📖 薄弱点强化：资本预算

Corporate Finance

I. Lesson Focus

II. The Problem

A manufacturing company is evaluating a new production line with an initial equipment outlay of CNY 8 million. The project will generate annual operating cash flows, but its life, salvage value, changes in net working capital, and appropriate cost of capital must be estimated accurately. Relying on vague notions such as “it will pay back eventually” or “the IRR looks high” can lead to accepting value-destroying projects or rejecting value-creating ones. Capital budgeting is tested almost every year on the CFA Level I exam, with heavy emphasis on correctly identifying incremental cash flows, ignoring sunk costs, separating financing costs from the project discount rate, and choosing the superior project among mutually exclusive alternatives.

III. Core Concepts and Decision Rules in Capital Budgeting

Capital budgeting is the process of making long-term investment decisions. The overriding goal is to accept projects that increase shareholder wealth, i.e., those with NPV > 0. The fundamental decision rule is maximization of Net Present Value (NPV). NPV is the present value of all expected incremental cash flows minus the initial investment and directly measures the increase in shareholder value.

Incremental Cash Flows are the key. They must satisfy three principles: - Consider only incremental changes relative to the status quo. - Use after-tax cash flows. - Include all relevant opportunity costs and externalities.

Common Cash Flow Pitfalls: - Sunk costs: Costs already incurred and irrecoverable; must be ignored (e.g., prior market research expense). - Opportunity costs: The forgone benefit from using an asset must be included. - Externalities (cannibalization or enhancement): Effects on other company products must be incorporated. - Changes in net working capital (ΔNWC): An increase at project start is a cash outflow; recovery at the end is a cash inflow.

IV. Primary Capital Budgeting Methods

1. Net Present Value (NPV)

$$ NPV = \sum_{t=1}^{n} \frac{CF_t}{(1+r)^t} - CF_0 $$ where $r$ is the project’s required rate of return (usually WACC or a risk-adjusted rate). Rule: Accept if NPV > 0. For mutually exclusive projects, select the one with the highest NPV.

2. Internal Rate of Return (IRR)

IRR is the discount rate that makes NPV = 0. Rule: Accept if IRR > required return. Limitations: Multiple IRRs possible with non-conventional cash flows; ranking conflicts with NPV for mutually exclusive projects due to size or timing differences.

3. Payback Period

Calculates the years required to recover the initial investment. Advantages: Simple and focuses on liquidity. Disadvantages: Ignores all cash flows after payback and ignores the time value of money. Discounted Payback corrects for time value but still ignores post-payback cash flows.

4. Profitability Index (PI)

$$ PI = \frac{\text{PV of future cash flows}}{CF_0} = 1 + \frac{NPV}{CF_0} $$ Accept if PI > 1. Under capital rationing, rank projects by descending PI.

5. Accounting Rate of Return (ARR)

ARR = Average net income / Average book value of investment. Based solely on accounting profit; ignores cash flows and time value. Generally not recommended for decision-making and rarely preferred on the exam.

V. Detailed Steps in Project Cash Flow Estimation

1. Initial investment (t=0): Equipment cost + installation + increase in NWC – after-tax proceeds from sale of old equipment.
2. Operating cash flow (OCF): $(S - C - D)(1 - T) + D$ or equivalently EBIT(1 – T) + Depreciation.
3. Terminal cash flow (final year): Final-year OCF + after-tax salvage value + recovery of NWC.

Discount Rate Selection: Most often the firm’s WACC. If project risk differs materially from the firm, adjust to an appropriate project-specific required return (e.g., CAPM for all-equity projects).

Worked Cases

Case 1: Conventional Project — NPV and IRR

Project requires CNY 5 million initial outlay and generates CNY 1.4 million after-tax operating cash flow annually for 5 years. No salvage value. Required return = 10%. Calculate NPV and IRR.

Solution:
NPV = –500 + 140 × PVIFA(10%, 5)
PVIFA(10%, 5) = 3.7908
NPV = –500 + 530.71 = +30.71 (accept the project).

Using a financial calculator or Excel, IRR ≈ 12.4% > 10%. Both metrics agree.

Case 2: Mutually Exclusive Projects and Ranking Conflict

Project A and Project B both require CNY 10 million initial investment. Project A has higher cash flows in early years; Project B has higher cash flows in later years. At 8% discount rate, NPV_A > NPV_B. At 15%, NPV_B > NPV_A. At the firm’s 10% required return, NPV_A = 1.85 million, NPV_B = 1.62 million. However, IRR_A = 14.2% and IRR_B = 15.8%.

