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Apply Valuation Models - CPA Bar

  1. A project has an NPV of $25,000 at a 10% discount rate and an NPV of -$8,000 at a 15% discount rate. Using linear interpolation, what is the approximate IRR?
    Answer: 13.8% IRR = Lower rate + [NPV at lower rate / (NPV at lower rate - NPV at upper rate)] x (Upper rate - Lower rate) = 10% + [$25,000 / ($25,000 + $8,000)] x 5% = 10% + (0.758 x 5%) = 10% + 3.79% = 13.8%. Option A assumes the IRR falls at the simple midpoint of the two rates. Option C is the upper bound rate where NPV is negative. Option D applies an incorrect interpolation formula.
  2. A company evaluates after-tax lease payments of $80,000 per year reduced to $60,000 after a 25% tax rate. The present value annuity factor for 5 years at 8% is 3.993. What is the present value of the after-tax lease payments?
    Answer: $239,580 After-tax annual lease payment = $80,000 x (1 - 0.25) = $60,000. PV of after-tax lease payments = $60,000 x 3.993 = $239,580. Option A applies the pre-tax lease payment to the annuity factor without the tax reduction. Option B multiplies the after-tax payment by 5 years without discounting. Option D applies the pre-tax payment and an incorrect annuity factor.
  3. A preferred stock pays a fixed annual dividend of $5,000 indefinitely. The required rate of return is 8%. What is the present value of this perpetuity?
    Answer: $62,500 PV of perpetuity = Annual payment / Discount rate = $5,000 / 0.08 = $62,500. Option A divides by 0.125 (a different rate). Option B reports the annual payment rather than the present value. Option C uses a 10% discount rate instead of 8%.
  4. Next year's FCFF is $8M; WACC 12%; growth 3%; debt $10M; excess cash $2M. Equity value?
    Answer: $80.9M Discount next year's FCFF at the perpetuity growth rate: 8 / (0.12 - 0.03) = 88.9M enterprise value. Then subtract the 10M debt and add the 2M excess cash: 88.9 - 10 + 2 = 80.9M. The tempting 88.9M is enterprise value, not equity value, because it skips the debt and cash adjustments.
  5. The net present value (NPV) method evaluates a capital investment by doing which of the following?
    Answer: Discounting all expected future cash flows to their present value and comparing the total to the initial investment outlay NPV discounts each expected future cash flow back to the present using the required rate of return, sums those present values, and subtracts the initial investment. A positive NPV indicates the investment creates value above the cost of capital. Option B describes the payback period. Option C describes the internal rate of return (IRR). Option D describes the accounting rate of return.
  6. A project requires an initial investment of $300,000 and generates after-tax cash flows of $120,000 (Year 1), $140,000 (Year 2), and $100,000 (Year 3). What is the payback period?
    Answer: 2.4 years Cumulative cash flows: End of Year 1 $120,000; End of Year 2 $260,000; remaining to recover = $300,000 - $260,000 = $40,000. Year 3 cash flow = $100,000. Fraction of Year 3 = $40,000 / $100,000 = 0.40. Payback = 2 + 0.40 = 2.4 years. Option B assumes the Year 2 cumulative total recovers the full investment. Option C assumes the investment is not recovered until the end of Year 3. Option D applies an incorrect fraction of the Year 3 cash flow.
  7. Project costs $500K and yields $120K forever. All-equity cost is 12%; tax 21%; debt $200K. Adjusted present value?
    Answer: $542,000 Value the unlevered project: 120,000 / 0.12 = 1,000,000. Subtract the 500,000 initial cost to get 500,000. Add the debt tax shield: 21% of 200,000 = 42,000. Total is 542,000. The tempting mistake is adding the tax shield to 1,000,000 and forgetting the 500,000 cost, giving 1,042,000.
  8. A company has EBITDA of $8,000,000. Three comparable companies trade at EV/EBITDA multiples of 7x, 8x, and 9x. Using the average multiple, what is the estimated enterprise value?
