Week 9: Capital Budgeting Section B Focus

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Master the FCF framework, NPV calculations, and project valuation for Section B (70 marks, ~95 minutes).

🎯 Exam Relevance: Capital budgeting is THE core Section B topic. You must know FCF construction, depreciation, ΔNWC, after-tax salvage, and NPV decision rules. Remember: 40-50% of marks come from interpretation, not just calculations!

🔑 The FCF Valuation Pipeline

Follow every step to maximize partial credit.

1️⃣ Identify Relevant Cash Flows (exclude sunk costs)
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2️⃣ Build Depreciation Schedule
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3️⃣ Calculate Operating Cash Flow (OCF)
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4️⃣ Compute ΔNWC for each year
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5️⃣ Calculate CAPEX & After-tax Salvage
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6️⃣ Sum Total CF = OCF + ΔNWC + CAPEX
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7️⃣ Discount at WACC → NPV
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8️⃣ Make Decision + Interpret

📐 Core Formulas

Operating Cash Flow (OCF)

OCF = EBIT × (1 - t) + Depreciation Or equivalently: OCF = (Sales - Costs - Depreciation) × (1 - t) + Depreciation OCF = Net Income + Depreciation

Free Cash Flow (FCF)

FCF = EBIT(1 - t) + Depreciation - CAPEX - ΔNWC

Change in Net Working Capital

ΔNWC = NWCt - NWCt-1 Note: Negative ΔNWC = cash outflow (NWC increasing) Final year: Full NWC recovery = positive cash inflow

After-Tax Salvage Value

After-tax Salvage = Selling Price - Tax on Gain Tax on Gain = (Selling Price - Book Value) × t If Book Value = 0 → Tax = Selling Price × t

NPV Decision Rule

NPV = Σ [CFt / (1 + r)t] NPV > 0 → ACCEPT NPV < 0 → REJECT

⚠️ Common Exam Traps

🚫 Trap #1: Including Sunk Costs

The $4,000 market research fee in Optimus Prime was a SUNK COST. It was already paid regardless of the project decision. Never include sunk costs in your FCF.

🚫 Trap #2: Forgetting NWC Recovery

In the final year, you must recover ALL Net Working Capital. This is a positive cash inflow often worth 5-10% of total project value.

🚫 Trap #3: Wrong Sign on ΔNWC

When NWC increases (more inventory/receivables needed), it's a cash OUTFLOW (negative). Only the final recovery is positive.

🚫 Trap #4: Forgetting Tax on Salvage

If you sell equipment above book value, you pay tax on the gain. After-tax salvage = Selling Price - (Gain × Tax Rate).

💡 Partial Credit Strategy

Even if your final NPV is wrong, you earn marks for: (1) correct formula identification, (2) proper setup, (3) intermediate calculations. Always show your work in a structured table format.

🧮 Interactive NPV Calculator

Practice the calculation workflow with this step-by-step calculator. Mirrors the exam approach.

Step 1: Project Parameters

Depreciation Schedule (MACRS 3-Year)

✏️ Practice Problem: Optimus Prime Corporation

This is the exact problem from Tutorial 9. Work through it step-by-step.

Scenario: Optimus Prime Corporation is considering purchasing equipment for $300,000 to increase revenues over 4 years.

Key Data:
  • Market research fee already paid: $4,000
  • Year 1 sales: $110,000 (growing at 10% annually)
  • Operating costs: 25% of sales
  • Initial NWC: $7,000; subsequent NWC: 12% of revenue
  • Salvage value in Year 4: $25,000
  • Tax rate: 34%; Required return: 7%

MACRS 3-Year Depreciation:
Year 1: 33.33% | Year 2: 44.44% | Year 3: 14.82% | Year 4: 7.41%

Question: Should Optimus Prime Corp purchase the equipment?
1
Identify Relevant Cash Flows
The $4,000 market research is a SUNK COST — it's already been paid regardless of the decision. Do NOT include it.
2
Depreciation Schedule
Year 1: $300,000 × 33.33% = $99,990
Year 2: $300,000 × 44.44% = $133,320
Year 3: $300,000 × 14.82% = $44,460
Year 4: $300,000 × 7.41% = $22,230
Total Depreciation = $300,000 ✓
3
Sales & Costs Projection
Year 1 Sales $110,000
Year 2 Sales (×1.10) $121,000
Year 3 Sales (×1.10) $133,100
Year 4 Sales (×1.10) $146,410

Operating Costs = 25% of Sales each year

4
Operating Cash Flow (Year 1 Example)
Sales $110,000
- Costs (25%) -$27,500
- Depreciation -$99,990
= EBT -$17,490
- Tax (34%) -$5,947 (tax saving!)
= Net Income -$11,543
OCF = NI + Depreciation $88,447
5
Net Working Capital (ΔNWC)
Year 0: Initial NWC -$7,000
Year 1: $13,200 needed - $7,000 prev -$6,200
Year 2: $14,520 needed - $13,200 prev -$1,320
Year 3: $15,972 needed - $14,520 prev -$1,452
Year 4: Full recovery +$15,972

⚠️ Don't forget Year 4 recovery!

