Question

What is the price of a coupon bond that has annual coupon payments of​ $85, a par value of​ $1,000, a yield to maturity of​ 10%, and a maturity of three​ years?

Answer 1

The price of the desired coupon bond can be found by discounting its future cash flows, which include annual $85 coupon payments and the $1,000 par value, based on a 10% yield to maturity over three years.

Step-by-step explanation:

We can calculate the price of a coupon bond that has annual coupon payments of $85, a par value of $1,000, a yield to maturity of 10%, and a maturity of three years by discounting each cash flow to the present value using the yield to maturity as the discount rate. The price of a bond is the sum of the present value of the future cash flows, which includes the annual coupon payments and the par value paid at maturity.

The formula for calculating the present value of each coupon payment is PV = C / (1 + r)^n, where PV is the present value, C is the coupon payment, r is the yield to maturity (expressed as a decimal), and n is the time period. The price of the bond is the sum of all these present values plus the present value of the par value to be received at maturity.

Answer 2

Let p be the price of the bond.
Annual coupons payment = 85
Par value (future value) is $1000.
So with a yield-to-maturity of 10% in three years,
p(1+10%) = 1000+3*85
solve for p
p=(1000+3*85)/1.10=1140.91

Note: since the coupon payment is not reinvested in the bond, the value is not compounded. Thus there is additional benefit if the payments are reinvested elsewhere. In other words, the yield-to-maturity actually under-estimates the potential yield.