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 1.50% to 8.50%, 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

As the face value of the Zero coupon bond is not given, let us assume the same to be $1000

Semi annual yield now = 7%/2 = 3.5% = 0.035

No of periods = 30*2 = 60

So, Price of Zero coupon bond today = 1000/1.035^60 = $126.93

Now if due to inflation, YTM becomes 8.5%

Semi annual yield = 8.5%/2 = 4.25% = 0.0425

No of periods = 30*2 = 60

So, Price of Zero coupon bond = 1000/1.0425^60 = $82.31

So, the price of the bond would decrease by = $126.93-$82.31 = $44.63 (Enter 44.63)

Please note that if the face value is taken as $100, the answer would be $4.46