Gmm co. plans to issue annual coupon bonds with 7.5% coupon rate to the public, maturing in 10 years. the face value of the bond is $1,000. you, as the cfo, want to decide how to set the price for the bond.
you notice that 2 years ago, your company issued a 15-year annual coupon bond with 8% coupon rate.
the current market price for the outstanding old bond is $950.

what is the fair price for the new 10-year annual coupon bond?

a. 1000

b. 924.70

c. 1024.70

d. 934.70

e. 1034.70

b. 924.70

Explanation:

First it's needed to calculate the YTM of the current bonds, issued 2 years ago, if we applied the Present Value formula to the Principal and Coupons we get the YTM to the current bonds.

With a market price of $950, we can find the YTM of these bonds today, when there are 13 years left until the expiration date, the YTM is 8,66%.

If we apply this 8,66% rate to the new bond issue, we can obtain the price that could be accepted for the market.

Bond Value  

Principal Present Value  =  F /  (1 + r)^t  

Coupon Present Value   =  C x [1 - 1/(1 +r)^t] / r  

YTM of the Bond that was issued 2 years ago.  

The price of this bond it's $340 + $610 = $950  

Present Value of Bonds $340 = $1,000/(1+0,0866)^13    

Present Value of Coupons $610 =  $80 (Coupon) x 7,63  

7,63 =   [1 - 1/(1+0,0866)^13 ]/ 0,0866  

The bond price to be issued:    

The price of this bond it's $436 + $489 = $924,70    

Present Value of Bonds $436 = $1,000/(1+0,0866)^10      

Present Value of Coupons $489 =  $75 (Coupon) x 6,52    

6,52 =   [1 - 1/(1+0,0866)^10 ]/ 0,0866    

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