Questions: A bond yield is defined as the rate that discounts all future cash flows and make its present value equal to the current market price. Given a 2-year bond with semiannual coupon payments of 5 and a face value of 100, and a current market price of 91, what is the yield of this bond? (Round your answer to two decimal places.)

Solution Steps

To find the yield of the bond, we need to solve for the yield rate \( y \) that satisfies the equation where the present value of all future cash flows equals the current market price. The cash flows include the semiannual coupon payments and the face value at maturity. We can use the following equation:

\[ 91 = \frac{5}{(1 + y/2)^1} + \frac{5}{(1 + y/2)^2} + \frac{5}{(1 + y/2)^3} + \frac{5 + 100}{(1 + y/2)^4} \]

This equation can be solved numerically using Python.

The bond has semiannual coupon payments of \( C = 5 \) and a face value of \( F = 100 \). The cash flows occur at the end of each period for 2 years, resulting in a total of 4 cash flows: \( C, C, C, \) and \( C + F \).

The present value \( PV \) of the bond's cash flows must equal the current market price \( P = 91 \). The equation can be expressed as:

\[ 91 = \frac{5}{(1 + y/2)^1} + \frac{5}{(1 + y/2)^2} + \frac{5}{(1 + y/2)^3} + \frac{105}{(1 + y/2)^4} \]

By solving the equation for \( y \), we find that the yield is approximately \( y \approx 0.15398222 \). To express this as a percentage, we multiply by 100:

\[ \text{Yield} = 0.15398222 \times 100 \approx 15.398222 \]

Rounding this to two decimal places gives us \( 15.4 \).

Final Answer