Question

1. Aerospace Co. is considering increasing the amount of debt in its capital structure. The treasurer is worried about the ramifications of that action on the firm’s cost of capital. The following information may be relevant to your analysis.

- The company’s capital structure is as follows (figures are in book values): Short-Term Bank Debt	$ 7.2 million
Long-Term Bond	30.0
Preferred Stock	5.6
Common Equity (8.60 million shares)	136.0
Total	$178.8 million

The bank debt is currently costing 9.2%.

- The bonds have a fixed 11% annual coupon and mature in fourteen years. The price of the bonds are $109 (based on $100 par value).

- The preferred stock has 100 par value, pays an annual dividend of 6% of par, and is selling for $63¼ per share.

- The common stock is selling for $19 per share.

- The company’s marginal tax rate is 34%.

- The beta of the firm’s stock, given its current capital structure, is 0.9.

- Treasury bonds are currently yielding 7.1%.

- The market has historically earned 8.3% more than Treasury bonds.

If the company sells $10 million in bonds (at the prevailing market rate), and uses the proceeds to repurchase common stock, what will be Aerospace Co.'s weighted-average cost of capital?

i) Use the Beta (Unlevered) = E/V x Beta (Levered) relationship.

ii) Treat preferred stock as debt when calculating the weight of equity (E/V) for un-levering and re-levering the Beta.

Answer 1

Market value of Short term bonds = $7.2 million at cost of 9.2%

Market Value of Long term bonds = $109/$100* $30 million = $32.7 million

Yield r is given as

109 = 11/r * (1-1/(1+r)^14) +100/(1+r)^14

By hit and trial r =0.0979 or 9.79% which is the cost of bonds

Market Value of Preferred Stock = $63.25/$100* $5.6 million = $3.542 million

Cost of preferred stock = $6/$63.25 =9.486%

Market Value of Common Stock = $19/share*8.6 million shares = $163.40 million

Cost of Common stock = 7.1%+8.3%*0.9= 14.57% (from CAPM)

Unlevered Beta of common stock = E/V* levered beta = 163.40/(7.2+32.7+3.542+163.40)*0.9 = 0.7109775

After new bonds issue and repurchase

Value of New firm = Value of earlier firm + Tax benefit =(7.2+32.7+3.542+163.40)+0.34*10 = $210.242 million

Market Value of Long term bonds = $32.7 million+$10 million = $42.7 million

Market Value of Common Stock = $210.242 million -$42.7 million -$7.2 million -$3.542 million = $156.80 million

So, Levered beta = V/E*unlevered beta = 210.242/156.80*0.7109775 =0.9533

New cost of Common stock = 7.1%+8.3%*0.9533= 15.0124% (from CAPM)

So,

WACC

=7.2/210.242*9.2%*(1-0.34)+42.7/210.242*9.792%*(1-0.34)+3.542/210.242*9.486%+156.80/210.242*15.0124%

=12.8767% or 12.88%