Suppose you purchase a 30-year, zero-coupon bond with a yield to maturity of 6%.

Question

Suppose you purchase a 30-year, zero-coupon bond with a yield to maturity of 6%. You hold the bond for five years before selling it. a. If the bond's yield to maturity is 6% when you sell it, what is the internal rate of return of your investment? b.If the bond's yield to maturity is 7% when you sell it, what is the internal rate of return of your investment? c.If the bond's yield to maturity is 5% when you sell it, what is the internal rate of return of your investment. d. Even if a bond has no chance of default, is your investment risk free if you plan to sell it before it matures? Explain.

Explanation / Answer

Sale price = 100 / 1.0625 = 23.30.

     Return = (23.30 / 17.41)1/5 – 1 = 6.00%.

                  Since YTM is the same at purchase and sale,

                    Therefore, IRR = YTM= 6.00%

         Sale price = 100 / 1.0725 = 18.42.

         Return = (18.42 / 17.41)1/5 – 1 = 1.13%.

         Since YTM rises, IRR < initial YTM.

     Sale price = 100 / 1.0525 = 29.53.

    Return = (29.53 / 17.41)1/5 – 1 = 11.15%.

     Since YTM falls, IRR > initial YTM.

d.   Even without default, if one sell prior to maturity, are exposed to the risk that the YTM may change.

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