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Perform Capital Budgeting Analysis - CPA Bar

  1. A capital project uses straight-line depreciation of $80,000 per year. The tax rate is 25%. What is the annual depreciation tax shield?
    Answer: $20,000 Depreciation tax shield = Depreciation x Tax rate = $80,000 x 25% = $20,000. Depreciation is a non-cash expense that reduces taxable income; the tax savings from this reduction equals the depreciation amount multiplied by the tax rate. Option A is the full depreciation amount before the tax effect. Option B is the after-tax operating income effect of depreciation ($80,000 x 75%). Option C uses a 50% tax rate.
  2. A project requires an initial investment of $500,000 and generates after-tax cash flows of $150,000 per year for 5 years. The discount rate is 10% and the PV annuity factor for 5 years at 10% is 3.791. What is the NPV?
    Answer: $68,650 PV of cash flows = $150,000 x 3.791 = $568,650. NPV = $568,650 - $500,000 = $68,650. A positive NPV indicates the project creates value above the cost of capital. Option A sums undiscounted cash flows and subtracts the investment. Option C reports only one year's cash flow. Option D applies the correct formula but labels the sign incorrectly.
  3. A company is replacing equipment. The old machine has a book value of $50,000 and a current market value of $30,000. The tax rate is 30%. What are the after-tax proceeds from selling the old equipment?
    Answer: $36,000 Loss on sale = Book value - Market value = $50,000 - $30,000 = $20,000. Tax benefit from loss = $20,000 x 30% = $6,000. After-tax proceeds = Market value + Tax benefit = $30,000 + $6,000 = $36,000. Selling at below book value creates a tax-deductible loss that increases the after-tax proceeds above the market value. Option B ignores the tax benefit. Option C applies the tax rate to the market value rather than the loss. Option D uses book value instead of market value.
  4. A project has PV of future cash flows of $568,650 and an initial investment of $500,000. What is the profitability index?
    Answer: 1.14 PI = PV of future cash flows / Initial investment = $568,650 / $500,000 = 1.137, rounded to 1.14. This PI is consistent with the positive NPV of $68,650 from this project. Option B inverts the ratio. Option C uses an incorrect PV. Option D would imply NPV equals zero (the break-even PI).
  5. A company consistently approves capital projects with positive total NPV, yet company-wide ROIC has declined for three consecutive years. Which analytical concern does this pattern raise?
    Answer: Projects may be approved based on optimistic projections that are not achieved in practice; the gap between expected and actual project performance suggests biased forecasting, poor project selection, or inadequate post-implementation review of capital allocations A persistent ROIC decline despite an apparently sound capital approval process signals a disconnect between projected and actual project performance. This can result from: overly optimistic forecasts in project proposals (benefits overstated, costs understated), selection bias toward projects that look good on paper, or failure to track and learn from post-implementation performance. A rigorous capital allocation process should include systematic comparison of project outcomes against original forecasts to detect and correct persistent biases. Option A incorrectly attributes the problem to the NPV method itself. Option B incorrectly claims they are unrelated. Option C prioritizes a forecast metric over an outcome metric.
  6. A company has a capital budget of $1,000,000 and three independent projects: Project A (investment $400,000, NPV $120,000, PI 1.30), Project B (investment $600,000, NPV $180,000, PI 1.30), Project C (investment $500,000, NPV $100,000, PI 1.20). Under capital rationing, which combination maximizes total NPV within the budget?
    Answer: Projects A and C; total NPV $220,000 Feasible combinations within $1,000,000: A+C = $900,000 (NPV $220,000); B only = $600,000 (NPV $180,000); A only = $400,000 (NPV $120,000); A+B exceeds $1M. Projects A and C together generate the highest total NPV of $220,000. Although both A and B have the same PI (1.30), B alone generates only $180,000, while A+C generates $220,000. All three projects combined would require $1,500,000, exceeding the budget. The PI ranking confirms A and C should be selected over B alone.
  7. The profitability index (PI) is calculated as which of the following?
    Answer: Present value of future cash flows divided by the initial investment PI = PV of future cash flows / Initial investment. A PI greater than 1.0 indicates the project creates value (equivalent to a positive NPV). PI is particularly useful for capital rationing because it measures value created per dollar invested, allowing comparison of projects with different investment amounts. Option A is not a standard capital budgeting ratio. Option C describes an undiscounted return metric, not PI. Option D is a ratio used to assess whether an IRR-based hurdle is met, not the PI formula.
  8. Equipment costs $200,000 to purchase or can be leased with annual payments of $44,000 for 5 years paid at year beginning (annuity due). The tax rate is 25% and the PV annuity due factor for 5 years at 8% is 4.312. What is the present value of the after-tax lease payments?
