NPV and IRR

Finance Essentials II

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Course: Finance Essentials II

Lesson 2: NPV and IRR

With the financial projections complete, Marie's analysis focuses on how much each investment, on a standalone basis, contributes to the overall value of N-Style. Marie will utilize two tools, a Net Present Value (NPV) analysis and an Internal Rate of Return analysis (IRR), to examine and compare the two investments. The Net Present Value (NPV) of an investment represents the net value to the company, in Present Value terms, of a project or investment. The NPV equals the sum of the Present Value of net future cash flows minus the initial investment.

NPV The sum of the present values of an investment's cash flows. internal rate of return 1. When measuring yield, it is the rate that equates an asset's future cash flows with its current price. All interim cash flows are assumed to be reinvested at the same rate. 2. The discount rate at which the net present value of an investment equals zero. Abbreviated: IRR. present value 1. What an amount of money is worth today. 2. The amount of money that could be received today in exchange for the payment of a given amount of money at a future date or dates. Abbreviated: PV.

Are cash flows in the future always positive?

No. Future cash flows may be positive or negative. In any business operation, there will be cash inflows (i.e., revenues) and outflows (e.g., manufacturing costs and selling expenses). The best way to handle future cash inflows with concurrent future cash outflows is to net the two. Typically, the business decision-maker only cares about the net result. The NPV technique works just fine regardless of whether future cash flows are projected to be negative or positive.

In calculating the NPV, is the initial investment always subtracted from the sum of the PVs of future cash flows?

Yes. The purpose of using the discounting technique to convert the projected Future Values into Present Values is to make those Future Values comparable to the (present) value of the initial investment. Therefore, once the future cash flows are stated in Present Value terms, the initial investment is subtracted.

In the NPV analysis of the two expansion options, Marie integrates the concept of Terminal Value into the NPV equation. She must integrate the Terminal Value because each expansion option will have significant value beyond the cash flow projection period. In her NPV calculations, Marie adds the Present Value of the Terminal Value of the expansion to the Present Value of the projected five-year cash flows before subtracting the initial investment.

Are there other analytical tools that Marie can use besides NPV and IRR?

Yes. Other tools include the payback rule, discounted payback rule, average accounting rule, and profitability index. While these other tools exist, they are not as analytically sound nor as robust as NPV and IRR. As a result, NPV and IRR are the most common and widely-used analytical tools for evaluating projects and informing financial decision-making.

The three NPV boxes on the right side of the image above to shows the relationship of the initial investment to the sum of the PVs of the future net cash flows and the PV of the Terminal Value in each of three situations:

1. Positive NPV: In this situation, the sum of the project's future net cash flows and Terminal Value are projected to exceed the company's initial investment (outflow) on a Present Value basis. An investment with a positive NPV will create value for the company and is financially worth pursuing.

2. Negative NPV: Here, the sum of the project's future net cash flows and the Terminal Value are projected to be less than the company's initial investment (outflow) on a Present Value basis. In this situation, the company would be better off, from a financial perspective, not undertaking the investment.

3. NPV of Zero: In this situation, the sum of the project's future net cash flows and Terminal Value will exactly equal the company's initial investment (outflow) on a Present Value basis. In NPV analysis terms, this project meets the return requirements of the company and, financially speaking, should be pursued.

Should all projects with a positive NPV be automatically accepted and funded?

No, there are many factors that go into whether or not a project should be accepted and funded.

• The size of the required up-front investment • The company's tolerance for risk • The concentration of risk in one project • The firm's overall business and operations strategies • Internal policies and investment guidelines • Legal and public policy issues

The NPV analysis is a sound and rigorous framework for evaluating proposed capital expenditure projects, but such analyses should be used only as an input to the final decision, not the final determination.

Why undertake a project with a zero NPV?

The NPV analysis uses the Discount Rate to convert Future Values to Present Values and vice-versa. The Discount Rate chosen by a company for the NPV analysis is a rate that represents the required rate of return for investments of similar maturity and risk to the investment being analyzed. As a result, a zero NPV means that the project exactly meets the firm's investment requirements, which also means that it is a project worth undertaking from a financial perspective.

