Finance Quiz: Computing Wacc
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Computing WaccQuestion 1 of 20

A private company has a target debt-to-equity ratio of 0.6. The company can borrow at 8.0% pre-tax and has a 25% tax rate. To estimate its cost of equity, it uses a publicly traded comparable firm with an equity beta of 1.5, a debt-to-equity ratio of 0.8, and a 30% tax rate. The risk-free rate is 4.0% and the market risk premium is 5.6%. What is the private company's estimated WACC?

9.21%
10.05%
9.63%
10.88%
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Finance Quiz: Computing Wacc

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Question 1

A private company has a target debt-to-equity ratio of 0.6. The company can borrow at 8.0% pre-tax and has a 25% tax rate. To estimate its cost of equity, it uses a publicly traded comparable firm with an equity beta of 1.5, a debt-to-equity ratio of 0.8, and a 30% tax rate. The risk-free rate is 4.0% and the market risk premium is 5.6%. What is the private company's estimated WACC?

  1. 9.21%
  2. 10.05%
  3. 9.63% (correct answer)
  4. 10.88%
Explanation: This is a multi-step pure-play method calculation.
  1. Unlever the comparable company's beta: βAsset=βEquity/[1+(1−T)(D/E)]=1.5/[1+(1−0.30)(0.80)]=1.5/1.56=0.9615\beta_{Asset} = \beta_{Equity} / [1 + (1 - T)(D/E)] = 1.5 / [1 + (1 - 0.30)(0.80)] = 1.5 / 1.56 = 0.9615.
  2. Relever the asset beta to the private company's target capital structure: βEquity,Target=βAsset[1+(1−T)(D/E)]=0.9615×[1+(1−0.25)(0.60)]=0.9615×1.45=1.394\beta_{Equity, Target} = \beta_{Asset} [1 + (1 - T)(D/E)] = 0.9615 \times [1 + (1 - 0.25)(0.60)] = 0.9615 \times 1.45 = 1.394.
  3. Calculate the private company's cost of equity: rce=Rf+β(MRP)=4.0%+1.394(5.6%)=4.0%+7.806%=11.806%r_{ce} = R_f + \beta(MRP) = 4.0\% + 1.394(5.6\%) = 4.0\% + 7.806\% = 11.806\%.
  4. Determine the weights from the target D/E ratio of 0.6: wd=D/(D+E)=0.6/1.6=0.375w_d = D/(D+E) = 0.6/1.6 = 0.375 and we=E/(D+E)=1/1.6=0.625w_e = E/(D+E) = 1/1.6 = 0.625.
  5. Calculate WACC: WACC=(wd×rd(1−T))+(we×rce)=(0.375×8.0%×(1−0.25))+(0.625×11.806%)=2.25%+7.379%=9.629%WACC = (w_d \times r_d(1-T)) + (w_e \times r_{ce}) = (0.375 \times 8.0\% \times (1-0.25)) + (0.625 \times 11.806\%) = 2.25\% + 7.379\% = 9.629\%, which rounds to 9.63%.

Question 2

An analyst has gathered the following information for a company:

  • Target debt-to-equity ratio: 0.50
  • Pre-tax cost of debt: 7.2%
  • Cost of preferred stock: 8.5%
  • Cost of common equity: 13.0%
  • The company's target capital structure includes 10% preferred stock.
  • Marginal tax rate: 30%

An analyst has gathered the following information for a company:

