Capital Structure Question Solution

To relever the βe, we use the formula, βe = βu +(D/E)*(βu-βd). And the “Target D/E” was found by taking “Target D/V” divided by “1-Target D/V”. So we get the new βe, 1.3576. Then to get cost of equity, we use the CAPM formula, Re=Rf+β(EMRP), 11.7679%. Since we have get the cost of equity and cost of debt, we can determined the WACC, which is equal to Equity/Value*Cost of Equity+Debt/Value*Cost of Debt*(1-tax rate). In the end ,we arrived at 8.48%.

E[Rp ] = (1 − wTb )RF,b + wTb E[RTb ] = (1 − 1.1735) × 0.02 + 1.1735 × 0.04386 = 4.80%.

SQRT(2 * F * T / H) = (2 * 80 * 200,000 / 1.00)0.5

Taking the CAPM equation, we were able to figure out eh cost of equity and in its credit range

Then we will convert the scientific notation to 0.00025 and find it’s coefficient which is 4000.

Although the increased leverage decreases the amount of earnings available to stock holders from 496.9 million to 451.7 million for a total of 45.2 million dollars, it has a positive affect for the company’s tax structure. It actually reduces the company’s tax liability by 83 million dollars! Without the debt they have to pay 952.5 million dollars in taxes. However after an increase of 30% leverage, the new tax liability is 869.5 million dollars.

Given that we now have the values of Debt Beta (Assumed to be 0.25), Asset Beta (0.80), Equity Value, Debt Value and Asset Value, the value of equity beta has been calculated to be 0.98 based on the above equation.

By using the company return and the Value Weighted Returns of the Market, we derived the companies’ levered equity betas and then unlevered them.

It seems then that companies should fully leverage the company or a least come close to doing so but there is a probability that the company enters financial distress as its leverage (D/E) increases. Financial distress can be very costly for companies, and the cost for this scenario is shown in the current market value of the levered firm's securities. Investors factor the potential for future distress into their assessment of the present value (this is where PV of distress costs is subtracted from un-levered company value and the PV of the tax-shield.) The value for the costs

The estimated beta of firm is about 1.27. This figure is retrieved from a reliable website-www.finance.yahoo.com.

Weight of Equity = 71%; Equity Cost of Capital = 12%; Weight of Debt = 29%; Debt Cost of Capital = 4.55%

Ast = 0.93 * b * d/100 = 0.93 * 300 * 607 /100 = 1696.99 mm2

From this set of problems, we can see that leverage is good for the firm. Leverage has increased the value of the firm as a whole and increased the price per share. Although the cost of debt increases the firm's risk because it increases the probability of default and bankruptcy, therefore shareholders will require higher rates of return on the equity they provide, debt also provides tax savings. And we can see that in table 4, where we calculated the total value of the firm as the pure business cash flows plus the tax savings. Another reason why debt increases firm value is the fact that it reduces WACC, because the cost of debt is generally lower than the cost of equity. Another option that shareholders can do is using homemade leverage. Shareholders should pay a premium for the shares of a levered firm when the addition of debt increases value.

As negative aspects of debt, e.g. personal tax loss and bankruptcy costs however do exist in reality, Miller (1977) elaborates that leverage will either have no or a negative effect on the firm’s value, hence untaxed firms should favor equity.

Let us assume that a firm has an EBIT level of $50,000, cost of debt 10%, the total value of debt $200,000 and the WACC is 12.5%. Let us find out the total value of the firm and the cost of equity capital (the equity capitalization rate).