NPV analysis can help you judge whether a specific investment is worth pursuing. The NPV analysis may also be used to compare investments, as the investment with the highest NPV creates the most economic value for the shareholders. The Net Free Cash Flows for each of the two investment options for N-Style are shown above. For the sake of this example, it will be assumed that all the cash flows occur at the end of the year. The Net Present Value of each investment is calculated by:

1. Summing the Present Values of the future Net Free Cash Flows through the Terminal Year and the Present Value of the Terminal Value of the investment

2. Subtracting the initial investment from this sum

Marie uses the same Discount Rate of 17.5%, the WACC of N-Style, that her boss Rob Gordon used in his valuation of N-Style

discount rate 1. The borrowing rate that the Federal Reserve charges to its member banks for short term

loans (usually in times of emergency). 2. The rate used to determine present and future values. 3. The rate that measures how far a discount instrument like a T-Bill trades below par.

The result of NPV analysis shows that even with the higher initial investment, the Southern Expansion creates significantly more economic value for the shareholders of N-Style than the Northern Expansion does. However, being a responsible and conscientious analyst, Marie does not recommend pursuing the Southern Expansion on the basis of the NPV analysis alone. She continues her quantitative examination with an Internal Rate of Return (IRR) analysis.

Will it ever make sense to choose the investment with a lower NPV?

There can be several different reasons for choosing an investment with a lower NPV. For example, it might be that the higher NPV project requires a larger investment and the budget won't allow for such an outflow. Another reason may involve the nature of the project itself and internal (company policy) or external (legal or regulatory) restrictions on such investments.

Does the choice of Discount Rate impact the results of the NPV analysis?

The results for a Net Present Value analysis are sensitive to the Discount Rate chosen. Higher Discount Rates penalize cash flows occurring farther into the future relative to cash flows occurring closer to the present.

Therefore, an investment that has a higher percentage of cash flows occurring farther off in the future is less attractive the higher the Discount Rate.

Analysts performing an NPV analysis should develop an understanding of the sensitivity of the decisions being made relative to changes in the Discount Rate.

Will I always use only one Discount Rate for a project?

No, but that is a very sophisticated question whose answer is beyond the scope of this course. Typically, only one Discount Rate is used for a project. A more sophisticated analysis may use different Discount Rates for different time periods in the project's life. Generally, different Discount Rates are used to recognize changing levels of risk during the project's life, or to more precisely identify the costs of funding a project over a long period of time.

The general formula for calculating NPV is depicted above. Please note that if you are comparing investment alternatives that all have the same initial investment (I), you can ignore this factor when calculating NPVs. After all, subtracting the same number from the sum of the NPVs for each project will not affect the results of the analysis.

Why is Terminal Value missing from the equation on this screen?

Terminal Value is missing simply because this formula is in a different form from the one you saw earlier. The use of Terminal Value in the Present Value formula is both a mechanical convenience and a way of thinking about cash flows that is useful in valuing an on-going firm whose cash flows theoretically

stretch into perpetuity. Terminal Value does not, however, have to be explicitly identified in a Present Value formula for the formula to work properly. Terminal Value is the value assigned to an on-going concern, as of the Terminal Year, for all cash flows projected after the Terminal Year. Mechanically, Terminal Value is useful because the Terminal Year is the year a company reaches competitive equilibrium. Typically, net cash flows are assumed to be constant after this point. This has the mathematical effect of reducing the calculation of perpetual cash flows to a simple expression. If T is the Terminal Year, r is the Discount Rate, and CT+1 is the cash flow in the year following the Terminal Year, the Terminal Value in year T is simply: TV = CT+1/r By discounting this value to the present, you can arrive at the Terminal Value in Present Value terms. Logically speaking, deriving the Terminal Value allows you to understand how much of a company's (or project's) value derives from the period after the company (or project) reaches competitive equilibrium versus the period that comes before. This is useful because the period leading up to the Terminal Year often includes disproportionate profits that cannot be expected to occur indefinitely as competitors catch up. Regarding the formula on this screen, it is a general formula that works for all Present Value calculations. It is a particularly useful formula when dealing with projects with finite lives, for which the concept of Terminal Value doesn't apply, or for situations when the concept of Terminal Value may apply but is not material or interesting enough to specifically call attention to it. This formula can easily be converted to the formula using Terminal Value, and vice-versa.

What happens if the cash flows occur all throughout a year and not just at year-end?

In this course, we have made the simplifying assumption that all cash flows occur at year-end simply because adding modeling complexities would serve no purpose. In real life, analysts make judgments when performing an NPV analysis as to the level of complexity necessary given the circumstances at hand. How to handle the timing of the cash flows is one such area of judgment. As a general rule, when the cash flows can be predicted to occur on specific dates, the Discount Rate is adjusted for the actual time period involved and the cash flows are discounted from those actual dates. When dealing with cash flows that are expected to occur during a specific time interval but the exact timing is uncertain (e.g., revenues over a quarter), simplifying assumptions are made. The assumptions may include choosing the midpoint of the time period and discounting the revenues from that date. When making these assumptions, the analyst must judge how sensitive the final decision is to the assumptions being made.