  • Target debt-to-equity ratio: 0.50
  • Pre-tax cost of debt: 7.2%
  • Cost of preferred stock: 8.5%
  • Cost of common equity: 13.0%
  • The company's target capital structure includes 10% preferred stock.
  • Marginal tax rate: 30% Based on the information provided, what is the company's weighted average cost of capital (WACC)?
  1. 10.34%
  2. 10.16% (correct answer)
  3. 8.97%
  4. 10.88%
Explanation: First, determine the capital structure weights. Let V be total firm value. We are given that the weight of preferred stock, wp=P/V=0.10w_p = P/V = 0.10. This means the combined weight of debt and equity is wd+we=1−0.10=0.90w_d + w_e = 1 - 0.10 = 0.90. We are given a target debt-to-equity ratio, D/E=0.50D/E = 0.50. This ratio also applies to the weights: wd/we=0.50w_d / w_e = 0.50, so wd=0.50×wew_d = 0.50 \times w_e. Substitute this into the combined weight equation: 0.50we+we=0.90⇒1.5we=0.90⇒we=0.600.50w_e + w_e = 0.90 \Rightarrow 1.5w_e = 0.90 \Rightarrow w_e = 0.60. The weight of debt is wd=0.50×0.60=0.30w_d = 0.50 \times 0.60 = 0.30. The weights are: wd=30%w_d=30\%, wp=10%w_p=10\%, and we=60%w_e=60\%. Now, calculate the WACC: WACC=(wd×rd(1−T))+(wp×rp)+(we×re)=(0.30×7.2%×(1−0.30))+(0.10×8.5%)+(0.60×13.0%)=(0.30×5.04%)+0.85%+7.80%=1.512%+0.85%+7.80%=10.162%WACC = (w_d \times r_d(1-T)) + (w_p \times r_p) + (w_e \times r_e) = (0.30 \times 7.2\% \times (1 - 0.30)) + (0.10 \times 8.5\%) + (0.60 \times 13.0\%) = (0.30 \times 5.04\%) + 0.85\% + 7.80\% = 1.512\% + 0.85\% + 7.80\% = 10.162\%, or 10.16%.

Question 3

A firm has two outstanding bond issues. The first issue has a market value of $30 million and a yield-to-maturity of 6.0%. The second issue has a market value of $70 million and a yield-to-maturity of 9.0%. The company's target capital structure is 40% debt and 60% equity. The cost of equity is 14% and the tax rate is 30%. What is the firm's WACC?

  1. 10.50%
  2. 10.29%
  3. 11.10%
  4. 10.67% (correct answer)
Explanation: When calculating WACC with multiple debt issues, you need to find the weighted average cost of debt before applying the overall capital structure weights. First, calculate the weighted average cost of debt from the two bond issues. The total debt market value is $30M + $70M = $100M. The weighted average yield is: $30100×6.0%+70100×9.0%=1.8%+6.3%=8.1%\frac{30}{100} \times 6.0\% + \frac{70}{100} \times 9.0\% = 1.8\% + 6.3\% = 8.1\% $ Next, apply the tax shield to get the after-tax cost of debt: 8.1% \times (1 - 0.30) = 8.1% \times 0.70 = 5.67% Finally, use the target capital structure weights in the WACC formula: WACC = (0.40 \times 5.67%) + (0.60 \times 14.0%) = 2.27% + 8.40% = 10.67% Answer D (10.67%) correctly follows this three-step process. Answer A (10.50%) likely uses an incorrect debt weighting or miscalculates the weighted average yield. Answer B (10.29%) appears to make an error in applying the tax shield, possibly using the wrong tax rate or forgetting to weight the debt costs properly. Answer C (11.10%) probably forgets to apply the tax shield entirely, using the pre-tax weighted average cost of debt of 8.1% instead of the after-tax rate of 5.67%. Remember: with multiple debt issues, always calculate the market-value weighted average cost first, then apply the tax shield, then apply your target capital structure weights. Don't skip the debt weighting step—it's a common WACC trap.

Question 4

A firm's target capital structure consists of 30% debt and 70% equity. The firm is evaluating a project and needs to determine its WACC. The firm's bonds have a yield to maturity of 6.8%. The firm's marginal tax rate is 25%. An analyst provides two estimates for the cost of equity: 11.5% based on the Dividend Discount Model, and 12.5% based on CAPM. After review, the firm's management decides the CAPM estimate is the most appropriate measure of equity cost. What is the firm's WACC?

  1. 9.58%
  2. 9.93%
  3. 10.28% (correct answer)
  4. 10.79%
Explanation: The question requires the test-taker to select the correct cost of equity from two estimates and then compute the WACC.
  1. Select the appropriate cost of equity. The problem states that management considers the CAPM estimate of 12.5% to be the most appropriate. The DDM estimate is extraneous information.
  2. Calculate the after-tax cost of debt: rd(1−T)=6.8%×(1−0.25)=5.1%r_d(1 - T) = 6.8\% \times (1 - 0.25) = 5.1\%.
  3. Calculate WACC using the target weights and selected component costs: WACC=(wd×rd(1−T))+(wce×rce)=(0.30×5.1%)+(0.70×12.5%)=1.53%+8.75%=10.28%WACC = (w_d \times r_d(1-T)) + (w_{ce} \times r_{ce}) = (0.30 \times 5.1\%) + (0.70 \times 12.5\%) = 1.53\% + 8.75\% = 10.28\%.

