Question

Please solve clearly and explain all steps

A man buys a 22-year, 496 coupon bond with annual coupon payments and a YTM of 7.5% at issuance. Four vears later, he decides to sell the bond when the YTM rate drops to 5.5%. For what prices does he first buy the bond, and then sell it? He buys for $924.67 and sells for $982.05 He buys for $831.31 and sells for $628.40 He buys for $924.67 and sells for $628.40 He buys for $628.40 and sells for $831.31 He buys for $982.05 and sells for $924.67

Answer 1

Calculations are as below:

At 7.5% YTM:

Current price of the bond = V =?

Face value of bond = F = 1,000

Annual interest payment (I) = 1,000 × 4% = 40

Yield to maturity (YTM) = 0.075

Number of remaining years (n) from the date of current bond price = 22

V = (I / YTM) [{(1 + YTM)^n – 1} / (1 + YTM)^n] + [F / (1 + YTM)^n]

    = (40 / 0.075) [(1.075^22 – 1) / 1.075^22] + [1,000 / 1.075^22]

    = 533.33 (3.9089 / 4.9089) + (1000 / 4.9089)

    = 533.33 × 0.79628 + 203.71

    = 424.69 + 203.71

    = 628.40

At 5.5% YTM:

Current price of the bond = V =?

Face value of bond = F = 1,000

Annual interest payment (I) = 1,000 × 4% = 40

Yield to maturity (YTM) = 0.055

Number of remaining years (n) from the date of current bond price = 22 – 4 = 18

V = (I / YTM) [{(1 + YTM)^n – 1} / (1 + YTM)^n] + [F / (1 + YTM)^n]

    = (40 / 0.055) [(1.055^18 – 1) / 1.055^18] + [1,000 / 1.055^18]

    = 727.27 (1.621466 / 2.621466) + (1000 / 2.621466)

    = 727.27 × 0.618534 + 381.47

    = 449.84 + 381.47

  = 831.31

Answer: 4^th option