Hi,

I am new to Finance and having a tough time understanding the concept. Here is the question:

Jack Hammer invests in a stock that will pay dividends of $2.00 at the end of the first year; $2.20 at the end of the second year; and $2.40 at the end of the third year. Also, he believes that at the end of the third year he will be able to sell the stock for $33. What is the present value of all future benefits if a discount rate of 11 percent is applied? (Round all values to two places to the right of the decimal point.)
I am assuming this is the formula to use PVa = A x PV ifa (n=3, i=11%), however how do I calculate the a and ifa?

Thanks!:)

I don't know what your book is calling a and ifa. Since you'd be taking your values and multiplying by a factor, I presume the ifa is a factor. But is the a supposed to stand for annuity, cause this isn't an annuity. Since you're also only doing this with n = 3, as though that's the only equation you have to do, I might assume you're trying to make it an annuity. But I'm just guessing on that.

It would help a lot if we knew what you thought this was supposed to be as opposed to just having this equation.

An annuity is when there are equal payments at equal time periods. i.e. an exact equal series of payments. Like a loan payment that's the same every month, or the same $2000 put into your IRA each year, etc. This is 4 totally different amounts and is therefore not an annuity. Having payments doesn't make it an annuity - having equal payments at equal times does. The factor wouldn't know how to account for the 4 different values you have. You'll have to do all 4 numbers individually.

So it's not an annuity. Assuming the ifa was a factor, how you "calculate" depends on the method you're using. Generally if the equation is set up like this (i.e. a value times a factor), they're using charts. If you were working it out algebraically, you'd have the full equation. If you were using a financial calculator, chances are you'd just be plugging all the numbers in and not be multiplying by factors. So I would have to assume this is using charts. In which case you don't "calculate" it. You get it off the charts. Using the i = 11%. But the n is going to be different for each of your 4 individual ones you have to figure out.

Here's how to solve:

You have to discount all future cashflows back to the present value.

So PV of the $2 dividend at the end of the first year is 2/(1+11%).
PV of the $2.20 dividend at the end of the second year is 2.2/(1+11%)^2.
PV of the $2.40 dividend at the end of the third year is 2.4/(1+11%)^3.
PV of the $33 stock sale at the end of the third year is 33/(1+11%)^3.

Add all these PV's up to get the present value of all future benefits, and essentially the price that the stock should be selling for.