A company issues a ten-year $1000 bond at par with a coupon rate of 6% paid semi-annually.The YTM at the beginning of the third year of the bond (8 years left to maturity)is 7.8%.What is the new price of the bond?

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The new price of the bond can be calculated using the present value of its future cash flows, which include the semi-annual coupon payments and the principal amount at maturity. The formula for the present value of an annuity (for the coupon payments) and a lump sum (for the principal repayment) is used here. Given a coupon rate of 6% on a $1000 bond, the semi-annual coupon payment is $1000 * 6% / 2 = $30. With 8 years left to maturity and payments made semi-annually, there are 16 payments remaining. The YTM of 7.8% annually is 3.9% semi-annually. The present value of the bond is calculated as the sum of the present value of the annuity (coupon payments) and the present value of the lump sum (principal repayment). Using the present value formulas:$$ PV = \frac{C}{r} \left(1 - \frac{1}{(1 + r)^n}\right) + \frac{F}{(1 + r)^n} $$Where:- $PV$ = Present Value of the bond- $C$ = Semi-annual coupon payment = $30- $r$ = Semi-annual YTM = 3.9% or 0.039- $n$ = Total number of payments = 16- $F$ = Face value of the bond = $1000Plugging in the values:$$ PV = \frac{30}{0.039} \left(1 - \frac{1}{(1 + 0.039)^{16}}\right) + \frac{1000}{(1 + 0.039)^{16}} $$$$ PV ≈ $894.35 $$Therefore, the new price of the bond is approximately $894.35.

A Company Issues a Ten-Year $1000 Bond at Par with a Coupon