Suppose you purchase a 30-year, zero-coupon bond with a yield to maturity of 5.9

ID: 2733163 • Letter: S

Question

Suppose you purchase a 30-year, zero-coupon bond with a yield to maturity of 5.9%. You hold the bond for five years before selling it.

a. If the bond’s yield to maturity is 5.9% when you sell it, what is the internal rate of return of your investment?

b. If the bond’s yield to maturity is 6.9% when you sell it, what is the internal rate of return of your investment?

c. If the bond’s yield to maturity is 4.9% 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.

Let we assume face value of bond is $ 1,000

(a) Purchase price of zero-coupon bond = 1,000/(1.059)30 = $ 179.11

Selling price of zero-coupon bond = 1,000/(1.059)25 = $ 238.56

Internal rate of return = (238.56/179.11)1/5 - 1

Internal rate of return = 1.058 - 1 = 0.058*100 = 5.8%

Since, the YTM is the same as internal rate of return.

(b)

Purchase price of zero-coupon bond = 1,000/(1.059)30 = $ 179.11

Selling price of zero-coupon bond = 1,000/(1.069)25 = $ 188.61

Internal rate of return = (188.61/179.11)1/5 - 1

Internal rate of return = 1.0098 - 1 = 0.0098*100 = 0.98%

Since, the internal rate of return is lower than YTM.

(c)

Purchase price of zero-coupon bond = 1,000/(1.059)30 = $ 179.11

Selling price of zero-coupon bond = 1,000/(1.049)25 = $ 302.42

Internal rate of return = (302.42/179.11)1/5 - 1

Internal rate of return = 1.11 - 1 = 0.11*100 = 11%

Since, the YTM is the greater than internal rate of return.

(d) If we sell prior to maturity,we are exposed to the risk that YTM may change. Even if a bond has no chance of default.

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