Corporate Finance Fundamentals
Module 4: Capital Budgeting - Evaluating Investment Decisions
Module Overview
Welcome to Module 4! Now we put the time value of money to work. Capital budgeting is about answering one of the most important questions in business: Which investments should we make?
Every day, companies decide whether to:
- Build a new factory
- Launch a new product
- Replace old equipment
- Acquire another company
- Expand into new markets
These decisions can make or break a company. Make good investment decisions, and you create wealth. Make bad ones, and you destroy it. This module teaches you how to evaluate these opportunities systematically.
Learning Objectives:
By the end of this module, you will be able to:
- Calculate Net Present Value (NPV) and make investment decisions
- Compute Internal Rate of Return (IRR) and understand its uses
- Evaluate projects using Payback Period and Discounted Payback
- Calculate Profitability Index for ranking projects
- Understand when to use each evaluation method
- Apply capital budgeting techniques to real business decisions
- Recognize common pitfalls in investment analysis
Estimated Time: 5-6 hours
4.1 Introduction to Capital Budgeting
What is Capital Budgeting?
Capital budgeting (also called investment appraisal or capital expenditure analysis) is the process of evaluating and selecting long-term investments that are worth more than they cost.
"Capital" refers to long-term assets:
- Property, plant, and equipment
- New product lines
- Research and development projects
- Acquisitions
- Technology systems
"Budgeting" refers to planning:
- Which projects to pursue
- How much to invest
- When to invest
- How to finance investments
Why Capital Budgeting Matters
Large Amounts: Capital investments typically involve significant sums—millions or billions of dollars.
Long-Term Impact: Decisions affect the company for years or decades. Once a factory is built, you're committed.
Irreversibility: Many investments are difficult or impossible to reverse. You can't easily "undo" a factory or an acquisition.
Strategic Importance: Capital investments shape the company's future direction and competitive position.
Example: Tesla's Gigafactories
- Investment: Billions of dollars
- Commitment: Decades
- Impact: Determines production capacity and competitiveness
- Risk: If demand doesn't materialize, massive losses
Example: Kodak's Digital Photography
- Invented digital camera technology in 1975
- Chose not to pursue it (protecting film business)
- Competitors invested in digital
- Result: Kodak filed for bankruptcy in 2012
Good capital budgeting decisions create value. Bad ones can destroy companies.
The Capital Budgeting Process
Step 1: Idea Generation
- Identify potential investment opportunities
- Sources: R&D, competitive analysis, strategic planning
Step 2: Analysis and Evaluation
- Estimate cash flows
- Assess risks
- Apply evaluation techniques (NPV, IRR, etc.)
Step 3: Decision Making
- Compare alternatives
- Select projects that create value
- Reject projects that destroy value
Step 4: Implementation
- Execute approved projects
- Allocate resources
- Manage the project
Step 5: Post-Audit
- Compare actual results to projections
- Learn from successes and failures
- Improve future capital budgeting
Types of Capital Budgeting Decisions
1. Expansion Projects
- New factories
- New product lines
- New markets
- Objective: Grow the business
2. Replacement Projects
- Replace old equipment with new
- Upgrade technology
- Objective: Maintain or improve efficiency
3. Regulatory/Safety Projects
- Required by law or regulation
- Environmental compliance
- Safety improvements
- Objective: Meet legal requirements
4. Other Projects
- Research and development
- Executive jets
- Employee facilities
- Objective: Various (may not be purely financial)
Cash Flows vs. Accounting Profits
Critical Principle: Capital budgeting decisions are based on cash flows, not accounting profits.
Why cash flows?
- Cash is what you can spend, invest, or distribute
- Accounting profits include non-cash items (depreciation)
- Timing matters—cash flow timing affects NPV
- Cash flows measure actual economic benefit
Example: A project shows $1 million accounting profit but generates zero cash flow (all tied up in receivables and inventory). Which matters more for investment decisions? Cash flow!
Relevant Cash Flows
Only incremental cash flows matter—cash flows that occur because of the project.
Include:
- Initial investment (outflow)
- Operating cash flows from the project
- Terminal cash flow (project end)
- Tax effects
- Working capital changes
Exclude:
- Sunk costs: Already spent, can't be recovered
- Allocated overhead: Would exist anyway
- Interest payments: Captured in discount rate
- Financing cash flows: Separate from investment decision
Example: Sunk Costs You spent $100,000 researching a product. Now deciding whether to launch it. The $100,000 is a sunk cost—ignore it! Only consider future cash flows.
Project Cash Flow Components
1. Initial Investment (Year 0)
Initial Investment = Equipment Cost
+ Installation
+ Working Capital Increase
- After-tax proceeds from old equipment sale
2. Operating Cash Flows (Years 1-n)
Operating CF = (Revenue - Costs - Depreciation) × (1 - Tax Rate)
+ Depreciation
Or equivalently:
Operating CF = (Revenue - Costs) × (1 - Tax Rate) + (Depreciation × Tax Rate)
The second term is the depreciation tax shield—depreciation reduces taxes even though it's not a cash expense.
