Question

Moerdyk Corporation's bonds have a 15-year maturity, a 7.25% semiannual coupon, and a par value of $1,000. The going interest rate (rd) is 6.20%, based on semiannual compounding. What is the bond’s price? $1,047.19 $1,074.05 $1,101.58 $1,129.12 $1,157.35

Answer 1

Answer:

$1,101.58

Explanation:

Tenor: 30 times (15-year maturity * 2 for semiannual)

Coupon rate: 7.25% semiannual -> coupon received semiannual (PMT) = $1,000 * 7.25%/2 = $36.25

Face value (FV): $1,000

Yield To Date (YTD): 6.20% semiannual -> YTD per semiannual = 3.1% (=6.20%/2)

Bond’s price = present value of bond + present value of total coupon received semiannual

Present value of bond = FV/(1+ YTD) ^tenor = 1000/(1+3.1%)^30 = $400.1659

present value of total coupon received semiannual = 36.25/(1+3.1%)^30 + 36.25/(1+3.1%)^29+ ….. + 36.25/(1+3.1%)^1 = $701.4189

(we can use excel to calculate the PV of coupon received = PV(rate,tenor,-PMT) = PV(3.1%,30,-36.25) = 701.42)

⇒ Bond’s price = $400.1659+ $701.4189=  $1,101.58