### CFA Practice Question

A bond pays a coupon of \$1,000 after 6 months, \$1,000 after 1 year, \$3,500 after 1.5 years, and \$104,000 after 2 years. The spot annual interest rates for 0.5, 1, 1.5, and 2 years are 0.045, 0.055, 0.052, and 0.048, respectively. What is the value of this bond?
A. \$99,753.23
B. \$96,750.23
C. \$99,751.98
Explanation: We calculate the value of this exotic bond using the arbitrage-free valuation approach. We discount each of the four cash flows to the present, and sum the total. Notice that each spot rate is divided by 2 because the rates are annual but the coupons are paid semiannually. P = \$1,000 / (1 + 0.045/2) + \$1,000 / (1 + 0.055/2)^2 + \$3,500 / (1 + 0.052/2)^3 + \$104,000 / (1 + 0.048/2)^4 = \$(977.99 + 947.19 + 3,240.60 + 94,587.45) = \$99,753.23

User Comment
isida why are they dividing the spot rates by 2?? these rates are already semiannual rates
masha Q says the spot ANNUAL interest rates evern thought they are quoted for 0.5, 1 etc
humphrey why is it not (1+r)^0.5, (1+r)^1.5, etc.?
jason First: the rates are annual rates but we need to compound them semiannually, so we divide them by 2.
Second. as the compounding unit is 0.5 year, for 1.5 years (which is 3 units of hlaf-year period) it should be (1+r)^3 instead of (1+r)^1.5.
sireklove You can find this information on p164 of the Fixed Income Analysis text book.

PV(CF)= Cash Flow/[(1+Spot Rate/2)]^period
NickPash A and C are very close considering the amount of work you have to put to get the number. I did not calculate al the way and guessed C. Lesson learned. calculate all the way.
shiva5555 Is there a faster way on the calculator?
dipu617 Can it be done on BA II Plus?
dipu617 I can't do it in 1.5 minutes.... no way..........
Mikehuynh Forgot to divided by 2, luckily picked the correct answer.
leftcoast You don't have to be able to do every question in 1.5 minutes. It's expected that some will take longer some will take less.
asalonga7 i kinda wish we didn't have to use a BA2Plus for this exam. Any calculator with an extended display would make the calculations way faster
farhan92 ^except the NPV/IRR and Stats calculations...get your point though its the 21st Century surely these things can be sorted out now