📖 资本预算综合案例

Corporate Finance

I. Lesson Focus

This lesson integrates all capital budgeting tools and concepts covered in Corporate Finance. Candidates must be able to construct full project cash flows (including inflation, taxes, depreciation tax shields, net working capital changes, and terminal values), evaluate independent and mutually exclusive projects, handle unequal project lives with the equivalent annual annuity (EAA) approach, and optimize project selection under capital rationing. The focus is on applying NPV as the primary decision criterion while understanding when and why other metrics (IRR, payback, PI) may conflict or serve as supplementary tools.

II. The Problem

A manufacturing firm is evaluating three capital budgeting proposals: Project A is an independent expansion, while Projects B and C are mutually exclusive equipment replacement options. Cash flows are affected by inflation, corporate taxes, depreciation shields, recovery of net working capital (NWC), and differing project lives. Management must simultaneously consider profitability, speed of payback, cost of capital constraints, and shareholder value maximization to select the optimal combination. This mirrors the comprehensive capital budgeting scenarios frequently tested in the CFA Level I curriculum.

III. Core Capital Budgeting Decision Framework

The fundamental objective of capital budgeting is maximizing shareholder wealth. This is achieved by accepting all independent projects with NPV > 0 and, for mutually exclusive projects, selecting the one with the highest NPV.

Key evaluation metrics include: - Net Present Value (NPV): The present value of all project cash flows discounted at the cost of capital. Formula: $NPV = \sum_{t=0}^{n} \frac{CF_t}{(1+r)^t}$ - Internal Rate of Return (IRR): The discount rate that sets NPV = 0. When NPV and IRR conflict, NPV is always preferred. - Payback Period: Years required to recover the initial investment. It ignores the time value of money and cash flows beyond the cutoff. - Profitability Index (PI): $PI = \frac{PV\ of\ future\ CFs}{Initial\ Investment}$. Accept if PI > 1. - Equivalent Annual Annuity (EAA): Used for mutually exclusive projects with unequal lives. Convert NPV into an annual annuity: $EAA = \frac{NPV \times r}{1-(1+r)^{-n}}$

IV. Complete Project Cash Flow Estimation Steps

1. Initial Cash Flow (CF0): –Cost of fixed assets – installation costs + after-tax proceeds from sale of old assets – ΔNWC
2. Operating Cash Flow (OCF): $(Sales - Costs - Dep) \times (1-T) + Dep$, or equivalently $EBIT(1-T) + Dep$
3. Terminal Cash Flow: OCF in final year + after-tax salvage value + full recovery of NWC
4. Inflation Handling: Use nominal cash flows with nominal discount rates, or real cash flows with real discount rates. The CFA exam heavily tests the consistency principle.

Depreciation tax shield is a major source of value: PV of tax shield = $T_c \times Dep \times$ annuity factor.

V. Project Types and Decision Rules

• Independent Projects: Accept if NPV > 0 or IRR > cost of capital.
• Mutually Exclusive Projects: Select only one; always choose the highest NPV. When projects differ in size or life, adjust using incremental IRR or EAA.
• Capital Rationing: When funds are limited, rank by PI or optimize the combination that maximizes total NPV without exceeding the budget.

VI. Taxes and Depreciation Effects

Corporate tax rates are typically given (e.g., 25% or 30%). Accelerated depreciation methods (such as double-declining balance) accelerate tax shields, improving early cash flows and NPV. A common exam point is the after-tax salvage value: $After-tax\ salvage = Salvage - T_c \times (Salvage - Book\ value)$

Worked Cases

Case 1: Full NPV Calculation for an Independent Project (with Inflation and NWC)

Project requires an initial outlay of CNY 8 million and has a 5-year life. First-year sales revenue is CNY 2.2 million, growing at 6% inflation thereafter. Variable costs are 60% of revenue, fixed costs CNY 0.5 million per year. Straight-line depreciation to zero, tax rate 25%, nominal WACC = 12%. Salvage value at end of Year 5 is CNY 0.8 million. Initial NWC requirement is CNY 0.6 million, fully recovered at t=5.

