Math Problem Statement

Given the following calculate the WACC.

Given the following calculate the WACC.

Solution

To calculate the Weighted Average Cost of Capital (WACC), we use the formula:

WACC=(EV×rE)+(DV×rD×(1T))\text{WACC} = \left( \frac{E}{V} \times r_E \right) + \left( \frac{D}{V} \times r_D \times (1 - T) \right)

Where:

  • EE is the market value of equity (Weight of Equity in Total Capital Structure)
  • DD is the market value of debt (Weight of Debt in Total Capital Structure)
  • V=E+DV = E + D is the total value of capital (which is 100% in this case)
  • rEr_E is the cost of equity
  • rDr_D is the cost of debt (Pre-tax Yield on Debt)
  • TT is the tax rate

Steps:

  1. Calculate the Cost of Equity using the Capital Asset Pricing Model (CAPM): rE=Risk Free Rate+β×(Return on the Stock MarketRisk Free Rate)r_E = \text{Risk Free Rate} + \beta \times (\text{Return on the Stock Market} - \text{Risk Free Rate})

    Substituting the given values: rE=3.5%+1.3×(9.0%3.5%)=3.5%+1.3×5.5%=3.5%+7.15%=10.65%r_E = 3.5\% + 1.3 \times (9.0\% - 3.5\%) = 3.5\% + 1.3 \times 5.5\% = 3.5\% + 7.15\% = 10.65\%

  2. Weight of Debt (D/V) = 33%
    Weight of Equity (E/V) = 67%

  3. Pre-tax Yield on Debt (r_D) = 5.0%

  4. Tax rate (T) = 26.5%

Now, using these in the WACC formula:

WACC=(0.67×10.65%)+(0.33×5.0%×(10.265))\text{WACC} = \left( 0.67 \times 10.65\% \right) + \left( 0.33 \times 5.0\% \times (1 - 0.265) \right)

Let's compute this.The Weighted Average Cost of Capital (WACC) is approximately 8.35%.

Would you like more details or have any questions? Here are some related questions to explore further:

  1. How does an increase in the tax rate affect the WACC?
  2. What impact does a higher proportion of debt have on WACC?
  3. How is the cost of equity calculated using the CAPM model?
  4. Why is the after-tax cost of debt used in the WACC formula?
  5. How can WACC influence a company's investment decisions?

Tip: A lower WACC generally indicates cheaper access to capital, which can encourage investment.

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Math Problem Analysis

Mathematical Concepts

Finance
Weighted Average Cost of Capital (WACC)
Capital Structure
Cost of Equity
Cost of Debt

Formulas

WACC = (E/V * r_E) + (D/V * r_D * (1 - T))
r_E = Risk Free Rate + β * (Return on Stock Market - Risk Free Rate)

Theorems

Capital Asset Pricing Model (CAPM)
WACC Formula

Suitable Grade Level

University-level Finance