John is considering the purchase of Super Technology, Inc. bonds that were issued 7 years ago. When the bonds were originally sold they had a 25-year maturity and a 11.13 percent coupon interest rate, paid annually. The bond is currently selling for $1,015. Par value of the bond is $1,000. What is the yield to maturity on the bonds if you purchased the bond today?
Round the answers to two decimal places in percentage form.
use Excel or financial calculator.
To calculate the yield to maturity (YTM) on the Super Technology, Inc. bonds, we need to use the present value formula for bonds. The YTM is the rate at which the present value of all expected future cash flows (coupon payments and the final par value) equals the current market price of the bond.
Here are the details of the bond:
Face Value (Par Value): $1,000
Coupon Interest Rate: 11.13% (annual)
Time to Maturity: 18 years (25 years original maturity – 7 years since issuance)
Current Market Price: $1,015
To calculate the YTM, we’ll use a financial calculator or spreadsheet software like Excel. In Excel, you can use the “RATE” function to find the YTM. Here’s how to do it in Excel:
In a cell, enter the following formula:
=RATE(nper, pmt, pv, fv)
nper: The number of periods until maturity, which is 18 years.
pmt: The annual coupon payment, which is $1,000 (par value) * 11.13% (coupon rate) = $111.30.
pv: The current market price, which is -$1,015 (negative because it’s an outflow).
fv: The face value of the bond, which is $1,000.
Calculate the YTM by inputting these values into the formula:
=RATE(18, 111.30, -1015, 1000)
Press Enter, and Excel will calculate the YTM for you.
The YTM for the Super Technology, Inc. bond is approximately 10.87%.
In this case, the YTM of 10.87% represents the annualized rate of return you can expect if you purchase the bond at the current market price of $1,015 and hold it until maturity. Keep in mind that the YTM assumes you will reinvest coupon payments at the same rate, and it may not account for certain factors like taxes or transaction costs. However, it provides a useful estimate of the bond’s expected return under these assumptions.
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