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Consider two firms, With and Without, that have identical assets that generate identical cash flows. Without is an all-equity firm, with 1 million shares outstanding that trade for a price of $24 per share. With has 2 million shares outstanding and $12 million in debt at an interest rate of 5%.Assume that MM's perfect capital market conditions are met and that you can borrow and lend at the same 5% rate as With. You have $5000 of your own money to invest and you plan on buying With stock. Using homemade (un)leverage, how much do you need to invest at the risk-free rate so that the payoff of your account will be the same as a $5000 investment in Without stock?Group of answer choices$4000$5000$2500$0

Question

Consider two firms, With and Without, that have identical assets that generate identical cash flows. Without is an all-equity firm, with 1 million shares outstanding that trade for a price of 24pershare.Withhas2millionsharesoutstandingand24 per share. With has 2 million shares outstanding and 12 million in debt at an interest rate of 5%.Assume that MM's perfect capital market conditions are met and that you can borrow and lend at the same 5% rate as With. You have 5000ofyourownmoneytoinvestandyouplanonbuyingWithstock.Usinghomemade(un)leverage,howmuchdoyouneedtoinvestattherisk−freeratesothatthepayoffofyouraccountwillbethesameasa5000 of your own money to invest and you plan on buying With stock. Using homemade (un)leverage, how much do you need to invest at the risk-free rate so that the payoff of your account will be the same as a 5000 investment in Without stock?Group of answer choices400040005000250025000

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Solution

To calculate the amount you need to invest at the risk-free rate, you first need to understand the concept of homemade leverage. This is a strategy where an investor replicates the effects of corporate leverage by borrowing money and using it to invest in a company's stock.

In this case, you want to replicate the payoff of investing in Without, an all-equity firm, by investing in With, a leveraged firm, and in a risk-free asset.

First, calculate the total value of each firm. Without has 1 million shares at 24pershare,soitstotalvalueis24 per share, so its total value is 24 million. With has 2 million shares and 12millionindebt,soitstotalvalueisalso12 million in debt, so its total value is also 24 million.

Next, calculate the proportion of With's value that is financed by equity. This is 12million(thevalueoftheequity,whichisthetotalvalueminusthedebt)dividedby12 million (the value of the equity, which is the total value minus the debt) divided by 24 million (the total value), or 0.5.

Now, to replicate the payoff of a 5000investmentinWithout,youshouldinvest0.5ofyourmoney,or5000 investment in Without, you should invest 0.5 of your money, or 2500, in With's stock. The rest of your money, $2500, should be invested at the risk-free rate.

So, the answer is $2500.

This problem has been solved

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All of the following are arguments against using leverage, except: a. Lenders make you pay for inflation in the interest rate they charge b. You bring on the possibility of default and loss of your entire investment c. You lose flexibility or “financial slack" d. You increase the volatility of your total returns e. Equity may shrink if the market crashes Clear my choice

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