Questions: Related to Checkpoint 92 (Yield to maturity) Abner Corporation's bonds mature in 21 years and pay 9 percent interest annually. If you purchase the bonds for 725, what is your yield to maturity?

Related to Checkpoint 92 (Yield to maturity) Abner Corporation's bonds mature in 21 years and pay 9 percent interest annually. If you purchase the bonds for 725, what is your yield to maturity?
Transcript text: (Related to Checkpoint 92) (Yield to maturity) Abner Corporation's bonds mature in 21 years and pay 9 percent interest annually If you purchase the bonds for $\$ 725$, what is your yield to maturity?
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Solution

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Solution Steps

To calculate the yield to maturity (YTM) of a bond, we need to solve for the interest rate that equates the present value of the bond's future cash flows to its current price. The bond's future cash flows include annual interest payments and the repayment of the bond's face value at maturity. This is typically done using a numerical method such as the Newton-Raphson method or a financial library.

Step 1: Identify Given Data

We are given the following information:

  • Face value of the bond: \( F = \$1000 \)
  • Annual coupon rate: \( r = 0.09 \)
  • Years to maturity: \( n = 21 \)
  • Current price of the bond: \( P = \$725 \)
Step 2: Calculate Annual Coupon Payment

The annual coupon payment is calculated as: \[ C = F \times r = 1000 \times 0.09 = \$90.00 \]

Step 3: Define the Yield to Maturity (YTM) Equation

The yield to maturity (YTM) is the interest rate \( y \) that equates the present value of the bond's future cash flows to its current price. The equation is: \[ P = \sum_{t=1}^{n} \frac{C}{(1+y)^t} + \frac{F}{(1+y)^n} \]

Step 4: Solve for YTM

Using numerical methods, we solve for \( y \) in the equation above. The calculated yield to maturity is: \[ y = 0.1267 \]

Step 5: Convert YTM to Percentage

Convert the yield to maturity to a percentage and round to two decimal places: \[ \text{YTM\%} = y \times 100 = 0.1267 \times 100 = 12.67\% \]

Final Answer

\(\boxed{12.67\%}\)

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