3. Terminal Cash Flow (Final year)
Terminal CF = After-tax salvage value
+ Recovery of working capital
Example: Complete Cash Flow Estimation
Project details:
- Equipment cost: $100,000
- Revenue: $50,000/year
- Operating costs: $20,000/year
- Depreciation: $20,000/year (straight-line)
- Tax rate: 30%
- Project life: 5 years
- Working capital: $10,000 (recovered at end)
- Salvage value: $10,000
Initial Investment (Year 0):
Equipment: -$100,000
Working capital: -$10,000
Total: -$110,000
Operating Cash Flow (Years 1-5):
Revenue: $50,000
Operating costs: -$20,000
Depreciation: -$20,000
--------
Earnings before tax: $10,000
Tax (30%): -$3,000
--------
Net income: $7,000
Add back depreciation: +$20,000
--------
Operating cash flow: $27,000
Terminal Cash Flow (Year 5):
Operating CF: $27,000
Salvage value: $10,000
Tax on salvage (30%): -$3,000
Working capital recovery: $10,000
--------
Total Year 5 CF: $44,000
Project Cash Flows:
Year 0: -$110,000
Year 1: $27,000
Year 2: $27,000
Year 3: $27,000
Year 4: $27,000
Year 5: $44,000
Now we can evaluate this project!
4.2 Net Present Value (NPV)
The Gold Standard of Capital Budgeting
Net Present Value (NPV) is the most important and widely used capital budgeting technique.
Definition: The present value of all cash inflows minus the present value of all cash outflows.
NPV = Σ [CFₜ / (1 + r)ᵗ] - Initial Investment
Or:
NPV = PV of Benefits - PV of Costs
Decision Rule:
- NPV > 0: Accept the project (creates value)
- NPV < 0: Reject the project (destroys value)
- NPV = 0: Indifferent (project earns exactly the required return)
Why NPV is the Best Method
1. Considers Time Value of Money
- Properly discounts all cash flows
- A dollar today ≠ a dollar tomorrow
2. Considers All Cash Flows
- Includes every cash inflow and outflow
- Nothing is ignored
3. Measures Value Creation
- NPV is the dollar amount of value added
- Positive NPV = wealth creation
- Directly related to shareholder wealth maximization
4. Additive
- NPVs can be added together
- If Project A has NPV of $10M and Project B has NPV of $5M, combined NPV is $15M
5. Consistent with Goal of Firm
- Maximizes shareholder wealth
- Aligns with corporate objective
Calculating NPV: Step by Step
Example 1: Basic NPV Calculation
Project requires $50,000 investment and generates:
- Year 1: $20,000
- Year 2: $25,000
- Year 3: $30,000
Required return: 12%
Step 1: Calculate PV of each cash flow
Year 0: -$50,000 / (1.12)⁰ = -$50,000
Year 1: $20,000 / (1.12)¹ = $17,857
Year 2: $25,000 / (1.12)² = $19,930
Year 3: $30,000 / (1.12)³ = $21,347
Step 2: Sum all present values
NPV = -$50,000 + $17,857 + $19,930 + $21,347
NPV = $9,134
Decision: Accept! NPV > 0. The project creates $9,134 of value.
Example 2: Reject Project
Project requires $100,000 investment and generates:
- Year 1: $30,000
- Year 2: $30,000
- Year 3: $30,000
- Year 4: $30,000
Required return: 15%
Calculate NPV:
NPV = -$100,000 + $30,000/(1.15)¹ + $30,000/(1.15)² + $30,000/(1.15)³ + $30,000/(1.15)⁴
NPV = -$100,000 + $26,087 + $22,684 + $19,725 + $17,152
NPV = -$14,352
Decision: Reject! NPV < 0. The project destroys $14,352 of value.
Example 3: Using Annuity Formula
Same project as Example 2. Notice the cash flows are an annuity!
NPV = -$100,000 + $30,000 × [(1 - (1.15)⁻⁴) / 0.15]
NPV = -$100,000 + $30,000 × 2.855
NPV = -$100,000 + $85,650
NPV = -$14,350
Same answer (small rounding difference)—much faster calculation!
Example 4: NPV with the Previous Full Example
Remember our project with complete cash flows?
Year 0: -$110,000
Year 1: $27,000
Year 2: $27,000
Year 3: $27,000
Year 4: $27,000
Year 5: $44,000
Required return: 10%
Calculate NPV:
NPV = -$110,000 + $27,000/(1.10)¹ + $27,000/(1.10)² + $27,000/(1.10)³
+ $27,000/(1.10)⁴ + $44,000/(1.10)⁵
NPV = -$110,000 + $24,545 + $22,314 + $20,286 + $18,442 + $27,316
NPV = $2,903
Decision: Accept! NPV = $2,903 > 0. The project adds nearly $3,000 in value.
