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12-4 Valuing an American option: J & B Drilling Company has recently acquired a lease to drill for Natural gas in the remote region of southwest...

12-4 Valuing an American option: J & B Drilling Company has recently acquired a lease to drill for Natural gas in the remote region of southwest Louisiana and southeast Texas. The area has long been known for oil and gas production, and the company is optimistic about the prospects of the lease. The lease contract has a three-year life and allows J &B to begin exploration at any time up until the end of the three-year term.
J & B's engineers have estimated the volume of the natural gas they hope to extract from the leasehold and have placed a value of $25 million on it, on the condition that explorations begin immediately. The cost of developing the property is estimated to be $23 million (regardless of when the property is developed over the next three years). based on the historical volatilities in the returns of the similar investments and other relevant information, j & B's analysts have estimated that the value of the investment opportunity will evolve over the next three years.
The risk-free rate of interest is currently 5%, and the risk-natural probability of an uptick in the value of the investment is estimated to be 46.26%.

a. Evaluate the value of the leasehold as an American call option. What is the lease worth Today?

b. As one of J & B's analysts, what is your recommendation as to when the company should begin drilling?

19-20 After completing its capital spending for the year, Carlson Manufacturing has $1,000 extra cash. Carlson’s managers must choose between investing the cash in Treasury bonds that yield 8%, or paying the cash out to investors who would buy the bonds themselves.

a. If the corporate tax rate is 35%, what tax rate on ordinary income would make the investors indifferent between receive the dividend or letting Carlson invest to money?

b. If the answer to part (a) reasonable, Why and why not?

c. Suppose that the only investment choice is a stock that yields 12%. What personal tax rate will make stockholders indifferent of the outcome of Carlson’s dividend decision?

d. Is this a compelling argument for a low dividend payout
policy? Why and Why not?
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