If I want a 12% return and: I invest $18,000 in 900 shares of stock. I get .80 per share dividend at the end of each year for the next 4 years and I sell the stock at the end of 4 years for $22,500. (considering present value) I took the PV for a $1 annuity, 4 years, 12% (3.037) and now I'm stuck. Can anyone walk me through this?

So you're in a "hare-raising" business, eh? (Sorry... couldn't resist ;) )

The question is a bit unclear; it looks like you want to determine the net present value of this investment activity, using a discount rate of 12%? I'll assume that's the case; let me know if it's otherwise.

Your PV multiplier for 12%, 4 years is correct. When you then multiply the 3.037 by the amount of the annual dividend, the result is the present value of the dividend payments.

3.037 x 900 x 0.80 = 2,187. Note that this result is the PV of all four dividend payments together, not the PV of each one. So far, so good.

To that amount you need to add the PV of the sales price. Since it was sold at t = 4 (with t denoting time), it's \frac{22,500}{1.12^4} .

Now you've got the PV of the dividend stream, and the PV of the sales price. Add those two together, and compare that sum with the amount of the initial investment.

If PV(dividend stream) + PV(sales price) > Initial investment, the excess is the positive NPV of the overall investment. If on the other hand the Initial Investment exceeds the sum of the PVs, you have a negative NPV.

One interpretation is that a positive NPV means that your overall return-on-investment was greater than 12%; a negative NPV means ROI < 12%.

it didn't take all of my post. :<( I want to know if you can explain thie middle part to me. I can't figure out where the 1.12 came from. My textbook doesn't say anything about putting the years in the form of a power or dividing "that number" into the selling price. My yeeeeaaaars ago accounting classes are making me think I should just take the $18,000 and multiply times a future value of 1.574 (12%, 4 years) and if the return include dividends is equal to or greater than this number, I got my 12% return. Help?

The good news is that the concept underlying the PV of a single amount is a lot simpler than that of the PV of a level series of amounts.

Suppose I invest $100 for 4 years, at 12%. At the end of each year, then, I'll have 112% (or 1.12) of the beginning-of-year amount.

E.g. after one year I'll have $112. This amount will grow to $112 x 1.12 = $125.44 by the end of the second year.

Put another way, the end-of-second-year amount is the initial investment, multiplied by 1.12 (one year's growth), and then multiplied by 1.12 again (another year's growth), or...

100 x 1.12 x 1.12 = 125.44. This can be written as

100\ \times \ 1.12^2\ =\ 125.44

You can then see that after 4 years I'll have 100\ \times \ 1.12^4 \ = \ 157.351936

"Present value", or "discounting", is nothing more than 'unwinding' this compounding effect. You're asking the question, "If I ended up with $157.351936 after 4 years, and I know that I earned 12% all along, how much did I start with? (i.e., what's the "present value"?")

To answer that--i.e. to 'unwind' the compounding equation--you just divide both sides by the compound multiplier:

\frac{157.351936}{1.12^4} \ = \ 100

And so to generalize, the PV of some future amount F, using a discount rate of r (as a decimal; 0.12, e.g.), over n years, is

PV \ = \ \frac{F}{(1+r)^n}

Cheers!

LOL! Both the wine (I have that frequently myself), but, well, just excuse ArcSince - he has the most bizarre sense of humor. :p

And excuse my typing. ArcSine. And no, I haven't had any wine.

Yet.

Yet.

:)

... now it's a party. We'll get the good folks down the hall at "Food & Drink" to cater.