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List at least three factors that affect the MARK, and discuss how each one affects it. State whether each of the following involves debt financing or equity financing. (a) $10,000 taken from one partner's savings ac- count to pay for equipment repair (b) Issuance of preferred stock worth $1.3 mil- lion (c) Short-term loan of $75,000 from a local bank (d) Issuance of $3 million worth of 20-year bonds (e) Del Engineering buyback of $8 million of its own stock using internal funds Helical Products, Inc. uses an after-tax MARR of 12% per year. If the company's effective tax rate (federal, state, and local taxes) is 40%, determine the company's before-tax MARK. The owner of a small pipeline construction com- pany is trying to figure out how much he should bid in his attempt to win his first "big" contract. He estimates that his cost to complete the project will be $7.2 million. He wants to bid an amount that will give him an after-tax rate of return of 15% per year if he gets the job, but he doesn't know how much he should bid on a before-tax basis. He told you that his effective state tax rate is 7% and his effective federal tax rate is 22%. (a) The expression for determining the overall effective tax rate is state rate + (1 - state rate)(federal rate) What should his before-tax MARR be in order for him to make an after-tax MARK of 15% per year? (b) How much should he bid on the job?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.Compute the sample variance and standard deviation for the water absorbency data of Exercise 1.2 on page 13. Reference: Exercise 1.2 According to the journal Chemical Engineering, an important property of a fiber is its water absorbency. A random sample of 20 pieces of cotton fiber was taken and the absorbency on each piece was measured. The following are the absorbency values: 18.71 21.41 20.72 21.81 19.29 22.43 20.17 23.71 19.44 20.50 18.92 20.33 23.00 22.85 19.25 21.77 22.11 19.77 18.04 21.12 (a) Calculate the sample mean and median for the above sample values. (b) Compute the 10% trimmed mean. (c) Do a dot plot of the absorbency data. (d) Using only the values of the mean, median, and trimmed mean, do you have evidence of outliers in the data?In 2010, Brazil began construction of the Belo Monte hydroelectric dam on the Xingu River (which feeds the Amazon River). The project is funded by a consortium of investors and is ex- pected to cost $11 billion. It will begin producing electricity in 2015. Even though the dam will pro- vide clean energy for millions of people, environ- mentalists are sharply opposed. They say it will devastate wildlife and the livelihoods of 40,000 people who live in the area to be flooded. Assume that the funding will occur evenly over the 5-year period from 2010 through 2014 at $2.2 billion per year. The disbenefits are estimated to be $100,000 for each displaced person and $1 billion for wildlife destruction. Assume that the disbenefits will occur evenly through the 5-year construction period and anticipated benefits will begin at the end of 2015 and continue indefinitely. Use an interest rate of 8% per year to determine what the equivalent annual benefits must be to en- sure a B/C ratio of at least 1.0. In the United States, the average number of air- planes in the sky on an average morning is 4000. There are another 16,000 planes on the ground. Acrospace company Rockwell Collins developed what it calls a digital parachute-a panic-button technology that will land any plane in a pinch at the closest airport, no matter what the weather or geography and without the help of a pilot. The technology can be applied if a pilot is no longer capable of flying the plane or is panicked and con- fused about what to do in an emergency. Assume that the cost of retrofitting 20,000 commercial air-Measurements of scientific systems are always subject to variation, some more than others. There are many structures for measurement error, and statisticians spend a great deal of time modeling these errors. Suppose the measurement error X of a certain physical quantity is decided by the density function f(x) = [*(3-r'), -15251, elsewhere. (a) Determine * that renders f(x) a valid density function.(b) Find the probability that a random error in measurement is less than 1/2.(c) For this particular measurement, it is undesirable if the magnitude of the error (ie., (x]) exceeds 0.8. What is the probability that this occurs? Five independent coin tosses result in HHHHH. It turns out that if the coin is fair the probability of this outcome is (1/2)5 = 0.03125. Does this produce strong evidence that the coin is not fair? Comment and use the concept of P-value discussed inSection 1.1.The proportion of the budget for a certain type of industrial company that is allotted to environmental and pollution control is coming under scrutiny. A data collection project determines that the distribution of these proportions is given by f(y) = 5(1-V)'. OSys1. elsewhere. (a) Verify that the above is a valid density function. (b) What is the probability that a company chosen at random expends less than 10% of its budget on environmental and pollution controls? (c) What is the probability that a company selected at random spends more than 50% of its budget on environmental and pollution controls