Capital budgeting Study Guide

📖 Core Concepts Capital budgeting – allocating funds to long‑term, non‑core investments (machinery, plants, new products, R&D) to increase shareholder value. Hurdle rate – the minimum required return (usually the firm’s cost of capital) a project must exceed to be considered. Mutually exclusive projects – when only one project can be chosen; the one with the highest NPV wins. Present‑value (PV) annuity factor – the divisor used to turn a lump‑sum NPV into an equal yearly amount (the equivalent annuity). 📌 Must Remember NPV rule – accept any project with $NPV>0$; if capital is limited, pick the highest‑NPV mutually exclusive project. IRR rule – accept if $IRR$ exceeds the cost of capital; remember $IRR$ is the discount rate that makes $NPV=0$. Multiple IRRs – occur when cash‑flow signs change more than once; then the simple $IRR>$ cost‑of‑capital test is unreliable. MIRR – adjusts the IRR by assuming a realistic reinvestment rate for intermediate cash flows. Payback period – the time required to recover the initial outlay (non‑discounted). Discounted payback – same as payback but using discounted cash flows. Profitability index (PI) – $PI = \frac{\text{PV of future cash flows}}{\text{Initial investment}}$; rank projects when capital is scarce. Equivalent Annual Cost (EAC) – annual cost of owning/operating an asset; useful for projects with different lifespans. Real options – value the flexibility to alter future cash flows (e.g., expand, abandon) and are treated like financial options. 🔄 Key Processes NPV Calculation Forecast cash flows for each period. Discount each cash flow at the hurdle rate. Sum discounted cash flows and subtract the initial outlay. IRR Determination Set $NPV=0$ and solve for the discount rate $r$ (usually via trial‑and‑error or spreadsheet). MIRR Computation Compound all positive cash flows at the reinvestment rate to the project end. Discount all negative cash flows at the finance rate to time 0. Solve for the rate that equates the two values. EAC Conversion Compute $EAC = \frac{NPV}{\text{PV annuity factor (for project life)}}$. Project Ranking (Capital‑constrained) Exclude projects below the hurdle rate. Rank remaining projects by PI or NPV. Select in order until the budget is exhausted. 🔍 Key Comparisons NPV vs. IRR – NPV gives dollar value added; IRR gives a percentage return. NPV is always reliable; IRR can mislead with multiple rates or non‑conventional cash flows. Payback vs. Discounted Payback – Payback ignores time value of money; discounted payback incorporates it, giving a longer (more realistic) horizon. EAC vs. NPV – NPV compares total value; EAC translates that value into an annual cost, enabling comparison of projects with different lifespans. MIRR vs. IRR – MIRR assumes realistic reinvestment rates; IRR assumes reinvestment at the IRR itself (often unrealistic). ⚠️ Common Misunderstandings “Higher IRR always means a better project.” False when cash‑flow signs change or projects have different scales/lifespans. “Payback period is sufficient for decision‑making.” It ignores cash flows after recovery and the time value of money. “A positive NPV guarantees the best choice when capital is limited.” Not if another project has a higher NPV per dollar of capital; PI may be more appropriate. “Real options add value automatically.” Only if the firm can actually exercise the flexibility; otherwise the option value is zero. 🧠 Mental Models / Intuition “Add‑value test” – Think of NPV as a profit‑like number: if it’s positive, the project contributes to shareholder wealth. “Rate‑of‑return ceiling” – IRR is a ceiling; if the market’s cost of capital is above it, the project can’t cover its financing cost. “Annualizing lump sums” – EAC is like spreading a loan’s total cost evenly over its life; easier to compare with other yearly expenses. “Flexibility is an option” – Treat every managerial choice (delay, expand, abandon) as an option you can price with the same logic as a stock option. 🚩 Exceptions & Edge Cases Multiple IRRs – Occur with non‑monotonic cash flows; use NPV profile or MIRR instead. Mutually exclusive projects with different lives – Use EAC or convert to equivalent NPV over a common analysis horizon. Projects that are not repeatable – EAC assumes repeatability; avoid using it for one‑off assets. Capital constraints with identical NPVs – Choose the project with higher PI (more value per dollar invested). 📍 When to Use Which NPV – Default method when you have a reliable discount rate and want absolute value added. IRR – Useful for quick percentage‑return checks, especially when comparing to a known cost of capital; avoid if cash‑flow signs change. MIRR – Prefer when you need a realistic return figure with specified finance and reinvestment rates. Payback / Discounted Payback – Use only as a screening tool for liquidity risk, not as a final decision metric. Profitability Index – Ideal when the capital budget is binding and you must prioritize projects. EAC – Apply when projects have unequal, non‑repeatable lifespans and you need an annual cost comparison. Real Options – Deploy when the project contains significant managerial flexibility (e.g., the option to expand or abandon). 👀 Patterns to Recognize Positive NPV + IRR > hurdle → accept (unless multiple IRRs). NPV profile crossing zero more than once → look for multiple IRRs. Longer project life + similar NPV → lower EAC (better annual cost). High initial cash outflow with later large inflows → watch for high IRR but verify with NPV. Projects with identical NPVs but different initial costs → higher PI wins under capital scarcity. 🗂️ Exam Traps Choosing IRR over NPV for mutually exclusive projects – IRR can favor a lower‑NPV project if cash‑flow timing differs. Assuming a single IRR always exists – Cash‑flow sign changes can produce multiple IRRs; the test becomes ambiguous. Treating Payback as a “must‑meet” rule – It ignores cash flows after recovery and the discount rate, leading to over‑acceptance of poor projects. Applying EAC to non‑repeatable projects – The method assumes the project can be duplicated; using it otherwise misstates annual cost. Overlooking the impact of financing mix – Forgetting that debt vs. equity changes the weighted average cost of capital, which shifts the hurdle rate for NPV/IRR calculations. --- Keep this guide handy; focus on NPV and IRR fundamentals, remember the exceptions, and use the decision‑rules to navigate capital‑budgeting questions quickly.