 # perpetuity

A successful investor has decided to set up a scholarship fund for deserving students at her alma mater. 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 four years from today. The funds will be deposited into an account immediately and will grow at a rate of 4%, compounded semiannually, for the foreseeable future. How much money must the investor donate today to fund the scholarship? A. \$528,150. B. \$549,487. C. \$574,253. D. \$618,812.

i got 554K…no where close. anybody?

I am going with B You have to find the annualized rate of interest =1.02^4 =4.04% therefore the value of the perpetuity three years from now (remember that a perpetuity is valued one year from first cash flow) =25,000/0.0404 =\$618811.88 Now this has to be brought to present value by three years of the effective annual rate =\$618811.88/(1.0404^3) =\$549487.24 =B

PV perpetuity = PMT/(I/Y) I’m not sure if this is right but honestly, the question is not quite clear for me yet. Edit: Now I got it. Thanks Aussie.

aussie_jaco Wrote: ------------------------------------------------------- > Now this has to be brought to present value by > three years of the effective annual rate > > =\$618811.88/(1.0404^3) > =\$549487.24 > =B Except I would switch calculator in BGN mode, and go for A.

map1 Wrote: ------------------------------------------------------- > Except I would switch calculator in BGN mode, and > go for A. Doesn’t that effectively give you four years of discounting at the effective annual rate which is the amount of money that should have been invested last year?

I meant to say that the amount invested today has 4 years of interest, not 3, until 4 years from today. The amount calculated with 25,000/4.04% is correct.

sabaruch Wrote: ------------------------------------------------------- > i got 554K…no where close. > > anybody? got the same

thanks wasn’t annualizing for the perp

My thoughts are that if you look at the dividend discount model the first cash flow is from time period t+1 not t+0. This would lead to the perpetuity being valued at t=3 and not t=4?

so, is it B or A?

Oh the anticipation is just too much

It’s B. This was in the Schweser sample exam. 25,000/1.0404 = 618,811.88 PV of this for 4 years @ 4.04% = 528,150 (Option A) 528,150*1.0404 = 549,487.24

The key is “The funds will be deposited into an account immediately”

chad17 Wrote: ------------------------------------------------------- > It’s B. This was in the Schweser sample exam. > > 25,000/1.0404 = 618,811.88 > PV of this for 4 years @ 4.04% = 528,150 (Option > A) > 528,150*1.0404 = 549,487.24 I don’t get it. I get the value of the perpetuity as 618,811. Why don’t you then just get the PV of that: n = 8 i/y = 2 pmt = 0 FV=618,812 -> PV = 528,150 ? Why do you then do this bit: 528,150*1.0404 = 549,487.24 ??

Because the funds are being deposited immediately as opposed to the end of the period. Thus, one more period of interest needs to be accounted for.

right right, I thought that doing the PV calculation in BGN mde would account for that?

BGN mode is tricky, I don’t use that. Time lines work best for me. However, if you set the calc. in BGN mode and use N as 3, then you get that answer. I’m sure someone else on here can help you out, I’m not comfortable using BGN mode.

I see my problem, using BGN I put n=8, when it should have been n=6 (using semi-annual payments) my problem really was counting the correct number of periods from which to discount the perpetuity back thanks

I’m still not happy with this one! I get A, \$528,000 The cash goes in TODAY (year 0) It will go out 4 years from today… [--------[--------[--------[--------[ 0…1…2…3…4 …(1)…(2)…(3)…(4)… So this is 4 years worth of interest right? At year 0 = 528,000 At year 1 = (528k x 1.0404) = 549,000 At year 2 = (549k x 1.0404) = 571,000 At year 3 = (571k x 1.0404) = 594,000 At year 4 = (594k x 1.0404) = 618,000 What have I done wrong here? Thanks 528,000 x 1.0404 x 1.0404 x 1.0404 x 1.0404 = 618,000 NB ??? Ahhhh, just hit me… That 618,000 is actually the present value as of year 3 or something? Always get mixed up on these damn questions