**Net Present Value**

Net Present Value (NPV) is the gold standard analytic technique used in financial analysis and investment decision-making. And spreadsheets like Excel make it super easy to use. Lets talk about what NPV is, how its derived, and how to employ it.

In business we invest in projects that make money in the future. We pay now and intend to reap the rewards in the future. Usually a project or asset will make money as a stream of revenues and profits over years. It could also be a project whose main benefit is savings. We need the ability to calculate whether that stream of future cash flows is worth more than the money we need to invest to buy it or build it. NPV is the tool we use to make that analysis.

The way we look at decisions about whether to fund a project or calculate the value of an asset is to turn that stream of future dollars into today’s dollars.

If you need a primer on the time value of money, check out these two blog posts:

Then we compare that sum of present values to the cost; if the cost is more than the total present value, we don’t do the deal; if it is less, it is considered a good deal.

This is the way projects are analyzed and assessed as go or no go, and how income producing assets and acquisitions are valued for sale, purchase, merger or acquisition.

In those previous blog posts we analyzed and calculated the value of future cash flows and brought them back to present value. **Net Present Value** (NPV) takes this idea a step further and accounts for the transactional aspect.

We must “purchase” the future cash flows either by:

- Buying a bond or stock, or
- Acquiring a company, or
- Purchasing an income-producing asset, or
- Undertaking a project and incurring the costs of developing or building the income-producing asset.

Net present value “nets out” the cost of acquiring the future cash flows. NPV compares the cost in today’s dollars to the present value of projected income or benefits also in today’s dollars. The deal is only worth doing if the price is less than our assessment of the future benefits.

NPV is the main tool used to value assets and make decisions about projects, purchases, mergers, or acquisitions. The spreadsheets can get pretty complicated when they are populated with all the costs, revenue and expense projections, and assumptions about timing and risk, but the basic idea is always to compare the costs to the future benefits and compare them apples to apples by taking into account the time value of money.

NPV answers a simple question: does the present value of all the money coming in over the life of the project outweigh how much money we have to spend in order to receive it? Net present value is just that, it’s the net between the present value of these two streams: the money going out and the money coming in.

We need to determine whether NPV is greater than 0. If it’s greater than 0, then the costs are less than the benefits and we should do the project or make the investment.

The decision rule is whether NPV is bigger than 0 or less than 0. We can construct the formula for NPV by following along very closely with what we did in the prior blog post discounting cash flows. NPV is the gold standard but using it along with IRR makes for even better analysis and decision making. I will talk about IRR (internal rate of return) in a future blog post.

NPV is equal to the present value of what’s coming in off the project as cash flows minus the initial cost.

This formula is set up as the initial cost, which has a minus sign in front of it, plus Cash flow in period 1, discounted one period back, plus the cash flow in period two, discounted two periods back, plus the cash flow in period 3, discounted back three periods, you get the idea, plus all the other cash flows coming in discounted by their period.

What we are doing is taking the initial cost and weighing it against the present value of all the cash coming in. We “net” the two numbers. There’s a minus sign on the costs, and plus signs on all of the present value cash flows.

We are essentially looking at how all the money going out weighs against all the money coming in.

Think of it like a balance. If we know the initial investment and the stream of money coming in from the project in the future, we can measure the NPV as the difference between the two; its the net between those two streams.

As the initial investment becomes larger, the NPV become smaller. You can see that the NPV, whether it’s bigger than 0 or less than 0, depends on that balance between the money going out and the money coming in. Let’s work a problem and compute an NPV in practice.

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# NPV in Practice

Analyze the stream of cash flows and compute the NPV if the discount rate is 15%

EXAMPLE PROJECT

Today

Year: 0 1 2 Sum (NPV)

-$3,000 $1,500 $1800 $300

Let’s think about whether it’s worth it to do this project. In period 0, today, we need to spend $3,000 in order to receive the future cash flows. Is it worth it to spend that $3,000? What do we expect to get in return?

