Question

Suppose you buy a 2-year maturity tips (inflation-indexed) bond at its face value of $1,000 with a (real) coupon of 4.3% paid annually. Given an inflation rate of 8.45% each year, what would be the approximate real value of the coupon payment in the second year?

A) $43
B) $43.58
C) $86
D) $86.37

Answer 1

The calculation above shows how the nominal value of the coupon would increase due to the adjustment for inflation, resulting in a nominal payment of approximately $50.58.

Step-by-step explanation:

To calculate the real value of the coupon payment in the second year for a TIPS bond with a given inflation rate, we first need to adjust the principal to account for the inflation. Since the coupon rate is applied to the adjusted principal, we'll see an increase in the coupon payment proportional to the inflation rate.

The steps are as follows:

1. Adjust the principal by the inflation rate for the first year: $1,000 * (1 + 0.0845) = $1,084.50.
2. Calculate the new adjusted principal after the second year: $1,084.50 * (1 + 0.0845) = $1,176.36 approx.
3. Apply the real coupon rate of 4.3% to the adjusted principal for the second year coupon payment: $1,176.36 * 0.043 = $50.58 approx.

However, the question asks for the real value of the payment, implying that it's asking for the originally stated coupon value without accounting for the effect of inflation.

Since the real value is fixed and not influenced by inflation, the coupon payment's real value in the second year remains at $43 as stated in the bond terms