So i have this question:

Homemade leverage Companies A and B differ only in their capital structure. A is financed 30% debt and 70% equity; B is financed 10% debt and 90% equity. The debt of both companies is risk-free. Rosencrantz owns 1% of the common stock of A. What other investment package would produce identical cash flows for Rosencrantz?

This is the answer on the answer sheet:

The two firms ha ve equal value; let V represent the total value of the firm. Rosencrantz could buy 1% of Company B’s equity and borrow an amount equal to:

0.01 x (DA-DB)=0.002V

This investment requires a net cash outlay of 0.007V and provides a net cash return of

(0.01 x profits)-(0.03 x rf x V) where rf is the risk free rate of interest on debt. Thus , the two investments are identical.

I am having some problems understanding this answer. First of all , under what point would Rosencrantz buy 1% of company B's equity ? Couldn't he start with a different number?

Secondly, why would he borrow an amount equal to 0.01 x (DA-DB)=0.02. Why is DB being subtracted from DA?

Thirdly, why does this investment require a cash outlay of 0.007v and under what basis is the net cash return (0.01 x profits)-(0.03 x rf x V).

I have some learning disabilities and this really does not make any sense to me. Could somebody please explain how to answer this question in a clearer/simpler way or explain the steps the answer sheet in a clearer manner so that all these number i am having issues with make sense?

Thanks! I really appreciate it.


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