Question

Consider a bond with a 6% annual coupon and a face value of $1,000. Complete the following table. What relationships do you observe between years to maturity, yield to maturity, and the current price?

Short answer

The current yield will be:

Step-by-step solution

Step 1. Introduction

The total return expected if the bond is kept to maturity is known as yield to maturity. It can also be referred as the internal rate of return of bond if it is kept till maturity.

Step 2. Explanation

$$\begin{gathered} AnnualCoupon=\$1000\times 6\% \\ =\$60 \\ CaseI \\ CurrentMarketPrice=\$60\times \frac{1-{\left({\displaystyle \frac{1}{1.04}}\right)}^2}{0.04}+\$1000\times {\left(\frac{1}{1.04}\right)}^2 \\ =\$60\times 1.8861+\$1000\times 0.9246 \\ =\$1037.77 \\ CurrentYield=\frac{\$60}{\$1037.77} \\ =5.78\% \\ Case-II \\ CurrentMarketPrice=\$60\times \frac{1-{\left({\displaystyle \frac{1}{1.06}}\right)}^2}{0.06}+\$1000\times {\left(\frac{1}{1.06}\right)}^2 \\ =\$1,000 \\ CurrentYield=\frac{\$60}{\$1000} \\ =6\% \\ Case-III \\ CurrentMarketPrice=\$60\times \frac{1-{\left({\displaystyle \frac{1}{1.06}}\right)}^3}{0.06}+\$1000\times {\left(\frac{1}{1.06}\right)}^3 \\ =\$1000 \\ CurrentYield=\frac{\$60}{\$1000} \\ =6\% \\ Case-IV \\ CurrentMarketPrice=\$60\times \frac{1-{\left({\displaystyle \frac{1}{1.04}}\right)}^5}{0.04}+\$1000\times {\left(\frac{1}{1.04}\right)}^5 \\ =\$1089 \\ CurrentYield=\frac{\$60}{\$1089} \\ =5.51\% \\ Case-V \\ CurrentMarketPrice=\$60\times \frac{1-{\left({\displaystyle \frac{1}{1.08}}\right)}^5}{0.08}+\$1000\times {\left(\frac{1}{1.08}\right)}^5 \\ =\$920.16 \\ CurrentYield=\frac{\$60}{\$920.16} \\ =6.52\% \end{gathered}$$