## Bond Yields

You're looking at two bonds identical in every way except for their coupons and, of course, their prices. Both have 12 years to maturity. The first bond has a 10 percent coupon rate and sells for \$935.08. The second has a 12 percent coupon rate. What do you think it would sell for?

Because the two bonds are very similar, they will be priced to yield about the same rate. We first need to calculate the yield on the 10 percent coupon bond. Proceeding as before, we know that the yield must be greater than 10 percent because the bond is selling at a discount. The bond has a fairly long maturity of 12 years. We've seen that long-term bond prices are relatively sensitive to interest rate changes, so the yield is probably close to 10 percent. A little trial and error reveals that the yield is actually 11 percent:

Bond value = \$100 X (1 - 1/1.1112)/.11 + 1,000/1.1112 = \$100 X 6.4924 + 1,000/3.4985 = \$649.24 + 285.84 = \$935.08

With an 11 percent yield, the second bond will sell at a premium because of its \$120 coupon. Its value is:

Bond value = \$120 X (1 - 1/1.1112)/.11 + 1,000/1.1112 = \$120 X 6.4924 + 1,000/3.4985 = \$779.08 + 285.84 = \$1,064.92

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