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

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

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