Jackson Corporations Bonds Have 10 Years Remaining To Maturi ✓ Solved

Jackson Corporations Bonds Have 10 Years Remaining To Maturity In

Jackson Corporation’s bonds have 10 years remaining to maturity. Interest is paid annually, the bonds have a $1,000 par value, and the coupon interest rate is 9%. The bonds have a yield to maturity of 10%. What is the current market price of these bonds?

Paper For Above Instructions

In this paper, we will analyze the valuation of Jackson Corporation's bonds with specific characteristics: a 10-year remaining maturity, annual interest payments, a par value of $1,000, a coupon rate of 9%, and a yield to maturity (YTM) of 10%. Understanding how these variables influence bond pricing requires an examination of the bond valuation principles, relevant formulas, and the impact of interest rates on bond market prices.

Bonds are debt instruments whereby the issuer agrees to pay the bondholder periodic interest payments and repay the principal at maturity. The bond's market price is influenced by the comparison between its coupon rate and the current market interest rates (YTM). When the YTM exceeds the coupon rate, the bond tends to sell at a discount; when the YTM is lower than the coupon rate, it sells at a premium. Here, the YTM (10%) exceeds the coupon rate (9%), indicating that the bond will sell below par value.

Bond Valuation Formula

The present value (PV) of a bond can be calculated as the sum of the present value of the periodic coupon payments and the present value of the face value repayment at maturity. The formula is:

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

Where:

  • C = Annual coupon payment = Coupon rate × Par value
  • F = Face value of the bond (par value) = $1,000
  • r = Yield to maturity per period (annual in this case) = 10% or 0.10
  • n = Number of periods remaining = 10

Calculating the Bond Price

First, compute the annual coupon payment:

C = 9% × $1,000 = $90

Next, apply the present value formula:

Price = ($90 × (1 - (1 + 0.10)^-10) / 0.10) + ($1,000 / (1 + 0.10)^10)

Calculating step-by-step:

  • Calculate the present value of the coupon payments:
PV of coupons = $90 × (1 - (1 + 0.10)^-10) / 0.10


= $90 × (1 - (1 + 0.10)^-10) / 0.10


= $90 × (1 - (1.10)^-10) / 0.10


= $90 × (1 - 0.3855) / 0.10


= $90 × 0.6145 / 0.10


= $90 × 6.145


= $553.05
  • Calculate the present value of the face value:
PV of face value = $1,000 / (1.10)^10


= $1,000 / 2.5937


= approximately $385.54

Adding both components gives the bond's theoretical market price:

Price = $553.05 + $385.54 ≈ $938.59

Therefore, the current market price of Jackson Corporation's bonds is approximately $938.59.

Conclusion

This valuation reflects the impact of the higher YTM relative to the coupon rate, resulting in a bond price slightly below par. Investors considering purchasing this bond should expect to pay approximately $938.59, acknowledging that the bond's return aligns with the prevailing market interest rate environment.

References

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  • Ross, S. A., Westerfield, R., & Jaffe, J. (2013). Corporate Finance. McGraw-Hill Education.
  • Clark, G. L., & Monk, A. H. B. (2014). The Bond Market and Interest Rate Determination. Journal of Finance.
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