Question 5

A company has a WACC of 9.55%. Its target capital structure is 30% debt and 70% equity. The pre-tax cost of debt is 7.0%, and the corporate tax rate is 25%. What is the company's cost of common equity (rce)?

  1. 10.64%
  2. 12.11%
  3. 10.93%
  4. 11.39% (correct answer)
Explanation: This question tests your understanding of the Weighted Average Cost of Capital (WACC) formula and how to solve for the cost of equity when given other components. The WACC formula is: WACC=(E/V×re)+(D/V×rd×(1−T))WACC = (E/V \times r_e) + (D/V \times r_d \times (1-T)), where E/V is the equity weight, D/V is the debt weight, rer_e is the cost of equity, rdr_d is the pre-tax cost of debt, and T is the tax rate. To find the cost of equity, you need to rearrange the WACC formula. First, calculate the after-tax cost of debt: 7.0%×(1−0.25)=5.25%7.0\% \times (1 - 0.25) = 5.25\%. Then, calculate the debt component of WACC: 0.30×5.25%=1.575%0.30 \times 5.25\% = 1.575\%. Since the total WACC is 9.55%, the equity component must be: 9.55%−1.575%=7.975%9.55\% - 1.575\% = 7.975\%. Finally, solve for the cost of equity: 7.975%÷0.70=11.39%7.975\% ÷ 0.70 = 11.39\%. Choice A (10.64%) likely results from forgetting to apply the tax shield to the debt cost. Choice B (12.11%) appears to come from using the pre-tax cost of debt instead of the after-tax cost in the calculation. Choice C (10.93%) might result from calculation errors in the algebraic manipulation or rounding mistakes during intermediate steps. Remember this key strategy: always work backwards from WACC by isolating the unknown component. Calculate what you know first (the after-tax debt cost), subtract it from the total WACC, then divide by the appropriate weight to find your missing variable.

Question 6

A company maintains a target capital structure of 25% debt and 75% equity. Its most recent annual dividend (D0) was $2.00 per share, and it expects dividends to grow at a constant rate of 5% per year. The current stock price is $42.00. The company's pre-tax cost of debt is 8%, and its marginal tax rate is 30%. What is the company's WACC?

  1. 8.72%
  2. 8.90% (correct answer)
  3. 9.50%
  4. 5.15%
Explanation: The solution requires finding the cost of equity using the Dividend Discount Model (DDM), then calculating WACC.
  1. Calculate the cost of equity (rce). First, find the next expected dividend (D1): D_1 = D_0 \times (1+g) = \2.00 \times (1.05) = $2.10.Then,usetheDDMformula:. Then, use the DDM formula: r_{ce} = (D_1 / P_0) + g = ($2.10 / $42.00) + 0.05 = 0.05 + 0.05 = 10.0%$.
  2. Calculate the after-tax cost of debt: rd(1−T)=8.0%×(1−0.30)=5.6%r_d(1 - T) = 8.0\% \times (1 - 0.30) = 5.6\%.
  3. Calculate WACC using target weights: WACC=(wd×rd(1−T))+(wce×rce)=(0.25×5.6%)+(0.75×10.0%)=1.4%+7.5%=8.90%WACC = (w_d \times r_d(1-T)) + (w_{ce} \times r_{ce}) = (0.25 \times 5.6\%) + (0.75 \times 10.0\%) = 1.4\% + 7.5\% = 8.90\%.

Question 7

Cygnus Corp. has a stated target capital structure of 35% debt and 65% equity. The company currently has $50 million in book value of debt and $80 million in book value of equity. The market value of its equity is $150 million, and its debt is trading at 98% of its book value. The pre-tax cost of debt is 7%, the cost of equity is 11.96%, and the tax rate is 25%. What is the company's WACC?

