Question

Over the past year (from 1 year ago to today), the inflation rate was 5.26 percent, the risk-free rate was 7.86 percent, and the real rate of return for a bond was 9.38 percent. The bond was priced at 1,192.22 dollars one year ago and 1,212.7 dollars two years ago, pays annual coupons of 50.99 dollars, and just made a coupon payment. What is the price of the bond today?

Answer 1

Answer-

Let us consider the one year back Scenario

Given

Real rate of rerturn = 9.38 %
Inflation rate = 5.26 %

YTM includes real rate of return and inflation rate.

Real rate of return = ( 1 + nominal rate / 1 + inflation rate) - 1

9.38 % = ( 1 + nominal rate / 1 + 5.26 % ) - 1

9.38 % + 1 = (1 + nominal return) / ( 1 + 5.26 %)

1 + nominal rate = ( 1 + 9.38 %) x ( 1 + 5.26 %)

1 + nominal rate = ( 1 + 0.0938 ) x ( 1 +0.0526)

1 + nominal rate = ( 1.0938) x ( 1.0526)

1 + nominal rate = 1.15133

nominal rate = .1.15133 - 1

nominal rate = 0.15133

nominal rate = 15.133 %

YTM = 15.133 %

Present Value = PV = $ 1192.22 [ Considering one year back ]
Coupon Payment = PMT = $ 50.99
YTM = 15.133 %
Number of periods = 1
Furture value = FV = ?

FV = $ 1321.65

The price of the bond today = $ 1321.65

Note- The two years ago price of $ 1212.7 is not relevant as the YTM might be different at that time.