An n+m year annuity of $1 per year has it - 7% during the first m years and has iz 11% during the Smo.07 = 34, Smo.11 = 128. %3D remaining n years. m=18, n 26 Find the present value of this annuity a year before the first payment comes in.
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- You are considering a 10-year investment project. At present, the expected cash flow each year is 10,000. Suppose, however, that each years cash flow is normally distributed with mean equal to last years actual cash flow and standard deviation 1000. For example, suppose that the actual cash flow in year 1 is 12,000. Then year 2 cash flow is normal with mean 12,000 and standard deviation 1000. Also, at the end of year 1, your best guess is that each later years expected cash flow will be 12,000. a. Estimate the mean and standard deviation of the NPV of this project. Assume that cash flows are discounted at a rate of 10% per year. b. Now assume that the project has an abandonment option. At the end of each year you can abandon the project for the value given in the file P11_60.xlsx. For example, suppose that year 1 cash flow is 4000. Then at the end of year 1, you expect cash flow for each remaining year to be 4000. This has an NPV of less than 62,000, so you should abandon the project and collect 62,000 at the end of year 1. Estimate the mean and standard deviation of the project with the abandonment option. How much would you pay for the abandonment option? (Hint: You can abandon a project at most once. So in year 5, for example, you abandon only if the sum of future expected NPVs is less than the year 5 abandonment value and the project has not yet been abandoned. Also, once you abandon the project, the actual cash flows for future years are zero. So in this case the future cash flows after abandonment should be zero in your model.)In Example 11.1, the possible profits vary from negative to positive for each of the 10 possible bids examined. a. For each of these, use @RISKs RISKTARGET function to find the probability that Millers profit is positive. Do you believe these results should have any bearing on Millers choice of bid? b. Use @RISKs RISKPERCENTILE function to find the 10th percentile for each of these bids. Can you explain why the percentiles have the values you obtain?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?
- 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)?We must invest all our money in two stocks: x and y.The variance of the annual return on one share of stock x isvar x, and the variance of the annual return on one share ofstock y is var y. Assume that the covariance between theannual return for one share of x and one share of y is cov(x,y). If we invest a% of our money in stock x and b% in stocky, then the variance of our return is given by a2var xb2var y2ab cov(x, y). We want to minimize the variance of thereturn on our invested money. What percentage of the moneyshould be invested in each stock?We are considering investing in three stocks. The randomvariable Si represents the value one year from now of $1invested in stock i. We are given that E(S1) 1.15, E(S2) 1.21, E(S3) 1.09; var S1 0.09, var S2 0.04, var S3 0.01; cov(S1, S2) 0.006, cov(S1, S3) 0.004, and cov(S2,S3) 0.005. We have $100 to invest and want to have anexpected return of at least 15% during the next year.Formulate a QPP to find the portfolio of minimum variancethat attains an expected return of at least 15%.
- #17FAVORABLE UNFAVORABLEMARKET MARKETEQUIPMENT ( $) ($)Sub 100 300,000 –200,000Oiler J 250,000 –100,000Texan 75,000 –18,000For example, if Ken purchases a Sub 100 and ifthere is a favorable market, he will realize a profitof $300,000. On the other hand, if the market is unfavorable, Ken will suffer a loss of $200,000. ButKen has always been a very optimistic decisionmaker.(a) What type of decision is Ken facing?(b) What decision criterion should he use?(c) What alternative is best? #18Although Ken Brown (discussed in Problem 3-17) is the principal owner of Brown Oil, his brother Bob iscredited with making the company a financial success. Bob is vice president of finance. Bob attributeshis success to his pessimistic attitude about business and the oil industry. Given the information fromProblem 3-17, it is likely that Bob will arrive at a different decision. What decision criterion should Bobuse, and what alternative…A hardware company sells a lot of low-cost, highvolumeproducts. For one such product, it is equallylikely that annual unit sales will be low or high. Ifsales are low (60,000), the company can sell theproduct for $10 per unit. If sales are high (100,000),a competitor will enter and the company will be ableto sell the product for only $8 per unit. The variablecost per unit has a 25% chance of being $6, a 50%chance of being $7.50, and a 25% chance of being $9.Annual fixed costs are $30,000.a. Use simulation to estimate the company’s expectedannual profit.b. Find a 95% interval for the company’s annualprofit, that is, an interval such that about 95% ofthe actual profits are inside it.c. Now suppose that annual unit sales, variable cost,and unit price are equal to their respective expectedvalues—that is, there is no uncertainty. Determinethe company’s annual profit for this scenario.d. Can you conclude from the results in parts a and cthat the expected profit from a simulation is equalto…53. Why is the RISKCORRMAT function necessary?How does @RISK generate random inputs by default,that is, when RISKCORRMAT is not used
- Same situation as in the previous two problems this time the magnet s mass is 5.68 kg and the magnetic force pulling it to the right is 170.9 N. The length of the cord is 1.70 m, and the ceiling is 2.98 m above the floor. Suppose that you cut the cord and the magnet falls to the floor while still being pulled to the right by the force of 170.9 N. How long will it take the magnet to hit the floor? 0.848 s 0.403 s 0.707 s 0.495 sThe information contained in the table below shows the expected return and standard deviation for a risky asset and risk-free asset. Asset Expected Return Risk (Standard Deviation) Risky Asset 13.00% 27.00% Risk-Free Asset 2.50% 0.00% Coefficient of Risk Aversion 1.0 Required: Using the information in the tables above, determine the optimal allocation to the risky asset. Use the MIN functions to ensure no leverage is deployed.Suppose that Pizza King and Noble Greek stopadvertising but must determine the price they will chargefor each pizza sold. Pizza King believes that Noble Greek’sprice is a random variable D having the following massfunction: P(D $6) .25, P(D $8) .50, P(D $10) .25. If Pizza King charges a price p1 and NobleGreek charges a price p2, Pizza King will sell 10025( p2 p1) pizzas. It costs Pizza King $4 to make a pizza.Pizza King is considering charging $5, $6, $7, $8, or $9 fora pizza. Use each decision criterion of this section todetermine the price that Pizza King should charge.