📖 资本预算导论：概念与流程

Corporate Finance

I. Lesson Focus

This lesson introduces the fundamental concepts of capital budgeting, the decision-making process, and the primary evaluation techniques used by corporations to allocate scarce capital to long-term investment projects. Candidates must master the definitions, incremental cash flow principles, NPV, IRR, payback, and profitability index, along with their relative strengths, weaknesses, and potential conflicts.

II. The Problem

A manufacturing firm must decide whether to invest CNY 8 million in new production equipment that is expected to generate CNY 2.2 million in annual net cash inflows for five years, with a required rate of return of 10%. Should the project be accepted? If several mutually exclusive projects compete for limited capital, how should the firm rank them? Capital budgeting solves the core corporate-finance question of how to deploy limited long-term capital to maximize shareholder value.

III. Definition and Importance of Capital Budgeting

Capital budgeting is the process of planning, evaluating, and selecting long-term capital expenditure projects. These projects typically require large initial outlays and affect the firm’s cash flows, risk profile, and competitive position for 5–30 years.

Importance: - Decisions are largely irreversible; once capital is committed, recovery is difficult and costly. - Capital budgeting directly determines future profitability, risk, and firm value. - It is the primary mechanism for implementing corporate strategy (market expansion, efficiency gains, ESG upgrades).

IV. Core Decision Principles

1. Incremental Cash Flow Principle: Analyze only the additional cash flows generated by the project; ignore sunk costs.
2. After-Tax Cash Flow Principle: All analysis uses after-tax cash flows.
3. Opportunity Cost Principle: The value of resources in their best alternative use must be included.
4. Externality (Cannibalization/Synergy) Principle: Account for the project’s impact on the firm’s other operations.
5. Time Value of Money Principle: Cash flows occurring at different times must be discounted to a common point.

V. Primary Capital Budgeting Methods

Methods are divided into non-discounting and discounting techniques.

1. Non-Discounting Methods (Ignore Time Value)

• Payback Period: Years required to recover the initial investment from cumulative cash flows.
  Advantages: simple, intuitive, useful for liquidity and risk screening.
  Disadvantages: ignores cash flows after payback, ignores time value.
• Discounted Payback Period: Uses discounted cash flows; partially corrects for time value.

2. Discounting Methods (CFA Emphasis)

• Net Present Value (NPV)
  $$ NPV = \sum_{t=1}^{n} \frac{CF_t}{(1+r)^t} - CF_0 $$
  Decision rule: Accept if NPV > 0; reject if NPV < 0. For mutually exclusive projects, select the highest NPV.

• Internal Rate of Return (IRR)
  The discount rate that sets NPV = 0.
  Decision rule: Accept if IRR > required return (r).
  Pitfall: IRR and NPV can conflict for mutually exclusive projects due to differences in scale or cash-flow timing.

• Profitability Index (PI)
  $$ PI = \frac{\text{PV of future cash flows}}{\text{Initial investment}} $$
  or
  $$ PI = 1 + \frac{NPV}{\text{Initial investment}} $$
  Decision rule: Accept if PI > 1. Under capital rationing, rank by PI.

• Modified Internal Rate of Return (MIRR): Corrects IRR’s unrealistic reinvestment-rate assumption by assuming positive cash flows are reinvested at the firm’s cost of capital.

VI. Typical Capital Budgeting Process

1. Idea generation
2. Project screening and preliminary analysis
3. Detailed economic evaluation (NPV, IRR, etc.)
4. Project selection and ranking (independent vs. mutually exclusive)
5. Implementation and control
6. Post-audit: compare actual vs. forecasted results to improve future decisions.

Worked Cases

Case 1: Basic NPV and IRR Calculation

Project: CF₀ = –1,000,000; annual CF = 300,000 for 5 years; r = 10%.

$$ NPV = -1,000,000 + 300,000 \times \frac{1-(1.1)^{-5}}{0.1} = -1,000,000 + 1,136,160 = 136,160 $$ NPV > 0 → accept.
IRR ≈ 15.24% > 10% → same accept decision.

Case 2: NPV–IRR Conflict in Mutually Exclusive Projects

Project A: Investment 5 million, front-loaded cash flows, IRR = 18%, NPV(10%) = 0.8 million.
Project B: Investment 8 million, smoother cash flows, IRR = 15%, NPV(10%) = 1.3 million.

Decision: IRR ranks A higher, but NPV correctly ranks B higher because B creates more shareholder wealth. This conflict is a frequent CFA exam trap.

Case 3: Profitability Index under Capital Rationing

Capital budget limit = 10 million. Independent projects:
- X: Investment 4m, NPV 1.2m, PI = 1.30
- Y: Investment 6m, NPV 1.5m, PI = 1.25
- Z: Investment 5m, NPV 0.9m, PI = 1.18

Optimal combination: X + Y (total investment 10m, total NPV = 2.7m), superior to X + Z (total NPV = 2.1m).

Traps

Key Formulas

• $NPV = \sum_{t=1}^{n} \frac{CF_t}{(1+r)^t} - CF_0$
• IRR: discount rate that makes NPV = 0
• $PI = 1 + \frac{NPV}{\text{Initial investment}}$
• Discounted payback: periods until cumulative discounted cash flows equal initial outlay
• When NPV and IRR conflict, choose the project with higher NPV
• Under capital rationing, rank independent projects by descending PI

Practice Questions

Q1. Which of the following should not be included as an incremental cash flow in capital budgeting?
A. Additional taxes from the new project
B. Market research fee paid two years ago
C. Opportunity cost of factory space used
D. Salvage value at project end

Q2. A project requires an initial investment of 2 million and generates 600,000 annually for 5 years. At a 12% discount rate, the NPV is closest to:
A. –0.128 million
B. 0.164 million
C. 0.321 million
D. 0.487 million

Q3. When NPV and IRR conflict for two mutually exclusive projects, the superior decision criterion is:
A. Higher IRR
B. Higher NPV
C. Shorter payback
D. Higher PI

Q4. A profitability index greater than 1 implies:
A. IRR is less than the discount rate
B. NPV is positive
C. Payback exceeds project life
D. The project has negative cash flows

Q5. The main purpose of a post-audit in the capital budgeting process is to:
A. Generate initial project ideas
B. Compare actual outcomes with forecasts and improve future decisions
C. Calculate the project’s IRR
D. Determine the financing method

Q6. Which statement about the payback period is correct?
A. It considers all cash flows over the project’s life
B. It fully incorporates the time value of money
C. It is often used to measure liquidity and risk
D. It is superior to NPV for ranking mutually exclusive projects

Q7. In the calculation of MIRR, the reinvestment rate is typically assumed to be:
A. The project’s own IRR
B. The firm’s weighted average cost of capital (WACC)
C. The risk-free rate
D. Zero

Q8. If a project has a positive NPV, then its:
A. PI is less than 1
B. IRR is less than the discount rate
C. Discounted payback is necessarily shorter than project life
D. MIRR is greater than the discount rate

Answers

Takeaways

• Capital budgeting evaluates long-term projects on the basis of incremental after-tax cash flows; the fundamental accept/reject rule is NPV > 0.
• NPV is the theoretically preferred method; IRR may conflict with NPV for mutually exclusive projects—always follow NPV.
• Ignore sunk costs; include opportunity costs and project externalities.
• Under capital rationing, rank projects by profitability index.
• The full process includes idea generation, evaluation, selection, implementation, and post-audit.
• Payback methods are useful supplementary screens but cannot replace discounted cash-flow techniques.