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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.

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jepessoa

Answer:

current market price of the bond is $667

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

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