6
After-Tax Salvage Value
Selling Price $25,000
- Book Value (fully depreciated) $0
= Taxable Gain $25,000
Tax (34%) $8,500
After-tax Salvage $16,500
7
Total Cash Flows
Year 0Year 1Year 2Year 3Year 4
OCF—88,447105,22481,00180,031
ΔNWC-7,000-6,200-1,320-1,45215,972
CAPEX-300,000———16,500
Total CF-307,00082,247103,90479,549112,503
8
NPV Calculation
NPV = -307,000 + 82,247/(1.07)¹ + 103,904/(1.07)² + 79,549/(1.07)³ + 112,503/(1.07)⁴ NPV = -307,000 + 76,866 + 90,755 + 64,938 + 85,825 NPV = $11,383.81
✓ ACCEPT — NPV > 0, project creates value

IRR = 8.57% > 7% required return (consistent with NPV decision)

🎯 Interpretation (The Marks Everyone Misses!)

Remember: 40-50% of Section B marks come from interpretation, not calculations!

  • Decision: Accept the project since NPV = $11,383.81 > 0
  • Value Creation: The project adds ~$11,384 in shareholder wealth
  • Rate of Return: IRR of 8.57% exceeds the 7% hurdle rate
  • Risk Consideration: Sales growth assumption of 10% is key — sensitivity analysis would be prudent

Tutorial 9 Problem 1 - NWC Deep Dive: Need vs Recovery

Understanding the "Annual Need" and "Annual Recovery" approach to Net Working Capital.

🔑 The Key Insight: NWC is a Rolling Investment

Think of NWC like renting an apartment with a security deposit:

1
Move In (Year 0)
You pay a deposit to start — this is your initial NWC investment
2
Upgrade to Bigger Apartment (Years 1-4)
More sales = bigger "apartment" = bigger deposit needed. But you GET BACK your old deposit!
3
Move Out Completely (Project End)
When the project ends, you get your ENTIRE current deposit back!

⚠️ Why Does Recovery Happen Each Year?

NWC is made up of:

Inventory

Parts & supplies you buy

Accounts Receivable

Money customers owe you

Less: Accounts Payable

Money you owe suppliers

Recovery happens when you sell the inventory and collect receivables from the PREVIOUS period. The cash that was "trapped" becomes available again!

📐 The Formula

ΔNWC = Annual Need (this year) + Annual Recovery (last year's NWC) + Last Year Recovery (if project ends) Annual Need = NWC required THIS year (cash OUT) Annual Recovery = Getting back LAST year's NWC (cash IN) Last Year Recovery = Getting back THIS year's NWC at project end
Step 1 of 6
Project Start (Year 0)
Before operations begin, invest initial NWC of $7,000. This covers initial inventory and operating cash needed to start the project.
Cash Effect: -$7,000
Yr 0
Yr 1
Yr 2
Yr 3
Yr 4
Total NWC Invested: $7,000

📊 NWC Worksheet (Solution Format)

Click on "Annual Recovery" or "Last Year Recovery" rows to see explanations.

Year 0 Year 1 Year 2 Year 3 Year 4
Annual Need -$7,000 -$13,200 -$14,520 -$15,972 -$17,569
Annual Recovery ← click — +$7,000 +$13,200 +$14,520 +$15,972
Last Year Recovery ← click — — — — +$17,569
ΔNWC -$7,000 -$6,200 -$1,320 -$1,452 +$15,972

📗 What is Annual Recovery?

Each year, you recover the PREVIOUS year's NWC investment:

  • Year 1: Recover Year 0's $7,000 (sell Year 0 inventory, collect Year 0 receivables)
  • Year 2: Recover Year 1's $13,200
  • Year 3: Recover Year 2's $14,520
  • Year 4: Recover Year 3's $15,972

Think of it like this: The inventory you bought last year gets sold, and the receivables from last year get collected. That cash comes back to you!

