- CFA Exams
- CFA Level I Exam
- Topic 1. Quantitative Methods
- Learning Module 2. Time Value of Money in Finance
- Subject 2. Fixed Income Instruments and the Time Value of Money
CFA Practice Question
A 10-year government zero coupon bond is currently yielding 6.4%. If in 10 years, you expect a two year government zero coupon bond to provide a yield of 10.7%, what must the yield be on a 12-year zero coupon bond today in order for you to be indifferent between the 10-year bond and the 12-year bond?
A. 7.1%
B. 7.7%
C. 8.4%
Explanation: To be indifferent, both securities must yield the same total dollar amount at the end of the investment horizon, which, in this case, is 12 years.
Option II: Buy a 12-year bond.
(1.064)10 (1.107) 2 = (1 + x) 12
= 7.1%
where x is the yield on the 12-year bond.
Option I: Buy a 10-year bond and then a two-year bond.
Option II: Buy a 12-year bond.
When indifferent: Option I = Option II
(1.064)10 (1.107) 2 = (1 + x) 12
= 7.1%
where x is the yield on the 12-year bond.
User Contributed Comments 12
User | Comment |
---|---|
rgat | why isn't the 10 yr and 12 yr forwards not divided by 2?? |
mountaingoat | anyone help explain the logic behind the calculation: FV(10yr)*FV(2yr) = FV(12yr)? |
ridone | 6.4% is the yield in 10 of 12 years and 10.7% is the yield in 2 of 12 years hence (6.4x10/12)+(10.7x2/12)=7.11% |
jmelville | rgat - I think you don't need to divide by 2 since it's a zero coupon bond |
JeremyMartin | i thought we should always assume that coupon rates are semiannual? when should we assume that rates are annual or semiannual? |
YOUCANDOIT | good question |
danceadam | The above answer is wrong. You should always use semi annual rates when valuing zero coupon bonds. |
jfrank7 | The answer is the same if you assume semi-annual payments and divide the interest rates by 2. |
maria15 | Ridone - I like your take on the calculation. Thanks! |
birdperson | jfrank7 - i disagree! ((1 + (.064/2))^20 * (1 +(.107/2))^4 ) ^ (1/12) - 1 = 7.237% not 7.1% which you get following the solution provided by analystnotes! |
raywen8 | ^ (1/24) instead of ^ (1/12) |
ascruggs92 | that was way easier than I thought |