Apply Valuation Models
Help Questions
CPA Business Analysis and Reporting (BAR) › Apply Valuation Models
The net present value (NPV) method evaluates a capital investment by doing which of the following?
Determining the discount rate at which the present value of future cash flows equals the initial investment
Discounting all expected future cash flows to their present value and comparing the total to the initial investment outlay
Dividing average annual accounting income by the average book value of the investment over its life
Calculating the number of years required for cumulative undiscounted cash flows to recover the initial investment
Explanation
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.
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?
$1,051.40
$1,000.00
$972.00
$948.60
Explanation
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.
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?
$30.00
$52.00
$60.00
$75.00
Explanation
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.
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?
$40,000
$50,000
$62,500
$5,000
Explanation
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%.
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?
$239,580
$299,250
$319,440
$200,000
Explanation
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.
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?
$5,000,000
$2,300,000
$3,100,000
$4,200,000
Explanation
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.
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?
3.0 years
2.7 years
2.0 years
2.4 years
Explanation
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.
A DCF analysis values an acquisition target at $42,000,000 while a comparable company analysis values it at $56,000,000. Which response to the $14,000,000 gap is most analytically appropriate?
Use the lower DCF value as a conservative floor and proceed with that as the maximum offer
Average the two values to arrive at $49,000,000 as the offer price
Discard the comparable company analysis because market multiples are inherently more subjective than DCF
Investigate the assumptions driving the gap, since DCF value depends on growth and discount rate assumptions while comparable company multiples reflect what the market currently pays for similar businesses
Explanation
A significant gap between DCF and market multiple valuations usually signals that one or both methodologies contain assumptions worth scrutinizing. DCF is highly sensitive to terminal growth rate and discount rate inputs, while comparable company multiples may include a market-specific control premium or reflect current sector optimism. Understanding why the gap exists is more informative than arbitrarily averaging or discarding a method. Option A treats two different analytical conclusions as though they should be mechanically blended. Option B incorrectly dismisses market-based evidence. Option D accepts the lower value without understanding why the two methods diverge.
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?
The 12% growth assumption is acceptable if senior management endorses it
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
The model should be rerun using the 8% midpoint between historical and assumed growth
Acquisitions always generate synergies that justify assuming higher growth than historical rates
Explanation
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.
Project C has the highest NPV ($180,000) but the longest payback period (6 years) of all projects considered. Management proposes rejecting Project C in favor of Project D (NPV $95,000, payback 2 years). Which concern is most analytically relevant?
The payback period is more reliable than NPV for projects with long time horizons
Selecting Project D over Project C sacrifices $85,000 of shareholder value; the payback period ignores cash flows beyond the recovery point and does not account for the time value of money
Project C should be rejected because a 6-year payback period always signals excessive risk
Both projects should be accepted because both generate positive NPV and capital is unconstrained
Explanation
The payback period ignores all cash flows after the investment is recovered and does not discount future cash flows. A project with a long payback but high NPV may generate most of its value after the payback point. Overweighting payback leads to rejecting long-horizon, high-value projects in favor of faster-recovering, lower-value alternatives - exactly the tradeoff here. Option A makes an absolute rule about payback length that has no analytical basis. Option C inverts the well-established ranking of decision criteria. Option D is incorrect because the projects are implicitly mutually exclusive given that management is choosing between them.