Question

Consider a 5% 1 year to maturity coupon bond with a face value of $100. If the price of the bond is $90, what is the yield to maturity?

Answer 1

\(\mathrm{P}=\frac{C}{(1+y)^{1}}+\frac{C}{(1+y)^{2}}+\ldots+\frac{C}{(1+y)^{T}}+\frac{M}{(1+y)^{T}}\)

Where;

\(\mathrm{P}=\) market price of the bond

\(\mathrm{C}=\) interest payment (coupon)

\(\mathrm{M}=\) maturity value

\(\mathrm{T}=\) time to maturity

Price of bond = 5/(1+r) + 100/(1+r)

90 = 5/(1+r) + 100/(1+r)

r = 0.1667 or 16.67%, this is the yield to maturity.

The first term gives us the present value of the interest earned in one year and the second term gives us the present value of the face value of the bond after one year.

The yield to maturity is the interest rate that makes the present value of the cash flow of a bond equal to the market price.