Even Though Most Corporate Bonds In The United States 928388

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Suppose a German company issues a bond with a par value of €1,000, 15 years to maturity, and a coupon rate of 6.1 percent paid annually. If the yield to maturity (YTM) is 7.2 percent, what is the current price of the bond?

This problem involves calculating the price of a bond based on its future cash flows discounted at the YTM. The bond pays an annual coupon of €61 (6.1% of €1,000). The present value of the bond is the sum of the present values of all future coupons and the face value, discounted at the YTM. The general formula for bond price is:

Price = (C × [1 - (1 + r)^-n] / r) + (F / (1 + r)^n)

Where:

  • C = Annual coupon payment (€61)
  • F = Face value (€1,000)
  • r = Yield per period (0.072)
  • n = Number of periods (15)

Using these parameters, we can compute the bond's current price.

Paper For Above instruction

The analysis of bond valuation is fundamental in understanding fixed-income securities and the dynamics that influence their pricing in international markets. In the case of the German corporate bond, the essential task is to determine its current market value based on its future cash flows, discounted appropriately at the prevailing yield to maturity.

The bond in question has a face value of €1,000, a maturity of 15 years, and pays an annual coupon of €61 (which is 6.1% of €1,000). The YTM is given as 7.2%, which reflects investors' required rate of return given the company's credit risk and market conditions. Using the standard bond pricing formula, the market price is the sum of the present value of the coupon payments and the present value of the face value, discounted at the YTM.

Calculating the present value of coupon payments involves the annuity formula:

PV of coupons = C × [1 - (1 + r)^-n] / r

and the present value of the face value is:

PV of face value = F / (1 + r)^n

Plugging in the values: C = €61, F = €1,000, r = 0.072, n = 15, we find:

PV of coupons = €61 × [1 - (1 + 0.072)^-15] / 0.072

PV of coupons ≈ €61 × [1 - (1.072)^-15] / 0.072

PV of coupons ≈ €61 × [1 - 0.340] / 0.072

PV of coupons ≈ €61 × 0.660 / 0.072

PV of coupons ≈ €61 × 9.167 ≈ €558.4

PV of face value = €1,000 / (1.072)^15 ≈ €1,000 / 2.900 ≈ €344.8

By summing these two components, the current price of the bond is approximately €558.4 + €344.8 = €903.2.

Hence, the current market price of the bond is approximately €903.20, which reflects the present value of its expected future cash flows discounted at the prevailing YTM. This calculation demonstrates the principles of bond valuation and the importance of discount rates in determining bond prices in international financial markets.

References

  • Fabozzi, F. J. (2016). Bond Markets, Analysis, and Strategies. Pearson.
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  • Brigham, E. F., & Ehrhardt, M. C. (2016). Financial Management: Theory & Practice. Cengage Learning.
  • Hull, J. C. (2018). Options, Futures, and Other Derivatives. Pearson.
  • Ross, S., Westerfield, R., & Jaffe, J. (2019). Corporate Finance. McGraw-Hill Education.
  • Kolb, R. W. (2009). Contemporary Financial Markets and Institutions. Pearson.
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  • Krugman, P., Obstfeld, M., & Melitz, M. (2018). International Economics. Pearson.
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