Question
Asked Nov 7, 2019
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A company releases a​ five-year bond with a face value of​ $1,000 and coupons paid semiannually. If market interest rates imply a YTM of 8%, what should be the coupon rate offered if the bond is to trade at par?

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Expert Answer

Step 1

When the bond is trading at par, that is at a face value of $1,000 then the coupon rate on the bond is equal to the yield to maturity.

Bond Price is $1000

Face Value “FV” is $1000

r = semi-annual YTM = 4%

Number of period “n” is 10 (5*2)

It can be proved as follows:

[1 1(1r"]
FV
Bond Price C >
(1 r)
r
[1 1 (10.04)10]
1000
1000 C x
(1 0.04)10
0.04
1000
1000 1- 0.675564168825799]
1.0410
0.04
C x 8.11089577935504+ +675.56416882579
1000
c = $40
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[1 1(1r"] FV Bond Price C > (1 r) r [1 1 (10.04)10] 1000 1000 C x (1 0.04)10 0.04 1000 1000 1- 0.675564168825799] 1.0410 0.04 C x 8.11089577935504+ +675.56416882579 1000 c = $40

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Step 2

Annual Coupon = 2*$40

Annu...

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