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- A project does not necessarily have a unique IRR. (Refer to the previous problem for more information on IRR.) Show that a project with the following cash flows has two IRRs: year 1, 20; year 2, 82; year 3, 60; year 4, 2. (Note: It can be shown that if the cash flow of a project changes sign only once, the project is guaranteed to have a unique IRR.)In the financial world, there are many types of complex instruments called derivatives that derive their value from the value of an underlying asset. Consider the following simple derivative. A stocks current price is 80 per share. You purchase a derivative whose value to you becomes known a month from now. Specifically, let P be the price of the stock in a month. If P is between 75 and 85, the derivative is worth nothing to you. If P is less than 75, the derivative results in a loss of 100(75-P) dollars to you. (The factor of 100 is because many derivatives involve 100 shares.) If P is greater than 85, the derivative results in a gain of 100(P-85) dollars to you. Assume that the distribution of the change in the stock price from now to a month from now is normally distributed with mean 1 and standard deviation 8. Let EMV be the expected gain/loss from this derivative. It is a weighted average of all the possible losses and gains, weighted by their likelihoods. (Of course, any loss should be expressed as a negative number. For example, a loss of 1500 should be expressed as -1500.) Unfortunately, this is a difficult probability calculation, but EMV can be estimated by an @RISK simulation. Perform this simulation with at least 1000 iterations. What is your best estimate of EMV?Bruin Properties is in escrow to buy a 175,000 square foot shopping center in Camarillo, California for $35,000,000. Bruin Properties can borrow $24,000,000 fixed rate fully amortizing over 30 years at a 6.0% annual interest rate with equal monthly payments of principal and interest or it can borrow $28,000,000 fixed rate fully amortizing over 30 years at a 7.0% annual interest rate with equal monthly payments of principal and interest. What is the incremental annual borrowing cost for the additional $4,000,000 loan amount if each loan would be outstanding for the full 30 year term? a.13.0% b.12.4% c.11.5% d. 7.0%
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