  1. 10.25%
  2. 9.40%
  3. 9.61% (correct answer)
  4. 10.34%
Explanation: The correct approach is to use the firm's stated target capital structure weights for the WACC calculation. The information about current book and market values is provided to distract from the correct methodology.
  1. Use the target weights: wd=0.35w_d = 0.35 and wce=0.65w_{ce} = 0.65.
  2. Calculate the after-tax cost of debt: rd(1−T)=7.0%×(1−0.25)=5.25%r_d(1 - T) = 7.0\% \times (1 - 0.25) = 5.25\%.
  3. Use the given cost of equity: rce=11.96%r_{ce} = 11.96\%.
  4. Calculate WACC: WACC=(wd×rd(1−T))+(wce×rce)=(0.35×5.25%)+(0.65×11.96%)=1.8375%+7.774%=9.6115%WACC = (w_d \times r_d(1-T)) + (w_{ce} \times r_{ce}) = (0.35 \times 5.25\%) + (0.65 \times 11.96\%) = 1.8375\% + 7.774\% = 9.6115\%, which rounds to 9.61%.

Question 8

A firm has a target capital structure of 40% debt and 60% common equity. The firm's pre-tax cost of debt is 6.5%. The company's stock beta is 1.3, the risk-free rate is 3.5%, and the market risk premium is 6.0%. The marginal tax rate is 30%. What is the firm's weighted average cost of capital (WACC)?

  1. 8.60% (correct answer)
  2. 9.38%
  3. 11.33%
  4. 5.42%
Explanation: The WACC is calculated by weighting the after-tax costs of each capital component.
  1. Calculate the after-tax cost of debt: rd(1−T)=6.5%×(1−0.30)=4.55%r_d(1 - T) = 6.5\% \times (1 - 0.30) = 4.55\%.
  2. Calculate the cost of common equity using CAPM: rce=Rf+β(E(Rm)−Rf)=3.5%+1.3×6.0%=11.3%r_{ce} = R_f + \beta(E(R_m) - R_f) = 3.5\% + 1.3 \times 6.0\% = 11.3\%.
  3. Calculate WACC using the target weights: WACC=(wd×rd(1−T))+(wce×rce)=(0.40×4.55%)+(0.60×11.3%)=1.82%+6.78%=8.60%WACC = (w_d \times r_d(1-T)) + (w_{ce} \times r_{ce}) = (0.40 \times 4.55\%) + (0.60 \times 11.3\%) = 1.82\% + 6.78\% = 8.60\%.

Question 9

Andromeda Industries is determining its WACC. The firm's target capital structure is 70% equity and 30% debt. The company has 10-year, 8% annual coupon bonds outstanding with a par value of $1,000 that are currently trading at $1,038.50. The company's stock has a beta of 0.9. The risk-free rate is 4%, and the expected return on the market is 11%. The corporate tax rate is 25%. What is Andromeda's WACC?

  1. 8.90% (correct answer)
  2. 9.01%
  3. 9.46%
  4. 11.42%
Explanation: This is a multi-step calculation.
  1. Compute the pre-tax cost of debt (rd), which is the bond's yield-to-maturity (YTM). Using a financial calculator with N=10, PV=-1038.50, PMT=80 (8% of $1,000), and FV=1000, the calculated I/Y (YTM) is 7.50%.
  2. Compute the cost of equity (rce) using CAPM. The market risk premium (MRP) is E(Rm) - Rf = 11% - 4% = 7%. So, rce=Rf+β(MRP)=4%+0.9(7%)=10.3%r_{ce} = R_f + \beta(MRP) = 4\% + 0.9(7\%) = 10.3\%.
  3. Compute the WACC using the target weights: WACC=(wd×rd×(1−T))+(wce×rce)=(0.30×7.50%×(1−0.25))+(0.70×10.3%)=(0.30×5.625%)+7.21%=1.6875%+7.21%=8.8975%WACC = (w_d \times r_d \times (1-T)) + (w_{ce} \times r_{ce}) = (0.30 \times 7.50\% \times (1 - 0.25)) + (0.70 \times 10.3\%) = (0.30 \times 5.625\%) + 7.21\% = 1.6875\% + 7.21\% = 8.8975\%, which rounds to 8.90%.

Question 10

Rigel Inc. has a target capital structure that is 60% equity, 30% debt, and 10% preferred stock. The after-tax cost of debt is 4.0%, the cost of preferred stock is 7.0%, and the cost of equity is 11.5%. The company is considering a new project that is of similar risk to the existing firm. Information about flotation costs for new financing is available but deemed by the firm's analyst to be best handled by adjusting the project's initial investment rather than the discount rate. What is the correct WACC for evaluating this project?