Step-by-step calculation (selected years): - Revenues: Y1 = 2.2, Y2 = 2.332, Y3 = 2.472, Y4 = 2.620, Y5 = 2.777 (million) - Year 1 OCF: Revenue 2.2 – VC 1.32 – FC 0.5 – Dep 1.6 = EBIT –1.22; Taxes –0.305; NOPAT –0.915; OCF = –0.915 + 1.6 = 0.685 million - OCFs for Years 1–5: 0.685, 0.793, 0.907, 1.028, 1.156 million - Year 5 terminal CF = 1.156 + 0.8 × (1–0.25) + 0.6 = 2.356 million - NPV = –8 –0.6 + PV of OCFs + PV of terminal CF ≈ +0.428 million

Conclusion: NPV > 0, accept the independent project.

Case 2: Mutually Exclusive Projects with Unequal Lives (EAA Method)

Project X: Initial investment CNY 5 million, 4-year life, annual OCF CNY 1.8 million, WACC 10%, NPV = 0.924 million
Project Y: Initial investment CNY 7 million, 6-year life, annual OCF CNY 1.65 million, NPV = 1.186 million

Because lives differ, direct NPV comparison is invalid. Apply EAA:

• EAA_X = 0.924 × (0.10 / (1 – 1.10^{-4})) ≈ 0.2915 million
• EAA_Y = 1.186 × (0.10 / (1 – 1.10^{-6})) ≈ 0.2728 million

Decision: Although Project Y has higher NPV, Project X has the higher EAA and should be chosen.

Case 3: Project Selection under Capital Rationing Using PI

Budget ceiling CNY 10 million. Available projects:

Optimal combination: A + C (total investment 9m, total NPV 2.65m). Other feasible sets produce lower total NPV or exceed the budget.

Traps

Key Formulas

• $NPV = CF_0 + \sum_{t=1}^{n} \frac{CF_t}{(1+r)^t}$
• IRR solves $NPV = 0$
• $PI = 1 + \frac{NPV}{Initial\ Outlay}$
• $EAA = \frac{r \times NPV}{1 - (1+r)^{-n}}$
• $OCF = (S - C - D)(1-T) + D$
• After-tax Salvage = Salvage – $T_c \times (Salvage - Book\ Value)$
• Decision rule: Accept independent projects if NPV > 0; for mutually exclusive, select highest NPV; under rationing, maximize total NPV within budget

Practice Questions

Q1. When NPV and IRR conflict for two mutually exclusive projects of different sizes, which metric should be used?
A. The project with higher IRR
B. The project with higher NPV
C. The project with higher PI
D. The project with shorter payback

Q2. A project costs CNY 2 million and generates CNY 0.6 million annual OCF for 5 years at WACC = 10%. Its PI is closest to:
A. 0.92
B. 1.14
C. 1.38
D. 1.51

Q3. The correct way to incorporate inflation in capital budgeting is to:
A. Use real cash flows and the real discount rate
B. Use nominal cash flows and the real discount rate
C. Use any rate as long as it includes inflation
D. Ensure cash flows and discount rate use the same pricing basis (nominal or real)

Q4. The main purpose of the EAA method is to:
A. Compare projects with different initial investment sizes
B. Compare mutually exclusive projects with unequal economic lives
C. Calculate the payback period
D. Remove the effect of inflation

Q5. Equipment with a book value of CNY 0.3 million is sold for CNY 0.5 million. Tax rate is 25%. After-tax cash flow from salvage is:
A. 0.45 million
B. 0.425 million
C. 0.375 million
D. 0.50 million

Q6. Under capital rationing, the firm should select the combination of projects that:
A. Maximizes total PI
B. Maximizes total NPV without exceeding the budget
C. Maximizes average IRR
D. Minimizes total payback period

Q7. Which of the following is not added back when calculating operating cash flow?
A. Depreciation
B. Increase in net working capital
C. Non-cash charges
D. Deferred taxes (if non-cash)

Q8. If a project has a positive NPV, it follows that:
A. Its IRR is less than the cost of capital
B. Its PI is less than 1
C. It will increase shareholder wealth
D. Its payback period exceeds project life

Answers

Takeaways

• NPV remains the gold standard; for mutually exclusive projects always select the highest NPV.
• Use the EAA approach whenever project lives differ—never compare raw NPVs directly.
• Project cash flows must explicitly include depreciation tax shields, NWC changes, and after-tax salvage values.
• Inflation must be treated consistently (nominal-to-nominal or real-to-real).
• Under capital rationing, the goal is to maximize total NPV within the budget, not simply rank by PI.
• All capital budgeting decisions ultimately serve the objective of shareholder wealth maximization rather than IRR or payback alone.