Question

Find the duration of a 8% coupon bond making annual coupon payments if it has three years until maturity and a yield to maturity of 7.8%. What is the duration if the yield to maturity is 11.8%? (Do not round intermediate calculations. Round your answers to 4 decimal places.)

YTM	Duration
7.8% YTM
11.8% YTM

Answer 1

NUMBER OF YEARS CASH FLOWS DISCOUNTING FACTOR CASH FLOW * DF

@8%

1 80 0.9259 74.0720

2 80 0.8573 68.5840

3 1080 0.7938 857.3040

THEREFORE, THE DURATION OF THE BOND IS : PV OF THE CASH FLOWS/ PV OF THE BOND

PV OF CASH FLOWS = $999.96

THE PV OF THE BOND IS :

FV = $1000

PMT = 80

YTM= 7.8%

N = 3 YEARS

THEREFORE, THE PV IS = 1005.17

THE DURATION IS 0.9948

THE DURATION OF THE BOND WHEN THE YTM IS 11.8 WILL BE

THE PV OF THE BOND WILL BE :

FV= $1000

PMT = $80

N = 3 YEARS

YTM= 11.8

PV = $908.4158

SO THE DURATION WILL BE : $999.96/908.4158 = 1.1008