  1. 8.80% (correct answer)
  2. 9.12%
  3. 8.50%
  4. 9.35%
Explanation: The standard methodology for capital budgeting is to use a WACC that reflects the ongoing costs of capital and to account for flotation costs separately by increasing the initial project cost. The question directs the test-taker to this approach. Therefore, the flotation cost information is a distractor.
  1. Use the given component costs and target weights. The cost of debt is already provided on an after-tax basis.
  2. Calculate WACC: WACC=(wd×rd,AT)+(wps×rps)+(wce×rce)WACC = (w_d \times r_{d, AT}) + (w_{ps} \times r_{ps}) + (w_{ce} \times r_{ce}) = (0.30×4.0%)+(0.10×7.0%)+(0.60×11.5%)(0.30 \times 4.0\%) + (0.10 \times 7.0\%) + (0.60 \times 11.5\%) = 1.20%+0.70%+6.90%=8.80%1.20\% + 0.70\% + 6.90\% = 8.80\%.

Question 11

Vega Corp. plans to finance a new project using its target capital structure of 40% debt and 60% equity. Vega's current stock beta is 1.1, reflecting its historical debt-to-equity ratio of 0.25. The increased leverage of the new target structure is expected to raise the firm's equity beta to 1.3. The pre-tax cost of debt is 6.0%. The risk-free rate is 3.0%, the market risk premium is 5.0%, and the tax rate is 25%. What is the appropriate WACC to use for capital budgeting decisions?

  1. 6.90%
  2. 7.50% (correct answer)
  3. 8.50%
  4. 7.20%
Explanation: The WACC for new projects should be based on the firm's target capital structure and the corresponding component costs.
  1. The problem explicitly states that the beta corresponding to the new target leverage is 1.3. The current beta of 1.1 is irrelevant. Calculate the new cost of equity: rce=Rf+β(MRP)=3.0%+1.3(5.0%)=3.0%+6.5%=9.5%r_{ce} = R_f + \beta(MRP) = 3.0\% + 1.3(5.0\%) = 3.0\% + 6.5\% = 9.5\%.
  2. Calculate the after-tax cost of debt: rd(1−T)=6.0%×(1−0.25)=4.5%r_d(1-T) = 6.0\% \times (1 - 0.25) = 4.5\%.
  3. Use the target capital structure weights (40% debt, 60% equity) to calculate WACC: WACC=(wd×rd(1−T))+(wce×rce)=(0.40×4.5%)+(0.60×9.5%)=1.8%+5.7%=7.50%WACC = (w_d \times r_d(1-T)) + (w_{ce} \times r_{ce}) = (0.40 \times 4.5\%) + (0.60 \times 9.5\%) = 1.8\% + 5.7\% = 7.50\%.

Question 12

A company maintains a target capital structure of 25% debt and 75% equity. Its most recent annual dividend (D0) was $2.00 per share, and it expects dividends to grow at a constant rate of 5% per year. The current stock price is $42.00. The company's pre-tax cost of debt is 8%, and its marginal tax rate is 30%. What is the company's WACC?

  1. 8.72%
  2. 8.90% (correct answer)
  3. 9.50%
  4. 5.15%
Explanation: The solution requires finding the cost of equity using the Dividend Discount Model (DDM), then calculating WACC.
  1. Calculate the cost of equity (rce). First, find the next expected dividend (D1): D_1 = D_0 \times (1+g) = \2.00 \times (1.05) = $2.10.Then,usetheDDMformula:. Then, use the DDM formula: r_{ce} = (D_1 / P_0) + g = ($2.10 / $42.00) + 0.05 = 0.05 + 0.05 = 10.0%$.
  2. Calculate the after-tax cost of debt: rd(1−T)=8.0%×(1−0.30)=5.6%r_d(1 - T) = 8.0\% \times (1 - 0.30) = 5.6\%.
  3. Calculate WACC using target weights: WACC=(wd×rd(1−T))+(wce×rce)=(0.25×5.6%)+(0.75×10.0%)=1.4%+7.5%=8.90%WACC = (w_d \times r_d(1-T)) + (w_{ce} \times r_{ce}) = (0.25 \times 5.6\%) + (0.75 \times 10.0\%) = 1.4\% + 7.5\% = 8.90\%.

