)

Solutions

Expert Solution

Given for the bond,

Face value = $1000

Coupon rate = 18% semiannually

coupon = (18%/2)*100 = $90

Yield to maturity = 24% compounded semiannually

Duration is calculated as below table:

here, since it is a semiannual bond, discount factor = 1/(1+YTM/2)^(2*period)

PV of coupon = discount factor * coupon

Price = sum of all PV = $949.30

weight = PV of coupon/ price

duration of each coupon = year*weight

duration of the bond = sum of all duration = 0.96 years

In term of semiannual period, duration = 2*0.96 = 1.92 periods

Year Period Coupon Discount factor = 1/(1+YTM/2)^(2*year) PV of cash flow=coupon*discount factor weight = PV of Coupon/Price Duration = weight*year
0.5000 1 $                90.00 $                  0.89 $                80.36 0.0846 0.0423
1.0000 2 $          1,090.00 $                  0.80 $             868.94 0.9154 0.9154
Price $             949.30 Duration 0.96

jeff jeffy answered 1 year ago
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