Capital Budgeting Methods

Why This Matters

Capital budgeting is where financial mathematics meets real-world decision-making. Every time a company decides whether to build a new factory, launch a product, or acquire equipment, they're using these methods to answer one fundamental question: Will this investment create value? You're being tested on your ability to apply time value of money principles, understand discount rate mechanics, and evaluate investments using multiple criteria—not just plug numbers into formulas.

These methods connect directly to core concepts you'll see throughout financial mathematics: present value calculations, annuity structures, and rate-of-return analysis. The exam loves to test whether you understand why different methods give different answers and when each method is most appropriate. Don't just memorize formulas—know what each method captures, what it ignores, and how to choose between conflicting recommendations.

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Time Value Methods: The Gold Standard

These methods properly account for the fundamental principle that a dollar today is worth more than a dollar tomorrow. By discounting future cash flows, they reflect opportunity cost and provide theoretically sound investment criteria.

Net Present Value (NPV)

• Measures wealth creation directly—calculates the difference between present value of all cash inflows and outflows: $NPV = \sum_{t=0}^{n} \frac{CF_t}{(1+r)^t}$
• Decision rule is straightforward: accept if $NPV > 0$, reject if $NPV < 0$; represents the dollar amount added to firm value
• Considered the theoretically superior method because it accounts for time value of money, all cash flows, and provides an absolute measure of value creation

Internal Rate of Return (IRR)

• The discount rate that makes NPV equal zero—solve for $r$ in $\sum_{t=0}^{n} \frac{CF_t}{(1+r)^t} = 0$
• Accept if IRR exceeds the hurdle rate (cost of capital); intuitively appealing because it expresses return as a percentage
• Can produce multiple solutions or none with non-conventional cash flows, where sign changes occur more than once—this is a critical limitation

Profitability Index (PI)

• Ratio of present value to initial investment—calculated as $PI = \frac{PV \text{ of future cash flows}}{\text{Initial Investment}}$
• Accept if PI > 1, which mathematically guarantees a positive NPV; a PI of 1.15 means $1.15 of value per dollar invested
• Essential for capital rationing situations where you must rank projects by efficiency rather than absolute value creation

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Modified and Adjusted Methods

These techniques refine the basic approaches to address specific limitations or provide more realistic assumptions about reinvestment and project comparison.

Modified Internal Rate of Return (MIRR)

• Assumes reinvestment at the cost of capital, not the IRR itself—this is more realistic since earning the IRR on reinvested funds is rarely guaranteed
• Eliminates the multiple IRR problem by using a single reinvestment rate, producing one unique solution regardless of cash flow pattern
• Formula combines terminal value and present value: $MIRR = \left(\frac{FV \text{ of inflows}}{PV \text{ of outflows}}\right)^{1/n} - 1$

Discounted Payback Period

• Time to recover initial investment using discounted cash flows—addresses the major flaw of simple payback by incorporating time value
• More conservative than simple payback because discounted cash flows are smaller, resulting in longer payback periods
• Still ignores cash flows after recovery, meaning a project could have excellent returns beyond payback that go unrecognized

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Quick Assessment Tools

These simpler methods sacrifice theoretical rigor for ease of calculation and intuitive appeal. They're often used as initial screening tools rather than final decision criteria.

Payback Period

• Time required to recover initial investment from undiscounted cash flows—if you invest $100,000 and earn $25,000 annually, payback is 4 years
• Popular because it's simple and measures liquidity risk—shorter payback means faster capital recovery and less exposure to uncertainty
• Ignores time value of money and all cash flows after payback, making it theoretically flawed but practically useful as a screening tool

Accounting Rate of Return (ARR)

• Uses accounting profit, not cash flows—calculated as $ARR = \frac{\text{Average Annual Accounting Profit}}{\text{Initial Investment}}$
• Easy to compute from financial statements since it uses familiar accounting measures rather than requiring cash flow projections
• Does not discount future returns, ignoring time value of money entirely—least reliable method for investment decisions

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Specialized Comparison Methods

When projects have different lifespans or you need to compare ongoing costs rather than returns, these methods provide appropriate frameworks.

Equivalent Annual Cost (EAC)

• Converts total project cost into an annual figure—uses the annuity formula: $EAC = \frac{NPV \text{ of costs}}{\text{Annuity Factor}}$
• Essential for comparing projects with unequal lives—a 3-year project and 5-year project can't be compared directly by NPV alone
• Lower EAC is preferred when choosing between mutually exclusive projects that will be repeated indefinitely, common in equipment replacement decisions

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Quick Reference Table

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Self-Check Questions

1. Which two methods can give conflicting rankings for mutually exclusive projects, and what causes this conflict?

2. A project has an IRR of 15% and a cost of capital of 10%. If cash flows change sign three times, what problem might arise, and which alternative method addresses it?

3. Compare NPV and PI: when would they give the same accept/reject decision, and when might you prefer PI over NPV?

4. You're comparing two machines—one lasts 4 years, the other 7 years. Why is NPV alone insufficient, and what method should you use instead?

5. An FRQ asks you to evaluate a project using payback period and NPV. The payback is 3 years (acceptable) but NPV is negative. Which method should guide the decision, and why?