What would you pay for a bond that pays an annual coupon of $35, has a
face value of $1,000, matures in 7 years, and has a yield to
maturity(YTM)of 8%?
Hi pheifer-ga,
The implied purchase price is in the range $765.70 to $765.73.
The calculation is complex, so people usually use calculators with the
method built in. Multiple yield-to-maturity calculators are available
for free use on the World Wide Web. They typically have the purchase
price as an input, not an output, so to get this answer, I tried
various purchase prices until the yield to maturity came out at 8%.
I got three yield-to-maturity calculators to agree on the result
above.
Kiplinger.com offers a calculator at:
http://www.calcbuilder.com/cgi-bin/calcs/5.8/BON1.cgi/Kiplinger
I entered the following values to get a yield to maturity of 8.03%:
Price you paid: 76% (the calculator does not allow fractions of a
percent)
Face value: $1000
Coupon rate: 3.50%
Months to maturity: 84
Your coupon income is invested elsewhere at a rate of: 8%
Type of bond: This didn't matter, since I was looking at the taxable
yield.
The key to making this calculation work was entering 8% as the rate
earned on the coupon income invested elsewhere. The other calculators
apparently had this assumption built in.
SmartMoney.com's calculator is at:
http://www.smartmoney.com/onebond/index.cfm?story=bondcalculator
To get a yield of 8.00%, I entered:
Price: 76.57
Coupon rate: 3.5%
Matures on: Oct 2010 (7 years from now)
Finally, the MoneyChimp web site has an explanation of the calculation
at:
http://www.moneychimp.com/articles/finworks/fmbondytm.htm
with a calculator on a popup window from that page. To get a yield to
maturity of 8.000% with this calculator, I entered:
Current price: $765.70
Par value: $1000
Coupon rate: 3.5%
Years to maturity: 7
I found the MoneyChimp calculator the easiest to use. I used it to
find the exact range of cents in the purchase price that gave a yield
to maturity of 8.000%.
Search Strategy:
"yield to maturity" calculator
I hope this information is helpful. If you need any further
explanation, please ask for a clarification.
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