Question

Suppose you buy an inflation-indexed bond that will adjust with inflation and thus pay you $1,500 in real (inflation-adjusted) terms each year for the next five years, plus your real principal of $75,000 at the end of the fifth year. The nominal interest rate is 5 percent and the expected inflation rate is 3 percent. What is the present value of the bond? (Round to the nearest thousand dollars and pick the answer closest to the one you calculate.)

A. $65,000

B. $70,000

C. $74,000

D. $75,000

Answer 1

The bond is inflation indexed bond.

The coupon payment and principal amount are given in real terms.

So, real interest rate will be used to ascertain the present value of the bond.

Nominal interest rate = 5%

Expected inflation rate = 3%

Real interest rate = Nominal interest rate - Expected inflation rate = 5% - 3% = 2%

The real interest rate is 2%.

Calculate the present value of the bond -

PV = Coupon payment (P/A, i, n) + Principal repayment (P/F, i, n)

PV = $1,500(P/A, 2%, 5) + $75,000(P/F, 2%, 5)

PV = [$1,500 * 4.7135] + [$75,000 * 0.9057]

PV = $7,070.25 + $67,927.50

PV = $74,997.75

Thus,

The present value of the bond is closest to $75,000.

Hence, the correct answer is the option (D).