Question 13

Cygnus Corp. has a stated target capital structure of 35% debt and 65% equity. The company currently has $50 million in book value of debt and $80 million in book value of equity. The market value of its equity is $150 million, and its debt is trading at 98% of its book value. The pre-tax cost of debt is 7%, the cost of equity is 11.96%, and the tax rate is 25%. What is the company's WACC?

  1. 10.25%
  2. 9.40%
  3. 9.61% (correct answer)
  4. 10.34%
Explanation: The correct approach is to use the firm's stated target capital structure weights for the WACC calculation. The information about current book and market values is provided to distract from the correct methodology.
  1. Use the target weights: wd=0.35w_d = 0.35 and wce=0.65w_{ce} = 0.65.
  2. Calculate the after-tax cost of debt: rd(1−T)=7.0%×(1−0.25)=5.25%r_d(1 - T) = 7.0\% \times (1 - 0.25) = 5.25\%.
  3. Use the given cost of equity: rce=11.96%r_{ce} = 11.96\%.
  4. Calculate WACC: WACC=(wd×rd(1−T))+(wce×rce)=(0.35×5.25%)+(0.65×11.96%)=1.8375%+7.774%=9.6115%WACC = (w_d \times r_d(1-T)) + (w_{ce} \times r_{ce}) = (0.35 \times 5.25\%) + (0.65 \times 11.96\%) = 1.8375\% + 7.774\% = 9.6115\%, which rounds to 9.61%.

Question 14

A firm's target capital structure consists of 30% debt and 70% equity. The firm is evaluating a project and needs to determine its WACC. The firm's bonds have a yield to maturity of 6.8%. The firm's marginal tax rate is 25%. An analyst provides two estimates for the cost of equity: 11.5% based on the Dividend Discount Model, and 12.5% based on CAPM. After review, the firm's management decides the CAPM estimate is the most appropriate measure of equity cost. What is the firm's WACC?

  1. 9.58%
  2. 9.93%
  3. 10.28% (correct answer)
  4. 10.79%
Explanation: The question requires the test-taker to select the correct cost of equity from two estimates and then compute the WACC.
  1. Select the appropriate cost of equity. The problem states that management considers the CAPM estimate of 12.5% to be the most appropriate. The DDM estimate is extraneous information.
  2. Calculate the after-tax cost of debt: rd(1−T)=6.8%×(1−0.25)=5.1%r_d(1 - T) = 6.8\% \times (1 - 0.25) = 5.1\%.
  3. Calculate WACC using the target weights and selected component costs: WACC=(wd×rd(1−T))+(wce×rce)=(0.30×5.1%)+(0.70×12.5%)=1.53%+8.75%=10.28%WACC = (w_d \times r_d(1-T)) + (w_{ce} \times r_{ce}) = (0.30 \times 5.1\%) + (0.70 \times 12.5\%) = 1.53\% + 8.75\% = 10.28\%.

Question 15

A firm has two outstanding bond issues. The first issue has a market value of $30 million and a yield-to-maturity of 6.0%. The second issue has a market value of $70 million and a yield-to-maturity of 9.0%. The company's target capital structure is 40% debt and 60% equity. The cost of equity is 14% and the tax rate is 30%. What is the firm's WACC?

  1. 10.50%
  2. 10.29%
  3. 11.10%
  4. 10.67% (correct answer)
Explanation: When calculating WACC with multiple debt issues, you need to find the weighted average cost of debt before applying the overall capital structure weights. First, calculate the weighted average cost of debt from the two bond issues. The total debt market value is $30M + $70M = $100M. The weighted average yield is: $30100×6.0%+70100×9.0%=1.8%+6.3%=8.1%\frac{30}{100} \times 6.0\% + \frac{70}{100} \times 9.0\% = 1.8\% + 6.3\% = 8.1\% $ Next, apply the tax shield to get the after-tax cost of debt: 8.1% \times (1 - 0.30) = 8.1% \times 0.70 = 5.67% Finally, use the target capital structure weights in the WACC formula: WACC = (0.40 \times 5.67%) + (0.60 \times 14.0%) = 2.27% + 8.40% = 10.67% Answer D (10.67%) correctly follows this three-step process. Answer A (10.50%) likely uses an incorrect debt weighting or miscalculates the weighted average yield. Answer B (10.29%) appears to make an error in applying the tax shield, possibly using the wrong tax rate or forgetting to weight the debt costs properly. Answer C (11.10%) probably forgets to apply the tax shield entirely, using the pre-tax weighted average cost of debt of 8.1% instead of the after-tax rate of 5.67%. Remember: with multiple debt issues, always calculate the market-value weighted average cost first, then apply the tax shield, then apply your target capital structure weights. Don't skip the debt weighting step—it's a common WACC trap.

