10.1 Project Cash Flows: A First Look
The first step in evaluating a proposed investment is to identify the relevant cash flows. These are the incremental cash flows that come about as a direct consequence of the decision to take on a project. Any cash flow that would occur regardless of the project is not relevant.
The stand-alone principle simplifies this process by allowing us to view a project as a "minifirm," focusing only on its own incremental cash flows in isolation from the company's other activities.
10.2 Incremental Cash Flows
When identifying incremental cash flows, several pitfalls must be avoided.
- Sunk Costs: These are costs that have already been paid or are liabilities to be paid, regardless of whether the project is accepted or rejected. Sunk costs are irrelevant to the capital budgeting decision.
- Opportunity Costs: These are the valuable benefits that are given up by choosing a particular project. For example, if a project uses land the company already owns, the opportunity cost is the after-tax cash flow the land could have generated if sold or used for another purpose.
- Side Effects: The introduction of a new project can affect the cash flows of a company's existing projects. A negative side effect, like lost sales of an existing product due to a new product, is called erosion. These effects must be included in the incremental cash flow calculation.
- Net Working Capital (NWC): A project typically requires an initial investment in NWC (inventory, accounts receivable, etc.). This is a cash outflow at the beginning, but it is recovered at the end of the project's life, resulting in a cash inflow.
- Financing Costs: Interest payments, dividends, and other financing expenses are not included in the project's cash flows. We evaluate the project's cash flow from its assets, separate from how those assets are financed.
10.3 Pro Forma Financial Statements and Project Cash Flows
To calculate project cash flows, we first need to prepare pro forma (projected) financial statements. These statements, especially the income statement and balance sheet, summarize the project's future revenues, costs, and capital requirements.
Project Cash Flow Components
Project cash flow has three main components:
- Operating Cash Flow (OCF): Cash flow from the project's day-to-day operations.
- Capital Spending: The initial investment in long-term assets and any subsequent investments or salvage values.
- Changes in Net Working Capital (NWC): The initial investment in NWC and its subsequent recovery.
Formula: Project Cash Flow = OCF - Capital Spending - Change in NWC
Textbook Example: Shark Attractant Project
Projections: Sales = 50,000 units at $4/can. Variable Costs = $2.50/can. Fixed Costs = $17,430/year. Equipment Cost = $90,000 (3-year life, straight-line to zero). Initial NWC = $20,000. Tax rate = 21%.
Step 1: Pro Forma Income Statement
| Sales | $200,000 |
|---|---|
| Variable costs | 125,000 |
| Fixed costs | 17,430 |
| Depreciation ($90,000/3) | 30,000 |
| EBIT | $27,570 |
| Taxes (21%) | 5,790 |
| Net Income | $21,780 |
Step 2: Project Cash Flows
- OCF: $27,570 (EBIT) + $30,000 (Depreciation) - $5,790 (Taxes) = $51,780
- Capital Spending: -$90,000 at Year 0. Salvage value is zero.
- Change in NWC: -$20,000 at Year 0. +$20,000 in Year 3.
Final Cash Flows:
- Year 0: -$90,000 (CapEx) - $20,000 (NWC) = -$110,000
- Year 1 & 2: OCF = $51,780
- Year 3: OCF + NWC recovery = $51,780 + $20,000 = $71,780
10.4 More about Project Cash Flow
This section delves deeper into NWC and depreciation, which are often sources of confusion.
A Closer Look at NWC
Changes in NWC adjust for the difference between accounting revenues and costs and actual cash flows. An increase in NWC is a cash outflow, while a decrease is a cash inflow. The total NWC invested is typically recovered at the end of the project.
Tricky Area:
Remember that NWC is a crucial component of cash flow. An increase in accounts receivable means you haven't collected all your sales in cash, and an increase in accounts payable means you haven't paid all your costs in cash. Including changes in NWC correctly adjusts for these non-cash items.
