Question on TVM problem colleagues, discount, receive, investor, question

invic

Good day, colleagues!
I learn on Kaplan Shweser 2011 CFA Level 1. Now I`m on TVM concept.
Please explain me test question on page 132 #13:
An investor will receive an annuity of $4,000 a year for ten years. The first payment is to be received five years from today. At a 9% discount rate, this annuity`s worth today is closest to:
A. $16,684
B. $18,186
C. $25,671.
Answer:
Two steps: (1) Find the PV of the 10-year annuity: N=10, I/Y=9, PMT=-4000, FV=0,CPT-PV=25,670.63. This is the present value as of the end of Year 4, (2) Discount PV of the annuity back FOUR years: N=4, PMT=0, FV=-25,670.63, I/Y=9, CPT-PV=18,185.72.
I can not understand, why we need to
discount PV of the annuity back FOUR years???

hanvinh

For any such problems, drawing a timeline would be of great help to simplify the understanding of cash flow……..
Here, total time horizon is 14 years…..i.e. first 4 years from now, when we won’t have any cash flow and 10 years thereafter when we will get $4000 each year.
First of all draw the timeline….
t               =  0  1  2   3   4   5   6   7   8   9   10  11  12  13  14
Payment =  0  0  0   0   0  ($4000 each year till year 14………)
Now, calculate the PV of cash inflow till year ending ‘4’ by using PVIFA formula or calculator….
ie. ((4000*(1+9%)^(14-4))-1)/(9%*(1+9%)^(14-4)) = $ 25670.63
PV of cash flow at year 0 shall be= 25670.63/(1+9%)^4= $ 18185.72
Regards,
Kailas Kale

KungFuPanda

(1) if you discout the 10 years annuity using ordinary annuity, you would have to deposit the money in the beginning of year 4 to get the money in year 5 (End of year payment). In other words, to recieve it in 5 years, you need to deposit the money in year 4. Year 4 is thus the year you need (x) amount.
(2) Another way to do it, is that since the first payment comes in year 5…  you can find PV using annuity due or beginning payment for 10 years. This gives your a PV of 27980.99. Changing back to End payment, then discounting back 5 years gives you the 18,186.
TVM is simple when you think in terms of timing and when you get the money. If you master timing, you master TVM!
Hope that helps