How is risk accounted for in the NPV analysis?

There are two methods to account for risk in an NPV analysis. The first (and most important method) is to reflect the risk in the level of the Discount Rate: the higher the risk, the higher the Discount Rate. You may think of the Discount Rate as being composed of two parts: 1) a rate reflective of the cost of borrowing money or raising equity to fund the project, and; 2) a premium for the level of risk. The second method to account for risk is to conduct a sensitivity analysis. Using the same Discount Rate, vary the assumptions that underlie the cash flow projections to examine best-case, optimistic-case, and downside-case scenarios.

There is a direct relationship between the NPV of a project and its rate of return (all else held constant). The greater its NPV, the higher the return. Since the Discount Rate is the rate used to calculate the Present Values in the NPV analysis, this also means that there is a relationship among the project NPV, project rate of return, and the Discount Rate. This relationship is demonstrated in the image above and summarized below:

• Positive NPV: When the project has a positive NPV, the project is expected to produce a rate of return in excess of the Discount Rate. (Remember that the Discount Rate is equal to the Weighted Average Cost of Capital for the company, so the rate of return is higher than the firm's cost of capital.) This type of project is financially worth doing.

• Negative NPV: When the project has a negative NPV, the project is expected to produce a rate of return less than the Discount Rate. (Here the project is providing a rate of return that is lower than the company's cost of capital.) This type of project is financially not worth doing.

• NPV of Zero: In this situation, the project's rate of return is equal to the Discount Rate. This type of project is also worth undertaking financially, since it represents a case where the WACC is exactly equal to the projected rate of return.

discount rate 1. The borrowing rate that the Federal Reserve charges to its member banks for short term loans (usually in times of emergency). 2. The rate used to determine present and future values. 3. The rate that measures how far a discount instrument like a T-Bill trades below par.

To complete the quantitative side of the investment decision, Marie also performs an Internal Rate of Return (IRR) analysis. The IRR is equal to the Discount Rate that makes the Net Present Value (NPV) of all the cash flows of an investment (including those after the Terminal Year)

equal to zero. Think of the IRR as the breakeven Discount Rate. It's the point at which an investment goes from a negative NPV (i.e., an investment that is not worth undertaking from a financial perspective) to a positive NPV (i.e., one that is worth undertaking from a financial perspective). Roll over the boxes on the right side of the image to see how the IRR and the Discount Rate relate to the cash flows. Some organizations use the concept of a "hurdle rate," which represents the minimum rate of return an investment must earn in order to have financial merit. For these organizations, the IRR (or breakeven Discount Rate) is compared to the hurdle rate, and if IRR is less than this hurdle rate, the investment or project is rejected.

internal rate of return 1. When measuring yield, it is the rate that equates an asset's future cash flows with its current price. All interim cash flows are assumed to be reinvested at the same rate. 2. The discount rate at which the net present value of an investment equals zero. Abbreviated: IRR.

Do the IRR and NPV methods always produce the same investment recommendation?

Usually, but not always. NPV gives you an idea of the nominal size of investment values, while IRR focuses on rates of return. In evaluating projects, there can easily be cases where one project has a higher return but offers a smaller nominal value than another project. As a general rule, it's good practice to conduct both analyses when evaluating investment alternatives.

The process for determining the IRR is depicted above. Solving for the IRR is a mathematically iterative process whereby the NPV formula is solved numerous times until a Discount Rate (r) is chosen that results in an NPV of zero. IRR calculations assume the same Discount Rate across all cash flows for the same investment or project.

discount rate 1. The borrowing rate that the Federal Reserve charges to its member banks for short term loans (usually in times of emergency). 2. The rate used to determine present and future values. 3. The rate that measures how far a discount instrument like a T-Bill trades below par. cash flow A measure of all money that is received or paid out by an entity over a period of time.

The IRR analysis focuses on the rate of return only and ignores the actual magnitude of the cash flows. When dealing with budget constraints, or when faced with projects that have very different cash flows and initial investment requirements, the IRR should be used in conjunction with other methods. That is why Marie is using an NPV analysis as well. IRR calculations are more important when the decision-making is framed in terms of rates of return that must be achieved. If a company's investment guidelines require a minimum rate (a hurdle rate) to be achieved for an investment to be considered, then the key to evaluating that investment would be the IRR. For N-Style, the hurdle rate is 17.5%, the company's Weighted Average Cost of Capital. Marie will be looking to see if one or both of the investment options have a return higher than 17.5%.

