Net Present Value Rule

The net present value is the difference between an investment's market value and cost. In other words, it is the current value of the projected cash flows of an investment project, discounted back at an appropriate rate. 

The basic idea is to create value by identifying an investment worth more in the marketplace than it initially cost us to acquire. 

It is important to note that the net present value is a part of the capital budgeting process for any organization, including all the cash flows for expenses or profits of a product or investment used through the NPV to identify whether that product is worth it and profitable. 

Let’s look at an example:

Suppose you purchase an older house for $150,000 and spend another $50,000 on the repairs. So far, your total investment is $200,000. Once the work is complete, you place the house back into the marketplace and find it worth $250,000. 

The present market value now exceeds the cost of $200,000 by $50,000. So, in other words, the $50,000 is the value-added from managing this project.

Now, for this example, things worked out for us. We made profits and managed the project the right way. However, these things tend not to go so quickly in real-life scenarios. The real challenge is to identify whether or not investing that $200,000 was the right choice. 

It describes the goal of capital budgeting to determine whether investments or projects will be worth more than their cost. 

The net present value measures how much weight is created today by undertaking an investment. When it is positive, we know that the project is worth investing in, while when it is negative, we assume the opposite. 

How does Net Present Value work?

Based on our previous example, you can see how we would make our capital budgeting decision. The first step is to look at what other fixed-up properties were selling for in the market. 

Then we would get estimates of the cost of buying a particular property and compare it to the market prices.

So far, we have the estimated total cost and estimated market value.

If the difference is positive, we would consider investing in the project as it would have a positive estimated net present value. In our example, we have information on the market prices for other properties, which considerably simplifies the process. 

Most of the time, however, investors are left with indirect market information, making it more challenging to determine the estimate of their investments.

In other words, the NPV analysis determines the value of an investment, project, or any series of cash flows. It is an all-encompassing metric because it includes all revenues, expenses, and capital costs associated with an investment in its free cash flow (FCF).

It considers not only all revenues and costs but also the timing of each cash flow, which can significantly impact the present value of an investment. For example, it is preferable to see cash inflows earlier and cash outflows later than the opposite.

Estimating Net Present Value

Picture yourself starting a business to sell products online, and you estimate the costs accurately since you know what prices you can get each product for if you buy a sizeable quantity. Would that be a good investment?

The answer depends on whether the value of the business surpasses the initial cost, which means having a positive NPV.

The necessary procedure to find your NPV is the discounted cash flow valuation (DCF valuation).  It is the process of valuing an investment by discounting its future cash flows. 

Net Present Value Formula 

NPV = Σ Rt / (1 + i)^t

Where:

Rt = Net cash inflow - outflow during a single period. 

i = discount rate.

t = number of periods. 

The present value of the projected cash flows of an investment project is discounted back at an appropriate rate.

To see how we might estimate NPV, imagine your starting up a new landscaping business, and you believe that the cash revenues from your quotes, assuming everything goes as expected, will be $19,000 per year.

As a result, your cash costs will be $13,000 annually, and you will wind down the business after six years. The equipment will be worth $2,000 as salvage at the end of the six years. 

The project costs $26,000 to launch. Let’s use a 10 percent discount rate. Is this a good investment?

Answer:

First, we need to find the present value of future cash flows with a discount rate of 10%. The net cash flow would be $19,000 from cash inflow minus $13,000 from the cash outflow resulting in $6,000 and a lump sum of $2,000 in six years.

Then,

Present Value = $6,000 x (1 - 1/1.10^6)/ 0.10 + $2,000/1.10^6

= $6,000 x 4.355 + $2,000/1.772

= $26,130 + $1,128.67

= $27,258.67

So,

NPV = -$26,000 + $27,258.67 = $1,258.67, which means it is a good investment since the NPV is positive. 

Let’s say there are 2,000 shares of stock outstanding. What will be the effect of the price per share from taking it? 

Answer:

You will have a gain in the value of 1,258.67/2000 = $0.629 per share from taking this project. Since the NPV is positive, the effect of the price per share is favorable, while the opposite occurs when it is negative, resulting in a loss in value per share.  

It is important to note that it is much more complex when you come up with the cash flows and the discount rate. In the meantime, we will assume the estimations are given. 

Net Present Value Rule

As the goal of financial management is to increase shareholder value, this brings us to the net present value rule. 

