📖 资本预算中的现金流估算

Corporate Finance

I. Lesson Focus

This lesson explains how to correctly identify and estimate the incremental after-tax cash flows required for capital budgeting decisions. Candidates must master the classification of cash flows into initial outlay, operating cash flows, and terminal cash flow, the treatment of sunk costs, opportunity costs, externalities, net working capital, depreciation tax shields, and after-tax salvage values. These concepts are directly tested in NPV, IRR, and project selection questions.

II. The Problem

A manufacturing company is considering an 8 million yuan investment in a new automated production line. Management needs to determine exactly how much real “cash” the project will generate over its entire life. Which expenditures belong in the initial investment? Should sunk costs be included? Must the increase in working capital be deducted? At project termination, how should the after-tax proceeds from selling the equipment and the recovery of working capital be treated? Only after accurately estimating incremental cash flows for every year can NPV and IRR be calculated to decide whether the project adds value. An error in cash flow estimation will lead to a wrong decision even if the discount rate is calculated perfectly.

III. Fundamental Principles of Cash Flows in Capital Budgeting

The core concept in capital budgeting is incremental cash flow—the difference in the firm’s cash flows with the project versus without the project. Four principles must be followed strictly:

1. Consider only incremental cash flows: Measure only the cash changes caused directly by the project.
2. Ignore sunk costs: Costs already incurred and irrecoverable are irrelevant to the decision.
3. Include opportunity costs: The value of the best alternative use of a resource that is given up by undertaking the project.
4. Account for externalities: Positive or negative effects the project has on the rest of the firm’s cash flows (e.g., cannibalization).

IV. Time Classification of Project Cash Flows

Project cash flows are divided into three components:

• Initial investment cash flow (t = 0)
• Operating cash flows (t = 1 to n−1)
• Terminal cash flow (t = n)

Components of Initial Investment

• Cost of new fixed assets
• Installation and commissioning costs (capitalized)
• Increase in net working capital (ΔNWC)
• After-tax proceeds from sale of old assets (if a replacement project)
• Formula:
  Initial Outlay = Cost of new asset + Installation + ΔNWC − After-tax proceeds from sale of old asset

Operating Cash Flow Formula (Core Equation)

The most frequently used formula for operating cash flow (OCF) is:

$$ OCF = (S - C - D)(1 - t) + D $$

where
- S = incremental sales revenue
- C = incremental cash operating costs (excluding depreciation)
- D = incremental depreciation expense
- t = marginal corporate tax rate

An equivalent form is:

$$ OCF = (S - C)(1 - t) + Dt $$

This represents after-tax operating profit plus depreciation (a non-cash expense).

Components of Terminal Cash Flow

In the final year, in addition to normal OCF, include: - After-tax cash flow from sale of fixed assets: Sale price − Tax on (Sale price − Book value) - Recovery of net working capital: +ΔNWC (sign reversal) - Any cleanup or removal costs (if applicable)

V. Impact of Depreciation Methods on Cash Flows

CFA Level I emphasizes the difference between straight-line and accelerated depreciation (e.g., double-declining balance). Accelerated methods produce larger depreciation and tax shields early, resulting in higher early-period OCF and lower later OCF. Although total depreciation over the project life is the same, the NPV is usually higher under accelerated depreciation because of the time value of money.

VI. Treatment of Special Items

• Interest expense: Not included in operating cash flows (already reflected in the WACC discount rate) to avoid double-counting.
• Inflation: Match nominal cash flows with nominal discount rates and real cash flows with real discount rates; consistency is required.
• Cannibalization: Lost sales from existing products must be treated as a negative incremental cash flow.
• Allocated overhead: Only incremental overhead costs caused by the project are included; existing allocated costs are ignored.

Worked Cases

Case 1: Simple Expansion Project

A company plans a new production line with the following data: - Equipment cost: 5 million yuan, installation 0.5 million yuan, 5-year straight-line depreciation to zero salvage - Expected annual sales: 4 million yuan, annual cash operating costs 1.8 million yuan - Increase in net working capital: 0.6 million yuan - Tax rate 25%, required return 10%

Cash flow calculation:

Initial outlay (t=0): 5 + 0.5 + 0.6 = 6.1 million yuan

Annual depreciation D = 5.5 / 5 = 1.1 million yuan

Annual OCF (t=1 to 5):
OCF = (4 − 1.8 − 1.1)(1 − 0.25) + 1.1 = (1.1)(0.75) + 1.1 = 0.825 + 1.1 = 1.925 million yuan

Terminal year (t=5): OCF 1.925 + recovery of NWC 0.6 = 2.525 million yuan (zero salvage, no tax)

Case 2: Replacement Project with Opportunity Cost

A firm is replacing old equipment with new: - New equipment cost 8 million yuan, installation 0.8 million yuan, 5-year straight-line to residual value 0.5 million yuan - Old equipment current market value 1.8 million yuan, book value 1.2 million yuan - New equipment increases revenue by 1.5 million yuan and reduces cash costs by 0.8 million yuan annually - Increase in NWC 0.4 million yuan, tax rate 25%

