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A corporation has 10,000 bonds outstanding with a 6% annual coupon rate, 8 years to maturity, a $1,000 face value, and a $1,100 market price. The company’s 100,000 shares of preferred stock pay a $3 annual dividend, and sell for $30 per share. The company’s 500,000 shares of common stock sell for $25 per share and have a beta of 1.5. The risk free rate is 4%, and the market return is 12%. Assuming a 21% tax rate, what is the company’s Cost of bonds?

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Answer:

Year   Cashflow    DF@10%      PV           DF@3%     PV

               $                                 $                                  $

  0        (1,100)           1           (1,100)           1             (1,100)

1-8        47.4             5.3349  252.87      7.0197      332.73

 8       1,000             0.4665    465.5      0.7894       789.4

                                  NPV      (381.63)              NPV 22.13                    

Kd = LR     + NPV1/NPV1+NPV2    x (HR – LR)

Kd = 3       + 22.13/22.13 + 381.63   x (10 – 3)

Kd =  3       + 22.13/403.76 x 7

Kd = 3        + 0.38

Kd = 3.38%  

Explanation:

Cost of debt is calculated based on internal rate of return formula. In year 0, we will consider the current market price of the bond as cashflow. In year 1 to 8, we will consider the after-tax coupon as the cashflow. The after-tax coupon is calculated as R(1 - T).  R is 6% x $1,000 = $60 and tax is 21%. Thus, we have $60(1  - 0.21) = $47.4. then we will discount the cashflows for  8 years so as to obtain the internal rate of return. The internal rate of return represents cost of debt.

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