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 of the bond should be calculated using a financial calculator or spreadsheet by solving the equation: \$966 = \(\frac{\$100}{{(1+YTM)^1}}\) + \(\frac{\$1100}{{(1+YTM)^2}}\). Please note, your calculated YTM would be in decimal format; for a percentage, you need to multiply it by 100.

Step-by-step solution

Understanding the Concept of Effective Yield

The effective yield of a bond, also known as the yield to maturity (YTM), is the Internal Rate of Return (IRR) on the bond's cash flows: the initial cost (the price of the bond), the coupon payments, and the principal repayment. The equation to find it is: \(PV = \sum \frac{CF_t}{{(1+YTM)}^t}\), where PV is the present value or price of the bond (\$966), \(CF_t\) are the cash flows at period t (Coupon payments of \$100 after the first year and \$1100 after the second year), and t is the time period.

Setting up the Equation

By plugging in the known values into the equation we get: \$966 = \(\frac{\$100}{{(1+YTM)^1}}\) + \(\frac{\$1100}{{(1+YTM)^2}}\)

Solving the Equation

This problem requires the solution of a quadratic equation. While it can be solved by algebraic methods, the most efficient way to solve this equation is by using a financial calculator or computer-based tools, such as a spreadsheet.

Finding the Yield to Maturity (YTM)

The solution of the equation gives the YTM. The YTM is the bond's internal rate of return, given its price, coupon payments, and principal repayment.