NPV in Excel
Method 1: Using NPV function
Year Cash Flow
0 -110000
1 27000
2 27000
3 27000
4 27000
5 44000
=NPV(0.10, B2:B6) + B1
Important: Excel's NPV function assumes the first value is at Year 1, so add Year 0 separately!
Result: $2,903
Method 2: Manual calculation
Year Cash Flow Discount Factor Present Value
0 -110000 1 -110000
1 27000 =1/1.10^1 =B2*C2
2 27000 =1/1.10^2 =B3*C3
3 27000 =1/1.10^3 =B4*C4
4 27000 =1/1.10^4 =B5*C5
5 44000 =1/1.10^5 =B6*C6
NPV = SUM(D1:D6)
NPV Profile
An NPV profile shows how NPV changes as the discount rate changes.
Example:
Project cash flows:
Year 0: -$100,000
Years 1-5: $30,000 each
Calculate NPV at different rates:
Discount Rate NPV
0% $50,000
5% $29,890
10% $13,723
15% $634
20% -$10,102
25% -$19,008
Observations:
- NPV decreases as discount rate increases
- At 0% discount rate, NPV = sum of cash flows - investment
- There's a rate where NPV = 0 (approximately 15.2%)—this is the IRR!
Graph visualization:
- X-axis: Discount rate
- Y-axis: NPV
- Downward sloping curve
- Crosses x-axis at IRR
Multiple Projects: Accept/Reject vs. Ranking
Independent Projects:
- Projects don't affect each other
- Can accept multiple projects
- Rule: Accept all projects with NPV > 0
Example:
- Project A: NPV = $50,000 → Accept
- Project B: NPV = $30,000 → Accept
- Project C: NPV = -$10,000 → Reject
Accept both A and B.
Mutually Exclusive Projects:
- Can only choose one project
- Projects serve the same purpose or compete for resources
- Rule: Choose the project with highest NPV
Example:
- Location A for new factory: NPV = $45,000
- Location B for new factory: NPV = $60,000
- Location C for new factory: NPV = $40,000
Choose Location B (highest NPV).
Capital Rationing:
- Limited budget
- Can't accept all positive NPV projects
- Rule: Maximize total NPV within budget constraint
We'll cover this with Profitability Index later.
4.3 Internal Rate of Return (IRR)
What is IRR?
Internal Rate of Return (IRR) is the discount rate that makes NPV equal to zero.
In other words: the rate of return the project actually generates.
Mathematical Definition:
NPV = 0 = Σ [CFₜ / (1 + IRR)ᵗ]
Solve for IRR.
Decision Rule:
- IRR > Required Return: Accept the project
- IRR < Required Return: Reject the project
- IRR = Required Return: Indifferent
Intuition: If a project earns 20% (IRR) and you only require 12% (required return), it's a good investment!
Calculating IRR
IRR cannot be calculated algebraically for most projects—it requires trial and error or software.
Example 1: Simple Two-Period Project
Invest $1,000 today, receive $1,200 in one year. What's the IRR?
0 = -$1,000 + $1,200 / (1 + IRR)
$1,000 = $1,200 / (1 + IRR)
1 + IRR = $1,200 / $1,000
1 + IRR = 1.20
IRR = 0.20 = 20%
Simple! The project earns 20%.
Example 2: Multi-Period Project
Year 0: -$50,000
Year 1: $20,000
Year 2: $25,000
Year 3: $30,000
Set NPV = 0 and solve:
0 = -$50,000 + $20,000/(1+IRR) + $25,000/(1+IRR)² + $30,000/(1+IRR)³
This requires trial and error or Excel.
Using Excel:
Year Cash Flow
0 -50000
1 20000
2 25000
3 30000
=IRR(A1:A4)
Result: IRR = 22.4%
Interpretation: This project earns 22.4%. If your required return is less than 22.4%, accept the project.
IRR vs. NPV: Same Decisions?
For single, independent projects, IRR and NPV give the same accept/reject decision.
Example:
Required return: 12%
Year 0: -$50,000
Year 1: $20,000
Year 2: $25,000
Year 3: $30,000
NPV at 12%: $9,134 > 0 → Accept IRR: 22.4% > 12% → Accept
Same decision!
Why? When IRR > required return, NPV must be positive (and vice versa).
When IRR Gives Wrong Answer
IRR has several problems that NPV doesn't have:
Problem 1: Mutually Exclusive Projects
Example:
Required return: 10%
Project A:
Year 0: -$1,000
Year 1: $1,500
NPV = -$1,000 + $1,500/1.10 = $364
IRR = 50%
Project B:
Year 0: -$10,000
Year 1: $12,000
NPV = -$10,000 + $12,000/1.10 = $909
IRR = 20%
By IRR: Choose Project A (50% > 20%) By NPV: Choose Project B ($909 > $364)
Which is correct? NPV! Project B creates more value ($909 vs. $364).
Why IRR fails: It's a percentage, not a dollar amount. A 50% return on $1,000 is less valuable than a 20% return on $10,000.
Scale Problem: IRR doesn't consider project size.
