Question

A General Power bond with a face value of $1,000 carries a coupon rate of 8.4%, has 9 years until maturity, and sells at a yield to maturity of 7.4%. (Assume annual interest payments.)

a.	What interest payments do bondholders receive each year?

Interest payments

$

b.	At what price does the bond sell? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Price

$

c.	What will happen to the bond price if the yield to maturity falls to 6.4%? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Price will

(Click to select) rise/fall by $

Answer 1

Annual coupon = Par value * coupon rate

                              = 1000* 8.4%

                              = 84 /year

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Price of the bond could be calculated using below formula.

P = C* [{1 - (1 + YTM) ^ -n}/ (YTM)] + [F/ (1 + YTM) ^ -n]

Where,

                Face value = $1000

                Coupon rate = 8.4%

                YTM or Required rate = 7.4%

                Time to maturity (n) = 9 years

                Annual coupon C = $84

Let's put all the values in the formula to find the bond current value

P = 84* [{1 - (1 + 0.074) ^ -9}/ (0.074)] + [1000/ (1 + 0.074) ^9]

P = 84* [{1 - (1.074) ^ -9}/ (0.074)] + [1000/ (1.074) ^9]

P = 84* [{1 - 0.52597}/ 0.074] + [1000/ 1.90125]

P = 84* [0.47403/ 0.074] + [525.96976]

P = 84* 6.40581 + 525.96976

P = 538.08804 + 525.96976

P = 1064.0578

So price of the bond is $1064.06

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If YTM changes to 6.4%

                Face value = $1000

                Coupon rate = 8.4%

                YTM or Required rate = 6.4%

                Time to maturity (n) = 9 years

                Annual coupon C = $84

Let's put all the values in the formula to find the bond current value

P = 84* [{1 - (1 + 0.064) ^ -9}/ (0.064)] + [1000/ (1 + 0.064) ^9]

P = 84* [{1 - (1.064) ^ -9}/ (0.064)] + [1000/ (1.064) ^9]

P = 84* [{1 - 0.57217}/ 0.064] + [1000/ 1.74773]

P = 84* [0.42783/ 0.064] + [572.17076]

P = 84* 6.68484 + 572.17076

P = 561.52656 + 572.17076

P = 1133.69732

So price of the bond is $1133.7

Price will increase by = $1133.7 - $1064.06 = $69.64

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