This simple example demonstrates how to iterate to an IRR solution. The general IRR formula states that for a two-year project, when the following equation is true the Discount Rate equals the IRR. USD 700 / (1 + r) + USD 700 / (1 + r)2 - USD 1200 = 0 To calculate the IRR of this investment, we must iterate our way to the solution. When the Discount Rate r = 10% p.a., the NPV is USD 14.88, so r must be higher. When r = 15% p.a., the NPV = -USD 62.00, so r should be lower than 15% p.a., but higher than 10%. When r = 13% p.a., the NPV = -USD 32.33, so r should be lower than 13% p.a. but higher than 10% p.a. When r = 11% p.a., the NPV = -USD 1.23, so r should be lower than 11% p.a. but higher than 10% p.a.

When r = 10.50% p.a., the NPV = + USD 6.77, so r should be higher than 10.5% p.a., but lower than 11% p.a. If this process is continued until the NPV is zero, the IRR result (rounded to four decimal places) is 10.9226%.

Is there any way to determine the IRR besides doing this manual iteration?

Yes. Financial calculators or spreadsheet programs have automatic functions that will determine the IRR of any series of cash flows.

As Marie begins her IRR analysis of the two options, she is interested in two results: 1. Which investment has the higher projected IRR? The investment with the higher projected IRR represents the more attractive investment for N-Style to pursue. 2. Does the IRR exceed the established hurdle rate for N-Style's investments? Company policy dictates that the IRR of company investments must exceed a 17.5% hurdle rate.

Marie iterates her way to a point where the NPV of each investment is equal to zero. The results of those iterations are shown above. Remember that when the NPV of the investment is equal to zero, the Discount Rate equals the IRR for the investment. Therefore, the IRR for the Northern Expansion is 32.067% and IRR for the Southern Expansion is 34.3309%.

How are risk factors accounted for in the IRR analysis?

The IRR analysis accounts for risk in two ways. The first is to reflect the risk in the level of the required hurdle rate. The higher the risk of a project, the higher the required hurdle rate (i.e., the required return to undertake a project). The second way to account for risk is to conduct a sensitivity analysis. This analysis varies the

assumptions that underlie the cash flow projections in order to examine best-case, optimistic-case, and downside-case IRRs.

Marie reviews the outcome of the analysis in light of her two areas of interest: 1. Since the Southern Expansion has an IRR (34.3309%) that is higher than the Northern Expansion (32.067%), the Southern Expansion is the more attractive investment for N-Style. 2. The IRR of the Southern Expansion is well above the hurdle rate for investments at N-Style of 17.5%.

Can an investment still be a bad one even if the results of the NPV and IRR analysis are positive?

There is more to an investment decision than strict consideration of the financial results alone. A company must also consider its overall business and operations strategies, and how any particular investment contributes to its goals and objectives.

Additionally, firms must take internal policies and investment guidelines, as well as legal and public policy issues into account when making an investment.

After performing a quantitative and qualitative analysis, Marie feels confident in making her recommendation to the CFO Rob Gordon. Despite the fact that the Southern Expansion has a significantly higher initial investment, it is clearly the better choice for N-Style. Remember, Marie's analysis focused on how best to increase shareholder value by choosing the investment (i.e., creating assets) with the highest value to N-Style. For N-Style, the next step is deciding how to finance the Southern expansion and how to raise the needed funds in the most effective and inexpensive manner.

Can the difference in initial investment amounts affect which project is chosen?

The initial investment directly impacts a project's NPV and IRR. All else held constant, the higher the initial investment for a project, the lower the NPV and the IRR. The level of initial investment can have other impacts on the investment decision. Higher initial

investments require companies to raise more funds. Since companies have constraints on the amount of funds that can be raised at any time, it is quite possible that a company cannot afford to undertake a project, even if it is the best project under consideration. Further, companies typically face a wide array of possible projects, each with a required initial investment and all subject to an overall total constraint on funds availability. To maximize shareholder value in such circumstances, a company will typically choose a portfolio of projects that maximizes total NPV while remaining below the constraint on total funds (i.e., total initial investments) required. All else equal, it may be that several smaller projects are more valuable to shareholders than one larger project.