3. A bond with 3 years remaining to maturity has an annual coupon rate of 6.40%,

Question

3. A bond with 3 years remaining to maturity has an annual coupon rate of 6.40%, and a face value of $1,000. Assume the yield to maturity is 7.10% and answer the questions below. (You may use a financial calculator to get the PV of the bond in this problem - but show your calculator entries, i.e., 1000 FV, etc). a) (8 points) What is the duration of this bond? b) (7 points) If interest rates rise 0.25% from the given YTM, by what percent will the bond change in value? Show this 2 ways as we did in class; (using modified duration and the capital gains formula method).

Explanation / Answer

ANS 3

a) USING THE MACAULY DURATION FORMULA

DURATION = SUM{t*c/(1+i)^t} + n*m/(1+i)^n / P

t = TIME IN YEARS UNTILL MATURITY

c = COUPON PAYMENT AMOUNT IN DOLLARS

i = INTEREST RATE (YIELD TO MATURITY)

n = NUMBER OF COUPON PAYMENTS MADE

m = PAR VALUE (PAID AT MATURITY)

P = BOND'S CURRENT MARKET PLACE

DURATION = {3*$64/(1+7.10%)^3 + 2*$64/(1+7.10%)^2 + 1*$64/1+7.10%)^1 + 3*$1000/(1+7.10%)^3} / $1000

{ 156.30 + 111.60 + 59.75 + 2242 } / 1000

= 2.56965 YEARS

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