Problem 2: Non-Conventional Cash Flows
Conventional cash flows: Initial outflow, then inflows (-, +, +, +) Non-conventional: Multiple sign changes (-, +, -, + or +, -, +)
Example: Multiple IRRs
Year 0: -$1,000
Year 1: $3,000
Year 2: -$2,100
NPV at 10%: -$1,000 + $3,000/1.10 - $2,100/1.10² = -$11
This project has two IRRs: 10% and 20%!
Test:
At 10%: NPV = -$1,000 + $3,000/1.10 - $2,100/1.10² = -$11
At 20%: NPV = -$1,000 + $3,000/1.20 - $2,100/1.20² = $0
Both rates make NPV approximately zero!
Which IRR is "the" IRR? There's no good answer. IRR fails here.
NPV has no such problem: It always gives one clear answer.
Problem 3: Reinvestment Rate Assumption
IRR implicitly assumes project cash flows can be reinvested at the IRR.
NPV assumes cash flows are reinvested at the required return (discount rate).
Example:
Project with IRR of 50% and required return of 10%.
IRR assumes: Cash flows from the project can be reinvested at 50% NPV assumes: Cash flows can be reinvested at 10%
Which is more realistic? Usually NPV's assumption. If you could really reinvest everything at 50%, that would be your required return!
Modified IRR (MIRR)
Modified IRR fixes the reinvestment rate problem by assuming reinvestment at the required return.
Steps:
- Find future value of all cash inflows at the required return
- Find present value of all cash outflows at the required return
- Find the rate that equates these values
Formula:
MIRR = (FV of inflows / PV of outflows)^(1/n) - 1
Example:
Year 0: -$50,000
Year 1: $20,000
Year 2: $25,000
Year 3: $30,000
Required return: 12%
FV of inflows at 12%:
Year 1: $20,000 × (1.12)² = $25,088
Year 2: $25,000 × (1.12)¹ = $28,000
Year 3: $30,000 × (1.12)⁰ = $30,000
Total FV: $83,088
PV of outflows: $50,000 (already at Year 0)
MIRR:
MIRR = ($83,088 / $50,000)^(1/3) - 1
MIRR = (1.6618)^0.333 - 1
MIRR = 1.1846 - 1
MIRR = 0.1846 = 18.46%
Using Excel:
=MIRR(cash_flows, finance_rate, reinvest_rate)
=MIRR(A1:A4, 0.12, 0.12)
Result: 18.46%
MIRR is more realistic than IRR but still inferior to NPV for decision-making.
Summary: NPV vs. IRR
Use NPV when:
- Mutually exclusive projects
- Non-conventional cash flows
- You want to maximize value
- Different project scales
Use IRR when:
- Explaining returns to non-financial managers
- Single, independent projects
- You must communicate as a percentage
Best Practice: Always calculate NPV. Use IRR as supplementary information.
4.4 Payback Period
What is Payback Period?
Payback Period is the time required to recover the initial investment.
Formula:
Payback Period = Number of years until cumulative cash flows equal initial investment
Decision Rule:
- Accept if payback period < company's cutoff
- Reject if payback period > company's cutoff
Calculating Payback Period
Example 1: Even Cash Flows
Initial investment: $60,000
Annual cash flow: $15,000
Payback Period:
Payback = $60,000 / $15,000 = 4 years
Example 2: Uneven Cash Flows
Year 0: -$100,000
Year 1: $30,000
Year 2: $40,000
Year 3: $50,000
Year 4: $20,000
Cumulative cash flows:
Year 0: -$100,000
Year 1: -$70,000 (-$100,000 + $30,000)
Year 2: -$30,000 (-$70,000 + $40,000)
Year 3: +$20,000 (-$30,000 + $50,000)
Investment is recovered during Year 3.
More precisely:
- At end of Year 2: Still need $30,000
- Year 3 generates $50,000
- Fraction of Year 3 needed: $30,000 / $50,000 = 0.6
Payback Period = 2.6 years
Decision: If company's cutoff is 3 years, accept. If cutoff is 2 years, reject.
Advantages of Payback Period
1. Simple and Intuitive
- Easy to calculate
- Easy to understand
- No complex formulas
2. Liquidity Focus
- Favors projects that return cash quickly
- Important for cash-strapped companies
3. Risk Proxy
- Shorter payback = less risk
- Less time for things to go wrong
Disadvantages of Payback Period
1. Ignores Time Value of Money
- Treats all cash flows equally
- $1 in Year 1 = $1 in Year 10 (wrong!)
2. Ignores Cash Flows After Payback
- Only looks until investment recovered
- Ignores long-term profitability
Example:
Project A:
Year 0: -$100,000
Year 1: $100,000
Years 2-10: $0
Payback: 1 year
Project B:
Year 0: -$100,000
Year 1: $40,000
Year 2: $40,000
Year 3: $40,000
Years 4-10: $50,000/year
Payback: 2.5 years
Payback prefers Project A (1 year vs. 2.5 years).
