Question

You are called in as a financial analyst to appraise the bonds of Olsen’s Clothing Stores. The $1,000 par value bonds have a quoted annual interest rate of 10 percent, which is paid semiannually. The yield to maturity on the bonds is 8 percent annual interest. There are 10 years to maturity. Compute the price of the bonds based on semiannual analysis.

Answer 1

current market price of the bond is $667

Step-by-step explanation:

the formula to calculate yield to maturity (YTM) is:

YTM = [C + (F - P)/n] / [(F + P)/2]

• F = face value
• P = market price
• n = number of years x 2 =
• C = coupon

we just start replacing and solve for P:

• YTM = 8%
• C = 50
• F = 1,000
• n = 20

8% = [50 + (1,000 - P)/20] / [(1,000 + P)/2]

8% x (1,000 + P)/2 = 50 + (1,000 - P)/20

8% x (500 + 0.5P) = 50 + 50 - 0.05P

40 + 0.04P = 100 - 0.05P

0.04P + 0.05P = 100 - 40 = 60

0.09P = 60

P = 60 / 0.09 = 667