9.1: Investment Decision Criteria

Capital Budgeting Decision Rules

Once managers have identified a potential investment opportunity and estimated its expected cash flows, they must decide whether the project should be accepted or rejected. Capital budgeting decision rules provide a systematic way to evaluate these choices by comparing the value of future cash flows to the project’s initial cost using the time value of money.

Although capital budgeting techniques differ in form and interpretation, they all rely on the same underlying economic logic: a project creates value only if the present value of its expected benefits exceeds the cost of undertaking it.

Effective capital budgeting decision criteria should satisfy several key principles. In particular, good decision rules should:

1. Focus on cash flows rather than accounting earnings, because only cash flows can be reinvested, distributed to investors, or used to repay financing. Non-cash accounting items such as depreciation matter only to the extent that they affect taxes.
2. Incorporate the time value of money, recognizing that cash received sooner is more valuable than cash received later. Decision rules that ignore discounting can lead to systematically poor outcomes, especially for long-lived projects.
3. Account for project risk by using an appropriate required rate of return. Riskier projects must generate higher expected returns to justify investment.
4. Indicate whether the project adds value to the firm, rather than merely recovering costs or meeting arbitrary benchmarks.

No single method satisfies these criteria perfectly in every situation. As a result, financial managers typically rely on a combination of decision rules, each of which highlights a different dimension of project performance.

The four most commonly used capital budgeting evaluation methods are:

• Net Present Value (NPV)
• Internal Rate of Return (IRR)
• Payback Period (and Discounted Payback)
• Profitability Index (PI)

Each of these criteria approaches the investment decision from a different perspective. Some focus on absolute value creation, others emphasize rates of return, liquidity, or capital efficiency. In practice, firms often examine multiple measures before making a final decision.

In the sections that follow, we examine each technique in detail. We begin with Net Present Value (NPV) and Internal Rate of Return (IRR), then turn to the Payback and Profitability Index methods, before extending the analysis to risk, uncertainty, and capital constraints. Throughout the chapter, NPV serves as the benchmark decision rule against which other methods are evaluated.

Key Insight: Independent vs. Mutually Exclusive Projects

Before applying decision rules, it is important to recognize that capital budgeting problems come in two common forms. First, some projects are independent, meaning that accepting one project does not prevent the firm from accepting another. If resources are available and each project has a positive NPV, the firm can accept multiple independent projects because each one increases value.

Other decisions involve mutually exclusive projects, where choosing one alternative automatically rules out the other (for example, leasing versus buying, or building Plant A versus Plant B). In these settings, managers are not asking “Is this project acceptable?” but rather “Which option creates the most value?” This distinction is especially important because methods such as IRR can sometimes rank mutually exclusive projects differently than NPV. We return to this issue in more detail later in the chapter when we examine project ranking and capital rationing.

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1. Net Present Value (NPV)

Net Present Value (NPV) measures the dollar amount by which a project is expected to increase (or decrease) the value of the firm. It does so by subtracting the project’s initial investment from the present value of its expected future free cash flows.

\[ \text{NPV} = \sum_{t=1}^{T}\frac{\text{FCF}_t}{(1+r)^t} - \text{CF}_0 \tag{9.1} \]

where:

• \(\text{FCF}_t\) represents the project’s incremental free cash flow in period \(t\)
• \(r\) is the required rate of return, typically based on the firm’s weighted average cost of capital (WACC)
• \(\text{CF}_0\) is the initial investment, usually a cash outflow at time zero

Decision Rule: Accept the project if NPV > 0; reject the project if NPV < 0.

Interpretation: An NPV of $25,000 means the project is expected to increase shareholder wealth by $25,000 in today’s dollars after accounting for both time value of money and risk.

BA II Plus — NPV Calculation

Tip: Enter cash flows first, then set the discount rate in the NPV menu.

2ND → CLR WORK
CF
CF0 = -50000       ENTER
C01 = 15000        ENTER
F01 = 5            ENTER
NPV
I = 10             ENTER
↓ CPT → NPV  ⇒  6,985

Because the NPV is positive at a 10% required return, the project is expected to create value and should be accepted.

NPV is widely regarded as the theoretically superior capital budgeting criterion because it directly measures value creation and allows NPVs from multiple projects to be added together.

