CFA L1 / Corporate / M5. Capital Allocation
Module 5 · Corporate Issuers

Capital Investment and Capital Allocation

EN: NPV, IRR, payback period — and pitfalls.
VN: NPV, IRR, payback và các bẫy thường gặp.

1. Net Present Value (NPV) Core

About: NPV = sum of discounted future CFs minus initial outlay. Decision: accept if NPV > 0. The most theoretically-sound capital-allocation tool.Tóm tắt: NPV = tổng PV dòng tiền tương lai − outlay đầu. NPV > 0: chấp nhận. Công cụ allocation chuẩn nhất.
\[ NPV = -CF_0 + \sum_{t=1}^{N} \frac{CF_t}{(1 + r)^{t}} \]

Decision rule

  • NPV > 0 Accept — adds value.
  • NPV < 0 Reject.
  • Mutually excl. Pick highest NPV.
Practice problem

Initial $1,000 outlay. Cash flows of $400/year for 3 years. Required return 10%. NPV?

Show solution
PV(CF) = 400 × [1 − (1.10)^−3] / 0.10 = 400 × 2.4869
= 994.74
NPV = −1,000 + 994.74
≈ −$5.26 → Reject

2. Internal Rate of Return (IRR) Core

About: IRR = discount rate that makes NPV = 0. Decision: accept if IRR > required return. Pitfalls: multiple IRRs (sign changes), reinvestment assumed at IRR, mutually-exclusive disagreements with NPV.Tóm tắt: IRR = lãi suất khiến NPV = 0. IRR > required: chấp nhận. Bẫy: nhiều IRR, reinvestment, mâu thuẫn với NPV.
\[ \sum_{t=0}^{N} \frac{CF_t}{(1 + IRR)^{t}} = 0 \]

Decision rule

  • IRR > r Accept.
  • IRR < r Reject.
  • Pitfalls Multiple IRRs (sign changes); reinvestment assumed at IRR; can disagree with NPV in mutually-exclusive choices — NPV wins.
Practice problem

Initial outlay $1,000, single CF of $1,200 in 1 year. Compute IRR.

Show solution
−1000 + 1200/(1+IRR) = 0
1+IRR = 1.20
IRR = 20%

3. Payback & Discounted Payback Core

About: Payback = time to recover the outlay (undiscounted). Discounted payback corrects TVM. Both ignore CF AFTER payback — biased toward short-life projects.Tóm tắt: Thời gian thu hồi vốn. Discounted PB sửa TVM. Cả hai bỏ qua CF sau payback — thiên vị dự án ngắn.
  • Payback Time for cumulative undiscounted CF to reach 0. Ignores TVM and CF after payback.
  • Disc. payback Same but uses discounted CF — addresses TVM but still ignores post-payback CF.

4. Profitability Index (PI) Core

About: PI = PV(future CF) / outlay = 1 + NPV/outlay. Accept if PI > 1. Useful for ranking projects under capital rationing.Tóm tắt: PI = PV CF / outlay. PI > 1: chấp nhận. Hữu ích xếp hạng khi capital giới hạn.
\[ PI = \frac{PV(\text{future CF})}{|CF_0|} = 1 + \frac{NPV}{|CF_0|} \]

Accept if PI > 1. Useful for ranking when capital is constrained.

Practice problem

Initial outlay $500, PV of future CF = $620. Compute PI and decide.

Show solution
PI = 620/500
PI = 1.24 → accept (PI > 1, value-additive)

5. Real Options Concept

About: Optionality embedded in projects: timing (delay), sizing (expand/contract), flexibility (switch inputs/outputs), abandonment. Adds value beyond static NPV.Tóm tắt: Tính chọn lựa: timing, sizing, flexibility, abandonment. Cộng thêm giá trị ngoài NPV tĩnh.
  • Timing Delay investment until uncertainty resolves.
  • Sizing Expand or contract scope after launch.
  • Flexibility Switch inputs/outputs (price, technology).
  • Fundamental Abandon project to recoup salvage.