    Answer: $64,000,000 Average EV/EBITDA = (7 + 8 + 9) / 3 = 8x. Estimated EV = $8,000,000 x 8 = $64,000,000. Option A applies the lowest multiple (7x). Option C applies the highest multiple (9x). Option D applies a multiple of 10x, which is not supported by the peer data.
  9. Project A has an NPV of $50,000 and IRR of 18%. Project B has an NPV of $75,000 and IRR of 14%. Both projects exceed the 10% cost of capital. The projects are mutually exclusive. Which should be selected?
    Answer: Project B, because it creates more absolute value for shareholders at $75,000 versus $50,000, and both projects exceed the cost of capital For mutually exclusive projects, NPV is the preferred decision criterion because it measures the absolute dollar value created for shareholders. Project B's NPV of $75,000 exceeds Project A's $50,000, meaning Project B creates $25,000 more value. The IRR conflict arises because the projects likely differ in scale or timing - Project B may require a larger investment but generates more total value. Option A elevates IRR over NPV, which is the classic error in mutually exclusive project analysis. Option C is incorrect; when projects are mutually exclusive, only one can be chosen. Option D is a general overstatement about IRR's superiority.
  10. Under the income approach to fair value measurement, value is estimated by which of the following methods?
    Answer: Discounting expected future cash flows or earnings at a rate reflecting the risk of those cash flows The income approach estimates value by converting future economic benefits into a present value using an appropriate discount rate. Common income approach methods include DCF analysis and the capitalization of earnings. Option B describes the asset (or cost) approach, which values a business by reference to the net asset value. Option C describes the market approach using precedent transactions. Option D describes the replacement cost variant of the asset approach.
  11. A project requires an initial investment of $200,000 and generates after-tax cash flows of $60,000 (Year 1), $70,000 (Year 2), $80,000 (Year 3), and $50,000 (Year 4). Using a 10% discount rate and PV factors of 0.909, 0.826, 0.751, and 0.683 respectively, what is the project's net present value?
    Answer: $6,590 PV of cash flows: ($60,000 x 0.909) + ($70,000 x 0.826) + ($80,000 x 0.751) + ($50,000 x 0.683) = $54,540 + $57,820 + $60,080 + $34,150 = $206,590. NPV = $206,590 - $200,000 = $6,590. Option A applies the correct calculation but labels the sign incorrectly. Option C reports only Year 1 cash flows. Option D reports the total present value without subtracting the initial investment.
  12. The Gordon Growth Model produces an intrinsic value of $65 per share for a stock currently trading at $85 per share. Which statement best characterizes the analytical implication of this gap?
    Answer: The gap may indicate the market is pricing in higher future growth or a lower required return than the model assumed; the analyst should evaluate whether the model inputs are realistic before drawing a conclusion A model value below the market price does not automatically mean the stock is overvalued. The Gordon Growth Model is highly sensitive to the growth rate (g) and required return (r) inputs - small changes in these assumptions produce large changes in estimated value. The market price may reflect a more optimistic growth outlook, a different perception of risk, or factors the model does not capture. Before concluding the stock is overvalued, the analyst should stress-test the model assumptions and determine whether they are more or less realistic than what the market implies. Options A and B reach premature conclusions without examining model inputs. Option D is an overstated version of the efficient market hypothesis that dismisses analytical tools entirely.
  13. A stock pays an annual dividend of $3.00 per share. Dividends are expected to grow at 4% per year in perpetuity and the required rate of return is 10%. Using the Gordon Growth Model, what is the estimated intrinsic value per share?
    Answer: $52.00 Gordon Growth Model: P = D1 / (r - g). D1 = D0 x (1 + g) = $3.00 x 1.04 = $3.12. P = $3.12 / (0.10 - 0.04) = $3.12 / 0.06 = $52.00. Option A divides only D0 by the required rate of return, omitting the growth rate. Option B divides D1 by only the growth rate. Option D uses D0 in the numerator without the growth adjustment.
  14. A project requires an initial investment of $150,000 and generates equal annual after-tax cash flows of $40,000 for 5 years. The discount rate is 8% and the present value annuity factor for 5 years at 8% is 3.993. What is the project's net present value?
