Question

A bond has two years to mature. It makes a coupon payment of \(100 after one year and both a coupon payment of \)100 and a principal repayment of \(1000 after two years. The bond is selling for \)966. What is its effective yield?

Short answer

The effective yield is 12%.

Step-by-step solution

Explanation

The effective yield is the rate of interest at which the present value is discounted.

At the end of one year, the coupon payment will be $100, and at the end of two years, the payment will be $1100 (=$100 + $1000). The present value of the bond is $966.

According to the problem,

$$\begin{gathered} 966=100{\left(1+r\right)}^{-1}+1100{\left(1+r\right)}^{-2} \\ 966=\frac{100}{{\left(1+r\right)}^1}+\frac{1100}{{\left(1+r\right)}^2} \\ 966{\left(1+r\right)}^2=100\left(1+r\right)+1100 \\ 966+1932r+966r^2=100+100r+1100 \\ 966r^2+1832r-234=0 \\ r=\frac{-1832\pm \sqrt{{1832}^2-4\times 966\times \left(-234\right)}}{2\times 966} \\ =\frac{-1832\pm \sqrt{3356224+904176}}{1932} \\ =\frac{-1832\pm 2064.07}{1932} \\ =\frac{-1832+2064.07}{1932} \\ =\frac{232.07}{1932} \\ =0.1201 \\ =12\% \end{gathered}$$

The negative value of r is ignored; thus, the effective interest rate will be 12%.