60.1K

Verified Solution

Link Copied!

Two firms, U and L, generate exactly the same cash flows as each other every year. Each will earn $350 in a boom year and $100 in a slumpyear. In each year, there is a 50% chance of a boom and a 50% chance of a slump. U is entirely equity financed, and shareholders receive the entire income of the company as a dividend every year. Its shares are currently valued at $1,000. L has $800 of perpetual risk-free bondspayingan interest rate of 10%, and therefore $80 of L's income is paid out as interestevery year. There are no taxes, and investors can borrow at the risk-free rate.1a)(5 points)What shouldthe value of L's stockbe if there are no arbitrage opportunities?1b)(5 points)Suppose that you invest $40 in U's stock. Is there an alternative involving an investment in Ls securitiesthat would give identical payoffs to those from owning $40 of Us stock in both a boom and a slump? What is the expected annual payoff from such a strategy?1c)(5 points)Now,suppose that you invest $40 in L's stock.Is there an alternative portfolio involving an investment in Uthat would give identical payoffs to those from owning $40 of Ls stock in both a boom and a slump? What is the expected annual payoff from such a strategy?1d)(5 points)Show that the expected return of the alternative portfolio you constructed in part c is the same as the formula for the cost of equity on slide 38of the Unit3Financing Fundamentals slidespredicts that it should be.Note that the equity (E in the formula on the slide) here is the amount of capital that you invest out of pocket, while the debt (D in the formula on the slide) is the amount that you borrow to finance the transaction.Two firms, U and L, generate exactly the same cash flows as each other every year. Each will earn $350 in a boom year and $100 in a slumpyear. In each year, there is a 50% chance of a boom and a 50% chance of a slump. U is entirely equity financed, and shareholders receive the entire income of the company as a dividend every year. Its shares are currently valued at $1,000. L has $800 of perpetual risk-free bonds paying an interest rate of 10%, and therefore $80 of L's income is paid out as interest every year. There are no taxes, and investors can borrow at a risk-free rate.

1a)What should the value of L's stock be if there are no arbitrage opportunities?

1b)Suppose that you invest $40 in U's stock. Is there an alternative involving an investment in Ls securities that would give identical payoffs to those from owning $40 of Us stock in both a boom and a slump? What is the expected annual payoff from such a strategy?

1c)Now, suppose that you invest $40 in L's stock.Is there an alternative portfolio involving an investment in That would give identical payoffs to those from owning $40 of Ls stock in both a boom and a slump? What is the expected annual payoff from such a strategy?

1d)Show that the expected return of the alternative portfolio you constructed in part c is the same as the formula for the cost of equity on slide 38of the Unit3Financing Fundamentals slidespredicts that it should be.Note that the equity (E in the formula on the slide) here is the amount of capital that you invest out of pocket, while the debt (D in the formula on the slide) is the amount that you borrow to finance the transaction.

Answer & Explanation Solved by verified expert

See Answer