Practice question in schweser notes

CFA Level I
#1

In Module Quiz 6.3, An investor will receive an annuity of $4,000 a year for 10 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.
The answers are given as: 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 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. (LOS 6.e)

I don’t see why the PV=25,670.63 is at the end of year 4, I feel like it should be at the end of year 5.The question did not mention that the payment is an annuity due. Can someone explain pls?

#2

Step 1 is the value of an immediate annuity, so the PV will be as of the end of year 4. You could also do this problem as an annuity due at the end of year 5 and discount back by 5 years; this should also produce the same PV at time 0. (PV of annuity due at time 5 = 27980.98759)

The fastest way to do this problem is with the CF worksheet
CF 2nd CLR WORK
CF0 =0 c01=0 F01=4 c02=4000 f02=10
2nd quit
NPV I=9 CPT NPV 18,185.72205

#3

Clearly solved. Many thanks!