But Project B is clearly better! It generates cash for 10 years.
3. Arbitrary Cutoff
- What should the cutoff be? 2 years? 5 years?
- No theoretical basis
4. Can Reject Positive NPV Projects
- Project might have positive NPV but long payback
- Payback would reject it (wrong decision)
5. Can Accept Negative NPV Projects
- Project might have short payback but negative NPV
- Payback would accept it (wrong decision)
When to Use Payback
Appropriate situations:
- Preliminary screening (rough cut)
- Small projects where detailed analysis isn't worth the effort
- When liquidity is critical concern
- In countries with high political risk (get money out fast)
Never use as primary decision criterion for major capital investments.
4.5 Discounted Payback Period
Improvement Over Regular Payback
Discounted Payback Period addresses one major flaw: it accounts for time value of money.
Method: Discount all cash flows, then calculate payback using discounted values.
Calculating Discounted Payback
Example:
Year 0: -$100,000
Year 1: $40,000
Year 2: $40,000
Year 3: $40,000
Year 4: $40,000
Required return: 12%
Discount each cash flow:
Year 0: -$100,000 / 1.12⁰ = -$100,000
Year 1: $40,000 / 1.12¹ = $35,714
Year 2: $40,000 / 1.12² = $31,888
Year 3: $40,000 / 1.12³ = $28,472
Year 4: $40,000 / 1.12⁴ = $25,421
Cumulative discounted cash flows:
Year 0: -$100,000
Year 1: -$64,286 (-$100,000 + $35,714)
Year 2: -$32,398 (-$64,286 + $31,888)
Year 3: -$3,926 (-$32,398 + $28,472)
Year 4: +$21,495 (-$3,926 + $25,421)
Investment recovered during Year 4.
Precise calculation:
Fraction of Year 4: $3,926 / $25,421 = 0.15
Discounted Payback = 3.15 years
Compare:
- Regular payback: 2.5 years
- Discounted payback: 3.15 years
Discounted payback is always longer (because future cash flows are worth less).
Advantages Over Regular Payback
1. Considers Time Value of Money
- Properly discounts future cash flows
- More accurate assessment
2. Partially Addresses Risk
- Discounting reflects opportunity cost
- Higher risk → higher discount rate → longer discounted payback
Still Has Major Flaws
1. Still Ignores Cash Flows After Payback
- Same problem as regular payback
- Can reject good long-term projects
2. Still Has Arbitrary Cutoff
- What should it be?
- No clear answer
3. Not as Good as NPV
- Why not just use NPV?
- NPV is better in every way
When to Use Discounted Payback
Slightly better than regular payback for preliminary screening, but still inferior to NPV.
Best practice: Use as supplementary information alongside NPV, not as primary decision tool.
4.6 Profitability Index
What is Profitability Index?
Profitability Index (PI), also called Benefit-Cost Ratio, measures value created per dollar invested.
Formula:
PI = PV of Future Cash Flows / Initial Investment
or
PI = (NPV + Initial Investment) / Initial Investment
or
PI = 1 + (NPV / Initial Investment)
Decision Rule:
- PI > 1.0: Accept (creates value)
- PI < 1.0: Reject (destroys value)
- PI = 1.0: Indifferent
Interpretation: PI of 1.20 means you get $1.20 of present value for every $1.00 invested.
Calculating Profitability Index
Example 1:
Initial investment: $50,000
PV of cash inflows: $59,134
PI = $59,134 / $50,000 = 1.183
Or using NPV:
NPV = $9,134
PI = 1 + ($9,134 / $50,000) = 1.183
Decision: Accept (PI > 1.0)
Example 2:
Year 0: -$100,000
Year 1: $30,000
Year 2: $40,000
Year 3: $50,000
Year 4: $20,000
Required return: 12%
Calculate PV of inflows:
PV = $30,000/1.12 + $40,000/1.12² + $50,000/1.12³ + $20,000/1.12⁴
PV = $26,786 + $31,888 + $35,589 + $12,706
PV = $106,969
PI:
PI = $106,969 / $100,000 = 1.07
Decision: Accept (PI > 1.0)
PI vs. NPV
For single, independent projects: PI and NPV give same accept/reject decision.
- If NPV > 0, then PI > 1.0
- If NPV < 0, then PI < 1.0
For mutually exclusive projects: PI and NPV can conflict!
Example:
Project A:
Investment: $10,000
NPV: $3,000
PI = 1 + ($3,000 / $10,000) = 1.30
Project B:
Investment: $100,000
NPV: $15,000
PI = 1 + ($15,000 / $100,000) = 1.15
By PI: Choose Project A (1.30 > 1.15) By NPV: Choose Project B ($15,000 > $3,000)
Which is correct? NPV! Project B creates more value.
Why PI fails: It's a ratio. Project A has better return per dollar, but Project B creates more total value.
When PI is Useful: Capital Rationing
Capital rationing occurs when the company can't invest in all positive NPV projects due to budget constraints.
