Question

You own a 10-year bond and a 20-year bond, both of which are non-callable bond and pay a coupon of 7%. What is true about the change in value of your bonds, if interest rate falls from 12% to 8%?

The value of the 20-yr bond will decrease by $60 more than the 10-yr bond

The value of the 20-yr bond will decrease by $27 more than the 10-yr bond

The value of the 20-yr bond will increase by $60 more than the 10-yr bond

The value of the 20-yr bond will increase by $27 more than the 10-yr bond

.The value of the 20-yr bond will increase by $72 more than the 10-yr bond

Answer 1

Calculating Price of 20 year bond at 12%

Using TVM Calculation,

PV = [FV = 1,000, PMT = 70, N = 20, I = 0.12]

PV = $626.53

Calculating Price of 20 year bond at 8%

Using TVM Calculation,

PV = [FV = 1,000, PMT = 70, N = 20, I = 0.8]

PV = $901.82

Calculating Price of 10 year bond at 12%

Using TVM Calculation,

PV = [FV = 1,000, PMT = 70, N = 10, I = 0.12]

PV = $717.49

Calculating Price of 10 year bond at 8%

Using TVM Calculation,

PV = [FV = 1,000, PMT = 70, N = 10, I = 0.08]

PV = $932.90

DIfference in Change in Price = (901.82 - 626.53) - (932.90 717.49)

DIfference in Change in Price = $60

The value of the 20-yr bond will increase by $60 more than the 10-yr bond