    Answer: $9,720 PV of annuity = $40,000 x 3.993 = $159,720. NPV = $159,720 - $150,000 = $9,720. Option A subtracts the annual cash flow from the initial investment rather than computing PV. Option B reports the total undiscounted cash flows ($40,000 x 5 = $200,000). Option D applies the correct formula but labels the sign incorrectly.
  15. An acquisition generates a positive NPV only if the target achieves 12% annual revenue growth for 5 years. The target's historical growth rate is 4%. Which concern is most analytically important before proceeding?
    Answer: The acquisition's value depends on achieving three times the historical growth rate; sensitivity analysis should test whether value is preserved at growth rates closer to the historical baseline When an acquisition requires a substantial departure from historical performance to produce a positive NPV, the investment is highly sensitive to that assumption. Sensitivity and scenario analysis - testing NPV at historical growth (4%), a moderate improvement (8%), and the full assumption (12%) - reveals the range of outcomes and the probability that the deal creates value. Management endorsement does not make an aggressive assumption reliable, and synergies do not automatically triple a company's growth rate. Option C introduces an arbitrary midpoint without analytical justification. Option B is an unsupported generalization.
  16. A project requires an initial investment of $180,000 and generates annual cash flows of $50,000 (Year 1), $60,000 (Year 2), $70,000 (Year 3), and $40,000 (Year 4). What is the payback period?
    Answer: 3.0 years Cumulative cash flows: End of Year 1 $50,000; End of Year 2 $110,000; End of Year 3 $180,000. The initial investment is fully recovered at the end of exactly 3 years. Option A assumes an equal split that does not match the actual cash flow pattern. Option B extends to Year 4, which is unnecessary since the investment is recovered in Year 3. Option C calculates a fractional year based on incorrect cumulative totals.
  17. The internal rate of return (IRR) is best defined as which of the following?
    Answer: The discount rate at which the net present value of a project equals zero The IRR is the specific discount rate that sets NPV equal to zero - the rate at which the present value of future cash inflows exactly equals the initial investment. A project is accepted when its IRR exceeds the required rate of return. Option A is incorrect; higher discount rates reduce NPV rather than maximizing it. Option C describes the accounting rate of return. Option D describes the hurdle rate or cost of capital, which is used as the acceptance benchmark for IRR, not the definition of IRR itself.
  18. A bond has a face value of $1,000, an annual coupon rate of 6%, and 3 years to maturity. The market yield is 8%. The PV annuity factor for 3 years at 8% is 2.577 and the PV factor for Year 3 is 0.794. What is the bond's current price?
    Answer: $948.60 Annual coupon = $1,000 x 6% = $60. PV of coupons = $60 x 2.577 = $154.62. PV of face value = $1,000 x 0.794 = $794.00. Bond price = $154.62 + $794.00 = $948.62, approximately $948.60. When market yield exceeds coupon rate, bonds trade at a discount to face value. Option B is face value, which applies only when coupon rate equals market yield. Option C is a premium price, which would apply if the coupon rate exceeded the market yield. Option D applies an incorrect annuity factor.
  19. EV/EBITDA is 8x; EBITDA $40M; debt $80M; excess cash $20M. Equity value?
    Answer: $260M EV = 8 x 40 = $320M. Subtract net debt: debt $80M less cash $20M = $60M. Equity = 320 - 60 = $260M. The $240M trap subtracts all debt but forgets excess cash reduces net debt.
  20. A company applies the adjusted net asset method to value a private business. Book value of assets is $4,200,000. Unrecorded identifiable intangibles have a fair value of $800,000. Total liabilities are $1,900,000. What is the estimated equity value?
    Answer: $3,100,000 Adjusted total assets = Book value + Unrecorded intangibles = $4,200,000 + $800,000 = $5,000,000. Equity value = Adjusted assets - Liabilities = $5,000,000 - $1,900,000 = $3,100,000. Option A uses only book value assets minus liabilities, omitting the unrecorded intangibles. Option B reports only the book value of assets. Option C reports the adjusted asset total before subtracting liabilities.

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