Example:
Budget: $100,000
Available Projects:
| Project | Investment | NPV | PI |
|---|---|---|---|
| A | $40,000 | $8,000 | 1.20 |
| B | $50,000 | $11,000 | 1.22 |
| C | $60,000 | $9,000 | 1.15 |
| D | $30,000 | $7,500 | 1.25 |
All have positive NPV. Which to choose?
Strategy 1: Maximize Total NPV
- Choose combinations that maximize total NPV within budget
- Try: B + D = $50K + $30K = $80K investment, NPV = $18,500
- Try: A + C = $40K + $60K = $100K investment, NPV = $17,000
- Try: B + A = $90K investment, NPV = $19,000
Best: B + A gives highest total NPV ($19,000)
Strategy 2: Use PI to Rank
- Rank by PI: D (1.25), B (1.22), A (1.20), C (1.15)
- Select projects in order until budget exhausted
- D + B = $80K, NPV = $18,500
Both strategies work, but Strategy 1 (maximize total NPV) is slightly better in this case.
PI is helpful but not perfect for capital rationing.
Advantages of Profitability Index
1. Useful for Capital Rationing
- Helps rank projects by bang-for-buck
- Shows efficiency of capital use
2. Easy to Understand
- Ratio is intuitive
- "Get $1.25 for every $1 invested"
3. Consistent with NPV
- For accept/reject decisions on single projects
- Based on same PV calculations
Disadvantages of Profitability Index
1. Can Conflict with NPV
- For mutually exclusive projects
- NPV is superior
2. Scale Problem
- Like IRR, doesn't consider project size
- Small project can have high PI but low value creation
3. Not Perfect for Capital Rationing
- Maximizing total NPV is better
- PI ranking is approximate
When to Use PI
Good for:
- Screening multiple independent projects
- Capital rationing situations
- Comparing investment efficiency
Always use NPV as primary tool.
4.7 Comparing the Methods
Summary Table
| Method | Considers TVM? | Considers All CFs? | Direct Value? | Best Use |
|---|---|---|---|---|
| NPV | ✓ | ✓ | ✓ | Primary decision tool |
| IRR | ✓ | ✓ | ✗ | Supplementary info |
| MIRR | ✓ | ✓ | ✗ | Better than IRR |
| Payback | ✗ | ✗ | ✗ | Preliminary screening |
| Disc. Payback | ✓ | ✗ | ✗ | Better than payback |
| PI | ✓ | ✓ | ✗ | Capital rationing |
Decision Framework
Step 1: Calculate NPV
- Always do this first
- Accept if NPV > 0
- For mutually exclusive: choose highest NPV
Step 2: Calculate IRR (Optional)
- Provides percentage return
- Easy to communicate
- Useful for comparison to required return
Step 3: Calculate Payback (Optional)
- Quick liquidity check
- Understand how fast cash returns
- Risk assessment
Step 4: Calculate PI (If Relevant)
- Capital rationing situations
- Multiple independent projects
- Want to understand efficiency
Primary Rule: Use NPV for the final decision.
Real-World Practice
Survey Results: What do companies actually use?
Most Common (in order):
- IRR (75% of companies)
- NPV (75% of companies)
- Payback Period (57%)
- Profitability Index (12%)
Key Insight: Most companies use multiple methods (typically NPV + IRR + Payback).
Why IRR so popular?
- Easier to explain to non-financial managers
- "This project earns 25%" is simpler than "NPV is $2.3M"
- Psychological: people like percentages
Why NPV equally popular?
- Finance professionals know it's superior
- Required by best practice
- Most accurate measure of value creation
Best Practice: Calculate NPV (for decision) + IRR (for communication)
4.8 Special Topics in Capital Budgeting
Inflation and Capital Budgeting
Critical Rule: Be consistent with inflation treatment.
Two Approaches:
Approach 1: Nominal Terms
- Cash flows in nominal dollars (including inflation)
- Discount rate in nominal terms
Approach 2: Real Terms
- Cash flows in real dollars (constant purchasing power)
- Discount rate in real terms
Both give the same NPV if done consistently.
Example:
Project generates $100,000/year in real terms for 3 years.
- Real discount rate: 10%
- Inflation: 3%
- Nominal discount rate: 13.3% [(1.10 × 1.03) - 1]
Approach 1: Nominal
Year 1 nominal CF: $100,000 × 1.03 = $103,000
Year 2 nominal CF: $100,000 × 1.03² = $106,090
Year 3 nominal CF: $100,000 × 1.03³ = $109,273
NPV = $103,000/1.133 + $106,090/1.133² + $109,273/1.133³
NPV = $248,685
Approach 2: Real
NPV = $100,000/1.10 + $100,000/1.10² + $100,000/1.10³
NPV = $248,685
Same answer!
Common Mistake: Nominal cash flows with real discount rate (or vice versa). This gives wrong answer!
Equivalent Annual Annuity (EAA)
Problem: Comparing projects with different lifespans.
