11.1 Evaluating NPV Estimates
The primary challenge in capital budgeting is that the true market value of a project cannot be observed directly; it must be estimated. When a discounted cash flow (DCF) analysis results in a positive NPV, it's a good sign, but it's crucial to assess the reliability of that estimate. This is because our projections are based on assumptions that may be inaccurate, a risk known as forecasting risk (or estimation risk). We must avoid the "garbage in, garbage out" trap where inaccurate inputs lead to misleading results.
To mitigate this risk, the first step is to identify the project's specific sources of value. What makes this investment special? A basic principle of economics is that a highly competitive market will have few positive NPV projects, so we must be able to articulate why our project stands out from the competition.
11.2 Scenario and Other What-If Analyses
To assess forecasting risk, we use "what-if" analyses. The goal is to identify which variables are most critical to the project's success. We begin with a **base case** scenario using our initial, most-likely projections.
Scenario Analysis
This approach investigates changes in NPV by considering plausible alternative scenarios, such as a **best case** (optimistic) and a **worst case** (pessimistic) for all relevant variables simultaneously. This gives us a range of possible NPV outcomes and helps us gauge the potential for disaster.
Example: Scenario Analysis
A project has an initial cost of \$200,000, a five-year life, and a 12% required return. The following table shows the outcomes for the base, worst, and best cases, where each variable is adjusted to its most favorable or unfavorable value simultaneously.
| Scenario | Unit Sales | Price/Unit | Var. Cost/Unit | Fixed Costs | Net Present Value |
|---|---|---|---|---|---|
| Base Case | 6,000 | \$80 | \$60 | \$50,000 | \$29,624 |
| Worst Case | 5,500 | \$75 | \$62 | \$55,000 | -\$122,732 |
| Best Case | 6,500 | \$85 | \$58 | \$45,000 | \$201,915 |
Sensitivity Analysis
This is a variation of scenario analysis where we freeze all variables except for one. We then see how sensitive the NPV is to changes in that single variable. If the NPV is highly sensitive to a small change in a particular variable, it indicates a high degree of forecasting risk for that variable.
Example: Sensitivity to Unit Sales
Using the same base case, if we only vary the unit sales from 5,500 to 6,500, the NPV changes dramatically. The plot below illustrates this relationship. The steeper the line, the greater the sensitivity.
Figure 11.1: Sensitivity Analysis for Unit Sales
Simulation Analysis
Simulation analysis is an extended form of scenario analysis that allows all variables to vary simultaneously within a specified range, often thousands of times. It summarizes the results by calculating the average NPV and the percentage of scenarios with a negative NPV. While powerful, it can be complex and difficult to implement accurately.
11.3 Break-Even Analysis
Break-even analysis examines the relationship between sales volume and profitability. It helps answer the question, "How low can sales go before we start losing money?"
Fixed and Variable Costs
Variable costs (VC) change directly with the quantity of output. For example, direct labor and raw materials. **Fixed costs (FC)** do not change over a specified period, such as a lease payment or management salaries. Total costs (TC) are the sum of the two: \( TC = VC + FC \).
Accounting Break-Even
The accounting break-even point is the sales level that results in zero net income. It is calculated by covering fixed costs and depreciation with the contribution margin per unit. The formula is:
$$ \text{Accounting Break-Even Quantity (Q)} = \frac{FC + D}{P - v} $$
where \( FC \) is fixed costs, \( D \) is depreciation, \( P \) is price per unit, and \( v \) is variable cost per unit. A project that only breaks even on an accounting basis has a zero IRR and a negative NPV because it fails to recover its opportunity cost.
11.4 Operating Cash Flow and Break-Even
We can extend break-even analysis to focus on cash flow rather than net income. This gives us a clearer picture of a project's financial viability. The relationship between operating cash flow (OCF) and quantity sold (Q), ignoring taxes, is given by:
$$ OCF = (P-v) \times Q - FC $$
Break-Even Points
There are three key break-even points, each with a different implication for project evaluation.
- Cash Break-Even: The sales volume where OCF is zero. At this point, the project covers its variable and fixed costs but loses the initial investment entirely. The IRR is -100%.
- Accounting Break-Even: The sales volume where net income is zero. At this point, OCF equals depreciation, and the project's payback period equals its life.
- Financial Break-Even: The sales volume where NPV is zero. This is the most important measure for a financial manager. At this level, the project earns exactly its required return. The IRR equals the required return.
Tricky Area: Financial vs. Accounting Break-Even
Financial break-even is always higher than accounting break-even (assuming a positive required return and fixed costs) because it must cover not only the project's costs but also its opportunity cost of capital.
