Suppose an entrepreneur is deciding whether to take out a business loan from the Bank of...

 

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Suppose an entrepreneur is deciding whether to take out a business loan from the Bank of NY. The rate at which she can borrow is a random variable, which depends on the Bank of America's prime rate announcement. The Bank of America will make the rate announcement after the entrepreneur must decide whether to take out the loan from the Bank of NY Economic analysts have projected that there are five different rates that the Bank of America might announce and have assigned a probability to the likelihood of each rate. Call X the random variable that represents the rate that the Bank of America will announce and P(x) is the associated probability distribution function (PDF). The following is that PDF: 4/10 if x = 0.005 1/10 if x = 0.015 P (x) = 1/10 if x = 0.016 1/10 if x = 0.018 3/10 if x = 0.02 If the entrepreneur decides to borrow from the Bank of NY, she will pay a rate of X + .02. The entrepreneur needs to borrow $500, so if she borrows from the Bank of NY, the cost of borrowing is BCBSK = (X + .02)*500. Alternatively, the entrepreneur can borrow from her personal line of credit at a certain rate of .0372, and in that case the cost of borrowing would be BCLOC = .0372 * 500. Note, that this rate does NOT depend on the Bank of America's announcement. So, in summary, the entrepreneur must decide between borrowing $500 at the certain rate of 0.0372 or borrowing at the uncertain rate of X + .02. Next, suppose that the entrepreneur gains utility from the net wealth from the loan and her utility function is called U Wk , where Wk = 500 - BCk and k e {Bsk, LoC). (Bsk refers to the Bank of NY loan and LoC refers to the line-of-credit loan). 1. (1 point) If she borrows from the line of credit what is her wealth? Write out the formula and calculate the answer. 2. (3 points) If she borrows from the Bank of NY what is her expected wealth? In other words, find E WBsk = E [500 - (X + .02) * 500]. Show your work. Suppose an entrepreneur is deciding whether to take out a business loan from the Bank of NY. The rate at which she can borrow is a random variable, which depends on the Bank of America's prime rate announcement. The Bank of America will make the rate announcement after the entrepreneur must decide whether to take out the loan from the Bank of NY Economic analysts have projected that there are five different rates that the Bank of America might announce and have assigned a probability to the likelihood of each rate. Call X the random variable that represents the rate that the Bank of America will announce and P(x) is the associated probability distribution function (PDF). The following is that PDF: 4/10 if x = 0.005 1/10 if x = 0.015 P (x) = 1/10 if x = 0.016 1/10 if x = 0.018 3/10 if x = 0.02 If the entrepreneur decides to borrow from the Bank of NY, she will pay a rate of X + .02. The entrepreneur needs to borrow $500, so if she borrows from the Bank of NY, the cost of borrowing is BCBSK = (X + .02)*500. Alternatively, the entrepreneur can borrow from her personal line of credit at a certain rate of .0372, and in that case the cost of borrowing would be BCLOC = .0372 * 500. Note, that this rate does NOT depend on the Bank of America's announcement. So, in summary, the entrepreneur must decide between borrowing $500 at the certain rate of 0.0372 or borrowing at the uncertain rate of X + .02. Next, suppose that the entrepreneur gains utility from the net wealth from the loan and her utility function is called U Wk , where Wk = 500 - BCk and k e {Bsk, LoC). (Bsk refers to the Bank of NY loan and LoC refers to the line-of-credit loan). 1. (1 point) If she borrows from the line of credit what is her wealth? Write out the formula and calculate the answer. 2. (3 points) If she borrows from the Bank of NY what is her expected wealth? In other words, find E WBsk = E [500 - (X + .02) * 500]. Show your work.