Question

The total book value of the common stock of Company XYZ is $50 million and the total book value of its debt is $50 million. The debt of the company is trading at 100% of book value. The company has 5 million shares outstanding and they are selling for $14 per share. The beta of the stock is estimated to be 1,4, the expected market risk premium is 8% and the risk free rate is 4%. The tax rate is 35%. Assume that Company XYZ debt is risk-free.

a)      What is the required rate of return of Company XYZ stock?

b)      What is the weighted average cost of capital (WACC) of Company XYZ?

c)      What is the asset beta of Company XYZ?

d)      Discuss the Modigliani and Miller (MM) capital structure theory (without taxes). What happens to the expected return on equity when the debt-equity ratio in the company goes up? (you might want to draw a graph to illustrate your point)

Answer 1

Solution a

As per CAPM,

Required Return = Risk free rate + Expected Market Risk premium * Beta

                         = 4 + 8 * 1.4

                         = 15.20 % Answer

Solution b

Formula = Weight of debt * Cost of debt + Weight of Preferred stock * Cost of Preferred stock + Weight of Common stock * Cost of common stock

Particulars	Market Value	Weight	Cost	Calculation	WACC
Debt	50 Mn	50/120 = 41.67 %	4 * ( 1 - 0.35 ) = 2.6%	2.6 * 41.47%	1.08
Equity	5 Mn * 14 = 70 Mn	70/120 = 58.33 %	15.20%	15.20 * 58.33%	9.87
	120 Mn				9.95%

c)

> Formula

> Calculation

- Debt Equity ratio = Debt / Equity

                              = 50 / 70

                              = 0.7143

- Asset Beta = 1.4 / [ 1 + 0.7143 (1 - 0.35) ]

                              = 0.9561 Answer

d) MM Approach

• Modigliani and Miller advocate capital structure irrelevancy theory, which suggests that the valuation of a firm is irrelevant to the capital structure of a company. Whether a firm is highly leveraged or has a lower debt component in the financing mix has no bearing on the value of a firm.
• The Modigliani and Miller Approach further states that the market value of a firm is affected by its operating income, apart from the risk involved in the investment. The theory stated that the value of the firm is not dependent on the choice of capital structure or financing decisions of the firm.
• The second proposition of the M&M Theorem states that the company’s cost of equity is directly proportional to the company’s leverage level. An increase in leverage level induces higher default probability to a company. Therefore, investors tend to demand a higher cost of equity (return) to be compensated for the additional risk.

• Cost of levered equity = Cost of unlevered equity + Debt-to-equity ratio * ( Cost of unlevered equity - Cost of debt )

Hope you understand the solution.

Stay Safe!