A guide to evaluating investments using key financial criteria.
The Net Present Value (NPV) rule is the most important and conceptually sound method for evaluating investments. An investment's value is determined by the present value of its future cash flows. The NPV is the difference between the present value of an investment's future cash flows and its initial cost.
The goal of financial management is to create value for shareholders. Taking a project with a positive NPV directly increases shareholder wealth by that amount. A negative NPV project destroys value.
NPV Rule:
Accept the project if the NPV is positive.
Reject the project if the NPV is negative.
NPV Formula (Discounted Cash Flow Valuation):
$$ NPV = \sum_{t=1}^{N} \frac{CF_t}{(1+R)^t} - \text{Initial Cost} $$A new product will have cash flows of \$2,000 for the first two years, \$4,000 for the next two, and \$5,000 in the last year. The initial cost is \$10,000, and the discount rate is 10%. What is the NPV?
Since the NPV is positive, you should accept the project.
The payback period is the length of time required to recover the initial investment from a project's undiscounted cash flows. It's a simple "break-even" measure in an accounting sense.
Payback Period Rule:
Accept the project if the payback period is less than a prespecified cutoff point.
A project costs \$500 and has cash flows of \$100, \$200, and \$500 in Years 1, 2, and 3, respectively. What is the payback period?
Year 1: \$100 recovered.
Year 2: \$100 + \$200 = \$300 recovered. Still need \$200.
Year 3: The cash flow is \$500. We need to recover \$200.
$$ \text{Fraction of Year 3} = \frac{\text{Amount needed}}{\text{Cash flow in Year 3}} = \frac{\$200}{\$500} = 0.4 \text{ years} $$ $$ \text{Payback Period} = 2 + 0.4 = \textbf{2.4 years} $$The discounted payback period addresses a major flaw of the regular payback rule by considering the time value of money. It measures the time until the sum of a project's discounted cash flows equals the initial investment. This represents an economic or financial "break-even" point.
Discounted Payback Rule:
Accept the project if its discounted payback period is less than a prespecified cutoff point.
An investment costs \$300 and has cash flows of \$100 per year for five years. The required return is 12.5%. What is the discounted payback period?
Year 1: Discounted CF = $\frac{\$100}{1.125} = \$89$. Accumulated = $\$89$.
Year 2: Discounted CF = $\frac{\$100}{1.125^2} = \$79$. Accumulated = $\$89 + \$79 = \$168$.
Year 3: Discounted CF = $\frac{\$100}{1.125^3} = \$70$. Accumulated = $\$168 + \$70 = \$238$.
Year 4: Discounted CF = $\frac{\$100}{1.125^4} = \$62$. Accumulated = $\$238 + \$62 = \$300$.
The accumulated discounted cash flows equal the initial cost exactly in Year 4. Therefore, the discounted payback period is 4 years.
The Average Accounting Return (AAR) is a measure of a project's profitability based on its accounting figures, not cash flows. It is a ratio of average accounting profit to average book value over a project's life.
AAR Rule:
Accept the project if the AAR exceeds a target AAR.
A project costs \$500,000 and has a five-year life with straight-line depreciation to zero. The average net income is \$50,000. What is the AAR?
Average Net Income: \$50,000 (given)
Average Book Value: The initial book value is \$500,000 and the final is \$0. Since depreciation is straight-line, the average is the average of the beginning and ending values.
$$ \text{Average Book Value} = \frac{\text{Initial Cost} + \text{Final Value}}{2} = \frac{\$500,000 + 0}{2} = \$250,000 $$ $$ \text{AAR} = \frac{\$50,000}{\$250,000} = 0.20 = \textbf{20\%} $$The Internal Rate of Return (IRR) is the single discount rate that makes a project's NPV equal to zero. It represents the project's intrinsic rate of return. The IRR is closely related to the NPV and often leads to the same accept/reject decisions for simple projects.
IRR Rule:
Accept the project if the IRR exceeds the required return.
Reject the project if the IRR is less than the required return.
IRR Calculation:
$$ NPV = 0 = \sum_{t=1}^{N} \frac{CF_t}{(1+IRR)^t} - \text{Initial Cost} $$A project costs \$100 and pays \$60 per year for two years. What is the IRR?
Using trial and error or a financial calculator, we can find the IRR. For example, at a 10% discount rate, NPV = \$4.13. At a 15% discount rate, NPV = -\$2.46. The IRR is between these two values.
The exact IRR is approximately 13.1%.
The Modified Internal Rate of Return (MIRR) is a variation that addresses some of the IRR's flaws, such as the multiple rates of return problem. It modifies the cash flows first before calculating an IRR.
The Profitability Index (PI), also known as the benefit-cost ratio, measures the value created per dollar invested. It is the ratio of the present value of future cash flows to the initial investment.
PI Rule:
Accept the project if the PI is greater than 1.
Reject the project if the PI is less than 1.
No. A payback period less than the project's life only guarantees that the sum of the undiscounted cash flows is greater than the initial cost. Because the payback rule ignores the time value of money, a project can have a payback period less than its life but still have a negative NPV if the cash flows occur far in the future.
You can definitively state that the NPV is positive. The discounted payback period is the time it takes for the discounted cash flows to equal the initial cost. If this happens before the end of the project's life, it means there are still additional discounted cash flows to be received, making the total NPV positive.
Payback: The payback period must be less than the project's life. If NPV is positive, the cumulative cash flows eventually exceed the initial investment, so the payback period must exist. However, we cannot say for certain that the payback is less than a specific cutoff without more information.
Discounted Payback: The discounted payback period must also be less than the project's life. As seen in the previous question, a positive NPV guarantees a discounted payback that is less than the project's life.
