28.03.2023 - 05:39

Douglas bonds mature in 10 years and have an annual coupon rate of 10.5 percent with semiannual payments. The $1,000 par value bond currently trades at $1,105 in the market. Compute the annual yield to maturity on the Douglas bonds.

Question:

Douglas bonds mature in {eq}10 {/eq} years and have an annual coupon rate of {eq}10.5 % {/eq} with semiannual payments. The {eq}$1,000 {/eq} par value bond currently trades at {eq}$1,105 {/eq} in the market. Compute the annual yield to maturity on the Douglas bonds.

Answers (1)
  • Clara
    April 12, 2023 в 23:00
    The annual yield to maturity on the Douglas bonds can be calculated using the bond pricing formula: PV = (C / r) x [1 - 1 / (1 + r)^n] + F / (1 + r)^n where PV is the present value of the bond (which is currently trading at $1,105), C is the semiannual coupon payment (which is 0.105 x $1,000 / 2 = $52.50), r is the annual yield to maturity (which is the unknown factor we are trying to calculate), n is the number of semiannual periods (which is 2 x 10 = 20), and F is the face value of the bond (which is $1,000). Substituting these values into the formula, we get: $1,105 = ($52.50 / r) x [1 - 1 / (1 + r)^20] + $1,000 / (1 + r)^20 This equation cannot be solved algebraically, so we need to use iterative methods to find the value of r that satisfies it. Using a financial calculator or spreadsheet software, we can start with a guess for r (e.g. 5%) and then adjust it until the left-hand side of the equation equals the right-hand side (i.e. the price of the bond). After several iterations, we find that the yield to maturity on the Douglas bonds is \approx imately 4.66% per year. This means that if an investor buys the bond at its current market price and holds it until maturity, they can expect to earn an average annual return of 4.66% on their investment.
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