CPA Bar Quiz: Perform Capital Budgeting Analysis

What this quiz covers

This quiz focuses on Perform Capital Budgeting Analysis, giving you a quick way to practice the rules, question types, and explanations that matter most for CPA Bar.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

Question 1

1. $250,000
2. $68,650 (correct answer)
3. $150,000
4. -$68,650

Explanation: 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.

Question 2

1. $80,000
2. $60,000
3. $40,000
4. $20,000 (correct answer)

Explanation: 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.

Question 3

1. $36,000 (correct answer)
2. $30,000
3. $44,000
4. $50,000

Explanation: 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.

Question 4

1. $12,000
2. $12,758 (correct answer)
3. $55,650
4. $42,892

Explanation: After-tax annual cash flow = After-tax savings + Depreciation tax shield = ($90,000 x 0.75) + ($60,000 x 0.25) = $67,500 + $15,000 = $82,500. PV of cash flows = $82,500 x 3.791 = $312,758. NPV = $312,758 - $300,000 = $12,758. Option A uses an incorrect after-tax rate. Option C uses the full pre-tax savings as the cash flow base. Option D applies only the after-tax savings without the depreciation tax shield.

Question 5

1. Payback period is always the appropriate criterion for risk-averse decision makers
2. Shorter payback always indicates lower investment risk
3. 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 (correct answer)
4. Both projects carry equivalent risk because they operate in the same industry

Explanation: 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.

Question 6

1. The project should be accepted because the base-case NPV is positive at WACC
2. 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 (correct answer)
3. The 3% risk premium is excessive and should be ignored in the analysis
4. Any project with positive NPV at WACC should always be accepted regardless of risk adjustments

Explanation: 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.

Question 7

1. $165,000
2. $192,024
3. $158,500
4. $142,296 (correct answer)

Explanation: 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.

Question 8

1. NPV analysis must be incorrect if ROIC is declining simultaneously
2. ROIC and NPV measure fundamentally different things and cannot be compared
3. Individual project NPVs are the only relevant measure and company-wide ROIC should be ignored
4. 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 (correct answer)

Explanation: 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.

Question 9

1. 3.0 years
2. 2.7 years
3. 3.14 years (correct answer)
4. 4.0 years

Explanation: 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.

Question 10

1. Project B only; total NPV $180,000
2. Project A only; total NPV $120,000
3. All three projects; total NPV $400,000
4. Projects A and C; total NPV $220,000 (correct answer)

Explanation: 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.

Question 11

1. 15.0%
2. 16.0%
3. 16.9% (correct answer)
4. 18.0%

Explanation: 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.

Question 12

1. $20,120 (correct answer)
2. -$20,120
3. $73,320
4. $696,800

Explanation: PV of operating cash flows = $160,000 x 4.355 = $696,800. Terminal cash flows = Salvage $80,000 + NWC recovery $50,000 = $130,000. PV of terminal cash flows = $130,000 x 0.564 = $73,320. Total PV = $696,800 + $73,320 = $770,120. NPV = $770,120 - $750,000 = $20,120. Option B labels the sign incorrectly. Option C reports only the PV of terminal cash flows. Option D reports only the PV of operating cash flows.

Question 13

1. The project should be accepted because base-case NPV is positive
2. The 3% threshold is close enough to the 2.1% rate that the risk is acceptable
3. 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 (correct answer)
4. NPV analysis is not appropriate for capacity expansion decisions

Explanation: 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.

Question 14

1. $40,200
2. $68,220 (correct answer)
3. $128,220
4. -$68,220

Explanation: 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.

Question 15

1. Project Y; NPV $17,356
2. Project X; NPV $63,188
3. Project X; NPV $31,594 (correct answer)
4. Project Y; NPV $35,612

Explanation: Project X NPV = ($58,000 x 3.993) - $200,000 = $231,594 - $200,000 = $31,594. Project Y NPV = ($92,000 x 3.993) - $350,000 = $367,356 - $350,000 = $17,356. Project X has the higher NPV ($31,594 vs. $17,356) and should be selected for mutually exclusive projects. Option A selects the lower-NPV project. Options B and D use incorrect cash flow or investment amounts.

Question 16

1. 3.0 years
2. 2.75 years
3. 4.0 years
4. 3.45 years (correct answer)

Explanation: Cumulative cash flows: Year 1 $100,000; Year 2 $220,000; Year 3 $350,000. Remaining after Year 3 = $400,000 - $350,000 = $50,000. Year 4 fraction = $50,000 / $110,000 = 0.455. Payback = 3 + 0.455 = 3.45 years. Option A assumes Year 3 cumulative equals the investment. Option B produces a payback during Year 3 based on incorrect calculations. Option C assumes the investment is not recovered until all of Year 4's cash flow is received.

Question 17

1. The $200,000 book value should be included because it represents real economic value
2. The book value write-off confirms the original investment was poor and the new machine should be rejected
3. The $200,000 is a real cash outflow that must be included in the replacement NPV analysis
4. 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 (correct answer)

Explanation: 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.

Question 18

1. Management is correct that all project costs must be included in NPV analysis
2. The $800,000 R&D is a sunk cost; including it leads to rejecting a project that would create $680,000 of future value; only incremental future cash flows are relevant (correct answer)
3. Sunk costs should be included when they exceed $500,000
4. The NPV should include R&D to assess the overall program ROI for the innovation portfolio

Explanation: The R&D was completed last year and cannot be recovered regardless of the current decision. Including it is a sunk cost fallacy - allowing a past expenditure to distort a forward-looking decision. The decision should be: 'Given where we are now, does launching this product create future value?' The answer is yes ($680,000 NPV). Rejecting the launch would forgo $680,000 of value while not recovering a single dollar of the R&D. Management's desire to assess whether the total investment was worthwhile is understandable but represents a different analytical question from the current decision. Options A, C, and D either endorse or rationalize the inclusion of sunk costs.

Question 19

1. 0.83
2. 1.00
3. 1.20 (correct answer)
4. 1.50

Explanation: 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.

Question 20

1. Net present value divided by the IRR
2. Present value of future cash flows divided by the initial investment (correct answer)
3. Total undiscounted cash flows divided by the payback period
4. IRR divided by the weighted average cost of capital

Explanation: 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.