Question

You own a bond with a $1000 face value that pays a 12.2% annualised semiannual coupon rate and has 10 years to maturity. If the discount rate increases from 14% to 16% during the next two years of the bonds life, then what is the bond’s change in dollar value during the two-year period?

Select one: a. $-71.17 b. $72.83 c. $71.17 d. $-72.83

Answer 1

The original price of the bond is computed as shown below:

The coupon payment is computed as follows:

= 12.2% / 2 x $ 1,000 (Since the payments are semi annually, hence divided by 2)

= $ 61

The YTM will be as follows:

= 14% / 2 (Since the payments are semi annually, hence divided by 2)

= 7%

N will be as follows:

= 10 x 2 (Since the payments are semi annually, hence multiplied by 2)

= 20

Bonds Price = Coupon payment x [ [ (1 - 1 / (1 + r)n ] / r ] + Par value / (1 + r)n

= $ 61 x [ [ (1 - 1 / (1 + 0.07)20 ] / 0.07 ] + $ 1,000 / 1.0720

= $ 61 x 10.59401425 + $ 258.4190028

= $ 904.6538721

The new price of the bond is computed as shown below:

The coupon payment is computed as follows:

= 12.2% / 2 x $ 1,000 (Since the payments are semi annually, hence divided by 2)

= $ 61

The YTM will be as follows:

= 16% / 2 (Since the payments are semi annually, hence divided by 2)

= 8%

N will be as follows:

= 8 x 2 (Since the payments are semi annually, hence multiplied by 2)

= 16

Bonds Price = Coupon payment x [ [ (1 - 1 / (1 + r)n ] / r ] + Par value / (1 + r)n

= $ 61 x [ [ (1 - 1 / (1 + 0.08)16 ] / 0.08 ] + $ 1,000 / 1.0816

= $ 61 x 8.851369155 + $ 291.8904676

= $ 831.8239861

So, the price change is computed as follows:

= $ 831.8239861 - $ 904.6538721

= - $ 72.83

So, the correct answer is option d.

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