Your job pays you only once a year for all the work you did over the previous 12 months. Today, December 31, you just received your salary of $65,000, and you plan to spend all of it. However, you want to start saving for retirement beginning next year. You have decided that one year from today you will begin depositing 5 percent of your annual salary in an account that will earn 10 percent per year. Your salary will increase at 4 percent per year throughout your career. How much money will you have on the date of your retirement 40 years from today?

Your job pays you only once a year for all the work you did over the previous 12 months. Today, December 31, you just received your salary of $65,000, and you plan to spend all of it. However, you want to start saving for retirement beginning next year. You have decided that one year from today you will begin depositing 5 percent of your annual salary in an account that will earn 10 percent per year. Your salary will increase at 4 percent per year throughout your career. How much money will you have on the date of your retirement 40 years from today?

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter11: Simulation Models

Section: Chapter Questions

Problem 58P: Suppose you begin year 1 with 5000. At the beginning of each year, you put half of your money under...

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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?
Referring to the retirement example in Example 11.6, rerun the model for a planning horizon of 10 years; 15 years; 25 years. For each, which set of investment weights maximizes the VAR 5% (the 5th percentile) of final cash in todays dollars? Does it appear that a portfolio heavy in stocks is better for long horizons but not for shorter horizons?
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 are borrowing 25,000 and making monthly payments with 1% interest. Show that the monthly payments should equal 556.11. The key relationships are that for any month t (Ending month t balance) = (Ending month t 1 balance) ((Monthly payment) (Month t interest)) (Month t interest) = (Beginning month t balance) (Monthly interest rate) Of course, the ending month 60 balance must equal 0.
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.)
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?
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?
You have recently won the super jackpot in the WashingtonState Lottery. On reading the fine print, you discover that you have the following twooptions:a. You will receive 31 annual payments of $250,000, with the first payment beingdelivered today. The income will be taxed at a rate of 28 percent. Taxes will bewithheld when the checks are issued.b. You will receive $530,000 now, and you will not have to pay taxes on this amount.In addition, beginning one year from today, you will receive $200,000 each yearfor 30 years. The cash flows from this annuity will be taxed at 28 percent.Using a discount rate of 7 percent, which option should you select?
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?
Based on current dividend yields and expected capital gains, the expected rates of return on portfolios A and B are 11 % and 14 %, respectively. The beta of A is 0.8 % while that of B is 1.5. The T-bill is currently 6 %, while the expected rate of return of the S&P 500 index is 12 %. The standard deviation of portfolio A is 10 % annually, while that of B is 31 % , and that of the index is 20 %: If you currently hold a market index portfolio, would you choose to add either of these portfolios to your holdings? Explain. If instead you could invest only in bills and one of these portfolios, which would you choose, and why? Investor Y, who put K1 in large stocks (the S & P 500 portfolio) on December 31, 1925, and re-invested all dividends in that portfolio, would have ended on December 31, 2003, with K1992.80.
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…
You are saving for the college education of your two children. They aretwo years apart in age; one will begin college 15 years from today and the otherwill begin 17 years from today. You estimate your children’s college expenses to be$45,000 per year per child, payable at the beginning of each school year. The annualinterest rate is 7.5 percent. How much money must you deposit in an account eachyear to fund your children’s education? Your deposits begin one year from today.You will make your last deposit when your oldest child enters college. Assume fouryears of college.