Question 16

A company has a WACC of 9.55%. Its target capital structure is 30% debt and 70% equity. The pre-tax cost of debt is 7.0%, and the corporate tax rate is 25%. What is the company's cost of common equity (rce)?

  1. 10.64%
  2. 12.11%
  3. 10.93%
  4. 11.39% (correct answer)
Explanation: This question tests your understanding of the Weighted Average Cost of Capital (WACC) formula and how to solve for the cost of equity when given other components. The WACC formula is: WACC=(E/V×re)+(D/V×rd×(1−T))WACC = (E/V \times r_e) + (D/V \times r_d \times (1-T)), where E/V is the equity weight, D/V is the debt weight, rer_e is the cost of equity, rdr_d is the pre-tax cost of debt, and T is the tax rate. To find the cost of equity, you need to rearrange the WACC formula. First, calculate the after-tax cost of debt: 7.0%×(1−0.25)=5.25%7.0\% \times (1 - 0.25) = 5.25\%. Then, calculate the debt component of WACC: 0.30×5.25%=1.575%0.30 \times 5.25\% = 1.575\%. Since the total WACC is 9.55%, the equity component must be: 9.55%−1.575%=7.975%9.55\% - 1.575\% = 7.975\%. Finally, solve for the cost of equity: 7.975%÷0.70=11.39%7.975\% ÷ 0.70 = 11.39\%. Choice A (10.64%) likely results from forgetting to apply the tax shield to the debt cost. Choice B (12.11%) appears to come from using the pre-tax cost of debt instead of the after-tax cost in the calculation. Choice C (10.93%) might result from calculation errors in the algebraic manipulation or rounding mistakes during intermediate steps. Remember this key strategy: always work backwards from WACC by isolating the unknown component. Calculate what you know first (the after-tax debt cost), subtract it from the total WACC, then divide by the appropriate weight to find your missing variable.

Question 17

Andromeda Industries is determining its WACC. The firm's target capital structure is 70% equity and 30% debt. The company has 10-year, 8% annual coupon bonds outstanding with a par value of $1,000 that are currently trading at $1,038.50. The company's stock has a beta of 0.9. The risk-free rate is 4%, and the expected return on the market is 11%. The corporate tax rate is 25%. What is Andromeda's WACC?

  1. 8.90% (correct answer)
  2. 9.01%
  3. 9.46%
  4. 11.42%
Explanation: This is a multi-step calculation.
  1. Compute the pre-tax cost of debt (rd), which is the bond's yield-to-maturity (YTM). Using a financial calculator with N=10, PV=-1038.50, PMT=80 (8% of $1,000), and FV=1000, the calculated I/Y (YTM) is 7.50%.
  2. Compute the cost of equity (rce) using CAPM. The market risk premium (MRP) is E(Rm) - Rf = 11% - 4% = 7%. So, rce=Rf+β(MRP)=4%+0.9(7%)=10.3%r_{ce} = R_f + \beta(MRP) = 4\% + 0.9(7\%) = 10.3\%.
  3. Compute the WACC using the target weights: WACC=(wd×rd×(1−T))+(wce×rce)=(0.30×7.50%×(1−0.25))+(0.70×10.3%)=(0.30×5.625%)+7.21%=1.6875%+7.21%=8.8975%WACC = (w_d \times r_d \times (1-T)) + (w_{ce} \times r_{ce}) = (0.30 \times 7.50\% \times (1 - 0.25)) + (0.70 \times 10.3\%) = (0.30 \times 5.625\%) + 7.21\% = 1.6875\% + 7.21\% = 8.8975\%, which rounds to 8.90%.

Question 18

Vega Corp. plans to finance a new project using its target capital structure of 40% debt and 60% equity. Vega's current stock beta is 1.1, reflecting its historical debt-to-equity ratio of 0.25. The increased leverage of the new target structure is expected to raise the firm's equity beta to 1.3. The pre-tax cost of debt is 6.0%. The risk-free rate is 3.0%, the market risk premium is 5.0%, and the tax rate is 25%. What is the appropriate WACC to use for capital budgeting decisions?

