# Present Value

"Present value is what a dollar tomorrow is worth today."

So why are we interested that a dollar is worth more now than later? The reason is that it gives us a way to value a series of cash flows. If we can have a single number that values a cash flow, them we can compare cash flows to see which one is best. Let's consider a couple of cash flows:

What is so important about present value(PV)? Have your ever heard the expression "a bird in the hand is worth 2 in the bush?" PV is a little like that. A dollar today is worth more than a dollar a year from now. If it is not clear why, be sure to to watch the video on this page.

Now to determine how much more a dollar today is than a dollar a year from now, you have to think about interest rates. If your bank were offering 5% interest in a savings account, a dollar deposited now would be worth \$1.05 in one year. We could also say that a dollar in our account one year from now would be discounted by 5% to get our PV of \$.95. That is why the interest rate used for discounting is called the discount rate or sometimes the hurdle rate.

## An Example

 Year Cash Flow #1 Cash Flow #2 0 -\$15,000 -\$20,000 1 4,000 3,000 2 5,000 6,000 3 7,000 9,000 4 -2,000 6,000 5 4,000 1,000 6 5,000 6,000

Would you make the investment in cash flow #1 or cash flow #2? Surprisingly it depends on the discount rate. For a discount rate of 10%, cash flow #1 wins with a present value of \$1968 versus \$1871 for cash flow #2. At 8% cash flow #2 wins at \$3203 versus \$2950 for cash flow #1.

Now that is confusing! Why can't we just make a simple decision about which cash flow is the best? Well, we first need to find out what a good discount rate is.

## Discount Rate

The implication of the discount rate is that it is the minimum interest return that would be economical for us. If we are working with our savings, we might be satisfied with a hurdle rate that is about he same that we could expect on our savings or maybe 5%. If we are a company that is evaluating our capital budget, to see were we should invest our money to get the highest return, we would probably use our cost of money or the interest rate required to borrow money. Our interest cost might be 8%. Then we might add in something that would represent our expectation for inflation. We might decide that we will not accept any project that does not give a positive net present value with a 10% discount rate. When we are comparing cash flows, the winner is the one with the largest positive cash flow.

## The Winner Is....

Back to our example cash flows. Both cash flows have a positive net present value. (By the way, when we are netting or adding all the negative and positive present values together, then it is called net present value or NPV) Since the NPVs are positive they have passed the "test." So, if the 2 projects are not mutually exclusive then we want the one with the highest positive NPV.

## NPV or IRR?

When asked to evaluate cash flows some people prefer to use internal rate of return (IRR). Why? Because it is somewhat more intuitive than NPV. When you say that you have an IRR of 10% on a series of cash flows, it is like saying that you are earning 10% interest on your money. The method for calculating NPV is much easier than for IRR. However, with computers to help who cares?

What is the relationship between NPV and IRR? They are very intimately related. For a series of cash flows, the IRR is equal to the discount rate when the NPV=0. Expressed as an equation, it is:

If NPV = 0, then IRR = Discount Rate.

## Summary

PV and its summed up cousin, NPV are valuable methods for comparing cash flows. When we pick a discount rate that we are happy with we can compare cash flows to see which one is best. This process is used as the basis for capital budgeting.

NPV Calculator - Calculate the NPV for a series of cash flows.