Ch2. Capital Budgeting — Making Investment Decisions with NPV, IRR, and Payback Period

What Is Capital Budgeting?

Capital Budgeting: The process of analyzing the economic viability of long-term investment projects and deciding whether to invest.

Capital Budgeting Techniques:

Discounted Cash Flow (DCF-based):
  - NPV (Net Present Value)
  - IRR (Internal Rate of Return)
  - PI (Profitability Index)

Non-discounted:
  - Payback Period (PP)
  - Accounting Rate of Return (ARR)

NPV (Net Present Value)

NPV = Σ CF_t / (1+r)^t − Initial Investment

CF_t: Cash flow in period t
r:    Discount rate (cost of capital)

Investment Decision Rule:

NPV > 0 → Accept (increases firm value)
NPV = 0 → Indifferent
NPV < 0 → Reject

Example:

Initial investment: $10,000
Year 1 cash flow:    $6,000
Year 2 cash flow:    $7,000
Discount rate:       10%

NPV = $6,000/(1.10) + $7,000/(1.10)^2 − $10,000
    = $5,454.5 + $5,785.1 − $10,000
    = +$1,239.6 → Accept

IRR (Internal Rate of Return)

IRR: The discount rate at which NPV = 0.

0 = Σ CF_t / (1+IRR)^t − Initial Investment

→ Solve for IRR iteratively (trial and error or financial calculator)

Investment Decision Rule:

IRR > Cost of capital (r) → Accept
IRR < Cost of capital (r) → Reject

Problems with IRR:

① Multiple IRRs: If cash flow signs change more than once,
   multiple IRRs may exist
② Mutually exclusive projects: NPV and IRR may give
   conflicting rankings
   → NPV takes precedence in this case
③ Reinvestment assumption: IRR implicitly assumes
   interim cash flows are reinvested at the IRR rate
   (often unrealistic)

PI (Profitability Index)

PI = PV of future cash flows / Initial investment
   = (NPV + Initial investment) / Initial investment

PI > 1: Accept (equivalent to NPV > 0)
PI < 1: Reject

Use case: Ranking investments when capital is constrained.

Payback Period

Payback Period: The time required to recover the initial investment from project cash flows.

Decision rule: Accept if payback period ≤ target period

Drawbacks:

Ignores cash flows beyond the payback period
Ignores the time value of money
Focuses on liquidity rather than profitability

Discounted Payback Period: Calculates payback using discounted cash flows (accounts for time value of money).

When NPV and IRR Give Conflicting Signals

Comparing mutually exclusive projects:

Project A: NPV = $2,000,  IRR = 20%
Project B: NPV = $3,000,  IRR = 15%

NPV criterion → Choose B (greater value added)
IRR criterion → Choose A (higher rate of return)

→ NPV is the correct basis for decision
  (aligns with the goal of maximizing firm value)

Why they conflict: Differences in project scale or the timing of cash flows.

Key Concept Cards

NPV Rule ★★★★★ : Accept if NPV > 0. The most superior technique because it directly measures the increase in firm value. Memory tip: NPV = PV of future CFs − Investment; positive means accept

Limitations of IRR ★★★★★ : Multiple IRRs and conflicting results with NPV for mutually exclusive projects. In these cases, NPV takes precedence. Memory tip: IRR limitations = multiple values + mutually exclusive conflicts

PI and Capital Rationing ★★★★☆ : When capital is constrained, investing in descending order of PI maximizes total NPV. Memory tip: Capital rationing → rank by PI

Practice Quiz

Q. Initial investment $20,000; annual cash flows of$ 6,000 for years 1–5; discount rate 8%. What is NPV?

Annuity PV = $6,000 × [1−(1.08)^−5] / 0.08 =$ 6,000 × 3.9927 = $23,956. NPV =$ 23,956 − $20,000 = +$ 3,956 → Accept.

Q. Project A (NPV = $5,000, IRR = 25%) vs. Project B (NPV =$ 7,000, IRR = 18%). Which should you choose?

If mutually exclusive, choose B. NPV criterion takes precedence. A higher IRR does not necessarily mean greater value creation — NPV is the correct measure.

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