Steps: 1. Initial cash flow:
New asset outlay = 8 + 0.8 = 8.8 million
After-tax proceeds from old = 1.8 − (1.8−1.2)×0.25 = 1.8 − 0.15 = 1.65 million
ΔNWC = 0.4 million
Net initial outlay = 8.8 + 0.4 − 1.65 = 7.55 million yuan

1. Incremental annual depreciation: New = (8.8−0.5)/5 = 1.66 million; assume old was 0.6 million; ΔD = 1.06 million

2. Annual incremental OCF = (1.5 + 0.8 − 1.06)(1−0.25) + 1.06 = (1.24)(0.75) + 1.06 = 0.93 + 1.06 = 1.99 million yuan

3. Terminal year (t=5):
   After-tax salvage = 0.5 − (0.5−0)×0.25 = 0.375 million
   NWC recovery = 0.4 million
   Additional terminal cash = 0.375 + 0.4 = 0.775 million yuan

Case 3: Project with Cannibalization and Opportunity Cost

A beverage company launches a new flavor: - Initial investment 4.5 million yuan, 5-year straight-line depreciation to zero - New product expected revenue 3 million yuan, but reduces existing product revenue by 0.6 million yuan - New product cash costs 1.1 million yuan, increase in NWC 0.3 million yuan - The project uses an idle factory building that could be rented for 0.25 million yuan per year (pre-tax) - Tax rate 30%

Incremental revenue = 3 − 0.6 = 2.4 million yuan
Opportunity cost (forgone rent) = 0.25 million yuan (tax-adjusted in OCF)
Annual OCF = (2.4 − 1.1 − 0.9 − 0.25)(1−0.3) + 0.9 = (0.15)(0.7) + 0.9 = 0.105 + 0.9 = 1.005 million yuan
(depreciation = 4.5/5 = 0.9 million)

Initial outlay = 4.5 + 0.3 = 4.8 million yuan
Terminal year (t=5) cash flow = 1.005 + 0.3 = 1.305 million yuan (zero salvage)

Traps

Key Formulas

• Initial Outlay = Fixed asset cost + Installation + ΔNWC − After-tax proceeds from old asset
• $$ OCF = (S - C - D)(1-t) + D $$ or equivalently $$ (S - C)(1-t) + Dt $$
• Terminal CF = OCF_n + After-tax salvage value + Recovery of NWC
• Tax on salvage = t × (Sale price − Book value)
• Incremental cash flow = Cash flow with project − Cash flow without project
• Accelerated depreciation usually increases project NPV relative to straight-line due to time value of money

Practice Questions

Q1. In capital budgeting, sunk costs should be:
A. Included in the initial investment
B. Treated as an opportunity cost
C. Ignored completely
D. Recovered in the terminal year

Q2. A project has equipment cost of 6 million, installation 0.4 million, ΔNWC of 0.5 million, and after-tax proceeds from old equipment of 0.9 million. The initial investment cash flow is:
A. 6.0 million
B. 6.9 million
C. 6.0 million
D. 5.1 million

Q3. Which of the following should not be included in operating cash flow?
A. Depreciation tax shield
B. Incremental interest expense on project debt
C. Incremental sales revenue
D. Incremental cash operating costs

Q4. If a new project causes existing product sales to fall by 0.5 million, this effect should be:
A. Ignored because it is an internal transfer
B. Treated as a positive externality
C. Treated as a negative incremental cash flow
D. Included in the initial investment

Q5. Equipment with a book value of 0.3 million is sold for 0.5 million at a 25% tax rate. The tax on the sale is:
A. 0.05 million outflow
B. 0.05 million inflow
C. 0.20 million
D. Zero

Q6. Compared with straight-line depreciation, accelerated depreciation methods will usually:
A. Lower project NPV
B. Raise project NPV
C. Have no effect on NPV
D. Affect only IRR

Q7. In year 5 a project has OCF of 1.2 million, after-tax salvage cash flow of 0.4 million, and NWC recovery of 0.25 million. Terminal cash flow equals:
A. 1.20 million
B. 1.60 million
C. 1.85 million
D. 1.45 million

Q8. When calculating OCF, the correct treatment is:
A. Subtract interest expense from revenue before applying (1−t)
B. Exclude interest expense from the OCF calculation
C. Treat depreciation as a cash outflow
D. Ignore the effect of taxes

Answers

Takeaways

• Capital budgeting examines only incremental cash flows; sunk costs are always excluded.
• The core OCF formula is (S−C−D)(1−t)+D; depreciation affects cash flow only through its tax shield.
• Increases in net working capital are outflows at t=0 and must be added back at the project’s end.
• Salvage value is included on an after-tax basis using Sale − t(Sale − Book value).
• Interest expense is never subtracted in cash flows; it is already reflected in the discount rate.
• Opportunity costs and cannibalization must be treated as negative incremental cash flows.