Answered

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A bond has a $1,000 par value, 12 years to matu-rity, and an 8% annual coupon and sells for $980.
What is its yield to maturity (YTM)?

Sagot :

sqdancefan

Answer:

  8.269%

Step-by-step explanation:

You want the yield to maturity of a 12-year 8% annual coupon bond with $1000 par value selling for $980.

Yield

The yield of the bond has no closed-form formula, but can be found using graphical or iterative methods, or using a financial calculator. The attached calculator display shows the yield will be about 8.269%.

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Additional comment

The yield can be approximated by adding the change in bond value to the coupon value each year, relative to the average bond value over the period. The formula for this is ...

  YTM = [C + (FV-PV)/n] / [(FV+PV)/2]

where C is the coupon value each year, FV is the face value, PV is the present value (bond price), and n is the number of years.

In this problem, the estimated yield is ...

  YTM = [80 +(1000 -980)/12]/[(1000 +990)/2] ≈ 81.67/990

  YTM ≈ 0.08249 = 8.249%

This formula gives a way to calculate approximate yield without requiring a financial calculator or spreadsheet.

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