Depreciation (MACRS)
Depreciation is a non-cash expense that is relevant only because it creates a tax shield. The depreciation method used for capital budgeting is typically the Modified Accelerated Cost Recovery System (MACRS) as defined by the IRS. It assigns assets to a specific class (e.g., 3-year, 5-year, 7-year) to determine the depreciation schedule. The salvage value and economic life are not explicitly considered in the MACRS calculation.
Textbook Example: MACRS Depreciation
Problem: A car costing $12,000 is 5-year property. What is the yearly depreciation?
Solution: Using the 5-year MACRS percentages:
- Year 1: 20.00% × $12,000 = $2,400.00
- Year 2: 32.00% × $12,000 = $3,840.00
- Year 3: 19.20% × $12,000 = $2,304.00
- Year 4: 11.52% × $12,000 = $1,382.40
- Year 5: 11.52% × $12,000 = $1,382.40
- Year 6: 5.76% × $12,000 = $691.20
10.5 Alternative Definitions of Operating Cash Flow
There are three common ways to calculate OCF, all of which yield the same result if used correctly. The best approach is the one that's most convenient for a given problem.
- Bottom-Up Approach: Starts with net income and adds back non-cash expenses like depreciation. This is valid only if there is no interest expense.
\(OCF = \text{Net Income} + \text{Depreciation}\)
- Top-Down Approach: Starts with sales and subtracts cash costs and taxes, ignoring non-cash items like depreciation.
\(OCF = \text{Sales} - \text{Costs} - \text{Taxes}\)
- Tax Shield Approach: Separates the cash flow into two components: what the cash flow would be without depreciation and the tax savings from depreciation.
\(OCF = (\text{Sales} - \text{Costs}) \times (1 - T_C) + \text{Depreciation} \times T_C\)
10.6 Some Special Cases of DCF Analysis
This section covers three important and common special cases in DCF analysis.
Evaluating Cost-Cutting Proposals
The relevant cash flows for a cost-cutting project are the after-tax savings and the depreciation tax shield from the new equipment. You must also account for the initial investment and any after-tax salvage value.
Textbook Example: Cost-Cutting
Problem: A new system costs $200,000, has a 4-year life (straight-line depreciation), and saves $60,000/year (pre-tax). It frees up $45,000 in NWC. Salvage value is $30,000. Tax rate = 21%, required return = 16%. What is the NPV?
Solution:
- OCF: After-tax savings are $60,000 × (1 - 0.21) = $47,400. Depreciation is $50,000, so the tax shield is $50,000 × 0.21 = $10,500. OCF = $47,400 + $10,500 = $57,900/year.
- Initial Investment: -$200,000 (CapEx) + $45,000 (NWC inflow) = -$155,000.
- Terminal CF: After-tax salvage = $30,000 × (1 - 0.21) = $23,700. NWC outflow = -$45,000.
Total Cash Flows: Year 0: -$155,000. Years 1-3: $57,900. Year 4: $57,900 + $23,700 - $45,000 = $36,600.
$$NPV = -155,000 + \frac{57,900}{1.16^1} + \frac{57,900}{1.16^2} + \frac{57,900}{1.16^3} + \frac{36,600}{1.16^4} = -4,749$$
Setting the Bid Price
When bidding on a contract, the goal is to find the lowest price you can charge and still break even. This is the price that results in a zero NPV. You work backward from a zero NPV to find the required annual cash flow, and then the sales price per unit.
Evaluating Equipment Options with Different Lives
When comparing mutually exclusive projects with unequal lives, you cannot simply compare their NPVs. The correct method is to calculate the Equivalent Annual Cost (EAC) for each. The EAC is the amount of an annuity payment that has the same present value as the project's costs. You should choose the project with the lowest EAC.
Textbook Example: Equivalent Annual Cost (EAC)
Problem: Machine A: Cost $100, 2-year life, $10/year operating cost. Machine B: Cost $140, 3-year life, $8/year operating cost. Both use a 10% discount rate. Which to choose?