Figure 11.5: Operating Cash Flow and Sales Volume
11.5 Operating Leverage
Operating leverage is a measure of how a project's or firm's operating cash flow responds to a change in sales volume. A project with a higher proportion of fixed costs to total costs has a higher degree of operating leverage (DOL). This can be measured as:
$$ \text{DOL} = 1 + \frac{FC}{OCF} $$
A high DOL means that a small percentage change in sales volume can be magnified into a large percentage change in OCF and NPV. This increases a project's forecasting risk. Managers might consider alternative production methods with lower fixed costs to reduce DOL and lower the break-even point, especially for highly uncertain projects.
11.6 Capital Rationing
Capital rationing occurs when a firm has profitable (positive NPV) projects but lacks the necessary funds to undertake them. There are two types:
- Soft Rationing: This is a self-imposed constraint, often used for budgeting control within a large firm. It can be overcome if management truly believes a project is valuable.
- Hard Rationing: This occurs when a firm cannot raise capital for a project under any circumstances, typically due to financial distress or contractual limitations. In this situation, standard DCF analysis breaks down because the concept of a required return becomes ambiguous.
Chapter Review and Critical Thinking Questions
Use these questions to test your conceptual understanding of the chapter's topics. Click on each question to reveal the solution.
Solution: Forecasting risk is the possibility that a bad decision will be made because of errors in projected cash flows. The degree of forecasting risk would generally be greater for a new product. This is because a cost-cutting proposal's cash flows (cost savings) are usually more certain and easier to estimate than the cash flows for a new product, which depend on highly uncertain variables like sales volume and market share.
Solution: Sensitivity analysis examines how the NPV changes when only a single variable is altered, while all other variables are held constant. Scenario analysis, on the other hand, considers how NPV changes when several variables are altered simultaneously to reflect different possible states of the world (e.g., a best-case or worst-case scenario).
Solution: You should point out that this is flawed thinking. While average revenue and average cost are important for accounting profitability, capital budgeting focuses on marginal (or incremental) revenue and cost. A project can have a negative NPV even if average revenue exceeds average cost if it fails to cover its full cost of capital. You should also highlight that average cost includes sunk costs and irrelevant expenses, while marginal decisions should only be based on relevant incremental cash flows.
Solution: A no-layoff policy makes labor costs behave more like fixed costs rather than variable costs. This would significantly increase a company's degree of operating leverage (DOL). The company would have a higher fixed cost base, meaning that a small change in sales volume would have a magnified effect on operating cash flow and profitability.
Solution: Airlines have a high degree of operating leverage because they have very high fixed costs. The cost of purchasing or leasing airplanes, airport gate fees, and maintenance are largely fixed regardless of how many passengers are on a flight. Fuel is a major variable cost, but the high fixed costs mean that a small increase in passenger volume can lead to a large increase in operating cash flow.
Solution: As a shareholder, you should be most concerned with the financial break-even point. This is because the financial break-even point is the sales level at which a project earns exactly its required return. This is the only measure that truly reflects whether a project is creating value for the firm and, by extension, for its shareholders. The other two measures don't account for the time value of money or opportunity costs.
Solution: Assuming the project has fixed costs and a positive discount rate, the order would be: cash break-even, accounting break-even, and finally, financial break-even. This is because cash break-even only needs to cover cash fixed costs. Accounting break-even must cover cash fixed costs plus depreciation. Financial break-even must cover all cash costs plus the required return on the initial investment. This ordering will always apply as long as the assumptions hold true.
Solution: Soft rationing is a self-imposed limitation on capital spending. The firm could raise more capital if it chose to but has decided not to. Hard rationing occurs when a firm cannot raise capital for a project under any circumstances. With soft rationing, managers should prioritize projects with the highest profitability index. Hard rationing, however, creates a more ambiguous situation because it implies that a project's required return is so high that no projects are acceptable, which contradicts the goal of maximizing shareholder value.
Solution: The difficulty in raising capital for partnerships and proprietorships means that small businesses will often face **hard rationing**. They have limited access to external capital, which can force them to bypass profitable projects even if they have a positive NPV. This limits their growth potential and makes project selection based on NPV alone a less-than-perfect guide.
Solution: Your initial reaction should be one of cautious skepticism. While it is a good sign that all three scenarios (best, base, and worst) show a positive NPV, the results are only as good as the inputs. You should question whether the worst-case scenario is truly a realistic lower bound. It's possible the inputs for the worst case are still overly optimistic. You would want to investigate the assumptions, especially for the most critical variables, to ensure they are reasonable and not biased.