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A company needs $8 million in new capital for expanded composites manufacturing. It is offering small-denomination corporate bonds at a deep discount price of $800 for a 4% $1000 face value bond that matures in 20 years and pays the dividend semiannually. Find the nominal and effective annual rates, compounded semiannually, that this company is paying per investor

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jepessoa

Answer:

nominal interest rate = 4% annual

effective interest rate =  5.56% annual

Explanation:

the bond's nominal rate is basically the coupon rate

to calculate the bond's effective interest rate we must calculate its yield to maturity:

YTM = [coupon + [(face value - present value) / n]} / [(face value + present value) / 2]

  • coupon = $1,000 x 4% x 1/2 = $20
  • FV = $1,000
  • PV = $800
  • n = 40

YTM = [20 + [(1,000 - 800) / 40]} / [(1,000 + 800) / 2]

YTM = 25 / 900 = 2.777 semiannual ⇒ 5.56% annual

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