Value: 1.00 Point Barry’s Steroids Company Has $1,000 Par

value: 1.00 points Barry’s Steroids Company has $1,000 par value bonds outstanding at 13 percent interest

Barry’s Steroids Company has $1,000 par value bonds outstanding at 13 percent interest. The bonds will mature in 40 years. If the yield to maturity is 10 percent, what percent of the total bond value does the repayment of principal represent? Use Appendix B and Appendix D for an approximate answer and calculate your final answer using the formula and financial calculator methods. Do not round intermediate calculations. Round your final answer to 2 decimal places. Assume interest payments are annual.

Sample Paper For Above instruction

In evaluating the proportion of total bond value attributable to the repayment of principal, it is essential to understand the structure of bond valuation. Bonds are comprised of two primary components: the present value of future interest payments (coupon payments) and the present value of the face value (par value) repaid at maturity. Given a bond with a $1,000 par value, a 13% coupon rate, a 40-year maturity, and a yield to maturity (YTM) of 10%,we can analyze the composition of the bond's price to determine the principal's share.

First, the bond's annual interest (coupon payment) is 13% of $1,000, which equals $130. Since the interest payments are annual, the bond pays $130 each year for 40 years. To find the bond's current price, we use the present value formula for bonds, which sums the present value of the annuity of coupon payments and the present value of the face value:

Price = (Coupon payment × [1 - (1 + YTM)^-n ] / YTM) + (Face value / (1 + YTM)^n)

Where:

  • Coupon payment = $130
  • YTM = 10% or 0.10
  • n = 40 years
  • Face value = $1,000

Calculating the present value of the coupons:

PV_coupon = 130 × [1 - (1 + 0.10)^-40] / 0.10

Using a financial calculator or an Appendix B/Table 10-1 approximation, this equates approximately to PV_coupon ≈ $1,051.75.

Calculating the present value of the face value:

PV_face = 1000 / (1 + 0.10)^40 ≈ $94.60

Adding these gives the total bond price:

Total bond price ≈ $1,051.75 + $94.60 = $1,146.35

Therefore, the principal repayment ($1,000) as a percentage of the total bond value ($1,146.35) is:

(Principal / Total Bond Price) × 100 = ($1,000 / $1,146.35) × 100 ≈ 87.30%

In conclusion, at a yield to maturity of 10%, the repayment of the principal accounts for approximately 87.30% of the total bond value. This highlights the dominant role of principal repayment in the bond's valuation given the low YTM relative to the coupon rate, which causes the bond to trade at a premium.

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