Charli D'Amelio is an American influencer. She was a competitive dancer before launching her social media career in TikTok in $2019.$ Since then, she has become one of the most$-$followed social media personalities on the platform. Charli and her sister Dixie have started a private company $($D$$Amelio Family Enterprises$)$ that invests in venture capital, and in digital marketing firms, among other investments.

One of the firms they are exploring is called WebMediaAudience $4\mathrm{.}0($WMA$4\mathrm{.}0),$ a digital marketing firm which has the following capital structure: $$12$ million of debt $($with a debt beta of zero$)$ and $$24$ million of equity $($with an equity beta of $1\mathrm{.}5).$ The firm currently has no excess cash. The debt and equity values are both market values. In this question, assume that all of the assumptions of the Modigliani$-$Miller theorems hold $($no corporate or personal income taxes, no costs of financial distress, etc.$).$ Also, assume that the relevant risk$-$free rate is $3\%($effective annual rate$),$ that the expected return on the market portfolio is $8\%,$ and that the assumptions behind the CAPM hold.

Imagine that the D'Amelio sisters invest in the firm, but after they do so$,$ WMA$4\mathrm{.}0$ decides to implement a recapitalization strategy. In particular, the firms$$ management decides to issue $$1\mathrm{.}71$ million in equity $($common stock$),$ and use the proceeds to repurchase $$1\mathrm{.}71$M of the debt outstanding at the current market value, and invest remaining balances in risk$-$free financial instruments. Based on this financial transaction, what is: $($i$)$ the new asset beta of WMA$4\mathrm{.}0($i$.$e$.$ the beta of the firms$$ assets after the recapitalization transaction$),$ and $($ii$)$ the new expected return on equity after the firm implements the recapitalization plan above?

Charli D'Amelio is an American influencer. She was a competitive dancer before launching her social media career in TikTok in $2019.$ Since then, she has become one of the most$-$followed social media personalities on the platform. Charli and her sister Dixie have started a private company $($D$$Amelio Family Enterprises$)$ that invests in venture capital, and in digital marketing firms, among other investments.

One of the firms they are exploring is called WebMediaAudience $4\mathrm{.}0($WMA$4\mathrm{.}0),$ a digital marketing firm which has the following capital structure: $$12$ million of debt $($with a debt beta of zero$)$ and $$24$ million of equity $($with an equity beta of $1\mathrm{.}5).$ The firm currently has no excess cash. The debt and equity values are both market values. In this question, assume that all of the assumptions of the Modigliani$-$Miller theorems hold $($no corporate or personal income taxes, no costs of financial distress, etc.$).$ Also, assume that the relevant risk$-$free rate is $3\%($effective annual rate$),$ that the expected return on the market portfolio is $8\%,$ and that the assumptions behind the CAPM hold.

Imagine that the D'Amelio sisters invest in the firm, but after they do so$,$ WMA$4\mathrm{.}0$ decides to implement a recapitalization strategy. In particular, the firms$$ management decides to issue $$1\mathrm{.}71$ million in equity $($common stock$),$ and use the proceeds to repurchase $$1\mathrm{.}71$M of the debt outstanding at the current market value, and invest remaining balances in risk$-$free financial instruments. Based on this financial transaction, what is: $($i$)$ the new asset beta of WMA$4\mathrm{.}0($i$.$e$.$ the beta of the firms$$ assets after the recapitalization transaction$),$ and $($ii$)$ the new expected return on equity after the firm implements the recapitalization plan above?

Asset beta$=0\mathrm{.}86$ and expected return on equity$=10\%$

Asset beta$=0\mathrm{.}9$ and expected return on equity$=3\%$

Asset beta$=0\mathrm{.}9$ and expected return on equity$=5\%$

Asset beta$=1\mathrm{.}5$ and expected return on equity$=3\%$

Asset beta$=0\mathrm{.}86$ and expected return on equity$=3\%$

Asset beta$=0\mathrm{.}9$ and expected return on equity$=11\%$

Asset beta$=1\mathrm{.}0$ and expected return on equity$=3\%$

Asset beta$=0\mathrm{.}86$ and expected return on equity$=8\%$

Asset beta$=1\mathrm{.}0$ and expected return on equity$=8\%$

Asset beta$=1\mathrm{.}5$ and expected return on equity$=5\%$

Asset beta$=1\mathrm{.}5$ and expected return on equity$=8\%$

Asset beta$=0\mathrm{.}9$ and expected return on equity$=8\%$

Asset beta$=1\mathrm{.}5$ and expected return on equity$=10\mathrm{.}5\%$

Asset beta$=1\mathrm{.}0$ and expected return on equity$=5\%$

Asset beta$=0\mathrm{.}86$ and expected return on equity$=5\%$

Asset beta$=1\mathrm{.}0$ and expected return on equity$=10\%$Charli D'Amelio is an American influencer. She was a competitive dancer before launching her social media career in TikTok in $2019.$ Since then, she has become one of the most$-$followed social media personalities on the platform. Charli and her sister Dixie have started a private company $($D$$Amelio Family Enterprises$)$ that invests in venture capital, and in digital marketing firms, among other investments.

One of the firms they are exploring is called WebMediaAudience $4\mathrm{.}0($WMA$4\mathrm{.}0),$ a digital marketing firm which has the following capital structure: $$12$ million of debt $($with a debt beta of zero$)$ and $$24$ million of equity $($with an equity beta of $1\mathrm{.}5).$ The firm currently