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WACC Test Questions

I always get asked what are some questions for the exam, so I will try to give a few of many topics we will cover

 

Weighter Average Cost  of Capital
Suppose a firm has 1000 5 year zero coupon bonds outstanding (par value 1000) that have a YTM of 6%.  Moreover there are 500,000 shares outstanding with a Beta of 1.3.  If the expected return on the market is 10% and the risk free rate is 3% (we will use CAPM even with its problems).  Further assume the firm is expected to pay a 3.00 dividend and has a growth rate of 4%.  Assume a 30% tax rate.  (Be patient.  It will take a while)

What is the firm’s WACC?
WACC = (Weight of debt * cost of debt)  + (weight of equity * cost of equity)

The first step is to find the cost of debt.   Cost of debt:  YTM(1-T) = 6%(1-.2) = 4.8%

Second step find the  Cost of equity:  For this we can use CAPM (but realize CAPM has some problems) E(r) = rf + B(ERm-RF)  =  .03 + 1.3(.1-.03) = 12.1%
Next we will look at the weights.  The weights are fractions of the entire market value of the firm (debt and equity).   The weight of debt (Wd) = value of debt divided by value of  the sum of debt and equity.

 

Next we need to find the values of the debt and the equity.  The process is the same for each: To find the value of the debt, first find the value of each bond, then multiply by the number of bonds outstanding.

To find the value of the equity, find the value of each share of stock and multiply by the number of shares outstanding.   Value of the debt:  draw a time line:  find the price of the bond = 1000/1.06^5 = 747.26 there are 10,000 bonds outstanding so overall value = $7,472,581
Value of equity Price per share = Div(1)/(r-g) 3.00/(.121-.04)= $37.04 times 500,000 shares outstanding = $18,518.516

Weights

Overall value of the firm = $7,472,581 + 18,518,516 = $25,991,100 Fraction of debt:  7,472,581/$18,518,516 = .2875 so weight of equity = 1-.2875 = 71.25%
plugging everything back in: WACC = (Weight of debt * cost of debt)  + (weight of equity * cost of equity)
=.2875(.048) + .7125*(12.1) = 10.0%


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