### CFA Practice Question

Suppose the spot rates (annualized) for Treasuries are given as:

6 months = 1.31% (1/2 of annualized 6 month spot rate)
1 year = 1.92% (1/2 of annualized 1 year spot rate)
1.5 years = 2.37% (1/2 of annualized 1.5 year spot rate)
2 years = 2.96% (1/2 of annualized 2 year spot rate)

The Z-spread (annualized) is 1.24% for a 2 year maturity, 4% coupon (paid semi-annually) bond with face value of \$1,000. (Remember, these rates are calculated using 6-month periods.) The price of the bond is:
A. \$1,001.86
B. \$1,021.86
C. \$1,024.25
Explanation: You have to divide the Z-spread by 2 (to get the 6-month rate) and then add it to the spot rates.

User Comment
chantal can anyone explain pls ?
cwest020 I keep getting 996.72
jjhigdon I am also confused. 20/(1.0131+.0062) + 20/(1.0192+.0062)^2 + 20/(1.0237+.0062)^3 + 1020/(1.0296+.0062)^4 = 943.08. Why is that not right? The 6 month spot rates, even before adding the spread are less than the 1/2 year coupon rate, so the bond should be trading at a discount, right?
praj24 I'm really struggling with this, I've tried to calculate this price and I'm not getting the answer. Can anyone provide the right workings?

From my calculations I have:
6 mths = 1.31 + 0.62 = 1.93
1 Year = 1.92 + 0.62 = 2.54
1.5 Year = 2.37 + 0.62 = 2.99
2 Year = 2.96 + 0.62 = 3.58

Therefore PV of CFs:
20/(1.0193)^0.5 = 19.81
20/(1.0254) = 19.50
20/(1.0299)^1.5 = 19.14
1020/(1.0358)^2 = 950.71
Price = 1,009.16???

Also tried the same as JJ above but no luck.
Bedee Guess 1.009,16 is closest to the offered results, therefore Choice A is the correct one. Praj24's calc is the only feasible I am aware of. Don't forget u got many traps on the exam!

.5 Year = 1.31/2+.62 = 1.275%
1 Year = 1.92/2+.62 = 1.58%
1.5 year = 2.37/2+.62 = 1.805%
2 Year = 2.96/2+.62 = 2.10%

PV
Yr .5 = 20/1.01275 = 19.748
Yr 1 = 20/(1.0158)^2 = 19.38
Yr 1.5 = 20/(1.01805)^3 = 18.96
Yr 2 = 1020/(1.0210)^4 = 938.60

PV= 996.69

I don't see where I went wrong, pretty sure analyst notes is off.