“When the net present value of an investment is positive, it should be accepted; if it is negative, it should be rejected.”

Let’s look at another example using the proper steps.

A project in which you initially invested $72,500 provides consecutive annual cash flows of $14,700 for six years. Is this a good project if the discount rate is 7 percent?

Answer:

NPV = Σ Rt / (1 + i)^t

Present value = $14,700/ (1 + 0.07)^1 = $13,738.32

Present value = $14,700/ (1 + 0.07)^2 = $12,839.55

Present value = $14,700/ (1 + 0.07)^3 = $11,999.58

Present value = $14,700/ (1 + 0.07)^4 = $11,214.56

Present value = $14,700/ (1 + 0.07)^5 = $10,480.90

Present value = $14,700/ (1 + 0.07)^6 = $9,795.23

Total Present Value = $13,738.32 + $12,839.55 + $11,999.58 + $11,214.56 + $10,480.90 + $9,795.23 = $70,068.14

So,

NPV = $70,068.14 - $72,500 = (- $2,431.86)

We would reject this project with a required rate of 7 percent. 

Suppose you are asked to decide whether a new product should be launched. We expect the cash flows over the next four years to be $2,000 in the first two, then $4,000 for the third year, and $5,000 for the fourth. It will cost you $9,000 to start production. Use a 10% discount rate to evaluate the products. 

Answer:

Present value = $2,000/1.1 + $2,000/(1.1^2) + $4,000/(1.1^3) + $5,000/(1.1^4)

= $1,818 + $1,653 + $3,005 + $3,415 = $9,891

NPV = $9,891 - $9,000 = $891

The net present value is positive, so you should take on this project. 

For more practice, please view the video below. 

Excel NPV Functions

Excel has two net present value functions: NPV and XNPV. The two functions use the same math formula as shown above, but they save an analyst time by not having to calculate it in long form.

The standard NPV function =NPV() assumes that all cash flows in a series occur at regular intervals (i.e., years, quarters, and months) and ignores any fluctuation in those periods.

The XNPV function =XNPV() allows you to apply specific dates to each cash flow, which can be at irregular intervals. The function is beneficial because cash flows are frequently unevenly spaced, necessitating a higher level of precision.

Internal Rate of Return (IRR) vs. NPV

The internal rate of return, better known as the IRR, refers to the interest rate at which the investment's net present value equals zero. Another way to put it is the annual compound rate of return you can expect from a project or investment.

Consider, for example, a company considering purchasing a new piece of equipment for $25,000. After investing $25,000 into cash outflow, the equipment used by the business increases cash inflows by $6,000 yearly for eight years. 

The $6,000 inflow would be discounted using the discount rate of 7% for eight years. The investment is only profitable if the sum of all adjusted cash inflows and outflows is more significant than zero. A positive net cash inflow also indicates a greater rate of return than the 7% discount rate.

Present Value Sum = $35,827.79 - $25,000

 NPV = 10,827.79

Based on our example, we know that since there is a positive net cash inflow, our rate of return is higher than the discount rate.

Though the IRR is helpful, it is usually inferior to the NPV because too many assumptions are made about capital allocation and reinvestment risk.

In most cases, investors and business management consider NPV and IRR when considering projects.

A company's net present value

Analysts create a discounted cash flow DCF model in Excel to determine a business's value. This financial model will include revenues, expenses, capital costs, and business information.

Once the key assumptions have been established, the analyst can create a five-year forecast of the three financial statements (income statement, balance sheet, and cash flow)

Next, he calculates the firm's free cash flow to the firm (FCFF), also known as unlevered free cash flow (UFCF).

The company is valued beyond the forecast period using a terminal value. All future cash flows are discounted back to the present at the firm's weighted average cost of capital. To learn more, check out the course linked at the bottom of the article.

Challenges of NPV

Although net present value (NPV) is the most commonly used method to evaluate investment opportunities, it does have some drawbacks that should be carefully examined.

In NPV analysis, key challenges include:

• Too many assumptions to be made
• Sensitive to small changes in assumptions and drivers
• Easily manipulated to obtain the desired results
• Second- and third-order benefits/impacts may not be captured (i.e., on other parts of the business)
• The discount rate is assumed to be constant over time
• Performing accurate risk adjustment is a challenge (hard to obtain data on correlations and probabilities)

Researched & Authored by Michael Rahme | LinkedIn

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