Example:
Machine A:
- Cost: $10,000
- Life: 3 years
- Annual costs: $3,000
- NPV of costs: -$17,460 (at 10%)
Machine B:
- Cost: $15,000
- Life: 5 years
- Annual costs: $2,500
- NPV of costs: -$24,474 (at 10%)
Which is cheaper? Can't compare NPVs directly—different lifespans!
Solution: Equivalent Annual Annuity
Convert each NPV to equivalent annual cost.
Machine A:
$17,460 = EAA × [(1 - 1.10⁻³) / 0.10]
$17,460 = EAA × 2.4869
EAA = $7,020 per year
Machine B:
$24,474 = EAA × [(1 - 1.10⁻⁵) / 0.10]
$24,474 = EAA × 3.7908
EAA = $6,456 per year
Decision: Machine B is cheaper! ($6,456/year vs. $7,020/year)
Or in Excel:
=PMT(0.10, 3, 17460) → $7,020
=PMT(0.10, 5, 24474) → $6,456
Real Options in Capital Budgeting
Traditional NPV assumes: invest now or never.
Reality: Many projects have real options:
1. Option to Expand
- If project succeeds, can invest more
- Creates additional value beyond base case NPV
2. Option to Abandon
- If project fails, can stop and salvage assets
- Limits downside risk
3. Option to Wait
- Can delay investment to gather more information
- Uncertainty may resolve over time
4. Option to Switch
- Can change production methods or outputs
- Flexibility has value
Example: Option to Expand
Base Project:
- Investment: $10M
- NPV: $2M
Expansion Option:
- If demand is high (50% probability)
- Can invest additional $5M in Year 3
- Expansion NPV: $3M (if exercised)
Expected Value of Option:
Option value = 0.50 × $3M = $1.5M (PV)
Total Project Value:
Total = Base NPV + Option Value
Total = $2M + $1.5M = $3.5M
Traditional NPV ($2M) understates true value!
Real options analysis is advanced and beyond this course, but awareness is important: traditional NPV may undervalue flexible projects.
Sensitivity Analysis
Question: How sensitive is NPV to changes in assumptions?
Method: Vary one assumption at a time, recalculate NPV.
Example:
Base case:
- Investment: $100,000
- Annual revenue: $50,000
- Annual costs: $20,000
- Life: 5 years
- Discount rate: 12%
- Base NPV: $8,140
Test Sensitivity:
| Variable | -10% | Base | +10% |
|---|---|---|---|
| Revenue | -$9,870 | $8,140 | $26,150 |
| Costs | $15,350 | $8,140 | $930 |
| Discount rate | $14,590 | $8,140 | $2,620 |
Insights:
- Revenue most important (biggest NPV swing)
- Project vulnerable to revenue shortfall
- Less sensitive to cost changes
- Moderately sensitive to discount rate
Use: Identify key risks and focus management attention.
Scenario Analysis
Extension of sensitivity: Change multiple variables simultaneously.
Example Scenarios:
Best Case:
- Revenue: +20%
- Costs: -10%
- NPV: $52,300
Base Case:
- NPV: $8,140
Worst Case:
- Revenue: -20%
- Costs: +10%
- NPV: -$36,020
Expected NPV (with probabilities):
E(NPV) = 0.25 × $52,300 + 0.50 × $8,140 + 0.25 × (-$36,020)
E(NPV) = $13,075 + $4,070 - $9,005
E(NPV) = $8,140
(Same as base case if probabilities are symmetric)
Use: Understand range of outcomes and probability of loss.
Module 4 Practice Problems
Problem Set 1: NPV Calculations
-
Basic NPV: A project costs $75,000 and generates:
- Year 1: $25,000
- Year 2: $30,000
- Year 3: $35,000
- Year 4: $20,000
Required return: 11%
a. Calculate the NPV b. Should you accept the project?
-
NPV with Annuity: Investment: $200,000 Cash flows: $45,000/year for 7 years Required return: 13%
Calculate NPV using the annuity formula.
-
Complete Project: Equipment cost: $500,000 Working capital: $50,000 Revenue: $300,000/year Operating costs: $150,000/year Depreciation: $100,000/year (straight-line) Tax rate: 25% Project life: 5 years Salvage value: $50,000 Required return: 14%
a. Calculate operating cash flow for years 1-5 b. Calculate terminal cash flow c. Calculate NPV d. Decision?
Problem Set 2: IRR Analysis
-
Calculate IRR:
Year 0: -$80,000 Year 1: $25,000 Year 2: $30,000 Year 3: $35,000 Year 4: $30,000a. Calculate IRR (use Excel) b. If required return is 12%, accept or reject?
-
IRR vs. NPV: Required return: 10%
Project X:
- Investment: $50,000
- Year 1-3: $20,000/year
Project Y:
- Investment: $100,000
- Year 1-3: $45,000/year
a. Calculate NPV for both b. Calculate IRR for both c. If projects are mutually exclusive, which should you choose? d. Does IRR give the same answer as NPV?