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2. Internal Rate of Return (IRR)

The Internal Rate of Return (IRR) is the discount rate that makes the project’s NPV equal to zero. In practical terms, IRR represents the rate of return the project itself generates based on its expected cash flows.

\[ 0 = \sum_{t=1}^{T}\frac{\text{FCF}_t}{(1+\text{IRR})^t} - \text{CF}_0 \tag{9.2} \]

Decision Rule: Accept the project if IRR exceeds the required rate of return; reject the project if IRR is below the required rate.

Interpretation: If a project’s IRR is 14% and the firm’s cost of capital is 10%, the project earns a return that exceeds the firm’s minimum acceptable rate, suggesting value creation.

BA II Plus — IRR Calculation

Tip: Use the same cash flow worksheet you used for NPV, then compute IRR.

2ND → CLR WORK
CF
CF0 = -50000       ENTER
C01 = 15000        ENTER
F01 = 5            ENTER
IRR
CPT  ⇒  13.7%

Because the IRR of 13.7% exceeds the firm’s 10% hurdle rate, the project would be accepted under the IRR criterion.

Strengths: IRR is intuitive and widely used because it expresses project performance as a percentage return.

Limitations: IRR can produce misleading results when projects have unconventional cash flows, differ significantly in scale or timing, or when mutually exclusive projects are compared. In such cases, IRR rankings may conflict with NPV.

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3. Payback Period

The Payback Period measures how long it takes for a project to recover its initial investment from nominal (undiscounted) cash inflows.

\[ \text{Payback} = \text{Years before full recovery} + \frac{\text{Unrecovered cost at start of year}}{\text{Cash flow during year}} \tag{9.3} \]

Decision Rule: Accept the project if its payback period is less than or equal to the firm’s predetermined cutoff period.

Illustration

If a project requires an initial investment of $50,000 and generates annual cash inflows of $15,000, cumulative inflows reach $45,000 after three years. The remaining $5,000 is recovered during the fourth year.

The fraction of the fourth year required is $5,000 ÷ $15,000 = 0.33, yielding a payback period of 3.33 years.

Discounted Payback improves on the basic payback method by using present values of cash inflows, partially correcting for time value of money.

Advantages: Payback is simple to compute and emphasizes liquidity and early cash recovery.

Disadvantages: It ignores cash flows beyond the cutoff period and does not directly measure value creation, making it unsuitable as a primary decision rule.

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4. Profitability Index (PI)

The Profitability Index (PI) measures the present value of future cash inflows per dollar of initial investment. It is particularly useful when firms face capital rationing and must rank projects.

\[ \text{PI} = \frac{\sum_{t=1}^{T}\frac{\text{FCF}_t}{(1+r)^t}}{|\text{CF}_0|} \tag{9.4} \]

Decision Rule: Accept the project if PI > 1; reject the project if PI < 1.

Interpretation: A PI of 1.12 means that each $1 invested generates $1.12 in present value benefits, implying value creation.

BA II Plus Shortcut

Tip: If you already computed NPV, you can compute PI quickly using the relationship below.

PI = (NPV + |CF0|) / |CF0|

Using the earlier NPV example, PI = (6,985 + 50,000) ÷ 50,000 = 1.14, indicating acceptance.

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Comparing Capital Budgeting Decision Rules

Table 9.1. Comparison of common capital budgeting decision criteria and what each method emphasizes.

Criterion	Time Value of Money	Risk Reflected	Value Indicated	Primary Use
NPV	Yes	Yes	Dollar value	Primary decision rule
IRR	Yes	Yes	Percentage return	Communication and benchmarking
Payback	No (unless discounted)	Indirect	No	Liquidity screening
Profitability Index	Yes	Yes	Relative ratio	Capital rationing

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Managerial Application

In practice, firms rarely rely on a single capital budgeting metric. Instead, they use multiple criteria to gain a more complete understanding of project performance:

• NPV to assess value creation.
• IRR to communicate an intuitive rate of return.
• Payback to evaluate liquidity and early risk exposure.
• PI to rank projects when capital is limited.

When conflicts arise among methods, NPV should guide the final decision, as it directly measures changes in shareholder wealth.

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Practice Checkpoint

1. Compute NPV, IRR, and PI for a $100,000 project generating $25,000 per year for six years at an 8% discount rate.
2. Explain why the Payback method may be preferred for high-risk research and development projects despite its limitations.
3. When comparing mutually exclusive projects, explain why NPV is generally preferred over IRR.

Key Insight: “Cash flow is king and NPV wears the crown.”

Every capital budgeting technique ultimately traces back to the same question: if we invest $1 today, how many discounted dollars will it return tomorrow? Keep that question in mind, and the decision rules will always make sense.