Question

Microsoft has an equity value of $250B, but has only $10B in debt. Management decides they’d like to increase the D/(D+E) ratio to 40% and use the proceeds to repurchase shares of equity, i.e. a leveraged recapitalization.

a) Before the recapitalization, the debt is considered risk-free and the equity has a beta of 1.13; afterwards, the debt beta becomes 0.3. How much debt does Microsoft issue? By how much has this restructuring changed the riskiness of equity in Microsoft, i.e. what is
the equity beta after the recapitalization?

b. If the risk-free rate is 3% and the expected market return is 9%, what are the expected
returns to equity holders before and after the recapitalization?

Please answer all parts of this question.

Answer 1

a) Value of Firm = Debt + Equity = 10B + 250B = $260B

We know that According to Modigliani and Miller proposition I without taxes, Value of company is independent are of its capital structure, So after issuing of new debt, value of firm will not change.

Debt after recapitalization = 40% of value of firm = 40% of 260 = 104

Debt to be issued = Debt are recapitalization - Initial Debt = 104 - 10 = $94B

Debt issued by Microsoft = $94B

Now We know According to CAPM

Return of a security = Risk free rate + Beta x Market risk premium

Return of debt = Risk free rate + Debt Beta x market risk premium

Since before recapitalization debt is risk free, Return on debt = Risk free rate , so we get

Risk free rate = Risk free rate + Debt Beta x market risk premium

Debt Beta x market risk premium = 0

Debt Beta = 0 / Marekt risk premium

Debt beta = 0                              (as market risk premium is not equal to 0)

Hence Before recapitalization debt beta = 0

Equity = E = $250 B and Debt = D = $10B

So Asset Beta = [D/(D+E)][Debt Beta] + [E/(D+E)][Equity Beta] = [10/(10 + 250)][0] + [250/(10+250)][1.13] = (10/260)(0) + (250/260)(1.13) = 0 + 1.0865 = 1.0865

After Recapitalization Debt Beta = 0.3, D/(D+E) = 40% , so we get E/(D+E) = 1- D/(D+E) = 60%,

Now we have D/E = [ D/(D+E)] / [E/(D+E)] = 40% / 60% = 2/3

We know that Equity Beta = Beta Asset + (Beta Asset - Beta Debt)(D/E) = 1.0865 + (1.0865 - 0.3)(2/3) = 1.0865 + (0.7865)(2/3) = 1.0865 + 0.5243 = 1.6108

Hence Equity Beta after recapitalization = 1.6108

b) According to CAPM

Expected return to equity holders before recapitalization = Risk free rate + Equity beta before recapitalization(Market return - Risk free rate) = 3% + 1.13(9% - 3%) = 3% + 1.13 x 6% = 3% + 6.78% = 9.78%

Expected return to equity holders before recapitalization = 9.78%

Expected return to equity holders after recapitalization = Risk free rate + Equity beta after recapitalization(Market return - Risk free rate) = 3% + 1.13(9% - 3%) = 3% + 1.6108 x 6% = 3% + 9.6648% = 12.6648% = 12.66% (rounded to two decimal places)

Expected return to equity holders after recapitalization = 12.66%