CFA CFA I Exam
CFA Level I Chartered Financial Analyst (Page 88 )

Updated On: 26-Jan-2026

Which of the following statements is incorrect?

  1. NPV can be negative if the IRR is positive.
  2. Assuming a project has normal cash flows, the NPV will be positive if the IRR is less than the cost of capital.
  3. If IRR = k (the cost of capital), then NPV = 0.
  4. If the multiple IRR problem does not exist, any independent project acceptable by the NPV method will also be acceptable by the IRR method.
  5. The NPV method is not affected by the multiple IRR problem.

Answer(s): B

Explanation:

NPV is positive if IRR is greater than the cost of capital.



Alabama Pulp Company (APC) can control its environmental pollution using either "Project Old Tech" or "Project New Tech." Both will do the job, but the actual costs involved with Project New Tech, which uses unproved, new state-of-the-art technology, could be much higher than the expected cost levels. The cash outflows associated with Project Old Tech, which uses standard proven technology, are less risky--they are about as uncertain as the cash flows associated with an average project. APC's cost of capital for average risk projects is normally set at 12 percent, and the company adds 3 percent for high risk projects but subtracts 3 percent for low risk projects. The two projects in question meet the criteriafor high and average risk, but the financial manager is concerned about applying the normal rule to such cost-only projects. You must decide which project to recommend, and you should recommend the one with the lower PV of costs. What is the PV of costs of the better project?
Cash Outflows
Years:01234
Project New Tech1,500315315315315
Project Old Tech600600600600600

  1. 2,399
  2. 2,521
  3. 2,457
  4. 2,422
  5. 2,543

Answer(s): D

Explanation:

Recognize that (1) risky outflows must be discounted at lower rates, and (2) since Project New Tech is risky, it must be discounted at a rate of 12% - 3% = 9%. Project Old Tech must be discounted at 12%.
Tabular solution:
PV(New Tech) = -$1,500 - $315(PVIFA9%,4) = -$1,500 - $315(3.2397) = -$2,520.51. PV(Old Tech) = -$600 - $600(PVIFA12%,4) = -$600 - $600(3.0373) = -$2,422.38. PV(Old Tech) is a smaller outflow than NPV(New Tech), thus, Project Old Tech is the better project.



The management of Clay Industries have adhered to the following capital structure: 50% debt, 45% common equity, and 5% perpetual preferred equity. The following information applies to the firm: Before-tax cost of debt = 7.5% Combined state/federal tax rate = 35% Expected return on the market = 14.5% Annual risk-free rate of return = 5.25% Historical Beta coefficient of Clay Industries Common Stock = 1.15 Annual preferred dividend = $1.35 Preferred stock net offering price = $17.70 Expected annual common dividend = $0.45 Common stock price = $30.90 Expected growth rate = 11.75% Subjective risk premium = 3.8% Given this information, and using the Capital Asset Pricing Model to calculate the component cost of common equity, what is the Weighted Average Cost of Capital for Clay Industries?

  1. 15.31%
  2. 11.30%
  3. 9.92%
  4. 9.968%
  5. The WACC for Clay Industries cannot be calculated from the information.
  6. 10.05%

Answer(s): D

Explanation:

The calculation of the Weighted Average Cost of Capital is as follows: {fraction of debt * [yield to maturity on outstanding long-term debt][1-combined state/federal income tax rate]} + {fraction of preferred stock * [annual dividend/net offering price]} + {fraction of common stock * cost of equity}. The cost of common equity can be calculated using three methods, the Capital Asset Pricing Model (CAPM), the Dividend-Yield-plus-Growth-Rate (or Discounted Cash Flow) approach, and the Bond- Yield-plus-Risk-Premium approach. In this example, you are asked to calculate the cost of common equity using the Capital Asset Pricing Model (CAPM). This approach involves the following equation: {risk-free rate +beta[expected return on the market - risk-free rate]}.
Specifically, the calculation of the component cost of common equity using the CAPM is as follows: {[5.25% + 1.15(14.5%-5.25%]} = 15.888%. The after-tax cost of debt can be found by multiplying the yield to maturity on the firm's outstanding long-term debt (7.5%) by (1-tax rate). Using this method, the after-tax cost of debt is found as 4.875%. The calculation of the cost of perpetual preferred stock is relatively straightforward, simply divide the annual preferred dividend by the net offering price. Using this method, the cost of preferred stock is found as 7.627%. Incorporating these figures into the WACC equation gives the answer of 9.968%.



Buchanan Brothers anticipates that its net income at the end of the year will be $3.6 million (before any recapitalization). The company currently has 900,000 shares of common stock outstanding and has no debt. The company's stock trades at $40 a share. The company is considering a recapitalization where it will issue $10 million worth of debt at a yield to maturity of 10 percent, and use the proceeds to repurchase common stock. Assume the stock price remains unchanged by the transaction, and the company's tax rate is 34 percent. What will be the company's earnings per share if it proceeds with the recapitalization?

  1. $4.52
  2. $5.54
  3. $2.23
  4. $3.26
  5. $2.45

Answer(s): A

Explanation:

After issuing the debt, the company can repurchase $10,000,000/$40 = 250,000 shares leaving 650,000 shares outstanding. We still need to find the expected NI after issuing the debt. We're given the anticipated NI is $3.6 million. Thus, the EBIT (before the debt issue) can be found as follows: $3,600,000 = EBIT(1 - 0.34) or EBIT = $5,454,545.45. The company will pay $1,000,000 in interest after issuing the debt so the new EBT will be $5,454,545.45 - $1,000,000 = $4,454,545.45. Also, the new NI figure will be: $4,454,545.45(1 - 0.34) = $2,940,000. Finally, $2,940,000/650,000 = $4.52 is the EPS after the recapitalization.



Rollins Corporation is constructing its MCC schedule. Its target capital structure is 20 percent debt, 20 percent preferred stock, and 60 percent common equity. Its bonds have a 12 percent coupon, paid semiannually, a current maturity of 20 years, and sell for $1,000. The firm could sell, at par, $100 preferred stock, which pays a 12 percent annual dividend, but flotation costs of 5 percent would be incurred. Rollins' beta is 1.2, the risk-free rate is 10 percent, and the market risk premium is 5 percent. Rollins is a constant growth firm, which just paid a dividend of $2.00, sells for $27.00 per share, and has a growth rate of 8 percent. The firm's policy is to use a risk premium of 4 percentage points when using the bond-yield-plus-risk- premium method to find k(s). The firm's net income is expected to be $1 million, and its dividend payout ratio is 40 percent. Flotation costs on new common stock total 10 percent, and the firm's marginal tax rate is 40 percent. What is Rollins' cost of retained earnings using the bond-yield-plus-risk-premium approach?

  1. 16.6%
  2. 16.0%
  3. 16.9%
  4. 14.1%
  5. 13.6%

Answer(s): B

Explanation:

Cost of retained earnings (Bond yield plus risk premium approach): k(s) = 12.0% + 4.0% = 16.0%.



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