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Chapter 25 – Exercises & Cases

Multiple Choice Questions​

  1. Capital budgeting decisions typically involve:
    a) Short-term working capital changes
    b) Long-term investments with multi-year impact
    c) Only minor purchases
    d) Only replacement decisions
    Answer: b) Capital budgeting focuses on long-term investments.

  2. The payback period measures:
    a) Profit margin
    b) Time to recover initial investment
    c) Net present value
    d) Accounting profit
    Answer: b) Payback measures time to recover investment.

  3. Which method accounts for the time value of money?
    a) Simple payback
    b) ARR
    c) NPV
    d) Accounting profit
    Answer: c) NPV considers time value of money.

  4. The internal rate of return is:
    a) The discount rate that makes PV = FV
    b) The discount rate that makes NPV = 0
    c) The accounting rate of return
    d) The cash payback period
    Answer: b) IRR is the rate that makes NPV zero.

  5. The profitability index is useful when:
    a) Projects have no risk
    b) Capital is unlimited
    c) Capital rationing is required
    d) IRR cannot be calculated
    Answer: c) PI helps rank projects when capital is limited.

  6. The depreciation tax shield is:
    a) Depreciation expense minus tax
    b) Depreciation × (1 - tax rate)
    c) Depreciation × tax rate
    d) Tax expense × depreciation
    Answer: c) Depreciation tax shield = Depreciation × tax rate.

  7. Working capital investments:
    a) Are irrelevant for capital budgeting
    b) Reduce initial cash flow and are recovered at project end
    c) Increase cash flow each year
    d) Are the same as fixed costs
    Answer: b) Working capital reduces cash initially and is recovered later.

  8. A project with positive NPV and IRR below the hurdle rate should be:
    a) Accepted
    b) Rejected
    c) Deferred until IRR improves
    d) Compared to ARR
    Answer: b) If IRR is below hurdle, project should be rejected (even if NPV positive? Wait: positive NPV implies IRR > discount used. But if using different hurdle? That scenario inconsistent. Need adjust question.

Better adjust question: "A project with negative NPV but payback in 2 years should be?". rewrite Q8.**

  1. A project has a payback of 2 years but a negative NPV. The project should:
    a) Be accepted because payback is short
    b) Be rejected because it destroys value
    c) Be accepted if ARR is high
    d) Be accepted if IRR > 0
    Answer: b) Negative NPV indicates value destruction despite short payback.

  2. Luxembourg SMEs can reduce financing costs by:
    a) Ignoring risk assessments
    b) Using government-backed loans and grants
    c) Avoiding financial projections
    d) Using only equity financing
    Answer: b) Government-backed loans and grants can reduce costs.

  3. Government grants should be included in capital budgeting by:
    a) Ignoring them to be conservative
    b) Treating them as incremental cash inflows
    c) Deducting them from ARR only
    d) Recording them as liabilities only
    Answer: b) Grants are incremental cash inflows reducing net investment.

Questions​

  1. What are the key steps in the capital budgeting process? Why is each important?
  2. Compare the payback period and ARR methods. When might each be useful?
  3. Explain the time value of money. How is it applied in NPV analysis?
  4. Why is NPV considered the primary decision metric for capital investments?
  5. How does working capital affect project cash flows?
  6. Describe how depreciation impacts cash flows through the tax shield.
  7. What factors influence the cost of capital for Luxembourg SMEs?
  8. How do government grants and incentives influence investment decisions?
  9. What qualitative factors should be considered alongside financial metrics?
  10. Why is post-investment review important?

Problems Set A​

Problem A-1: Payback Calculation

Initial investment: €250,000. Annual cash inflows: €70,000 for first three years, €90,000 for years 4–5. Calculate the payback period.

Problem A-2: ARR Calculation

Investment: €150,000, salvage value €30,000, life 5 years. Annual accounting income: €28,000. Calculate ARR using average investment.

Problem A-3: Time Value of Money

What is the present value of receiving €40,000 annually for 4 years at 6%?

Problem A-4: NPV Calculation

Initial investment: €300,000. Cash inflows: €90k, €100k, €110k, €120k, €130k. Discount rate: 9%. Calculate NPV.

Problem A-5: Depreciation Tax Shield

Investment €200,000, straight-line depreciation over 5 years, no salvage. Tax rate 20%. Calculate annual depreciation tax shield.

Problems Set B​

Problem B-1: Discounted Payback

Investment €180,000. Cash inflows: €60k, €70k, €80k, €90k. Discount rate 8%. Calculate discounted payback.

Problem B-2: NPV vs. IRR

Project A: NPV €40k, IRR 18%. Project B: NPV €55k, IRR 15%. Projects are mutually exclusive. Which should be chosen and why?

Problem B-3: Cash Flow Estimation

Investment €120,000, depreciation €24,000 per year, tax rate 22%, operating income before depreciation and tax €60,000 per year. Calculate annual after-tax cash flow.

Problem B-4: Working Capital Recovery

Project requires €25,000 working capital at start. At end of 5-year project, working capital is released. How does this affect NPV?

Problem B-5: Luxembourg Grant Impact

Investment €400,000 qualifies for 15% grant paid at end of year 1. Determine net initial investment and cash flow impact.

Comprehensive Problem​

Comprehensive Problem 25: Evaluating the Second Location for Le Petit Bistro

Marie is considering opening a second location in Esch-sur-Alzette. The project involves:

  • Initial investment: €550,000 (construction €400k, equipment €150k)
  • Working capital: €80,000 (released at end)
  • Project life: 7 years
  • Annual revenues: €420k (Years 1–2), €480k (Years 3–7)
  • Operating cash expenses (excluding depreciation): 65% of revenue
  • Depreciation: Straight-line over 7 years (assume no salvage)
  • Tax rate: 20%
  • Discount rate: 9%
  • Financing: 60% debt at 4% interest, 40% equity (but use WACC for discount)
  • Grant: 10% of eligible investment (€400k construction qualifies) paid at end of Year 1
  • VAT: Recoverable but paid upfront (assume timing already handled)

Required:

  1. Estimate incremental operating cash flows for each year (revenues, expenses, depreciation, taxes).
  2. Include working capital investment and recovery.
  3. Incorporate grant cash flow in Year 1.
  4. Calculate NPV, IRR, and discounted payback period.
  5. Perform sensitivity analysis for revenue ±10%.
  6. Perform scenario analysis (optimistic: faster demand growth; pessimistic: slower growth, higher costs).
  7. Evaluate payback and ARR for comparison.
  8. Identify qualitative factors (staffing, brand impact, competition).
  9. Recommend accept or reject, with rationale.
  10. Prepare summary for bank financing (key metrics, sensitivity).

Cases​

Case 25-1: Equipment Replacement Decision

A Luxembourg manufacturing SME must decide whether to replace an old machine. The new machine costs €250,000, saves €60,000 per year in operating costs, and has a 6-year life with €20,000 salvage. The old machine can be sold for €30,000 now but has increasing maintenance costs. Analyze the replacement decision using NPV and qualitative factors.

Case 25-2: Digital Transformation Project

A Luxembourg financial services firm is considering a €800,000 digital platform to automate client onboarding. Benefits include faster onboarding, reduced errors, and improved compliance. However, the project also carries cybersecurity risk and requires staff training. Develop a balanced evaluation using capital budgeting and non-financial metrics.

Solutions are published in supplementary/instructor/solutions/chapter_25_solutions.md.