Answer:
- What is the fair price for the new 10-year annual coupon bond?
b. 924.70
Step-by-step 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