LEARNING OBJECTIVES
  1. Compile the WACC equation.
  2. Solve for WACC.

Now that we have calculated all of our component costs, calculating the WACC is simple. We plug into our formula and solve.


Table 12.1
 Components of WACC

Variable = Definition
r_{d} = Interest rate on firm's debt. Or the return on debt.
r_{d}(1 − T) = After-tax cost of debt.
r_{ps} = Return on preferred stock
r_{s} = Return on common stock
w_{d} = Weight (%) of debt used by company
w_{ps} = Weight (%) of preferred stock used by company
w_{s} = Weight (%) of common stock used by company
WACC = Weighted Average Cost of Capital
D_{PS} = Dividend of Preferred Stock
P_{PS} = Price of Preferred Stock
g = Growth rate of dividends of common stock
P_{0} = Price in time zero of a share of common stock
D_{0} = Dividend in time zero
D_{1} = Dividend in time 1


The weighted average cost of capital (WACC) takes the return from each component and then appropriately 'weights' it based on the percentage used for financing. The weights must sum to one and it is easiest to use decimals. In words the equation is:

Equation 12.7 WACC components (words)

WACC = (% of debt)(After-tax cost of debt) + (% of preferred stock)(cost of preferred stock) + (% of common stock)(cost of common stock)

Or WACC = (% of debt)(Before-tax cost of debt)(1−T) + (% of preferred stock)(cost of preferred stock) + (% of common stock)(cost of common stock)

Using symbols, the equation is:

Equation 12.8 WACC components (symbols)

WACC = w_{d}r_{d}(1 − T) + w_{ps}r_{ps} + w_{s}r_{s}
 


Worked Example: Falcons Footwear - CAPM to calculate rs

Falcons Footwear has 12 million shares of common stock selling for $60/share. They have 2 million shares of preferred stock selling for $85/share and $100 million in bonds trading at par. They are in the 40% tax bracket.

First, we calculate the total market value:

Total market value of common stock = 12 million * $60 each = $720 million
Total market value of preferred stock = 2 million shares * $85 each = $170 million
Total market value of bonds = $100 million trading at par = $100 million
Total market value = 720 + 170 + 100 = $990 million

From this, we get the weights:

Percentage of common stock = $720 / $990 = 72.7%
Percentage of preferred stock = $170 / $990 = 17.2%
Percentage of debt = $100 / $990 = 10.1%
Total equals = 100%

 

Then we plug in the weights and the component costs.

\text{WACC}=w_{d} r_{d}(1-T)+w_{ps} r_{ps}+w_{s} r_{s}
 
\text{WACC} =(0.101)(0.07)(1-0.4)+(0.172)(0.0882)+(0.727)(0.092)
\text{WACC} =0.0042+0.0152+0.0668=0.0862 or 8.62 \%


For Falcons Footwear the WACC is 8.62%.

KEY TAKEAWAY
  • The Weighted Average Cost of Capital is the component returns multiplied by their respective weights.


EXERCISES

  1. Calculate WACC given the following:

    r_{s} = \text{6 percent %}, \, r_{d} = \text{10%},  \, r_{ps} = \text{4%},  \, w_{d} = \text{40%},  \, w_{s} = \text{50%},  \, w_{ps} = 10%

  2. Calculate WACC given the following:

    r_{s} = \text{5.5%}, \, r_{d} = \text{4.5%}, \, r_{ps} = \text{7%}, \, w_{d} = \text{35%}, \,  w_{s} = \text{45%}, \,  w_{ps} = \text{20%}


Source: https://2012books.lardbucket.org/books/finance-for-managers/s12-05-weighted-average-cost-of-capit.html
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Last modified: Tuesday, 8 December 2020, 9:56 AM