Macbeth now decides to issue $5,000 of debt and to use the proceeds to repurchas

Question

Macbeth now decides to issue $5,000 of debt and to use the proceeds to repurchase stock. Suppose that Ms. Macbeth's investment bankers have informed her that since the new issue of debt is risky, debtholders will demand a return of 12.5%, which is 2.5% above the risk-free interest rate.

Recompute the return of assets (rA) and return on equity (rE)? (Do not round intermediate calculations. Round your answers to 3 decimal places.)

Suppose that the beta of the unlevered stock was .6. New capital structure is 50% debt financed. What will ?A, ?E, and ?D be after the change to the capital structure? (Round your answers to 1 decimal place.)

Explanation / Answer

After repurchase of stock, the capital structure of the company:

Equity = $5000

12.5% debt = $ 5000

Total capital employed = 5000 + 5000 = $10000

Operating income       = $1500

Less: Interest           = $ 625

Net operating income =   $875 (as there is no information, it has been assumed that there is no tax)

Return on Assets

= Operating Income / capital employed

= 1500 / 10000 = 0.15 = 15%

Return on Equity

= Net Operating Income / Equity

= 875 / 5000

= 0.175 = 17.5%

Part B

Making the assumptions that debt beta is zero,

The asset beta of the levered firm is given by the following equation:

Beta Equity = [ 1 + (1-T) (debt/equity) ] x (beta asset)

therefore,

Asset beta of the levered firm

= 6 / [ 1 + (1-T) (debt/equity) ]

= 6/ [ 1 + (1-0) 0.50 ]

= 6 / 1.50 = 4

Equity Beta is calculated using the CAPM formula:

Return on equity of the levered firm = 17.5%

Risk premium = 2.5%

Risk free rate = 12.5 - 2.5 = 10%

Applying CAPM,

17.5 % = 10% + Equity beta x risk premium

=> equity beta = 7.5% / 2.5% = 3

Calculation of debt beta:

Asset beta = [D/(D + E)] x debt beta + [E/(D + E)] x Equity beta

=> 4 = 0.50 x debt beta + 0.50 x 3

=> debt beta = 2.50 / 0.50 = 5

So for the levered firm,

Asset beta = 4

Equity beta = 3

debt beta = 5

=

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