need cash 4 years from today, use t = 3 to discout?

CFA Level I Quant
#1

In the Schweser practice exams (first book exam 2 morning session #20), they have what should be a pretty easy perpetuity question, but the wording about the timing of the cash flows is really throwing me off.

Need money for scholarsship blah blah blah “Her plan is for the fund to be capable of awarding 25,000 annually in perpetuity. The first scholarship is to be awarded and paid out exactly 4 years from today. The funds will be deposited into an account immediatly and grow at a rate of 4% compounded semiannually…”

So once you get the value of the perpetuity, I discounted it back by 4 periods using the EAR, because 4 years is 4 periods. I got the value of the perpetuit right, but in the answer sheet it says to use 3 periods:

“Note that since the first scholarship award is paid out in four years, the present value of the peretuity represents the amount that must be in the account at t=3”

I don’t understand this at all. Why must t = 3?

And if the money needs to be in the account before the four year mark, why don’t they use t = 7, with semiannual periods?

#2

You should review the formula of perpetuity. PV = CF/i PV is the value at time 0. The first cash flow is at time 1. In this question, the first cash flow needed is at time 4. The formula sums up the cash flows from time 4 to infinity and gives you the value at time 3. Therefore, you need to discount it 3 times to time 0.

#3

Oh, that’s right. Thanks.