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For the data of Exercise 1.4 on page 13, compute both the mean and the variance in "flexibility" for both company A and company B. Does there appear to be a difference in flexibility between company A and company B? Reference: Exercise 1.4: In a study conducted by the Department of Mechanical Engineering at Virginia Tech, the steel rods supplied by two different companies were compared. Ten sample springs were made out of the steel rods supplied by each company, and a measure of flexibility was recorded for each. The data are as follows: Company A: 9.3 8.8 6.8 8.7 8.5 6.7 8.0 6.5 9.27.0 Company B: 11.0 9.8 9.9 10.2 10.1 9.7 11.0 11.1 10.2 9.6 (a) Calculate the sample mean and median for the data for the two companies. (b) Plot the data for the two companies on the same line and give your impression regarding any apparent differences between the two companies.A public corporation in which you own common stock reported a WACC of 11.1% for the year in its report to stockholders. The common stock that you own has averaged a total return of 7% per year over the last 3 years. The annual report also men- tions that projects within the corporation are 75% funded by its own capital. Estimate the company's cost of debt capital. BASF will invest $14 million this year to upgrade its ethylene glycol processes. This chemical is used to produce polyester resins to manufacture products varying from construction materials to aircraft, and from luggage to home appliances. Eq- uity capital costs 14.5% per year and will supply 65% of the capital funds. Debt capital costs 10% per year before taxes. The effective tax rate for BASF is 36% (a) Determine the amount of annual revenue after taxes that is consumed in covering the interest on the project's initial cost. (b) If the corporation does not want to use 65% of its own funds, the financing plan may in- clude 75% debt capital. Determine the amount of annual revenue needed to cover the interest with this plan, and explain the ef- fect it may have on the corporation's ability to borrow in the future. A couple planning for their child's college educa- tion can fund part of or all the expected $100,000 tuition cost from their own funds (through an edu- cation IRA) or borrow all or part of it. The average return for their own funds is 7% per year, but the loan is expected to have a higher interest rate as the loan amount increases. Use a spreadsheet to generate a plot of the WACC curve with the esti- mated loan interest rates below and determine the best D-E mix for the couple.A recent environmental engineering graduate is try- ing to decide whether he should keep his presently owned car or purchase a more environmentally friendly hybrid. A new car will cost $26,000 and have annual operation and maintenance costs of $1200 per year with an $8000 salvage value in 5 years (which is its estimated economic service life). The presently owned car has a resale value now of $5000; one year from now it will be $3000, two years from now $2500, and 3 years from now $2200. Its operating cost is expected to be $1900 this year, with costs increasing by $200 per year. The presently owned car will definitely not be kept longer than 3 more years. Assuming used cars like the one presently owned will always be available, should the presently owned car be sold now, 1 year from now, 2 years from now, or 3 years from now? Use annual worth calculations at i = 10% per year and show your work. A pulp and paper company is evaluating whether it should retain the current bleaching process that uses chlorine dioxide or replace it with a proprie- tary "oxypure" process. The relevant information for each process is shown. Use an interest rate of 15% per year to perform the replacement study. Current Process Oxypure Process Original cost 6 -450,000 years ago, $ Investment cost -700,000 now, $ Current market 25,000 value, $ Annual operating - 180,00 0 -70,000 cost, $/year Salvage value, $ 50,000 Remaining life, 10 yearsABB Communications is considering replacing equipment that had a first cost of $300,000 five years ago. The company CEO wants to know if the equipment should be replaced now or at any other time over the next 3 years to minimize the cost of producing miniature background suppression sen- sors. Since the present equipment or the proposed equipment can be used for any or all of the 3-year period, one of the company's industrial engineers produced AW cost information for the defender and challenger as shown below. The values repre- sent the annual costs of the respective equipment if used for the indicated number of years. Determine when the defender should be replaced to minimize the cost to ABB for the 3-year study period using an interest rate of 10% per year. AW If Kept Stated Number of Number of Years, $ per Year Years Kept Defender Challenger -22,000 29.000 W N - -24,000 -26,000 -27,000 -25,000For the data shown, calculate the conventional B/C ratio at i = 6% per year. Benefits: $20,000 in year () and $30,000 in year 5 Disbenefits: $7000 in year 3 Savings (to government): $25,000 in years 1-4 Cost: $100,000 in year 0 Project life: 5 years Explain a fundamental difference between the modified B/C ratio and the profitability index. Gerald Corporation entered a public-private part- nership using a DBOM contract with the state of Massachusetts 10 years ago for railroad system upgrades. Determine the profitability index for the financial results listed below using a MARK of 8% per year. Investments: Year 0 $-4.2 million Year 5 $-3.5 million Net savings: Years 1-5 $1.2 million per year Years 6-10 $2.5 million per year A project had a staged investment distributed over the 6-year contract period. For the cash flows shown (next page) and an interest rate of 10% per year, determine the profitability index and deter- mine if the project was economically justified.The waiting time, in hours, between successive speeders spotted by a radar unit is a continuous random variable with cumulative distribution function Find the probability of waiting less than 12 minutes between successive speeders (a) using the cumulative distribution function of X; (b) using the probability density function of X. Determine the value c so that each of the following functions can serve as a probability distribution of the discrete random variable X: (a) f(x) = c(x2 + 4), for x = 0, 1, 2, 3; (b) f(x) = c() (->), for x = 0, 1, 2.Based on extensive testing, it is determined by the manufacturer of a washing machine that the time Y (in years) before a major repair is required is characterized by the probability density function f(y) = 10 -#/4, 920, elsewhere. (a) Critics would certainly consider the product a bargain if it is unlikely to require a major repair before the sixth year. Comment on this by determining A(Y > 6). (b) What is the probability that a major repair occurs in the first year