 # Timing problem in quantitative methos

Here is the question an investor wants to set up a scholarship fund. paying 25,000 annually in perpetuity. first payments is to be paid out exactly 4 YEARS FROM NOW. interest rate is 4% semiannual compounding. how much money need to donate today? A 528,150 B 549,487 C 574,253 D618,812 i did this using four years but answer states i should use 3 years. can some one explain?

I think this can be something similar to bond question where the PVn-1 = dividends I start getting from the nth yr… ans is B

If the payments start in yr 4, you do the PV in yr 3. So then you go back 3 years from that. achogogo Wrote: ------------------------------------------------------- > Here is the question > an investor wants to set up a scholarship fund. > paying 25,000 annually in perpetuity. first > payments is to be paid out exactly 4 YEARS FROM > NOW. interest rate is 4% semiannual compounding. > how much money need to donate today? > > A 528,150 > B 549,487 > C 574,253 > D618,812 > > i did this using four years but answer states i > should use 3 years. can some one explain?

First you have to calculate the present value that you need to fund such a perpetuity. The present value is \$618,812. Note that when you calculate the present value of the perpetuity, you are calculating it as of three years from now. Implicit in the ordinary perpetuity formula is the assumption that the first cash flow is arriving in one year’s time. Then you discount that value by three years to arrive at 549,487. In both calculations I used the equivalent annual rate of 4.04%. If you wanted to discount by four years instead of three, you could do so by altering your perpetuity formula. You would calculate the perpetuity and then add 25,000, the payment at the beginning of the fourth year, to get the value as of four years from now. That yields 643,812. Discount that by four years to get the same answer of \$549,487.

Can i just remember this and go to exam? I’m exhausted…

i dint get this one, do we calculate the value of the peretuity as 25000/.0816 = 306,372.5 or as 25000/.04=625000, I do not get B either way if I discount back 3 years!

I believe the correct interest rate to use is (1+.04/2)^2 = 4.04%.

why dou discount by 3 years?? first payment is 1 year from now, and theres 4 payments…mkaing it 4 years…

When you calculate present value of a perpetuity in end mode, the answer is the value one year before the first payment. If the first payment were to be made in one year, you would simply calculate the present value of the perpetuity. You would not calculate the present value, then discount it by another year. This trap for the unwary also arises frequently in the multi-stage dividend discount model.

Can we think of it as getting cash flow at t = 1,2,3,4 ? Does “paying 25,000 annually in perpetuity” mean that i pay 25k at year 1,2,3, and 4 with t=0 being today? If this is the correct setup, then we’d be discounting for 4 years right?

It is important to know the definition of a perpetuity. A perpetuity is a stream of cash payments that continues indefinitely.

You are paying 25k 4 years from now: t = 0 — 1 — 2 — 3 — 4 — 5… ------------------------25k-25k… so, let t’ = t-3 t’ = -3 — -2 — -1 — 0 — 1 — 2 ---------------------------25k—25k Now, at t’ = 0, you get PV’ =25k/i then at year -1, you need PV/(1+i) then at year -2, you need PV/(1+i)^2 then at year -3, you need PV/(1+i)^3 shift back to t and you have your value at t = 0. Edit: Change the semiannual interest rate to effective annual… didn’t completely read the problem…

It really helps to draw a time line.

Answer is B. Perpetuity 25000/0.04, that would be the value in year 3, not 4, since perpetuity, same as DDM, returns the value that is in a period n-1 (thats y DDM uses D1 not D0 to get current P0). If so you get perpetuity value in year 3 and discount semiannually, so its 2% , 6 payments, on a calculator, find PV. if you want to get perpetuity in year 4, you use year 5 payment, which is 25000*1.02^2, then you can discount 4 years back… Just remeber, as previous poster says, draw a timeline, and dont forget that it starts from 0, and one year is between 0 and 1, so on. thank you

oh crap, this is like DDM method huh, first payment is like D1 so we need to find the PV at P0, which is at really PV at t=3. Then we discount the PV for 3 years. Damn trickiness

yes this is what perpetuity is, ddm is just a perpetuity , with dividends