📘 What is Last Year Recovery?

This ONLY happens in the final year when the project ends!

In Year 4, you recover:

  • Annual Recovery: +$15,972 (Year 3's NWC, like normal)
  • PLUS Last Year Recovery: +$17,569 (Year 4's own NWC)

Since the project ends, you liquidate EVERYTHING: sell all remaining inventory, collect all outstanding receivables, pay off all payables. All that trapped cash is finally released!

🧮 Calculation Check

Year 1 ΔNWC:
Need: -$13,200
Recovery: +$7,000
Net: -$6,200
Year 4 ΔNWC:
Need: -$17,569
Recovery: +$15,972
Last Year: +$17,569
Net: +$15,972

Watch the Cash Flow Through Time

Click on any year to see the breakdown

Year 0
-$7,000
Year 1
-$6,200
Year 2
-$1,320
Year 3
-$1,452
Year 4
+$15,972
Annual Need (Out)
Annual Recovery (In)
Last Year Recovery (In)

Click a year to see details

🎯 The Big Picture

-$68,261
Total Need
+$68,261
Total Recovery
$0
Net Over Project Life

NWC is just timing! You put money in early and get it all back later. The only "cost" is the time value of money.

❓ Quick Concept Quiz

Test your understanding of capital budgeting concepts.

Progress: 0/5 answered

Q1: A company paid $50,000 for a feasibility study before deciding on a project. How should this be treated in the NPV analysis?

Correct: C — Sunk costs are costs already incurred regardless of the project decision. They should NEVER be included in NPV analysis.

Q2: Equipment is sold for $30,000 with a book value of $10,000. Tax rate is 30%. What is the after-tax salvage value?

Correct: B — Gain = $30,000 - $10,000 = $20,000. Tax on gain = $20,000 × 30% = $6,000. After-tax salvage = $30,000 - $6,000 = $24,000.

Q3: In Year 2, NWC requirement is $15,000 and was $12,000 in Year 1. What is ΔNWC for Year 2?

Correct: B — When NWC increases, cash is tied up (outflow). ΔNWC = $15,000 - $12,000 = $3,000 additional investment needed = -$3,000 in cash flow terms.

Q4: A project has NPV = -$5,000 and IRR = 9%. Required return is 10%. What should you do?

Correct: B — When NPV and IRR agree (NPV < 0, IRR 9% < 10% required), reject. NPV is the primary decision rule because it measures value creation.

Q5: Why do we add depreciation back when calculating Operating Cash Flow?

Correct: B — Depreciation reduces taxable income (providing a tax shield) but is NOT an actual cash outflow. We add it back because no cash left the company.

✅ Exam Day Checklist

Make sure you can do all of these before the exam.

FCF Calculation Skills

  • Calculate depreciation using MACRS or straight-line schedules
  • Compute OCF using both methods: NI + Depreciation OR EBIT(1-t) + Depreciation
  • Calculate ΔNWC correctly (remember: increase = outflow, recovery = inflow)
  • Compute after-tax salvage value with tax on gain/loss
  • Identify and exclude sunk costs and irrelevant overheads
  • Include opportunity costs and project externalities

Valuation Skills

  • Discount FCFs at WACC to get NPV
  • Calculate terminal value using perpetuity formula: TV = FCF / (r - g)
  • Convert Enterprise Value to Equity Value: EV - Debt + Cash
  • Calculate share price from Equity Value ÷ Shares Outstanding

Decision & Interpretation

  • Apply NPV decision rule: Accept if NPV > 0, Reject if NPV < 0
  • Interpret what NPV means for shareholder value
  • Identify key assumptions and sensitivity factors
  • Compare IRR to required return for consistency check

⏱ Time Management

  • Section B: ~95 minutes for 70 marks
  • Roughly 1.35 minutes per mark
  • Don't spend more than 40% of time on calculations — interpretation is half the marks!
  • If stuck, state assumption and continue for partial credit

📝 Formula Quick Reference

These will be on your formula sheet, but know how to USE them:

OCF = EBIT(1 - t) + Depreciation = NI + Depreciation FCF = OCF - CAPEX - ΔNWC ΔNWC = NWCt - NWCt-1 After-tax Salvage = Sale Price - (Gain × Tax Rate) where Gain = Sale Price - Book Value NPV = Σ [FCFt / (1 + r)t] Terminal Value = FCFn / (r - g) [Gordon Growth] Equity Value = Enterprise Value - Debt + Cash Share Price = Equity Value / Shares Outstanding