Profitability Index: The PI must be greater than 1.0. A positive NPV means the PV of future cash flows is greater than the initial cost, so their ratio must be greater than 1.0.
IRR: The IRR must be greater than the required rate of return. A positive NPV means the project is profitable at the required return, so the rate that makes NPV zero (the IRR) must be higher than the required return.
The payback period is calculated by summing a project's undiscounted future cash flows until they equal the initial investment. It provides a measure of how quickly a project recovers its initial cost. The decision rule is to accept a project if its payback period is less than a predetermined cutoff period.
The main problems are that it ignores the time value of money, disregards all cash flows that occur after the cutoff date, and uses an arbitrary cutoff point with no economic justification.
Advantages include its simplicity, its bias towards liquidity (favoring projects that recover cash quickly), and its rough adjustment for risk in later cash flows. It can be appropriate for small, routine investment decisions where the cost of a more detailed NPV analysis would be too high. It also serves as a simple screening tool to filter out projects that are obviously not worth pursuing.
The discounted payback period is calculated by summing a project's discounted cash flows until they equal the initial investment. It provides a measure of the time it takes to "break-even" in a financial sense, accounting for the time value of money. The decision rule is to accept a project if its discounted payback period is less than a prespecified cutoff.
Similar to the regular payback rule, it ignores cash flows beyond the cutoff date and requires an arbitrary cutoff period. It also lacks the simplicity of the regular payback method, making it only a marginal improvement.
The main advantage is that it incorporates the time value of money, making it a more financially sound measure. Yes, the discounted payback period will always be longer than the regular payback period (for a positive discount rate) because the future cash flows are being discounted to a smaller value, so it takes longer for them to sum up to the initial investment.
The AAR is the ratio of average net income to average book value. It provides a measure of a project's profitability based on accounting numbers. The decision rule is to accept a project if its AAR exceeds a predetermined target AAR.
The AAR's problems include ignoring the time value of money and using an arbitrary cutoff rate. The most troubling feature is that it uses accounting data (net income and book value) rather than cash flows and market values, so it is not a true economic rate of return. Its main redeeming quality is that the necessary information is almost always available and easy to compute.
NPV is calculated by finding the present value of all future cash flows and subtracting the initial investment. It provides a direct measure of how much value an investment adds to the firm. The NPV rule is to accept a project if its NPV is positive.
NPV is superior because it accounts for the time value of money, considers all cash flows, and provides a direct measure of value creation. An NPV of $2,500 means the project is expected to increase the total value of the firm's shares by $2,500.
The IRR is the discount rate that makes a project's NPV equal to zero. It provides a rate of return inherent to the project's cash flows. The IRR rule is to accept a project if its IRR is greater than the required return.
For conventional projects, IRR and NPV will almost always lead to the same accept/reject decision. However, NPV is superior for mutually exclusive projects or those with nonconventional cash flows, as IRR can give misleading results or multiple answers. A manager might prefer IRR for its intuitive appeal as a percentage return.
Managers use IRR because it's easy to understand and communicate. It's a quick way to gauge a project's profitability. A situation where IRR might be more appropriate is if the required return is unknown. If the IRR is very high, a manager can be confident the project is a good investment without needing an exact discount rate.
The PI is the ratio of the present value of a project's future cash flows to its initial investment. It measures the value created per dollar invested. The decision rule is to accept a project if its PI is greater than 1.0.
PI is directly related to NPV: a project has a PI > 1 if and only if its NPV > 0. A PI might be preferred when a firm has a limited budget and needs to rank projects to maximize the value from that limited capital (capital rationing).
For a perpetual project, the payback period is $I/C$. The IRR is the rate that makes NPV zero, so $I = C/IRR$, which means $IRR = C/I$. Therefore, for a perpetuity, the IRR is the reciprocal of the payback period. This implies that for long-lived projects with constant cash flows, a shorter payback period corresponds to a higher IRR, making the payback rule a decent approximation of the IRR rule in this specific case.
Reasons might include avoiding trade barriers and tariffs, reducing transportation costs, adapting products to local tastes more easily, and building a stronger brand presence in a key market. It could also be a strategic move to hedge against currency fluctuations or to gain access to a skilled labor force.
The main difficulty in applying all these criteria is forecasting future cash flows and an appropriate discount rate. The payback period is the easiest to implement because it requires no discounting. The NPV and IRR are the most difficult because they require a reliable estimate of the cash flows over the project's entire life and an accurate discount rate.
Yes, the criteria are applicable. Not-for-profit entities also have scarce resources and should seek to maximize the value created by their investments. They should make decisions based on the project's social value or mission impact relative to its cost, a concept similar to NPV.
Yes, governments should also use these techniques. Projects like building a bridge or a power plant have costs and benefits that can be analyzed using NPV, although the benefits (e.g., social welfare, reduced pollution) can be difficult to quantify financially.
The term is used because the MIRR is not a true internal rate of return. Its value depends on an externally supplied discount or reinvestment rate. Since there are different ways to calculate it and no single best method, its value can be easily manipulated, which diminishes its usefulness as a standalone measure.
Yes, the claim is correct. The reason is that a positive NPV project implies that the firm can earn at least the required return on its cash flows. The NPV calculation can be seen as a two-step process: compounding all cash flows to a single future value at the required return and then discounting that back to the present. If the cash flows are reinvested at any rate other than the required return, the NPV will change, which is why the NPV method implicitly assumes reinvestment at the required return.
Yes, the claim is correct. The IRR is, by definition, the rate that makes the present value of future cash inflows equal to the initial investment. This implies that if all intermediate cash flows are compounded at the IRR, the future value of those cash flows will exactly equal the initial investment compounded at the same rate. This inherent assumption is one of the main criticisms of the IRR method, as it may not be a realistic reinvestment rate.