    Answer: $142,296 After-tax annual lease payment = $44,000 x (1 - 0.25) = $33,000. PV of after-tax lease payments (annuity due) = $33,000 x 4.312 = $142,296. Option A uses the pre-tax payment without the tax reduction. Option B applies the pre-tax payment to the annuity due factor. Option C uses a different annuity factor.
  9. Two mutually exclusive options have: Option A with NPV $320,000 and IRR 16%; Option B with NPV $240,000 and IRR 22%. The WACC is 10%. Which should be selected and why?
    Answer: Option A should generally be selected because NPV measures absolute value created; for mutually exclusive projects where scale differs, NPV maximization aligns with shareholder value better than IRR maximization For mutually exclusive projects, NPV is the preferred criterion because it directly measures the dollar value created for shareholders. Option A's higher NPV ($320,000 vs. $240,000) means it creates $80,000 more value. Option B's higher IRR reflects a better return rate on a smaller scale but generates less absolute value. The IRR-NPV conflict typically arises when projects differ in scale or cash flow timing. IRR maximization does not equate to shareholder value maximization when scale differences exist. Options A and B each elevate a single metric without the correct reasoning. Option C is directionally correct but incomplete in its reasoning.
  10. Project L has a payback of 4.5 years and NPV of $420,000. Project S has a payback of 1.8 years and NPV of $95,000. A risk-averse CFO proposes selecting Project S for its faster payback. Which concern is most analytically relevant?
    Answer: Selecting Project S sacrifices $325,000 of value; payback ignores cash flows beyond the recovery point and does not discount for time value of money Choosing Project S over Project L gives up $325,000 of NPV ($420,000 - $95,000). The payback period has two known limitations: it ignores all cash flows after the payback point (which is where much of Project L's value may be generated) and it does not apply time value discounting. While faster payback does reduce some forms of liquidity risk, it is an incomplete metric for value creation. A risk-averse investor should consider a risk-adjusted NPV or scenario analysis rather than relying on payback as a proxy for risk. Options A and B overstate the reliability of payback as a risk measure. Option D is an unsupported assumption.
  11. A $5,000,000 factory expansion generates positive NPV at the base-case demand forecast. Sensitivity analysis shows NPV turns negative if annual demand grows below 3%. Current industry demand growth is 2.1%. Which conclusion is most analytically sound?
    Answer: The project requires demand growth exceeding the current industry rate to be NPV-positive; the break-even demand assumption is above the observable market trend, making this a high-risk investment requiring additional scrutiny before approval The sensitivity analysis reveals that this project is viable only if demand outpaces current market conditions. The break-even threshold (3%) is above the observable industry growth rate (2.1%), meaning the base-case forecast implicitly assumes either above-market company performance or a market acceleration. This is a significant analytical concern: if demand follows industry trends, the project destroys value. The decision should involve rigorous assessment of what competitive advantages justify the above-market demand assumption, or consideration of a phased or smaller investment. Option A accepts the base case without acknowledging the sensitivity finding. Option B dismisses a meaningful 0.9-percentage-point gap relative to an NPV threshold. Option D incorrectly rejects NPV methodology.
  12. A project requires an initial investment of $600,000 and generates after-tax operating cash flows of $120,000 per year for 8 years, plus a $60,000 after-tax salvage value at the end of Year 8. The PV annuity factor at 10% for 8 years is 5.335 and the Year 8 PV factor is 0.467. What is the NPV?
    Answer: $68,220 PV of operating cash flows = $120,000 x 5.335 = $640,200. PV of salvage = $60,000 x 0.467 = $28,020. Total PV = $640,200 + $28,020 = $668,220. NPV = $668,220 - $600,000 = $68,220. Option A omits the salvage value from the calculation. Option C adds the undiscounted salvage to the PV of operating cash flows. Option D applies the correct formula but labels the sign incorrectly.
  13. A project has an NPV of $85,000 at a 12% discount rate and an NPV of -$20,000 at an 18% discount rate. Using linear interpolation, what is the approximate IRR?
    Answer: 16.9% IRR = Lower rate + [NPV at lower rate / (NPV at lower rate + |NPV at upper rate|)] x (Upper rate - Lower rate) = 12% + [$85,000 / ($85,000 + $20,000)] x (18% - 12%) = 12% + (0.810 x 6%) = 12% + 4.86% = 16.86%, approximately 16.9%. Option A uses an equal split between the two rates. Option B underestimates the interpolation result. Option D is the upper bound where NPV is negative.
  14. A capital project has EBIT of $300,000, a tax rate of 25%, and depreciation of $80,000. What is the after-tax operating cash flow?
