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I have a question. A company is worth 1 million dollars, in terms of present value of revenues, discounted at rate R. Can I borrow 1 million dollars from a bank and buy the company? If the bank charges me R, I am indifferent?

Or, can I issue a bond for 1 million, with coupon R? Am I indifferent too?

Do these things happen? Do businesses ask for credit or issue bonds in order to buy companies?

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    $\begingroup$ This question has a few questions in it (“am I indifferent?”, “does this happen?”) which does not match the format of this website. Could you edit out the “Am I indifferent?” queries, as they do not fit the question title; you can make them a different question. (As a quick answer, yes this happens - look up “leveraged buyout.”) $\endgroup$ – Brian Romanchuk Dec 6 '17 at 21:39
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    $\begingroup$ It's called "leveraged buyout". $\endgroup$ – Alecos Papadopoulos Dec 6 '17 at 22:33
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I have a question. A company is worth 1 million dollars, in terms of present value of revenues, discounted at rate R. Can I borrow 1 million dollars from a bank and buy the company?

Yes. It is done all of the time.

Can I borrow 1 million dollars from a bank and buy the company? If the bank charges me R, I am indifferent?

No, you are not indifferent unless there is a mandatory repayment schedule. This is a riskless contract to you otherwise. If there is no better rate of return for you, then you begin to repay the loan, but if a new opportunity develops at $R'>R$ then you stop repaying the loan. If there is no mandatory repayment schedule then you would always opt for the loan as you can require the bank to keep a bad opportunity and you can keep any good opportunity.

In periods where $R$ is the superior opportunity, you repay the loan until it is fully repaid. In periods where $R'$ dominates the original opportunity, you send the cash flow into the new opportunity. The loan is acting as if it were a free option contract.

There is an implicit cost to not taking the loan.

None of this necessarily holds if there is a repayment schedule or if there is a loan rate of return which does not equal $R$.

As to bonds, again it is the terms and conditions that matter. In the real world bonds are costly to issue. It appears here that bonds and bank loans are identical so you would be indifferent to using a bond or a loan, but not indifferent to buying the firm on credit since the bank or bondholders will accept taking all of the risk for the return $R$.

If the return $R$ were risky and there were cash repayment obligations, then it is difficult to determine if you would be indifferent or prefer to borrow because the option requires exercise making it a forward contract and not an options contract unless there is also the capacity to prepay. You would be strictly indifferent if and only if there existed a mandatory principal repayment scheme. Otherwise, assuming that at the moment, no opportunity $R'>R$ existed, then you would take the loan and buy the firm.

This entirely depends upon the bank accepting the profit of the firm as the interest payment. This would never happen in the real world.

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