Question

a. Company x has 25,000 bonds outstanding that trade at par
value (each bond has a par value of $1,000). Companies with similar characteristics have
their bonds trading at a yield of 5.5%. The company also has 2 million shares of common
stock outstanding. The stock has a beta of 1.2 and sells for $50 a share. The risk free rate
is 2% and the market risk premium is 5%. The company’s tax rate is 30%. What is the
company’s weighted average cost of capital?
b. Company x now wishes to change its capital structure
to have a weighted average cost of capital of 6.75%. What debt ratio (debt to total firm
value) is needed for the firm to achieve its targeted weighted average cost of capital?
c. Suggest one strategy the firm could use to implement this preferred change to the capital
structure. Show your calculations for the steps needed to implement this change to match
the preferred WACC in (b).

Answer 1

a. Weigghted Average Cost of Capital:

Weighted Average Cost of Capital = 7.17%

Note:

1. Yield given is assumed to be before tax. Hence for WACC computation, after tax cost of yield is considered

2. Cost of Common Stock is determined using the CAPM formula:

Return on Equity = Risk Free Rate + (Beta *(Market Rate - Risk Free Rate)) where (Market Rate - Risk Free Rate) is the Expected Market Premium

3. Weighted Average Cost of Capital = (Cost of bond (after tax) * Propotion of Bond to Total Capital) + (Cost of common stock * Propotion of Common Stock to Total Capital)

Workings:

b. Required WACC = 6.75%

Weighted Average Cost of Capital = (Cost of bond (after tax) * Propotion of Bond to Total Capital) + (Cost of common stock * Propotion of Common Stock to Total Capital)

Assume Propotion of Bond to Total Capital = X

Thus,Propotion of Common Stock to Total Capital = 1-X

Cost of bond (after tax) = 3.85%

Cost of Common Stock = 8%

Replacing the values in the equation,

6.75% = (X*3.85%)+((1-X)*8%)

6.75% = 0.0385X+8%-0.08X

0.08X-0.0385X = 8%-6.75%

0.0415X=1.25%

X = 1.25%/0.0415X = 30.12%

Thus, Propotion of Bond to Total Capital = 30.12% or 30% and

Propotion of Common Stock to Total Capital = (1-30.12%) = 69.88% or 70%

Thus, Debt ratio (debt to total firm value) = 30.12% or 30%

c.

Total Value of firm under current capital structure= Value of debt + Value of Common stock = $25,000,000 + $100,000,000 = $125,000,000

Under revised capital structure of Debt ratio being 30.12%, value of debt needs to be $125,000,000 * 30.12% = $37,650,000.

Increase in Debt required = $37,650,000 - $25,000,000 = $12,650,000

To achieve this revised capital structure, the firm can adopt the strategy of Leveraged Buyback. Under Leveraged Buyback strategy, the firm will buy-back its common stock by raising debt.

To prove the above, assuming the company raises $12,650,000 at after tax yeld of 3.85% and buys-back $12,650,000 of common stock with the funds at the current selling price.

Revised Debt Value = $25,000,000 + $12,650,000 = $37,650,000

Revised Common Stock value = $100,000,000 - $12,650,000 = $87,350,000

Debt Ratio = $37,650,000 + ($37,650,000+$87,350,000) = 30.12%

Common Stock Ratio = $87,350,000 + ($37,650,000+$87,350,000) = 69.88%

Weighted Average Cost of Capital = (Cost of bond (after tax) * Propotion of Bond to Total Capital) + (Cost of common stock * Propotion of Common Stock to Total Capital)

= (3.85%*30.12%)+(8%*69.88%)

= 1.160%+5.590% = 6.750% (target WACC)