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

1. 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)

2. NPV (Net Present Value)

NPV = \sum \frac{CF_t}{1+r}^t − \text{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%

\begin{aligned} NPV &= \$6,\frac{000}{1.10} + \$7,\frac{000}{1.10}^2 − \$10,000 \\ &= \$5,454.5 + \$5,785.1 − \$10,000 \\ &= +\$1,239.6 \to \text{Accept} \end{aligned}

3. 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:

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

4. PI (Profitability Index)

\begin{aligned} PI &= \text{PV of future cash flows} / \text{Initial investment} \\ &= (NPV + \text{Initial investment}) / \text{Initial investment} \end{aligned}

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

Use case: Ranking investments when capital is constrained.

5. 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).

6. 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.

7. 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

8. 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.