- CFA Exams
- CFA Exam: Level I 2021
- Study Session 15. Fixed Income (2)
- Reading 46. Understanding Fixed-Income Risk and Return
- Subject 1. Sources of Return

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**CFA Practice Question**

An 8%, 20-year, $100-face value bond is selling for par. What is the required amount of reinvestment income necessary to earn the yield to maturity (semi-annual compounding)?

B. $220.10

C. $380.10

A. $160.00

B. $220.10

C. $380.10

Correct Answer: B

YTM=8% (par bond) reinvestment income = {4 [(1.04)

^{40}-1]/.04 -160} = {380.10-160} = $220.10###
**User Contributed Comments**
17

User |
Comment |
---|---|

zhaojiang |
N=40, I/Y =4,PV=0, PMT=4, CPT FV=380.10 380.10-(20*8)=$220.10 |

melissatt |
where did that 160 come from? Why 20 x 8 ? |

haarlemmer |
8(annual interest)* 20(# years in total) |

wroger |
must subtract coupon payments |

AlexYuen |
what abt the principal repayment? Should it not be subtracted too? |

tagr |
Yes, if you use N=40, I/Y=4, PV=-100, PMT=0, CPT FV=480.10 480.10-(20*8)-100=$220.10 |

julescruis |
good comment tagr |

steved333 |
SUBTRACT COUPON PMTS!!! |

prachirp |
Fv=480.10 less 100 (par value) Less 20*8=160 (interest) =220.10 Simple steps. |

mrushdi |
Generaly we have to deduct par value or purchase cost from total cash flows? |

moneyguy |
compute FV of zero-coupon bond then subtract coupon payments and Purchase Price |

jonan203 |
guys, it is simply the future value of an annuity less the sum of the annual coupon payments. FVa - (coupon payment * years) = reinvestment income |

jonan203 |
HP12C: 4 <enter><enter> 1.04 <enter> 40 <y^x> 1 <minus><times> .04 <divide> 160 <minus> |

johntan1979 |
For those who are still confused about the 20 x 8, that is actually the coupon interest which needs to be subtracted to get reinvested income. In actuality, it should be annual coupon rate x face value x annual periods i.e. 0.08 x 100 x 20 |

janglejuic |
thanks johntan1979. without face value it did not make any sense to multiply not converted (8 to 0.08) annual coupon percentage and annual period |

fzhou |
If you're confused with when to subtract coupon payments when not to, please compare this question with question 1 in the same quiz section. In question 1, "total dollar return from coupon AND reinvestment income", therefore you don't have to remove the coupon part; but in this question, it only asked for reinvestment income, therefore you have to subtract the coupon payments from FV. |

pigletin |
330 should be the reinvestment income (reinvested coupons) 220 is the interest on interest (the amount in excess of the coupons) |