- CFA Exams
- CFA Exam: Level I 2021
- Study Session 2. Quantitative Methods (1)
- Reading 6. The Time Value of Money
- Subject 4. The Future Value and Present Value of a Series of Equal Cash Flows (Ordinary Annuities, Annuity Dues, and Perpetuities)

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**CFA Practice Question**

If you owed $200 at the end of each year for the next three years, the present value of the obligation would be ______.

B. the same as it would be if you had to pay $300 today and $300 at the end of three years

C. less than it would be if you had to pay $300 today and $300 at the end of this year

A. less than it would be if you owed all $600 at the end of three years

B. the same as it would be if you had to pay $300 today and $300 at the end of three years

C. less than it would be if you had to pay $300 today and $300 at the end of this year

Correct Answer: C

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**User Contributed Comments**
20

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

Laurel |
Need an explanation on why the selected choice is the correct answer. |

Claudio |
because all other choices are wrong! |

Iyer |
We know that $100 today is more valuable than $100 3 yrs from now. why (a) is wrong: 200 you pay at the end of first yr is greater than 200 tht you pay after 3 yrs. Similary $200 that you pay fater 2 yrs is greater than $200 tht you pay after 3 yrs. and $200 that you pay after 3 yrs is the SAME as $200 after 3 yrs. Summing all three, we get $600 after 3 yrs is less than ($200 after 1 yr+ $200 after yr. 2 + $200 after yr. 3). (b)by similar argument choice b is wrong. $ 600 now is greater than ($200 after yr1 + $200 after yr2+ $200 after yr.3) why the selecte choice is correct: you are paying the $ 600 before 3 yrs wheras in wheras in the former case you pay $600 only at the end of 3 yrs. |

stranger |
(a) The longer the period the lesser is its present value, hence choice a is incorrect. (b) Here 300 today has PV=300, in our case the PV's of all amounts will be lesser. |

suraj |
Calculating the present value in each condition. If we were to pay it in 3 equal installments of 200 with a fictional rate of intrest as 10% then PV would be calculated as 200/1.1 + 200/1.21+ 200/1.31 where the denominator repersents the (1+r)^n or PV1=200 [1/0.1 -1/0.1(1.1)^3] PV1=497 PV2= All 600 after 3 years PV2=600/1.1^3=450 PV3=300 today and 300 at end of 3 years => 300 +300/(1.1)^3=390 PV4=300 today and 300 at the end of this year 300+300/1.1=572 hence for a.. it is 472 v/s 450 for b its 472 v/s 390 C is 472 v/s 573 which happens to be right |

aguns |
intelligent analysis by suraj. thnx |

stefdunk |
kudos to suraj, I just used logical reasoning, like ayer and stranger |

imroark |
If I interpret (A) correctly, it is equivalent to a Single Cash Flow of $600 at the end of 3 years. At an assumed Rate of 10%, the PV works out to $798.6. Instead if I pay $200 at the end of each year for 3 years, the PV is $497.4, which is less than $798.6. So, I think the answer ought to be (A). (Open for crticism) |

imroark |
The answer's right. Got my formula wrong the last time! |

ehc0791 |
If the interest rate is positive, then the answer is right. What if the interest rate is 0 or negative (deflation)? |

tom1980 |
but the point is that no one would lend u the money and give u the interest or no interest. |

StanleyMo |
i would think of factor inflation where money become smaller each year. |

wundac |
The selected choice is the only correct answer since An annuity due payment PV: PV=PV of a regular annuity*(1+r). Thus the importance of knowing your formula. |

Spawellian |
just pick any arbitrary interest rate and work out the PVs by drawing timelines. The same relationships should hold for any level of i |

8thlegend |
I really don't think you need to do any calculation. Just think of it as a mortgage. If put a down payment, you pay less on interest. So just by just looking at C you are working with $300 payment instead of $600 like the other 2 |

endurance |
The easy way is to use the cash flow menu on BAII if you can't reason the basics. CF0 = 0, CF1 = 200, CF2 = 200, CF3 = 200 I = 10 percent - Compute NPV = 497.37 Okay, then compare with the other cash flow assumptions - I is the same in all: A) NPV = 450.79, B)+C) = 498.12 Answer is C, because 497.37 is less than 498.12 |

nohuchi |
200/1.1 + 200/1.21+ 200/1.31 where the denominator repersents the (1+r)^n or PV1=200 [1/0.1 -1/0.1(1.1)^3] PV1=497 PV2= All 600 after 3 years PV2=600/1.1^3=450 PV3=300 today and 300 at end of 3 years => 300 +300/(1.1)^3=390 PV4=300 today and 300 at the end of this year 300+300/1.1=572 |

jjh345 |
Don't look at complicated math for this problem. Simple: Depreciation of the dollar from inflation. Assume your dollar is worth less tomorrow than it is today. If you pay more sooner, rather than later, it's "more" expensive, because the dollar depreciates over time. |

ibrahim18 |
I assumed no interest rate. They should have told us to assume an interest rate. |

amodkale |
suraj's analysis is all incorrect. He is conveniently assuming that there is 600 terminal inflow. I used PMT 200, N 3, I/Y 1 and PV comes to 588 (which is real value), then I applied 300 which I would received at the end of 3 years as one time flow at 1% interest which gave me present value of 291 so C option's value came 591 which proves C option is incorrect. |