What are the cash flows coming in off the project? We have a cash flow of $1,500 coming in at the end of year one. And we’ve got a cash flow of $1,800 coming in at the end of year two. If we just sum up the cash flows, a minus 3000 (it is minus because it is a cost) plus 1500 plus 1800, we get an answer of $300. This project is generating cash. It’s profitable in this sense. The money coming in is bigger than the money going out.

That’s the sum of all the cash flows, but that’s without any discounting. We haven’t accounted for the fact that we have to wait a year to get the $1,500, and then wait another year after that to get the $1,800. Remember: to use money you have to pay; there is a cost of capital. So what do we have to pay? In this case, we have to pay that 15% discount rate. That is the cost of capital in this example.

Today

Year: 0 1 2 Sum (NPV)

-$3,000 $1,500 $1800 $300

Present

Value: 1500/(1.15)^{1} 1800/(1.15)^{2}

NPV

@15% -$3,000 + $1,304.35 + $1,361.06 = **-$334.59**

We need to adjust the cash flows for the time value of money by discounting them to the present value. We take that $1,500 and discount it one period at 15% and we get $1,304.35. Then we take the $1,800 and discount it two periods at 15% and we get $1,361.06. Now when we sum the present value of all those cash flows, we get *minus *$334.59, which tells us that the project destroys value. It’s not worth doing.

It’s a profitable project, but we don’t want to do it. Why would we ever not want to do a project that’s profitable? It all comes down to the 15% discount rate. That 15% indicates what the hurdle rate is for the profitability of the project. This project might be profitable, but it is not profitable enough to justify the required 15% return. If we, our bosses, or our investors require a 15% return to take the risk of that project, we’re not going to be able to deliver it to them with a project like this.

Let’s examine what some of the main drivers are in that net present value calculation. First is cash flow. Obviously, more cash is better than less. The second is the timing. The further the cash flow is out in the future, the deeper it gets discounted.

And the third driver is the discount rate. The higher the discount rate, the deeper the cash flows get discounted and the lower the NPV. The lower the discount rate, the less discounting, the better the project. Lower discount rates, higher NPV. Higher discount rates, lower NPV.

Here is another example on the white board:

Net present value is the benchmark metric. It is our best capital budgeting tool. It incorporates the timing of the cash flows and it takes into account the opportunity cost, because the discount rate quantifies, in essence, what else could we do with the money.

The fact that we’re discounting implicitly incorporates the opportunity cost. And it incorporates **risk**. If we think the project is a lot riskier, what can we do? We can increase the discount rate to reflect that risk.

NPV is **objective** in the sense that, if we have good forecasting and good discount rates, we can lay this out and calculate it in a way that is presentable and explainable to anybody. It’s an arm’s length metric. NPV is transparent, we could sit down together with a spreadsheet and go over it and explain all of the assumptions to each other.

Net present value weighs the costs and benefits of cash coming in versus cash going out, and gives us an objective, arm’s length, and transparent metric for capital budgeting.

Spreadsheets like Excel make implementing NPV analysis a breeze. Here is a screen shot of NPV laid out in Excel:

To sum it all up:

## Here is the formula laid out in general terms:

**NPV = -C _{0} + C_{1}/(1+i) + C_{2}/(1+i)^{2 }+…+ C_{T}/(1+i)^{T}**

-C0 = Initial Investment

C = Cash Flow

i = Discount rate

T = Time

## Remember the main drivers of NPV are:

**Cash Flow**. Obviously, more cash is better than less.**Timing**. The further the cash flow is out in the future, the deeper it gets discounted.**Discount Rate**. The higher the discount rate, the deeper the cash flows get discounted and the lower the NPV. The lower the discount rate, the less discounting, the better the project. Lower discount rates, higher NPV. Higher discount rates, lower NPV.

This blog post is excerpted from my book MBA ASAP Understanding Corporate Finance. It is available from Amazon as a paperback, eBook for Kindle, and audiobook. The audiobook is also available from Audible.