Perpetuity receiving, discount, payments, decided

toocfatoo

In 10 years you will begin receiving $155 dollars per year in perpetuity from your grandparent's family trust fund (first payment is exactly 10 years from today). You consider these payments essentially risk free and have decided to discount them at a constant risk free rate of 6.5%. What is the present value today of these future cash flows?

a. 1353
b. 2385
c. 1270
d. 146

I am thinking it's c.
Please help.

Kiakaha

1st step: Apply the perpetuity formula

A/r=155/0.065=2,385 (rounded)

This way you've discounted the perpetuity to the date 9 years from today, that is, just one period before the mentioned first payment 10 years from today.

2nd step: discount to today

2,385/(1+0.065)^9=1,353.

I guess your issue is whether to discount for 10 periods or 9 after applying the perpetuity formula. Just think about this:

If you apply the perpetuity formula to a string of payments starting one period from today, you get the equivalent amount today, right? That is, one year before the first payment. So, if you just apply the formula to a string starting in 10 periods, you will get its equivalent value in 9 periods from today, that is, one before the first payment.

Just draw a line as it's explained in the books and you will get it easily. And remember to be careful with annuity dues.



Edited 2 time(s). Last edit at Sunday, October 3, 2010 at 03:44AM by Fdez.

Beatnik

Thanks Fdez. I really appreciate your help and explanations.