Problem Set 3: Payback Period
-
Regular Payback:
Year 0: -$120,000 Year 1: $30,000 Year 2: $40,000 Year 3: $50,000 Year 4: $60,000Calculate the payback period.
-
Discounted Payback: Same cash flows as Problem 6, discount rate = 11%
Calculate the discounted payback period.
Problem Set 4: Profitability Index
-
Calculate PI: Investment: $90,000 PV of inflows: $115,000
a. Calculate PI b. Calculate NPV c. Should you accept?
-
Capital Rationing: Budget: $150,000
Project Investment NPV A $60,000 $18,000 B $70,000 $21,000 C $50,000 $12,000 D $80,000 $20,000 a. Calculate PI for each project b. Rank by PI c. Which projects should you accept to maximize NPV?
Problem Set 5: Comparing Methods
-
Comprehensive Analysis: A project requires $250,000 investment and generates:
- Years 1-6: $60,000/year
- Year 7: $80,000
Required return: 12%
Calculate: a. NPV b. IRR c. Payback period d. Discounted payback e. Profitability Index f. Based on all methods, should you accept?
Problem Set 6: Real-World Application
-
Equipment Replacement: Current equipment:
- Book value: $200,000
- Remaining life: 5 years
- Annual operating costs: $80,000
- Salvage value in 5 years: $20,000
New equipment:
- Cost: $350,000
- Life: 5 years
- Annual operating costs: $40,000
- Salvage value in 5 years: $50,000
Current equipment can be sold today for $150,000. Tax rate: 30% Required return: 10%
Should you replace? Calculate incremental NPV.
-
New Product Launch: Development cost (sunk): $500,000 Production equipment: $2,000,000 Working capital: $300,000 Expected sales: 100,000 units/year at $50/unit Variable cost: $25/unit Fixed costs: $1,000,000/year Depreciation: $400,000/year Tax rate: 25% Project life: 5 years Required return: 15%
a. Calculate annual operating cash flow b. Calculate NPV (ignore sunk cost!) c. Should you launch?
Problem Set 7: Advanced Topics
-
Equivalent Annual Annuity: Machine A: Cost $40,000, lasts 3 years, annual costs $8,000 Machine B: Cost $60,000, lasts 5 years, annual costs $6,000
Discount rate: 9%
Which machine has lower equivalent annual cost?
-
Sensitivity Analysis: Base case NPV: $50,000
Calculate NPV if: a. Sales volume decreases 15% b. Price decreases 10% c. Costs increase 20% d. Discount rate increases from 10% to 12%
(You'll need to make reasonable assumptions about base values)
Additional Resources
Excel Templates
Download practice files:
- NPV and IRR Calculator
- Capital Budgeting Template
- Sensitivity Analysis Tool
- Payback Calculator
Case Studies
Practice with real-world capital budgeting decisions:
- Manufacturing expansion
- Technology investment
- Acquisition analysis
- Product launch evaluation
Further Reading
Books:
- "Capital Budgeting: Theory and Practice" by Pamela Peterson and Frank Fabozzi
- "Investment Valuation" by Aswath Damodaran (advanced)
Online:
- Corporate Finance Institute tutorials
- Investopedia capital budgeting articles
Looking Ahead to Module 5
You now know how to evaluate investment opportunities systematically. You can calculate NPV, IRR, and other metrics to make sound capital budgeting decisions.
But there's a critical piece missing: How do we account for risk?
Not all projects are equally risky. A government bond is different from a startup investment. Module 5 explores Risk and Return:
- How to measure risk
- The relationship between risk and return
- Portfolio diversification
- Systematic vs. unsystematic risk
- Introduction to the Capital Asset Pricing Model (CAPM)
These concepts will help you determine the appropriate discount rate for your NPV calculations.
Prepare for Module 5 by:
- Understanding that riskier projects require higher returns
- Reviewing basic statistics (mean, variance, standard deviation)
- Thinking about your own risk tolerance
Summary
Congratulations on completing Module 4! You can now:
✓ Calculate Net Present Value and use it to make investment decisions ✓ Compute Internal Rate of Return and understand its limitations ✓ Calculate Payback Period and Discounted Payback Period ✓ Use Profitability Index for capital rationing ✓ Compare and choose among different evaluation methods ✓ Apply capital budgeting techniques to real business decisions ✓ Understand special topics like inflation, real options, and sensitivity analysis
Capital budgeting is where corporate finance theory meets real-world impact. The decisions you've learned to analyze determine which products get developed, which factories get built, and ultimately, which companies succeed.
Every major business decision involves capital budgeting concepts. You now have the tools to evaluate these decisions rigorously.
Ready for the next level? Proceed to Module 5: Risk and Return to learn how to account for uncertainty in your analyses.
"In the business world, the rearview mirror is always clearer than the windshield." — Warren Buffett
Capital budgeting is about looking through the windshield—making the best decisions possible with the information available. You now have the tools to see clearly.
See you in Module 5!