“Calculating the Market Price of a Zero-Coupon Bond: A Financial Analysis of Tom Inc.’s 30-Year Bond with an 11.58% Semi-Annual Yield to Maturity”

QUESTION

15 years ago, Tom Inc issued zero-coupon bonds with a maturity date of 30 years and a face value of $1,000. Presently, the bond exhibits a semi-annually compounded yield to maturity of 11.58 percent. May I inquire about the prevailing market price of the bond?

Please ensure that the answer is rounded to two decimal places.

Perform computations utilizing the Microsoft Excel software or a dedicated financial calculator.

ANSWER

“Calculating the Market Price of a Zero-Coupon Bond: A Financial Analysis of Tom Inc.’s 30-Year Bond with an 11.58% Semi-Annual Yield to Maturity”

Calculating the market price of a zero-coupon bond requires a financial calculator or spreadsheet software like Microsoft Excel. In this case, we have a zero-coupon bond issued by Tom Inc. with a face value of $1,000, a maturity date of 30 years, and a semi-annually compounded yield to maturity (YTM) of 11.58 percent. To find the current market price of this bond, we can use the present value formula:

��=��(1+�/�)��

Where:

  • PV = Present Value (Market Price)
  • FV = Face Value ($1,000)
  • r = Semi-annual Yield to Maturity (11.58% or 0.1158 as a decimal)
  • n = Number of compounding periods per year (2 for semi-annual)
  • t = Number of years to maturity (30 years)

Now, let’s calculate the market price of the bond step by step:

  1. Convert the annual yield to a semi-annual yield by dividing it by 2: �=0.1158/2=0.0579
  2. Calculate the number of compounding periods (n) over the life of the bond: �=2∗30=60
  3. Plug these values into the present value formula: ��=1000(1+0.0579/2)2∗30
  4. Calculate the present value using a calculator or spreadsheet software:

��=1000(1+0.02895)60

��≈1000(1.02895)60

Now, let’s calculate the present value using a calculator or spreadsheet:

PV ≈ 1000 / (1.02895)^60

PV ≈ 1000 / 3.284067

PV ≈ $304.17 (rounded to two decimal places)

So, the prevailing market price of the Tom Inc. zero-coupon bond with a face value of $1,000, a maturity date of 30 years, and a semi-annually compounded yield to maturity of 11.58 percent is approximately $304.17. This is the amount an investor would be willing to pay for the bond in today’s market given the specified yield to maturity.

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