Question

Consider an investor who, on January 1, 2019, purchases a TIPS bond with an original principal of $107,000, an 8 percent annual (or 4 percent semiannual) coupon rate, and 15 years to maturity.

a. If the semiannual inflation rate during the first six months is 0.3 percent, calculate the principal amount used to determine the first coupon payment and the first coupon payment (paid on June 30, 2019).

b. From your answer to part a, calculate the inflation-adjusted principal at the beginning of the second six months.

c. Suppose that the semiannual inflation rate for the second six-month period is 1.0 percent. Calculate the inflation-adjusted principal at the end of the second six months (on December 31, 2019) and the coupon payment to the investor for the second six-month period.

Answer 1

a. The inflation-adjusted principal amount used to determine the first coupon payment on June 30, 2019, is found by multiplying the original par value ($107,000) by the semiannual inflation rate of 0.3%. Thus, the principal amount is $107,000 * 1.003 = $107,321.

b. The inflation-adjusted principal at the beginning of the second six months is $107,321 (as calculated in part a).

c. The inflation-adjusted principal at the end of the second six months is calculated by multiplying the beginning principal value (i.e. at the beginning of the second six months of $107,321 by the semiaanual inflation rate of 1%). Thus the principal amount at the end of second six months (On December 31, 2019) is $108,394.20 ($107,321 * 1.01). Therefore, the coupon payment to the investor for the second six month period is $4,335.77 ($108,394.20 * 4%).