Question

1- You are considering the purchase of a $1,000 par value bond with an 6.5% coupon rate
(with interest paid semiannually) that matures in 12 years. If the bond is priced to provide
a required return of 8%, what is the bond’s current price?

2- Two bonds have par values of $1,000. One is a 5%, 15-year bond priced to yield 8%. The
other is a 7.5%, 20-year bond priced to yield 6%. Which of these has the lower price?
(Assume annual compounding in both cases.)

3- Three years ago you purchased a 10% coupon bond that pays semiannual coupon pay-
ments for $975. What would be your bond equivalent yield if you sold the bond for cur-
rent market price of $1,050?

Answer 1

1]

price of bond is calculated using the PV function in Excel with these inputs :

rate = 8% / 2 (annual yield converted to semiannual yield)

nper = 12 * 2 (12 years to maturity with 2 semiannual coupon payments each year)

pmt = 1,000 * 6.5% / 2 (semiannual coupon payment = face value * coupon rate / 2)

fv = 1,000 (face value of bond receivable on maturity)

PV is calculated to be $885.65

2]

price of bond 1 is calculated using the PV function in Excel with these inputs :

rate = 8% (annual yield)

nper = 15 (15 years to maturity)

pmt = 1,000 * 5% (annual coupon payment = face value * coupon rate)

fv = 1,000 (face value of bond receivable on maturity)

PV is calculated to be $743.22

price of bond 2 is calculated using the PV function in Excel with these inputs :

rate = 6% (annual yield)

nper = 20 (15 years to maturity)

pmt = 1,000 * 7.5% (annual coupon payment = face value * coupon rate)

fv = 1,000 (face value of bond receivable on maturity)

PV is calculated to be $1,172.05

the price of bond 1 is lower

3]

realized return over 3 years = ($1,050 - $975) / $975 = 7.69%

BEY = 2 * [(1 + yield)^0.5 - 1]

BEY = 7.55%