  1. 6.90%
  2. 7.50% (correct answer)
  3. 8.50%
  4. 7.20%
Explanation: The WACC for new projects should be based on the firm's target capital structure and the corresponding component costs.
  1. The problem explicitly states that the beta corresponding to the new target leverage is 1.3. The current beta of 1.1 is irrelevant. Calculate the new cost of equity: rce=Rf+β(MRP)=3.0%+1.3(5.0%)=3.0%+6.5%=9.5%r_{ce} = R_f + \beta(MRP) = 3.0\% + 1.3(5.0\%) = 3.0\% + 6.5\% = 9.5\%.
  2. Calculate the after-tax cost of debt: rd(1−T)=6.0%×(1−0.25)=4.5%r_d(1-T) = 6.0\% \times (1 - 0.25) = 4.5\%.
  3. Use the target capital structure weights (40% debt, 60% equity) to calculate WACC: WACC=(wd×rd(1−T))+(wce×rce)=(0.40×4.5%)+(0.60×9.5%)=1.8%+5.7%=7.50%WACC = (w_d \times r_d(1-T)) + (w_{ce} \times r_{ce}) = (0.40 \times 4.5\%) + (0.60 \times 9.5\%) = 1.8\% + 5.7\% = 7.50\%.

Question 19

A firm has a target capital structure of 40% debt and 60% common equity. The firm's pre-tax cost of debt is 6.5%. The company's stock beta is 1.3, the risk-free rate is 3.5%, and the market risk premium is 6.0%. The marginal tax rate is 30%. What is the firm's weighted average cost of capital (WACC)?

  1. 8.60% (correct answer)
  2. 9.38%
  3. 11.33%
  4. 5.42%
Explanation: The WACC is calculated by weighting the after-tax costs of each capital component.
  1. Calculate the after-tax cost of debt: rd(1−T)=6.5%×(1−0.30)=4.55%r_d(1 - T) = 6.5\% \times (1 - 0.30) = 4.55\%.
  2. Calculate the cost of common equity using CAPM: rce=Rf+β(E(Rm)−Rf)=3.5%+1.3×6.0%=11.3%r_{ce} = R_f + \beta(E(R_m) - R_f) = 3.5\% + 1.3 \times 6.0\% = 11.3\%.
  3. Calculate WACC using the target weights: WACC=(wd×rd(1−T))+(wce×rce)=(0.40×4.55%)+(0.60×11.3%)=1.82%+6.78%=8.60%WACC = (w_d \times r_d(1-T)) + (w_{ce} \times r_{ce}) = (0.40 \times 4.55\%) + (0.60 \times 11.3\%) = 1.82\% + 6.78\% = 8.60\%.

Question 20

Rigel Inc. has a target capital structure that is 60% equity, 30% debt, and 10% preferred stock. The after-tax cost of debt is 4.0%, the cost of preferred stock is 7.0%, and the cost of equity is 11.5%. The company is considering a new project that is of similar risk to the existing firm. Information about flotation costs for new financing is available but deemed by the firm's analyst to be best handled by adjusting the project's initial investment rather than the discount rate. What is the correct WACC for evaluating this project?

  1. 8.80% (correct answer)
  2. 9.12%
  3. 8.50%
  4. 9.35%
Explanation: The standard methodology for capital budgeting is to use a WACC that reflects the ongoing costs of capital and to account for flotation costs separately by increasing the initial project cost. The question directs the test-taker to this approach. Therefore, the flotation cost information is a distractor.
  1. Use the given component costs and target weights. The cost of debt is already provided on an after-tax basis.
  2. Calculate WACC: WACC=(wd×rd,AT)+(wps×rps)+(wce×rce)WACC = (w_d \times r_{d, AT}) + (w_{ps} \times r_{ps}) + (w_{ce} \times r_{ce}) = (0.30×4.0%)+(0.10×7.0%)+(0.60×11.5%)(0.30 \times 4.0\%) + (0.10 \times 7.0\%) + (0.60 \times 11.5\%) = 1.20%+0.70%+6.90%=8.80%1.20\% + 0.70\% + 6.90\% = 8.80\%.