Question

ANSWER: 1415.31

John is considering acquiring a couple of Citigroup bonds, which were initially offered with a face value of $1000, a coupon rate of 12% per year (paid semiannually), and a maturity of 12 years. However, these bonds already paid 3 coupons and John is planning to buy them now, right before the next coupon payment (hence coupon received at John’s time “zero”). Find the pure price of each Citigroup bond if the current market interest rate for similar financial assets is 7% per year (compounded semiannually). Note: round your answer to two decimal places, and do not include spaces, currency signs, plus or minus signs, nor commas.

Answer 1

ans:

Since three coupons have already been paid, so John gets first coupon at t=0 for him.

Total coupons that John receives is from 4th to 24th (as semiannual payments) = 21

time remainig to maturity = 10 years as he purchases right before first coupn payment.

coupon amount = 12/100 * 1000 = $120 = $60 semi annualy

so,

PV of all future payments = 60*(1-(1+0.035)^-20)/0.035 = $852.744

payment received at t=0 = $60

pv of face value to be received at end of tenure of bond = 1000/(1+0.035)^20 = 502.565

so, pure price of each bond = 60+852.744+502.565 = 1415.31