Time Value of Money Question!!

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Valuestrats

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It will cost $20,000 a year for four years when an 8-year old child is ready for college. How much should be invested today if the child will make the first of four annual withdrawals 10- years from today? The expected rate of return is 8%.
So the first part of this is:
N=4 I=8 PMT=20,000 PV=66,242.54
I really don’t understand why the second part is:
N=9? I=8 FV=66,242.54 PV=33,137.76
Why is N=9, shouldn’t N=10 since the withdrawal is 10 years from today??

Please help, thanks so much
 
As per my understanding what you have done in first part is you have calculated P.V. of the four annual payments at 9th year so in order to calculate the P.V. as at 0 year you have to discount it over the period of 9 years.
Alternatively, what could have done is :-
N=3, I/Y=8, PMT=-20,000
CPT PV=> 51,542, this is the PV at 10th year of 3 annual payments in year 11,12,13 now add 20,000 to be paid on 10th year in it to arrive at 71,542 this is the PV of all the 4 payments at 10th year.
Now, you can use following
N=10, I/Y=8, FV=-71,542
CPT PV=>33,138.
I hope this is the answer.
 
This is correct.
Valuestrats. If you wanted to use N=10 then you initially have to use BGN mode in your first calc.
BGN: N=4 I=8 PMT = -20 FV=0 CPT PVT = 71541
END: N=10 I=8 PMT=0 FV=71541 CPT PV= £33,138
I find that drawing the timeline helps show where the PV and FV are, then it’s just a case of think about the N.
Hope this helps. If you need a better explanation then please let me know.
Pok
 
You can also use the cash flow calculator. Specify that CF0=0, CF1-CF9 = 0, CF10-13=20,000 and calculate NPV given IR of 8%.
or calculate the NPV as the difference of two perpetuities - one that starts on year 10 and another one that starts on year 14: (20/8%)/1.08^9-(20/8%)/1.08^13=33.14 (in thousands)
 
Yeah, tuition is one of those sneaky subjects. You have to remember that it’s due at the beginning of each of those four years, not the end.
 
maratikus wrote:
You can also use the cash flow calculator. Specify that CF0=0, CF1-CF9 = 0, CF10-13=20,000 and calculate NPV given IR of 8%.
or calculate the NPV as the difference of two perpetuities - one that starts on year 10 and another one that starts on year 14: (20/8%)/1.08^9-(20/8%)/1.08^13=33.14 (in thousands)
Click to expand...
I like this first example. Does this solve the problem with using BGN and END that I sometimes get confused with?
 
Thanks for your help guys. The only thing I don’t understand is, if today is time 0, and you will make a annual payment 10 years from today, so 10 periods total has passed by. Why do we use 9, when 10 periods have passed by. Can anyone explain this logic without using numbers?
The only thing that makes some sort of sense for me is that it’s just a rule, problem is I don’t understand the logic behind this. Please help!
-The present value of a perpetuity or annuity is valued one period before the first payment.
-The present value of an ordinary annuity gives the value of the payments one period before the first payment.
 
Draw a timeline. Label it periods 0 (8years old) to 10 (18 years old) to 13 (21 years old). First payment is at period 10.
I think you’re getting confused based on what is beginning and what is end. In this question, you are using an ordinary annuity. An ordinary annuity makes payment at the end of a period. So think of it this way: you are actually paying at the end of period 9 and not the beginning of period 10 (yes, it’s exactly the same). This is why you’re discounting 9 periods instead of 10. Therefore, as same as your second bullet point, the PV of an ordinary annuity is at period 9, one period before the first payment (period 10).
If it’s easier for you to discount it 10 years, you can you an annuity-due. An annuity-due makes payment at the beginning of the period. So in this case, beginning of period 10 (which is the same as end of period 9). Therefore, the PV of an annuity-due is at period 10.
Hope that made sense.
EDIT: Whoops, I thought I quoted. Anyways, this response is aimed at OP’s post directly (1) above.
 
Notice that the first of four withdrawals is ten years from *today*. Ten years from today is the same as N=9.
 
I like to think it this way. If I invest in a bank deposit today (t=0), I would earn an interest payment only at the end of the year which is actually (t=1). So, when I need money at t=10, beginning of the year, I’d only get an interest payments for 9 periods I had invested.
I hope it helps to clear the concept. I guess understanding when to use Begin and End function in the calculator would also help.
 
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