In 1997, the U.S. Treasury issued "Treasury inflationprotected securities" (TIPS). These are fixed-income securities that are inflation indexed toprotect their value against inflation. Like conventional bonds they have a fixed coupon rate and maturity date, but the face value is periodically adjusted for inflation by multiplying the original face value by the ratio of the Consumer Price Index (CPI) at the current date to the $\mathrm{CPI}$ at the original issue date. Each semiannual coupon payment is the inflation-adjusted face value times the fixed coupon rate. At maturity, the bondholder receives the maximum of the inflation-adjusted face value or the original face value. Hence, if deflation occurs, the bondholder is guaranteed not to lose on the face value.

You observe the following prices of two 10 -year inflation-adjusted bonds:

Bond 1: $P_{1}=77.92, C_{1}=3 %, F_{1}=100$

Bond 2: $P_{2}=100.00, C_{2}=6 %, F_{2}=100$,

where $P$ is the price, $C$ is the coupon rate, and $F$ is the original face value.

(a) Compute the price of a theoretical 10-year inflation-adjusted zero-coupon bond with original face value of 100.

(b) Does your answer in (a) depend on the rate of inflation? Justify your answer.