Quant Question: Ordinary Annuity / Annuity Due

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Scotty88

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I am having trouble understanding the explanation to this question, could someone help me understand the time line or if there is a mistake?
Qu: Debbie planning for daughter's college tuition. Her daughter will go to college in 5 years time and the required funds for tuition are $20,000 per year for 4 years, paid at beg of each year. Investments will return 7% per year. How much should Debbie set aside now?
The answer says:
Step 1: Calculate pv of regular annuity paying $20,000 each year for 4 years: N=4, I/Y=7, PMT=20,000;FV=0, CPT PV = 67,744
Step 2: Calculate sum required to generate the lump sum at beg of year 4: 67,744/1.07 to the power 4 = $51,682.
Now what I don't understand mostly is the timeline to this problem, why do we calculate money needed at BEG year 4 when she doesnt go to college for 5 years? Wouldn't she pay at end year 4, beg year 5?
 
I agree - if the problem is correctly stated, she should need to set aside 67744/1.07^5 not 67744/1.07^4. Oops.
 
I tried to solve your question without looking at the explanation and got the same answer.
Basically, first I calculated N = 4, I/Y = 7% and PMT = 20000 and PV = 67744 in END MODE.
But the problem is that this cash flow is in end mode, I multiply this by 1.07 to get it into BEG mode, which is 72486
I set this as the future value and make n = 5, the PV is exactly equal to 51682.
The only difference between my solution and yours is that I adjusted for BEG before calculating how much I have to set aside.
 
Basically, we need more money because we need the first payment at the end of 5 years. If we only use END mode, we will miss one year (the payment at the start of year 6 or end of year 5)
 
draw a timeline. It looks to be correctly solved
0 is now
1,2,3,4 – nothing
5, 6, 7, 8 => 20 K for 4 years.
you need money at the beginning of year 5 onwards.
discounting the 20K for 4 years at 7% gives you 67.744K at the end of year 4.
now discount that back 4 years…. to get 51.682 K.
 
^^ don’t you mean you need money at beg of year 6??
yeah i don’t bother with the annuity due, just work it like an annuity.
if u work it like a regular annuity, instead of being 9 years in total, there are 8 to be accounted for. this is b/c the last payment is at the BEGINNING of year 9, so in a reg annuity, it’s the same as END of year 8.
so u first discount the 4 years with the 20 000 payment, and get ur 67 744.23 number. this number represents the amount needed ONE YEAR BEFORE the 1st 20 000 payment. so instead of discounting 5 years to get to TODAY, you are now discounting back 4 years (b/c ur already a year before the 20 000 pmt, which is equal to 4 years from now) to get ur 51 682 figure.
 
on the timeline 20k is needed at years 5,6,7,8. the most obvious but time consuming method is to discount 20k by 7% for 5,6,7,8 yrs and then sum them up. the alternative is to use the annuity method on your calc. i think that’s where you seem to be confused. the ordinary annuity starts 1 period away, whereas annuity due starts now. so the first 20k payment (at yr 5) is one period (1 yr in this case) into the future from the PV=67,744 (i.e yr 4 on timeline). discounting PV at yr four by 7% for 4yrs would give you the right answer. i would try to avoid changing calc mode to BGN because it is time consuming and could really mess your whole exam up if you forget to change back to END mode. i suggest you brush up on annuities.
 
you can also use the CF function on your calc to determine the NPV of a series of CF’s
Here CFO=0, CF1=20, F1=4, Hit NPV, enter rate 7
Gives you 67.744 directly.
 
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