Question

U.S. Treasury 30 year maturity, zero coupon bonds are currently selling in the marketplace with a yield to maturity of 7.00%. Even though the bonds have a coupon rate of 0.00%, please assume semi–annual compounding, which is the bond market convention? If inflation increased unexpectedly, forcing the nominal required rate of return on these Treasury bonds to increase by 1.75% to 8.75%, by what dollar amount would the current market price of these bonds decrease? Enter your answer rounded to two decimal places. Do not enter $ or comma in the answer box. For example, if your answer is $12,300.456 then enter as 12300.46 in the answer box.

Answer 1

Sol:

Period (n) = 30 years, (Semiannual) = 30 x 2 = 60

Yield to maturity (r) = 7%, (Semiannual) = 7% / 2 = 3.5%

Par value (FV) = 1000 (assumed)

Zero coupon bond price = FV / (1 + r)^n

Zero coupon bond price = 1000 / (1 + 3.5%)^60

Zero coupon bond price = 1000 / (1.035)^60

Zero coupon bond price = 126.93

Now nominal required rate of return increase by 1.75% to 8.75%

Yield to maturity (r) = 8.75%, (Semiannual) = 8.75% / 2 = 4.375%

Zero coupon bond price = 1000 / (1 + 4.375%)^60

Zero coupon bond price = 1000 / (1.04375)^60

Zero coupon bond price = 76.60

Dollar amount decrease of these bonds will be = 126.93 - 76.60 = 50.33

Therefore dollar amount decrease of these bonds is 50.33