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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?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?A 5-year annuity of ten $5,300 semiannual paymentswill begin 9 years from now, with the first payment coming 9.5 years from now. If thediscount rate is 12 percent compounded monthly, what is the value of this annuityfive years from now? What is the value three years from now? What is the currentvalue of the annuity?
- Complete the following table and draw a graph showing how bond pricefor each bond changes over time as they move towards their maturitydates. Describe the relationship between bond prices and timeremaining for maturity.YearsreminingtomaturityBOND ACoupon rate = 8% p.a.Market interest rate =6% p.a.BOND BCoupon rate = 6% p.a.Market interest rate =6% p.a.BOND CCoupon rate = 4% p.a.Market interest rate =6% p.a.109876543210Audrey Sanborn has just arranged to purchase a $550,000vacation home in the Bahamas with a 20 percent down payment. The mortgage hasa 6.1 percent stated annual interest rate, compounded monthly, and calls for equalmonthly payments over the next 30 years. Her first payment will be due one monthfrom now. However, the mortgage has an eight-year balloon payment, meaning thatthe balance of the loan must be paid off at the end of Year 8. There were no othertransaction costs or finance charges. How much will Audrey’s balloon payment bein eight years?Let Xi be the price (in dollars) of stock i one year fromnow. X1 is N(15, 100) and X2 is N(20, 2025). Today I buythree shares of stock 1 for $12/share and two shares of stock2 for $17/share. Assume that X1 and X2 are independentrandom variables.a Find the mean and variance of the value of my stocksone year from now.b What is the probability that one year from now I willhave earned at least a 30% return on my investment?c If X1 and X2 were not independent, why would it bedifficult to answer parts (a) and (b)?
- Rollo Megabux has $1 million to invest in stocks orbonds. The percentage yield on each investment during thecoming year depends on whether the economy has a goodor a bad year (see Table 17). It is equally likely that theeconomy will have a good or a bad year.a If Rollo is risk-neutral, how should he invest hismoney?b For $10,000, Rollo can hire a consulting firm toforecast the state of the economy. The consulting firm’sforecasts have the following properties:P(good forecast|economy good) .80P(good forecast|economy bad) .20Should Rollo hire the consulting firm? What are EVSIand EVPI? Economy EconomyHas Good Has BadYear YearYield on stocks 22% 10%Yield on bonds 16% 14%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.I have a accounting firm and someone from real estate wants to invest and give my firm all her accounts but in return wants equal ownership of my firm, but i dont want to giver her equal ownership but wants her to invest in my firm , what are alternatives that i can offer her without giving her half ownership. Elaborate
- Suppose you are going to receive $20,000 per year forfive years. The appropriate interest rate is 7 percent.a. What is the present value of the payments if they are in the form of an ordinaryannuity? What is the present value if the payments are an annuity due?b. Suppose you plan to invest the payments for five years. What is the future valueif the payments are an ordinary annuity? What if the payments are an annuitydue?c. Which has the highest present value, the ordinary annuity or annuity due? Whichhas the highest future value? Will this always be true?Your job pays you only once a year for all the work you didover the previous 12 months. Today, December 31, you just received your salaryof $65,000, and you plan to spend all of it. However, you want to start saving forretirement beginning next year. You have decided that one year from today youwill begin depositing 5 percent of your annual salary in an account that will earn10 percent per year. Your salary will increase at 4 percent per year throughout yourcareer. How much money will you have on the date of your retirement 40 years fromtoday?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…