A few years ago, Michael purchased a home for $394,000. Today, the home is worth $520,000. His remaining mortgage balance is $166,000. Assuming Michael can borrow up to 80 percent of the market value of his home, what is the maximum amount he can borrow?
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A few years ago, Michael purchased a home for $394,000. Today, the home is worth $520,000. His remaining mortgage balance is $166,000. Assuming Michael can borrow up to 80 percent of the market value of his home, what is the maximum amount he can borrow?
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- 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?Suppose you begin year 1 with 5000. At the beginning of each year, you put half of your money under a mattress and invest the other half in Whitewater stock. During each year, there is a 40% chance that the Whitewater stock will double, and there is a 60% chance that you will lose half of your investment. To illustrate, if the stock doubles during the first year, you will have 3750 under the mattress and 3750 invested in Whitewater during year 2. You want to estimate your annual return over a 30-year period. If you end with F dollars, your annual return is (F/5000)1/30 1. For example, if you end with 100,000, your annual return is 201/30 1 = 0.105, or 10.5%. Run 1000 replications of an appropriate simulation. Based on the results, you can be 95% certain that your annual return will be between which two values?A European put option allows an investor to sell a share of stock at the exercise price on the exercise data. For example, if the exercise price is 48, and the stock price is 45 on the exercise date, the investor can sell the stock for 48 and then immediately buy it back (that is, cover his position) for 45, making 3 profit. But if the stock price on the exercise date is greater than the exercise price, the option is worthless at that date. So for a put, the investor is hoping that the price of the stock decreases. Using the same parameters as in Example 11.7, find a fair price for a European put option. (Note: As discussed in the text, an actual put option is usually for 100 shares.)
- 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.)A local finance company quotes a 16 percent interest rate onone-year loans. So, if you borrow $26,000, the interest for the year will be $4,160. Because you must repay a total of $30,160 in one year, the finance company requiresyou to pay $30,160y12, or $2,513.33, per month over the next 12 months. Is this a15 percent loan? What rate would legally have to be quoted? What is the effectiveannual rate?Solve for the future worth of each of the given series of payments: (a) $12,000 at the end of each six-month period for 12 years at 8% compounded semiannually. (b) $8,000 at the end of each quarter for 6 years at 12% compounded quarterly. (c) $6,000 at the end of each month for 5 years at 6% compounded monthly.
- A trust officer at the Blacksburg National Bank needs to determine how to invest $100,000 in the following collection of bonds to maximize the total annual return (before tax). Bond Annual Return Maturity Risk Tax-Free A 9.5% Long High Yes B 8.0% Short Low Yes C 9.0% Long Low No D 9.0% Long High Yes E 9.0% Short High No The officer wants to invest as least 50% of the money in short-term issues and no more than 50% in high-risk issues. At least 30% of the funds should go in tax-free investments, and at least 40% of the total annual return should be tax free. Suppose the decision variable represents the amount of money invested in bond for . Formulate a linear programming (LP) model to solve the optimal strategy. 1. Write down the constraint using the defined decision variables requiring “invest as least 50% of the money in short-term issues”. 2. Write down the constraint using the defined decision…Assume “Jane” saves $10,000 per year for 10 years starting at age 25. At age 35 she no longer is able to save but leaves her accumulated savings invested until age 65 when she retires. Assume “John” does not begin saving until age 35, but then saves $10,000 per year until age 65 when he also retires. Assume John and Jane invest their entire wealth in the same mutual fund. Who accumulates a larger retirement nest egg? 1. Answer this question by building an Excel spreadsheet that allows you to show the difference in wealth at age 65 assuming an annual rate of return of 8%. Make sure your model allows you to change the assumed rate of return and automatically recalculate the difference in wealth at age 65. 2. At what assumed rate of return are John and Jane’s wealth at age 65 equal? Use “Goal Seek” in order to find this rate of return. 3. Create a graph to clearly show how final wealth for John and Jane depends on the rate of return. Start at 0% and increase the rate of return in…Bilbo Baggins wants to save money to meet threeobjectives. First, he would like to be able to retire 30 years from now with a retirementincome of $23,000 per month for 20 years, with the first payment received 30 yearsand 1 month from now. Second, he would like to purchase a cabin in Rivendell in10 years at an estimated cost of $320,000. Third, after he passes on at the end of the20 years of withdrawals, he would like to leave an inheritance of $1,000,000 to hisnephew Frodo. He can afford to save $2,100 per month for the next 10 years. If hecan earn an 11 percent EAR before he retires and an 8 percent EAR after he retires,how much will he have to save each month in Years 11 through 30?
- My current income is $40,000. I believe that I owe$8,000 in taxes. For $500, I can hire a CPA to review mytax return; there is a 20% chance that she will saveme $4,000 in taxes. My utility function for (disposableincome) (current income) (taxes) (payment toaccountant) is given by x where x is disposable income.Should I hire the CPA?You are planning to save for retirement over the next 30 years.To do this, you will invest $800 a month in a stock account and $350 a month in abond account. The return of the stock account is expected to be 11 percent, and thebond account will pay 6 percent. When you retire, you will combine your money intoan account with an 8 percent return. How much can you withdraw each month fromyour account assuming a 25-year withdrawal period?I need help with everything, please. hint: you will need to define one variable for total funds needed; one variable for each for 2 securities. and five variables for investment in savings at the beginning of each year. The 6th year will be 1.04 times the 5th-year saving variable. Formulate the problem and submit the formulation - no need to solve 1. As part of the settlement for a class action lawsuit, Hoxworth Corporation must provide sufficient cash to make the following annual payments (in thousands of dollars): Year Payment 1 190 2 215 3 240 4 285 5 315 6 460 The annual payments must be made at the beginning of each year. The judge will approve an amount that, along with earnings on its investment, will cover the annual payments. Investment of the funds will be limited to savings (at 4% annually) and government securities, at prices and rates currently quoted in The Wall Street…