    Answer: $305,000 After-tax operating cash flow = NOPAT + Depreciation = (EBIT x (1 - Tax rate)) + Depreciation = ($300,000 x 0.75) + $80,000 = $225,000 + $80,000 = $305,000. Adding back depreciation is necessary because it is a non-cash charge deducted in computing EBIT. Option B is NOPAT only, without adding back depreciation. Option C adds depreciation to EBIT before applying the tax rate. Option D applies an incorrect tax calculation.
  15. In capital budgeting, the term 'incremental cash flow' refers to which of the following?
    Answer: The change in total cash flows that directly results from accepting the capital project, including all effects on other parts of the business Incremental cash flows are the changes in total company cash flows attributable to the investment decision - including all side effects such as cannibalization of existing products, changes to shared overhead, and any other ripple effects on the business. Properly identifying incremental flows requires comparing the company's total cash flows with vs. without the project. Option B describes undiscounted total cash flows, not incremental flows specifically. Option C describes after-tax operating cash flow, not the incremental concept. Option D incorrectly excludes side effects; cannibalization and other cross-business impacts are integral to correct incremental analysis.
  16. Equipment purchased three years ago for $600,000 has a current book value of $200,000. A new machine costing $500,000 would save $90,000 per year in operating costs over 7 years. A manager opposes replacement because of the $200,000 book value write-off. Which capital budgeting principle best addresses this argument?
    Answer: The $200,000 book value is a sunk cost; the replacement decision should be based on whether the PV of $90,000 annual savings justifies the $500,000 investment net of after-tax disposal proceeds from the old machine The $200,000 book value represents a past cost that cannot be recovered - whether the equipment is kept or sold, this value does not re-enter as cash. The accounting loss from writing it off is a non-cash charge that affects reported income but not the economic analysis. The correct analysis compares the cost of replacement ($500,000 minus after-tax proceeds from selling the old machine) to the PV of future savings ($90,000 per year for 7 years). Option A treats an accounting figure as an economic cost. Option B conflates a reporting loss with investment merit. Option C incorrectly treats book value as a future cash outflow.
  17. A project has a present value of future cash flows of $720,000 and requires an initial investment of $600,000. What is the profitability index?
    Answer: 1.20 PI = PV of future cash flows / Initial investment = $720,000 / $600,000 = 1.20. A PI of 1.20 means each dollar invested generates $1.20 of present value - $0.20 of net value per dollar deployed. Option A inverts the formula. Option B would imply NPV of zero (break-even). Option D applies an incorrect denominator of $480,000.
  18. A project has positive NPV of $45,000 at the company's WACC of 12%. The project involves a new market with no prior company experience. The CFO adds a 3% risk premium, reducing NPV to -$28,000 at 15%. Which analytical conclusion is most appropriate?
    Answer: The project's viability depends critically on whether 12% or 15% appropriately reflects the risk of this specific investment; management should validate the risk premium before deciding When a modest change in the discount rate flips NPV from positive to negative, the investment's acceptance hinges on the accuracy of the risk adjustment. The WACC reflects the average risk of the company's existing operations; a new-market project may legitimately warrant a higher rate. The analytical imperative is to validate whether 3% is the right incremental risk premium based on the specific characteristics of this project - market risk, execution uncertainty, competitive dynamics - rather than accepting or dismissing it arbitrarily. Options A and D ignore the risk signal. Option C dismisses the risk premium without analytical basis.
  19. In capital budgeting, which of the following is considered irrelevant to an investment decision?
    Answer: Sunk costs that have already been incurred and cannot be recovered regardless of the decision made Sunk costs are past expenditures that cannot be changed regardless of the current decision. Including them in capital budgeting analysis leads to biased decisions - the project should be evaluated on future incremental cash flows only. Option B (opportunity costs) is highly relevant because choosing this investment forecloses other uses of the capital. Option C (incremental cash flows) is the foundation of proper capital budgeting analysis. Option D (terminal cash flows) must be included because they affect the project's total return.
  20. A project requires an initial investment of $240,000 and generates cash flows of $60,000 (Year 1), $90,000 (Year 2), $80,000 (Year 3), and $70,000 (Year 4). What is the payback period?
    Answer: 3.14 years Cumulative cash flows: End of Year 1 $60,000; Year 2 $150,000; Year 3 $230,000. Remaining after Year 3 = $240,000 - $230,000 = $10,000. Year 4 fraction = $10,000 / $70,000 = 0.143. Payback = 3 + 0.143 = 3.14 years. Option A assumes the full investment is recovered exactly at Year 3. Option B calculates an earlier payback based on incorrect cumulative totals. Option D assumes recovery requires the full Year 4 cash flow.

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