Question

Kilgore Natural Gas has a $1,000 par value bond outstanding that pays 11 percent annual interest. The current yield to maturity on such bonds in the market is 10 percent. Compute the price of the bonds for these maturity dates:

25 years 15 years 4 years

Answer 1

Price of the bond is the sum of cash flows from holding the bond till maturity discounted at yield-to-maturity (YTM) rate. Since the interest is annual, the cashflow during the year is coupon interest calculated as $1,000 x 11% i.e. $110. During the last year of the period, the holder will get the principal of $1,000 back along with the interest for that period i.e. $1,110. Thus we can calculate the price for bond as follows:

The fina result will be as follows:

Thus prices of the bond for 25 years, 15 years and 4 years are $1,090.77, $1,076.06 and $1,031.70 respectively. This can be calculated in another way using PV function in Excel as well. The syntax is "=-PV(rate,nper,pmt,[FV],[type]). rate is discounting rate i.e. YTM i.e. 10%. nper is no. of periods. That will be the holding period. pmt is payments i.e. coupon payments of $110. FV is the future value i.e. redemption value of $1,000. You can ignore type. Hence price of bond for 25 years can be calculated as using the function as: =-PV(10%,25,110,1000). The result will be $1,090.77.

Happy Learning.