Solution:
- Machine A PV: \(PV = -100 - \frac{10}{1.10} - \frac{10}{1.10^2} = -117.36\). Annuity factor for 2 years at 10% is 1.7355.
\(EAC = \frac{-117.36}{1.7355} = -67.62\)
- Machine B PV: \(PV = -140 - \frac{8}{1.10} - \frac{8}{1.10^2} - \frac{8}{1.10^3} = -159.89\). Annuity factor for 3 years at 10% is 2.4869.
\(EAC = \frac{-159.89}{2.4869} = -64.30\)
Conclusion: Machine B is cheaper on an equivalent annual cost basis, so it is the better choice.
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: In the context of capital budgeting, an opportunity cost is the value of the benefit that is foregone by choosing to use a particular asset for a project instead of its next-best alternative. For example, if a company uses land it already owns for a new project, the opportunity cost is the after-tax cash flow that could have been realized from selling the land.
Solution: A firm would prefer to use MACRS depreciation because it is an accelerated method. This means that a larger portion of the depreciation is taken in the early years of an asset's life. This leads to higher tax shields and therefore higher cash flows and NPV in the early years of a project. The time value of money makes cash flows received sooner more valuable.
Solution: The assumption that a firm recovers all of its net working capital is generally reasonable for a project with a finite life. As the project winds down, inventory is sold off, receivables are collected, and accounts payable are paid. This frees up the cash that was tied up in working capital. However, this assumption might not be valid if some inventory becomes obsolete, or if some accounts receivable are never collected.
Solution: This statement is flawed. The stand-alone principle allows us to separate a project's cash flows from the rest of the firm's operations. However, it does not mean we should include financing costs. The financing decision (how to fund a project) is separate from the investment decision (whether the project itself is profitable). By excluding financing costs, we can focus on the cash flow generated by the project's assets. The cost of financing is captured in the discount rate used to calculate NPV, not in the cash flows themselves.
Solution: EAC analysis is appropriate when comparing mutually exclusive projects with unequal lives that must be replaced indefinitely. It is used because the NPVs of projects with different lives are not directly comparable. EAC finds the annual cost of each project, allowing for a fair comparison. A key implicit assumption is that the replacement projects will have the same costs and cash flows as the original, which may not hold true due to technological changes or inflation.
Solution: This statement is incorrect. While depreciation is a noncash expense, it is a tax-deductible expense. This means it reduces a firm's taxable income and, therefore, its tax bill. The tax savings from depreciation, known as the depreciation tax shield, are a very real cash flow benefit that must be included in a project's cash flow analysis.
Solution: The publisher must consider several incremental cash flow issues. The primary concern is erosion. The sales of the new, lower-priced book will likely cannibalize sales of the existing, higher-priced book. The publisher must account for the lost profits from the original book when evaluating the new project. Other considerations include new production costs, marketing expenses, and whether the new version will attract students who would not have purchased the original, thereby expanding the market.
Solution: The term "erosion" typically refers to the cannibalization of sales of an existing product by a new one. The damage to Porsche's reputation is a broader side effect of the new project. While a loss of reputation could lead to a decline in sales (erosion) of other Porsche models, the reputational damage itself is a separate, more abstract negative consequence that is difficult to quantify but must be considered in the overall qualitative analysis of the project.
Solution: A company might enter a market late if it believes it can bring a unique competitive advantage to the table. In Porsche's case, it might have been its reputation for high performance, which could have allowed it to compete at the high end of the market. Late entry can also allow a firm to learn from the mistakes of its predecessors and adopt more efficient production technologies. The success of early entrants can also prove that a market exists, reducing market risk for later entrants.
Solution: Porsche should assume that the initial high profit margins will not be maintained as the market becomes more competitive. As a basic principle of economics, high profits attract new competitors, which drives prices down and squeezes margins. Porsche might be able to maintain a higher-than-average margin due to its strong brand image and the high performance of its vehicles, but it would be unrealistic to assume that the initial "supernormal" profits would last forever.