Calculating Net Present Value and Mutually Exclusive Investments. All About Mutually Exclusive Investments.

Net Present Value and Mutually Exclusive Investments

We know that if a project has a positive net present value then we should accept that project because it's gonna add wealth to the firm but what if we have a mutually exclusive investment opportunity something where we only really have one option.

Let's say we have a vacant lot so here's our lot and let's say that we could build different types of buildings on this lot you can build the commercial types of buildings we could build the residential type of building or we could just sell a lot as it stands right now and just takes the cash.

So we've got these different investment opportunities we could have three different investment opportunities that we could do with this lot and we can't do all three of them, right? They're mutually exclusive. We can't build a commercial building here and at the same time just sell a lot as is with nothing built on it at all. So we can look at the different cash flows for each of these opportunities and say okay which is the best one and ultimately what we're gonna want to do is we're gonna pick the one with the highest net present value.

So I want to walk you through an example:

So let's say that we have three choices of what to do with that lot. We take a look at the different cash flows that we could have and so you can see our cash flows and it's over two years we'll say in year 0 here's the cash flow that's upfront, right? If we're making an investment or if we selling a lot as is we're just gonna get money upfront right and we're not gonna have any cash flows later so it's actually gonna be positive if we sell as-is. 

Let's look at those three options so we could build residential homes on this lot or we could build a commercial building like a shopping mall or something and then we could just say you know what we're not gonna build anything at all we're just gonna leave the lot vacant and just sell it as is. So when we look at these different opportunities we've got here's our stream of cash flows and then we can look at our cost of capital and our cost of capital might differ based on the project, right? So we might have a Cost of Capital of 12% for building residential but if we build a commercial we decide it's 9%. So we can go then and calculate a net present value for each of these different investment opportunities and compare them. 

Again we can't do all of these, right? We can't build a shopping mall and at the same time build a bunch of homes in the exact same spot that's just not possible. So if we're gonna go and calculate the net present value for each of these for the residential we just have what would that be negative 300 - (400 over 1.12) + (1100 over 1.12 squared) and the reason for that is you could just take a look at my net present value article if this is hard for you to understand but you can see our negative cash flows at upfront and then in the first year and then the positive cash flow in year two when we go and sell our homes, right?

So we're basically saying over the first two years we're gonna have some negative cash flows and then when it starts we're gonna sell the homes in year two. So then we just apply our cost of capital 12% to discount this back so the net present value ends up being $220 for building the residential homes.

Now with the commercial, we're gonna have negative 750 that's this the investment we're making to build this building upfront, and then in the first year, the cash flows are a little different than the residential. We get all the cash in year one and we get the same amount and we're going to have a different discount rate though and we gonna have here $259 for our net present value.

And then selling as is we're just getting cash upfront, so we don't have to discount any cash flows in period one or two back to the present because there are no cash flows. We're just selling the property as it currently stands as a vacant lot we don't even have worried about the cost of capital and so as is going to be a net present value of $175.

Now we can only do one of these projects, they all have a positive net present value, right? They're all going to add wealth to the firm so what we're gonna do is we want to pick the one with the highest net present value. So forget about anything else that's going on and just look at the net present value because that's telling you that this project the build commercial project has the highest NPV at 259 which means that building commercial is going to add the most wealth to our firm.