The current price of a non-dividend-paying stock is $30. Over the next six months it is expected to rise to $36 or fall to $26. Assume the risk-free rate is zero. I. What long position in the stock is necessary to hedge a short call option when the strike price is $32? Give the number of shares purchased as a percentage of the number of options that have been sold.
II. What is the value the call option?
III. What long position in the stock is necessary to hedge a long put option when the strike price is $32? Give the number of shares purchased as a percentage of the number of options purchased option.
IV. What is the value of the put option.
V. What is the risk neutral probability of the stock price moving up?

Abakery wants to determine how many trays of doughnuts it should prepare each day. demand is normal with a mean of 5 trays and standard deviation of 1 tray. if the owner wants a service level of at least 95%, how many trays should he prepare (rounded to the nearest whole tray)? assume doughnuts have no salvage value after the day is complete.

Which of the following are considered needs? check all that apply

Lavage rapide is a canadian company that owns and operates a large automatic car wash facility near montreal. the following table provides data concerning the company’s costs: fixed cost per month cost per car washed cleaning supplies $ 0.70 electricity $ 1,400 $ 0.07 maintenance $ 0.15 wages and salaries $ 4,900 $ 0.30 depreciation $ 8,300 rent $ 1,900 administrative expenses $ 1,400 $ 0.03 for example, electricity costs are $1,400 per month plus $0.07 per car washed. the company expects to wash 8,000 cars in august and to collect an average of $6.50 per car washed. the actual operating results for august appear below. lavage rapide income statement for the month ended august 31 actual cars washed 8,100 revenue $ 54,100 expenses: cleaning supplies 6,100 electricity 1,930 maintenance 1,440 wages and salaries 7,660 depreciation 8,300 rent 2,100 administrative expenses 1,540 total expense 29,070 net operating income $ 25,030 required: calculate the company's revenue and spending variances for august.