TVM Ques 18

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FeRMioN

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While attempting TVM questions.
CFA L1 Curriculum > TVM > Page 296 > Ques 18

The ques mentions cost payable at the beginning of the year. However, in the solution, this “beginning” concept is not taken into consideration. Something wrong somewhere ?

Thoughts, please!
 
I don’t think there’s anything wrong. You can choose to consider it as a regular annuity if you’re sensitive to the adjustments you need to make (a timeline usually helps with this). This is true because a payment at a beginning of year X is, for all practical purposes, a payment at the very end of year X-1. With this in mind, here are two ways to arrive at the same answer:
>>regular annuity (calculator in END mode all the time):
we have 4 payments of 20k each starting 18 years from now (ie. at the beginning of year 18). The PV of those is 70,919. Notice that this is the PV at the beginning of Year 17 (since it’s a regular annuity). Now this is the FV of the regular annuity with 17 payments. Set i=0.05, n=17, PV=0, and PMT should get you the right answer.
>>annuity due (calculator in BGN then END):
Start with BGN mode. Calculate the PV of an annuity due with 4 payments of 20k at 5%. That should give you 74,465. Notice that this is the PV at the beginning of year 18 (=end of year 17). We need to discount it at 5% to bring it to the PV at the beginning of year 17; that is, again, 70,919. This is our FV for the regular annuity. Switch back to END mode and repeat from above.
Notice that in both cases we choose the beginning of year 17 as our FV. This is because, for a regular annuity, that’s when the 17th payment is acutally made. Try to visualize the timeline: payment 1 is made at the end of year0, p2 at year1_end… p17 at year16_end (or equivalently, beginning of year 17).
Hopefully this made sense.
 
Thanks for the detailed response.
I do understand the timeline equivalence concept. However, my thought process is due to the confusing wording. In the starting, the question says that payment starts 18 years from now (this is in accordance of the solution given and your reasoning). But the problem is that later in the question it also states that these four payments of 20K each are at the beginning of the year.
I presume that these are - begin of yr18, begin of yr19, begin of yr20 and begin of yr21
So when I discount, the PV would accumulate at the begin of yr17 or end of yr 16. Then I would have to multiply it with 1.05 to get the cash flow at end of yr17 - later equating and this getting a diff answer.
I do understand it is a case of interpretation, however, the wording seems confusing so that the interpretation appears towards an alternate answer.
 
FeRMioN wrote:
So when I discount, the PV would accumulate at the begin of yr17 or end of yr 16. Then I would have to multiply it with 1.05 to get the cash flow at end of yr17 - later equating and this getting a diff answer.
Click to expand...
If you extend it to the end of yr17, it implies 18 payments instead of 17. Notice that the present is year 0, and between year 0 and beginning of year n, there are n payments; between year 0 and the end of year n, there are n+1 payments. Check it.
The second part of the question asks for an n=17 annuity, which means you should be concerned with the beginning of year 17 (=end of year 16).
 
The ques say “If she starts next year and makes 17 payments”.
Thus it is clear that the payments are - End yr1, End yr2,…… End yr17
Hence, I had accumulated both sides at End yr 17.
 
FeRMioN wrote:
The ques say “If she starts next year and makes 17 payments”.
Click to expand...
Yeah, what that means is that the first payment will not be made now, but in a year (ie. next year). That doesn’t mean the end of year 1 because that would essentially be 2 years from the present T0.
 
I do not agree.
T0 essentially means end of Year 0 (as per time line convention) - unless we refer specifically to the beginning of year 0.
orang3eph wrote:
Yeah, what that means is that the first payment will not be made now, but in a year (ie. next year). That doesn’t mean the end of year 1 because that would essentially be 2 years from the present T0.
Click to expand...
 
It’s your right to be wrong, and I shall not interrupt heretofore. But just to set the record straight on what the convention really is, you should know that T0 is T0 no matter what, and it strictly refers to the very present. The end of year 0 is the beginning of year 1 and that’s one period away. This shall become clear upon inspection of any timeline in reading 5 or elsewhere.
 
Thanks orang3eph - I do appreciate that you have spent time to reply to my query. I will go through the material and check again. Perhaps, I needed a different point of view of think about this and that is what you have given me - something to explore with a fresh perspective.
 
Thank You Arif Irfanullah for this detailed effort.
However, the only problem that I am facing is in interpretation of the “english” used in the question.
Like you mentioned in the video… the college starts 18 years from now => also, you have also elaborated on the timeline that this is “End of yr 18”
Now, the 4 payments are to be made at the “beginning” of each year - so that these should be “Begin of yr18”, “Begin of yr 19” and so on - is that not so?
Whay are we interpreting that the “1st payment at the beginning of the year” means the “end of year 18” ?
 
The questions is phrased in a somewhat confusing manner so we have to use some common sense.
The child is starting college at end of year 18 which is exactly the same as saying start of year 19. Hence the first payment is beginning of year 19. Making the first payment at the start of year 18 would be mean that the the first payment is made one year before the child starts. This would not make sense.
 
The questions is phrased in a somewhat confusing manner so we have to use some common sense.
The child is starting college at end of year 18 which is exactly the same as saying start of year 19. Hence the first payment is beginning of year 19. Making the first payment at the start of year 18 would be mean that the the first payment is made one year before the child starts. This would not make sense.
 
That is also possbile sometimes - some institutes do ask the students to deposit the fees in advance. Well, maybe not one year in advance, though :)
We would not be landing into this confusion, if the question had just mentioned - “beginning of academic year”.
Beginning of year generally implies beginning of calculation or timeline year !
 
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