What is the present value of this investment?

Question

My professor for my online class is basically useless. Please help me understand how to compute this. I have a financial calculator. And if you can tell me how, not just the answer.

An investment offers $15,000 per year for 12 years. If an investor can earn 8.35% annually on other investments, what is the present value of this investment? If its current price is $110,000, should the investor buy it?

I am putting PMT=15000, N=12, I/Y=8.35, PV=121,435.71; is that right??

Answer 1

Stick the $110,000 in for the PV everything else is correct (pmt = -15000 / n=12 / fv=0 ) and solve for the rate of return which should yield you 8.53% which would make it better than 8.35%.  Also make sure your payments are end of period and not beginning of period - which is why you were getting the 121k.

Yet another way to look at it is to stick the 8.35% interest in and solve for the payment which would be $14,862.  Again that's not as much at $15k so it would be better than other currently available investments - hypothetically speaking.

But the PV which was your question is $111,019.60 so $110k is a bargain for that.  Anything less than that would be good...more would be not as good as the 8.35% that we know we'd get.

Good luck...and get a Texas Instruments BAII Plus...if you don't have one it's a much better financial calculator than a HP 12c

Jeff

Answer 2

I made two scenarios. Both of these are grounded on the fact that the present time is now. First is that you have an investment period at Year 0. Cash inflow would begin at the following year at Year 1. Second is that the investment and the initial cash inflow occur at the same year.

I used excel. I made a cash flow that looked like this (based on the first assumption).

Year 0  -110000

Year 1  15000

Year 2  15000

and so on until Year 12...

I used 8.35% as the discount rate and calculated for the NPV. The answer was $ 1,019.60. Since this is greater than 0, this would imply that the cash flows would be sufficient to recover the investment and generate an additional value of 1,019.60. Therefore, this investment is profitable. Buy it.

Under the second scenario, there would be no year 0. Year 1 cash flow would be -95000 (-110000 + 15000). NPV I calculated is still greater than 0.

In any case, investment is worthwile.

Answer 3

Somehow I got a different result assuming cash flows are made at the end of the year (even if I assume the contrary I still don't get your number). I do not have a financial calculator, but I used excel =PV(8.35%, 12, 15000, 0, 0) I got $111,019.6

In all cases, the investor should make this investment because it's PV is higher than the initial investment of $110,000