NPV and the investment decision
Capital budgeting decides which long-term projects a firm should invest in. Net present value is the gold-standard method.
What capital budgeting covers
Capital budgeting evaluates long-term investments such as new factories, equipment, products, acquisitions, and research projects. These decisions involve large sums, shape a firm's future for years, and are hard to reverse, so careful analysis is essential.
Net present value
Net present value discounts all expected future cash flows at the project's required return (cost of capital) and subtracts the initial investment: \(NPV = -I_0 + \sum_{t=1}^{n} \frac{CF_t}{(1+r)^t}\). If NPV is positive, the project is expected to earn more than the required return and increase shareholder wealth.
NPV = -I_0 + \sum \frac{CF_t}{(1+r)^t}The NPV rule
Accept projects with positive NPV; reject those with negative NPV. When choosing between mutually exclusive projects, choose the one with the highest NPV. NPV accounts for the time value of money, uses all cash flows, and measures value added in dollars.
Choosing the discount rate
The discount rate should reflect the risk of the project's cash flows, typically the firm's weighted average cost of capital for average-risk projects, adjusted up for riskier projects and down for safer ones. Using one company-wide rate for all projects can lead to accepting too many risky projects and too few safe ones.
Relevant cash flows
Only incremental cash flows matter: changes in the firm's cash flows caused by the project. Include initial investment, operating cash flows after tax, changes in working capital, and salvage value. Exclude sunk costs, include opportunity costs, and account for side effects such as cannibalising sales of existing products.
Depreciation and taxes
Depreciation is not a cash flow itself, but it reduces taxable income, creating a tax shield equal to depreciation x tax rate. Operating cash flow = (revenue - costs) x (1 - tax rate) + depreciation x tax rate. Faster depreciation increases the present value of tax savings.
Working capital in projects
Projects often require extra inventory and receivables, an initial cash outflow for working capital. This working capital is usually recovered at the end of the project, an inflow. Ignoring working capital overstates NPV.
Worked example
A project costs 100,000 dollars and generates 30,000 dollars a year for 5 years. At a 10% cost of capital, the present value of the inflows is \(30{,}000 \times 3.791 = 113{,}730\). NPV = 113,730 - 100,000 = 13,730 dollars, so the project should be accepted. At a 15% rate, the annuity factor is 3.352, PV = 100,560, and NPV is only about 560.
Key takeaways
Capital budgeting evaluates large, long-lasting investments. NPV discounts future cash flows at the cost of capital and subtracts the investment; accept positive NPV projects and choose the highest NPV among exclusive options. The discount rate should match project risk. Use incremental after-tax cash flows, including working capital and opportunity costs, excluding sunk costs. Depreciation creates tax shields.
Flashcard
Evaluating long-term investments
Check your understanding
Two mutually exclusive projects have NPVs of 40,000 and 65,000 dollars. Which should the firm choose?