The Present Value of a Projected Perpetuity

CFA Level I Quant
#1

The Present Value of a Projected Perpetuity Consider a level perpetuity of £100 per year with its first payment beginning at t = 5. What is its present value today (at t = 0), given a 5 percent discount rate?

I have a doubt I did PV = A/r and got the value of 2000 euro, this 2000 euro should be t = 5, right?

Than I made a time line of

T=5 - 2000 euro

T=4 - 1904,76 euro

T=3 - 1814,06 euro

T=2 - 1727,68 euro

T=1 - 1645,41 euro

T=0 - 1567,06 euro

What I`m doing wrong?

#2

Payments for years 1-4 = 0, payments for years 5, 6, 7, 8,9…forever = 100/year.

PV at time 4 = 100/0.05 = 2,000

PV at time 0 =2,000/(1.054) = 1,645.40

#3

I should have done T=4 - 2000 euro as in T=5 it alredy starts paying dividends so the value would be higher than 2000 euro

FV = 2000 euro

N = 4

r = 5

PV = 1645,40 euro

Now that`s the right answer

#4

:+1: :slightly_smiling_face: