Question

Consider a bond with 10 years to maturity, paying fixed semi-annual coupons at a rate of 6% on a notional principal of $100,000. a. What is the value of the bond, if it trades at a yield-to-maturity of 4%? b. What is the percentage change in bond value if the yield increases to 6%? c. How would the answer to a) and b) change if the maturity were 20 years? d. How would the answer to a) and (b) change if the coupon rate were 15%?

Answer 1

a) N = 10 x 2 = 20

PMT = 6% x 100,000 / 2 = 3,000

FV = 100,000

I/Y = 4% / 2 = 2%

Computing Present Valueof (N, PMT, FV, I/Y)

Present Value = $116,351.43

Hence, the value of the bond, if it trades at a yield-to-maturity of 4% is $116,351.43

b) If I/Y = 6% / 2 = 3%

PV => $100,000

% Change = 100,000 / 116,351.43 - 1

% Change = -14.05%

c) If N = 20* 2 = 40

PV = $127,355.48

% Change = 100,000 / 127,355.48 - 1

% Change = -21.48%

d) If N = 20 =

I/Y = 4%/2 = 2%

PMT = 15% x 100,000 / 2 = 7,500

PV (N,I/Y,PMT) = $189,932.88

When I/Y = 6%/2 = 3%

PV = $166,948.64

% Change = 166,948.64 / 189,932.88 - 1

% Change = -12.10%