Hi, I have difficulty in understanding one solution to a question which listed on Reading #5 — The Time Value of Money, pp 137. Question No.13, SCHWESER NOTES LEVEL I BOOK 1, --------------------------------------------------------------------------------------------------- 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: B Solution: Two steps: (1) Find the PV of the 10-year annuity: N = 10; I/Y = 9; PMT = -4,000; FV = 0; CPT —> PV = 25,670.63. This is the present value as o f the end ofYear 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. ------------------------------------------------------------------------------------------------ My questions, I think at Step 1, the N should = 5, because we are looking for the present value as of the end of Year 4, why the author say the N = 10?
Step 1 is finding the PV of the 10 annual cash flows as at time 4, i.e. as an annuity immediate; step 2 discounts the result from step 1 by 4 years back to time 0. N is the number of payments, not the deferral period.
You could also do this in the CF worksheet:
CF0=0, C01=0, F01=4, C02=4000, F03=4000
2nd, Quit, NPV, I=9, CPT NPV=18,185.722
n is the number of payments; there are 10 payments, so n = 10.
The best thing you can do in these situations is to draw a timeline:
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
$4k $4k $4k $4k $4k $4k $4k $4k $4k $4k
If you treat the annuity as an ordinary annuity (payment at the end of the year, calculator in END mode), then calculating the present value gives the value at time t = 4; you then need to discount it 4 more years to get the present value today.
If you treat the annuity as an annuity due (payment at the beginning of the year, calculator in BEG mode), then calculating the present value gives the value at time t = 5; you then need to discount it 5 more years to get the present value today.
Obviously, you get the same value each way.
You will recieve TEN incomes, they are not paid this year, but at the end of year 4, so calculate the PV of 10 cash flows of 4000 and then bring them to the present 4 periods. You will get those 18k.
the first step is to calculate the present value of hte annuity. the annuity has 10 payments. thus n = 10
HI all, thank you very much. 
Especially thank you to S2000magician and breadmaker.
I really happy we have so many volunteers helping people.
I am taking some time to digest all reply. So excited to see a detailed explanation.
My pleasure.
Pleasure