# Net Present Value vs. The Payback Method.

I mentioned in some of our previous articles how net present value is superior to the payback method when it comes to evaluating whether or not to accept a project. People generally just use the payback rule because it's simplicity and then it's easier to calculate than NPV. I just want to give you some of the intuition in this article why NPV is superior. So let's focus on a specific example here,

So we've got a project that we're thinking about taking on. The cash flows for this project are going to be one upfront investment which is negative \$400. That we're spending on this project and then that investment is going to yield cash flows of \$150 annually for 3 years and then beyond that, there's not going to be any more cash flow. So this is just a 3-year project that's going to yield these cash flows and require this upfront investment of \$400. Now I need a couple of other things before we go and calculate the payback method or the payback rule.

We're going to need to know the required number of years we need to have the investment recouped within 3 years. We decide on the investments, we would like to have the money back within three years to be repaid. Then in terms of calculating NPV, we're going to need to know the cost of capital and we'll say that for our firm for this project it's 12%.

So let's calculate the payback method first because that's simpler, So for payback, we're going to take \$400 so that's our investment and now we're going to divide that by the annual increase in sales. The increase in revenue \$150 dollars a year. Divide that \$400 by the increase in sales or I can say increase in cash flow

So when we take that \$400 upfront investment of cash and divide it by the \$150 increase in cash flow for the next 3 years. Now we're soon to see what the amount of time it's going to take to pay back this investment, it's actually going to be 2.6 repeatings I'll just round it to 2.67. So what that means is that this is going to take 2.67 years to pay back this investment. This initial \$400 we're going to pay that back two-thirds of the way through the year.

If you think about it, it makes sense because if we summed up all the cash flows together all the positive cash flows for the three periods it comes out to \$450. In the initial investment is \$400 so we know that \$450 obviously is greater than \$400 so we know we are going to recoup before year three here and and and so we can see that it makes sense that right about 2.67 year is when we've gotten our money back so that's the payback method.

### Now let's go and let's calculate the net present value.

So for NPV now we're taking into consideration the time value of money and so we're going to have negative -400 upfront and then we're going to have plus 150 over (1+ our cost of capital) which is 1.12 plus 150 over 1.12 squared, the reason being this is period as we're discounting back two periods and now the third cash flow we've got to add again here so 150 divided by 1.12 to the third.

So we're discounting each of the cash flow back and then we're going to add that negative of front cash flow we're going to end up with a negative -39.8 well I'll just round it, we'll say negative -40. Now if we think about our payback we said if we pay this back within three years we should accept right? To accept would be the decision for payback because there are 2.67 years that we're going to the investments can be paid back within is less than our required return for our firm.

We say if it pays back within 3 years do it, well it pays back in 2.67 years so the payback rule says accept. However the NPV we know that if it's a negative NPV project which we have here negative -40, we should reject this project according to the NPV. Now as I've mentioned to you before if there's a difference between NPV and the payback rule you go with NPV. Now, why is it makes sense why we have conflicting recommendations here from NPV and payback?

Well, the thing is that the payback rule is not discounting these cash flows to the current period. It's not taking into consideration the time value of money, if you don't know what I mean by the phrase time value of money I strongly suggest you go back and check out one of our other articles on the time value of money.

Basically, the \$150 at the end of year three is not worth the same as \$150 at the end of year one or so forth, right? A dollar three years from now is not worth the same as a dollar now because a dollar now could have been invested and so we're discounting that future dollar back to the present in year three. We're discounting that 150 back to the present and the payback does not take into consideration that. It just says let's just take the done discounted cash flows and just to see how quickly we get them back.

So another kind of thing in this, this one is in illustrate here, but let's just say that we had the project an actual additional five years or an additional two years. Let's say the project went five years in total

Let's say now that we add cash flows of 150 in year 4 and 150 in year five. Now I'm not going to go through all the calculations but now we would actually have an NPV here, if it went five years now we would have an NPV that would be positive and it'd be 141. Now I'm just going to change around a few things here so if you get a little confused just read again. So now we've added a couple years and I just want to show you how things change. So if we add a cash flow of 150 and not changing like the cost capital or anything we're going to have an NPV that's positive and would say accept.

However let's say that we also changed one other thing, where we said that the required payback for the firm instead of three years let's say that it was two years. Now let's compare that scenario, now we've got the only thing we changed was the payback required amount of years to pay back the investment and we've extended the cash flows a little bit and the reason I did that is I want to show you something.

So now with this set of cash flows here the payback method would actually say that you should reject this project and why? because we're still paying back the investment within 2.67 years. Now you might say "hey that's weird why is this still 2.67? We've actually added some cash flows here. well here's the thing payback method does not account for any cash flows beyond this period. Here all it looks at is how long does it take for us to get these cash flows back. These cash flows could go into infinity and the payback rule is not going to concern itself with that. It just says at what point do we break even, what point do we get the cash flow back in a few.

So if you say well look we need it within two years well actually we're not going to get it back for 2.67 years I guess we should reject the project. well if you've got these cashflows extending out and out and into the future, you might be giving up a project that has a lot of cash flow that's happening later in the project.

Now NPV is superior because NPV is actually factoring that in it's saying "okay account for these additional cash flows will discount them to the present value and in that case, it would actually have this positive NPV of 141 and so just by changing a few of the parameters here and adding some additional cash flows see that now, in this case, NPV is again superior because NPV is taking into consideration cash flows beyond the period when the investment has been paid back.

Now you might say well hey you just kind of change the date here with the payback period is you know you just kind of arbitrarily change it well that's another disadvantage to the payback rule, to begin with, is that this whole idea of all it has to be paid back within two years or has to be paid back within four years or five, that's this arbitrary who decides that? Why is that amount of time? The NPV when we think about NPV all working with NPV is we're saying look let's take a look at the cash flows and now we're going to net all this out and we're going to see what is the wealth added to the firm and if a project is adding wealth to the firm all else equal then you want to be doing that project.

Payback is inferior to NPV it may be easier to calculate buts inferior for all these reasons right it's not considering the time value of money it's not looking at cash flows beyond the point where you've actually just repaid and recouped your initial costs and it's just relying on just this arbitrary figure of how long it is that someone decided the investment should repay themselves.