Waco Industries Inc Likes To Open A Branch In Houston And Ne

Waco Industries Inc Likes To Open A Branch In Houston And Need To Ra

Waco Industries, Inc. plans to open a new branch in Houston and intends to raise capital by issuing a 20-year corporate bond with an 8% coupon rate, a par value of $1,000. As an investor, you have a required rate of return of 7% and want to determine the maximum price you are willing to pay for this bond. Additionally, analyze what occurs if you pay more or less than this amount, and then evaluate the bond’s price if your required rate of return is 12%. Provide detailed calculations to support your answers.

Paper For Above instruction

The decision to invest in bonds hinges critically on understanding the relationship between the bond’s coupon rate, market interest rates, and the investor’s required rate of return. In this context, Waco Industries is issuing a bond with a 20-year maturity, an 8% fixed coupon rate, and a par value of $1,000. The investor’s required rate of return is essential in determining the fair value or present price of the bond. This paper explores these concepts through detailed financial calculations, elucidating how varying required rates of return influence bond pricing and the implications of paying above or below the fair value.

Bond Valuation Fundamentals

The value of a bond is the present value of its future cash flows, which primarily consist of periodic coupon payments and the repayment of the face value at maturity. The general formula for bond valuation is:

\[ P = \sum_{t=1}^{n} \frac{C}{(1+r)^t} + \frac{F}{(1+r)^n} \]

Where:

- \( P \) = present price of the bond

- \( C \) = annual coupon payment (\$1,000 × 8% = \$80)

- \( r \) = required rate of return per period

- \( F \) = face value of the bond (\$1,000)

- \( n \) = number of years remaining until maturity (20 years)

Calculating Bond Price at a 7% Required Return

Given the investor’s required return of 7% (or 0.07), we calculate the bond’s fair value using the present value of an annuity formula for coupon payments and the present value of a lump sum for the face value:

\[ P_{7\%} = C \times \left( \frac{1 - (1 + r)^{-n}}{r} \right) + F \times (1 + r)^{-n} \]

Plugging in the numbers:

\[ P_{7\%} = 80 \times \left( \frac{1 - (1 + 0.07)^{-20}}{0.07} \right) + 1000 \times (1 + 0.07)^{-20} \]

First, compute the present value factor for 20 years at 7%:

\[ (1 + 0.07)^{20} \approx 3.87 \]

\[ (1 + 0.07)^{-20} \approx \frac{1}{3.87} \approx 0.2584 \]

Then, the present value of coupons:

\[ 80 \times \left( \frac{1 - 0.2584}{0.07} \right) = 80 \times \left( \frac{0.7416}{0.07} \right) \approx 80 \times 10.583 \approx 846.64 \]

And the present value of the face value:

\[ 1000 \times 0.2584 \approx 258.40 \]

Adding these together:

\[ P_{7\%} \approx 846.64 + 258.40 = \$1105.04 \]

Thus, the maximum price an investor requiring a 7% return would pay for Waco’s bond is approximately \$1105.04.

Implications of Paying More or Less

- If the investor pays more than \$1105.04, the bond’s yield will fall below the investor’s required rate of return, making it less attractive relative to other investments.

- If the investor pays less than \$1105.04, the yield will be higher than 7%, indicating a more attractive investment opportunity because the cash flows provide a higher return relative to the purchase price.

Calculating Bond Price at a 12% Required Return

Now, suppose the investor’s required rate of return increases to 12% (or 0.12). Using the same process:

\[ (1 + 0.12)^{20} \approx 9.646 \]

\[ (1 + 0.12)^{-20} \approx \frac{1}{9.646} \approx 0.1037 \]

Calculate the present value of coupons:

\[ 80 \times \left( \frac{1 - 0.1037}{0.12} \right) = 80 \times \left( \frac{0.8963}{0.12} \right) \approx 80 \times 7.469 \approx 597.52 \]

Calculate the present value of the face value:

\[ 1000 \times 0.1037 \approx 103.70 \]

Total bond price:

\[ P_{12\%} \approx 597.52 + 103.70 = \$701.22 \]

At a 12% required return, the fair value of the bond drops to approximately \$701.22.

Conclusion

Bond prices are inversely related to required rates of return. When an investor’s required return decreases (e.g., from 12% to 7%), the bond’s price increases, reflecting a higher valuation of future cash flows. Conversely, when the required return rises, the bond’s price declines because future cash flows are discounted more heavily. Paying more than the fair price at the 7% required return indicates overpayment, reducing the effective yield; paying less is advantageous, offering a higher return. These calculations demonstrate crucial principles in bond investment decisions, enabling investors to assess risk, determine fair value, and optimize returns.

References

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  • Ross, S. A., Westerfield, R. W., & Jaffe, J. (2019). Corporate Finance. McGraw-Hill Education.
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  • Investopedia. (2023). Bond Pricing and Yield. Retrieved from https://www.investopedia.com
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