Question

I-Consider a firm whose only asset is a plot of vacant​ land, and whose only liability is debt of $ 14.5 million due in one year. If left​ vacant, the land will be worth $ 10.5 million in one year.​ Alternatively, the firm can develop the land at an upfront cost of $ 19.5 million. The developed land will be worth $ 34.1 million in one year. Suppose the​ risk-free interest rate is 9.7 % ​, assume all cash flows are​ risk-free, and assume there are no taxes. a. If the firm chooses not to develop the​ land, what is the value of the​ firm's equity​ today? What is the value of the debt​ today? b. What is the NPV of developing the​ land? c. Suppose the firm raises $ 19.5 million from the equity holders to develop the land. If the firm develops the​ land, what is the value of the​ firm's equity​ today? What is the value of the​ firm's debt​ today? d. Given your answer to part ​(c​), would equity holders be willing to provide the $ 19.5 million needed to develop the​ land?

II- If it is managed​ efficiently, Remel,​ Inc., will have assets with a market value of $ 50.1​million,$ 99.2​million, or $ 148.9 million next​ year, with each outcome being equally likely.​ However, managers may engage in wasteful empire​ building,which will reduce the market value by $ 5.2 million in all cases. Managers may also increase the risk of the​ firm, changing the probability of each outcome to 48 %,10 %​,and 42 %​,respectively.

a. What is the expected value of​ Remel's assets if it is run​ efficiently?

Suppose managers will engage in empire building unless that behavior increases the likelihood of bankruptcy. They will choose the risk of the firm to maximize the expected payoff to equity holders.

b. Suppose Remel has debt due in one year as shown below. For each​ case, indicate whether managers will engage in empire​ building, and whether they will increase risk. What is the expected value of​ Remel's assets in each​ case?

i.​ $44.6 ​million, ii. $46.8 ​million, iii. $82.1 ​million, iv. $95.7million.

c. Suppose the tax savings from the​ debt, after including investor​ taxes, is equal to 9 % of the expected payoff of the debt. The proceeds from the​ debt, as well as the value of any tax​ savings, will be paid out to shareholders immediately as a dividend when the debt is issued. What is the expected value of​ Remel's assets, including the tax​ savings, for each debt level in part ​(b​)?

Which debt level in part ​(b​) is optimal for​ Remel?

Answer 1

I- answer

a.

if the land is not being developed

liability due in one year= $14.5 million

value of vacant land in 1 year = $10.5 million

risk free rate = 9.7%

Equity = 0

Debt = value of vacant land in 1 year / (1+ 0.097)^ = 10.5 million / (1+ 0.097)^1 = $9.57 million

b.

If land is developed

value of developed land in 1 year = $34.1 milliom

cost of development = $19.5 million

Present value of land = (value of developed land in 1 year - value of vacant land in 1 year)/ / (1+ 0.097)^1 = (34.1 million – 10.5 million)/ 1.097 = $21.51 million

NPV = Present value of land - cost of development = $21.51 million - $19.5 million

NPV = $2.01 million

c.

firm debt today = 14.5 million / (1+ 0.097)^1 = $13.22 million

firm raise equity = $19.5 million

equity value today= = (value of developed land in 1 year – liability due in one year)/ (1+ 0.097)^1 = (34.1 million - 14.5 million)/ (1+ 0.097)^1 = $17.87 million

d.

NPV= 17.87 million - $19.5 million

= -1.63 million < 0

As the NPV investment is negative, the equity holders will not be willing to accept the deal.