Question

Masterson, Inc., has 4.1 million shares of common stock outstanding. The current share price is $84, and the book value per share is $11. The company also has two bond issues outstanding. The first bond issue has a face value of $70 million, has a coupon rate of 5.1%, and sells for 98% of par. The second issue has a face value of $50 million, has a coupon rate of 5.60%, and sells for 108% of par. The first issue matures in 20 years, the second in 12 years. The most recent dividend was $3.95 and the dividend growth rate is 5 percent. Assume that the overall cost of debt is the weighted average of that implied by the two outstanding debt issues. Both bonds make semiannual payments. The tax rate is 21 percent. What is the company’s WACC?

Answer 1

Answer:

The answer is "8.37%".

Explanation:

$\text{MV of equity} = \text{equity price} \times \text{number of outstanding shares}$

                     $=84 \times 4100000\\\\=344400000$

$\text{MV of Bond1}=\text{Par value} \times \text{bonds outstanding} \times \text{age of percentage}$

                      $=1000 \times 70000 \times 0.98 \\\\=68600000$

$\text{MV of Bond2}=\text{Par value} \times \text{bonds outstanding} \times \text{age of percentage}$

                      $=1000 \times 50000 \times 1.08 \\\\=54000000$

$\text{MV of firm} = \text{MV of Equity} + \text{MV of Bond1}+ \text{MV of Bond 2}$

                  $=344400000+68600000+54000000\\\\=467000000$

$\text{Weight of equity W(E)} = \frac{\text{MV of Equity}}{\text{MV of firm}}$

                                     $= \frac{344400000}{467000000}\\\\=0.7375$

$\text{Weight of debt W(D)}= \frac{\text{MV of Bond}}{\text{MV of firm}}$

                                  $= \frac{122600000}{467000000}\\\\=0.2625$

Equity charges

By DDM.  

$\text{Price = new dividend} \times \frac{(1 + \text{rate of growth})}{( \text{Equity expense-rate of growth)}}$

$84 = 3.95 \times \frac{(1+0.05)}{(\text{Cost of equity}- 0.05)}\\\\84 = 3.95 \times \frac{(1.05)}{(\text{Cost of equity} - 0.05)}\\\\84 = \frac{4.1475}{ (\text{Cost of equity} - 0.05)}\\\\\text{Cost of equity} -0.05 = \frac{4.1475}{84}\\\\\text{Cost of equity} -0.05 = 0.049375\\\\\text{Cost of equity} = 0.049375 + 0.05\\\\\text{Cost of equity} = 0.099375 \\\\\text{Cost of equity} \% = 9.9375 \% \ \ \ or \ \ \ 9.94 \%$

Debt expenses  

Bond1

$K = N \times 2$

$Bond \ Price = \sum [ \frac{\text{(Semi Annual Coupon)}}{(1 + \frac{YTM}{2})^k}] + \frac{Par\ value}{(1 + \frac{YTM}{2})^{N \times 2}}$

$k=1\\\\K =20 \times 2\\\\980 = \sum [ \frac {(5.1 \times \frac{1000}{200})}{(1 + \frac{YTM}{200})^k}] + \frac{1000}{(1 + \frac{YTM}{200})}^{20 \times 2}\\\\k=1\\\\\ YTM1 = 5.2628923903\\\\Bond2$

$K = N \times 2$

$Bond \ Price = \sum [ \frac{\text{(Semi Annual Coupon)}}{(1 + \frac{YTM}{2})^k}] + \frac{Par\ value}{(1 + \frac{YTM}{2})^{N \times 2}}$

$k=1\\\\K =12 \times 2$

$1080 =\sum [\frac{(5.6 \times \frac{1000}{200})}{(1 + \frac{YTM}{200})^k}] +\frac{1000}{(1 +\frac{YTM}{200})^{12 \times 2}} \\\\k=1\\\\YTM2 = 4.72$

$\text{Company debt costs} = YTM1 times \frac{(MV \ bond1)}{(MV \ bond1+MV \ bond2)}+YTM2 \times \frac{(MV \ bond2)}{(MV \ bond2)}$

The cost of the debt for the company:

$= 5.2628923903 \times \frac{(68600000)}{(68600000+54000000)}+4.72 \times \frac{(68600000)}{(68600000+54000000)}$

Business debt cost=$5.02 \%$

after taxation cost of debt:  

$= \text{cost of debt} \times (1- tax \ rate)\\\\= 5.02 \times (1-0.21)\\\\= 3.9658$

$WACC= \text{after debt charges} \times W(D)+equity cost \times W(E)$

            $=3.97 \times 0.2625+9.94 \times 0.7375 \\\\ =8.37 \%$