Correct Decision: Choose Project A because it has the higher NPV. NPV directly measures the absolute increase in shareholder wealth. The conflict arises from different reinvestment rate assumptions: IRR assumes reinvestment at the IRR, while NPV assumes reinvestment at the cost of capital.

Case 3: Comprehensive Case with NWC, Salvage, and Sunk Cost

A firm is considering new equipment costing CNY 2 million plus CNY 0.2 million installation. An old machine with book value CNY 0.3 million can be sold for CNY 0.5 million (tax rate 25%). The project requires an additional CNY 0.4 million in net working capital. Project life = 4 years. Annual revenue CNY 1.8 million, cash operating costs CNY 0.6 million, straight-line depreciation CNY 0.55 million per year to zero book value. Salvage value at end of year 4 = CNY 0.25 million. Required return = 12%.

Incremental Cash Flows: - Year 0: –(2.0 + 0.2) + (0.5 – 0.3) × (1 – 0.25) – 0.4 = –2.2 + 0.15 – 0.4 = –2.45 million - Annual OCF = (1.8 – 0.6 – 0.55)(1 – 0.25) + 0.55 = 0.65 × 0.75 + 0.55 = 1.0375 million - Year 4 terminal cash flow = 1.0375 + 0.25 × (1 – 0.25) + 0.4 = 1.0375 + 0.1875 + 0.4 = 1.625 million

NPV is positive (approximately CNY 0.684 million). Accept the project. Note: A prior CNY 0.15 million market study is a sunk cost and is correctly excluded.

Traps

Key Formulas

• $NPV = \sum \frac{CF_t}{(1+r)^t} - CF_0$
• IRR: discount rate that sets NPV = 0
• $PI = \frac{\text{PV of future CFs}}{\text{Initial investment}} = 1 + \frac{NPV}{\text{Initial Outlay}}$
• Operating cash flow: $OCF = (S - C - D)(1 - T) + D$
• After-tax salvage = Salvage – $T × ($Salvage – Book value$)$
• Initial CF = –Cost – Installation – ΔNWC + After-tax proceeds from old asset
• When NPV and IRR conflict, NPV is the superior criterion
• Discounted payback incorporates time value but still ignores cash flows beyond the cutoff

Practice Questions

Q1. Which of the following should not be included in a project’s initial cash flow?
A. Installation costs
B. Feasibility study fee paid six months ago
C. Increase in net working capital
D. After-tax proceeds from sale of old equipment

Q2. When mutually exclusive projects differ in scale, the most likely reason for a conflict between NPV and IRR rankings is:
A. Different reinvestment rate assumptions
B. Different depreciation methods
C. Different tax rates
D. Different project lives

Q3. A project requires an CNY 8 million initial investment and is expected to produce CNY 2 million annual cash flows for 5 years. The required return is 10%. The project’s profitability index is closest to:
A. 0.75
B. 1.05
C. 1.24
D. 1.52

Q4. The correct formula for operating cash flow is:
A. (Sales – Costs)(1 – Tax rate)
B. (Sales – Costs – Depreciation)(1 – Tax rate) + Depreciation
C. EBIT – Taxes
D. Net Income + Interest

Q5. Which statement about the payback period is least accurate?
A. The payback period ignores all cash flows after the payback date.
B. Discounted payback incorporates the time value of money.
C. A shorter payback period always implies a higher NPV.
D. Payback is primarily used to assess liquidity risk.

Q6. A project whose cash flows change sign three times is most likely to have:
A. Multiple IRRs
B. A permanently negative NPV
C. A PI less than 1
D. An excessively long discounted payback

Q7. Under capital rationing, a firm should primarily rank projects by:
A. Accepting all projects with NPV > 0
B. Descending order of IRR
C. Descending order of profitability index
D. Smallest initial investment

Q8. A project has an NPV of CNY 1.2 million and an initial investment of CNY 6 million. Its profitability index is:
A. 0.20
B. 1.20
C. 1.50
D. Not calculable

Answers

Takeaways

• NPV is the gold standard in capital budgeting; for mutually exclusive projects always select the highest NPV.
• Sunk costs are never included; opportunity costs and externalities must be included.
• Financing costs are already embedded in WACC; never deduct interest again in cash flows.
• When IRR and NPV conflict, trust NPV.
• Non-conventional cash flows may produce multiple IRRs; examine the NPV profile.
• Under capital rationing, rank by profitability index rather than IRR or total NPV.