Q7.1    The normalized passband edge angular frequency Wp is - 0.2
   The normalized stopband edge angular frequency Ws is - 0.4
   The desired passband ripple Rp is - 0.5 dB
   The desired stopband ripple Rs is - 40 dB

In Matlab:

Q7.X1 Design a fixed window FIR filter satisfying the specifications in Q7.1. Plot the magnitude and phase responses. Also include magnified plots of passband and stopband showing how well the filter satisfies the design specifications.

at 25 C, a solution is prepared by adding 50 ml of 0.2 M NaOH to 75 ml of 0.1 M NaOH. What is the total concentratoin of hydorxide ion in the solution? Assume volumes are additive.

Q7.1    The normalized passband edge angular frequency Wp is - 0.2
   The normalized stopband edge angular frequency Ws is - 0.4
   The desired passband ripple Rp is - 0.5 dB
   The desired stopband ripple Rs is - 40 dB

In Matlab:

Q7.X1 Design a Butterworth lowpass filter satisfying the specifications in Q7.1. Plot the magnitude and phase responses. Also include magnified plots of passband and stopband showing how well the filter satisfies the design specifications.

Copper is added to steel in amounts greater than 0.2% but less than 1.5% as it strengthens, hardens and reduces corrosion of the product. The amount of copper in a steel product is determined by digesting the steel product with strong acid, converting all copper species to the Cu+1 ion, complexing the Cu+1 ion to form a light absorbing species by reaction with neocuproine, and extracting the coloured complex with isoamyl alcohol for analysis by UV/VIS spectrophotometry at the 454 nm absorbance wavelength. A 0.2108 g sample of a standard steel sample containing 0.42% of copper was analysed by the above process and a final 10.00 mL volume of the isoamyl extract was obtained. The copper complex of this solution gave an absorbance of 0.481 using a 1.00 cm cuvette. A 0.2892 g sample of a steel product that was being manufactured was analysed as above using the same procedure and equipment and a final 10.00 mL volume of the isoamyl extract was obtained. The copper complex of this solution gave an absorbance of 0.632 using a 1.00 cm cuvette. A blank solution carried through the same procedure gave an absorbance of 0.038. What is the percentage of copper in the manufactured steel product? Is the copper in this steel product within the specified range given above. Note. You have to take into consideration the absorbance of the blank solution to solve the problem.

Your employer is considering a capital project that involves installing a new manufacturing facility(to manufacture a new product) at a cost of $30,800,000. The facility will be built on land that was purchased in 2018 for $1,250,000. If the facility is not built on this land, the land will remain unused. The new manufacturing facility, if built, will be depreciated on a straight-line basis over five years, to a salvage value of $2,000,000. If the facility is built, the production there will cause an immediate increase in Inventory of $1,300,000. It will also cause immediate increases in Accounts Receivable of $5,900,000, Accounts Payable of $850,000, and Long-Term Debt of $15.2million.

If built and produced, the new product is expected to generate annual sales of $20,375,000 by the end of the first year. Sales are expected to increase 8% per year. COGS expense is expected to be of $9,780,000 during the first year. Thereafter, COGS is expected to remain at a constant percentage of Sales. Because operating efficiency is expected to improve each year, SG&A expense is expected to remain at $3,750,000 for each of the five years of the project. At the end of the project’s five-year life, production will cease, and the manufacturing facility will be sold for an estimated $4,500,000. At that time, Inventory, Accounts Receivable and Accounts Payable will return to their pre-project levels.

If the project is implemented, it will likely increase sales of the company’s existing complimentary products. The net impact of those sales is expected to be a $2,225,000 annual increase in pre-tax profits.

Your employer’s tax rate is 21%. The firm has 5 million shares of common stock outstanding. The firm requires a 11% rate of return on capital projects of this risk.

Prepare a discounted cash flow analysis to determine whether your employer should implement this capital project. Your analysis should reveal answers to each of the following questions. Clearly label all cells. Highlight the cells that answer the following questions:

1. What is the initial investment amount (Year 0)?
2. What are the total cash flows each year (Years 1-5)
3. What is the NPV?
4. What is the IRR?

Discounted Cash Flow Analysis (Model) Excel Case:

Your employer is considering a capital project that involves installing a new manufacturing facility(to manufacture a new product) at a cost of $30,800,000. The facility will be built on land that was purchased in 2018 for $1,250,000. If the facility is not built on this land, the land will remain unused. The new manufacturing facility, if built, will be depreciated on a straight-line basis over five years, to a salvage value of $2,000,000. If the facility is built, the production there will cause an immediate increase in Inventory of $1,300,000. It will also cause immediate increases in Accounts Receivable of $5,900,000, Accounts Payable of $850,000, and Long-Term Debt of $15.2million.

If built and produced, the new product is expected to generate annual sales of $20,375,000 by the end of the first year. Sales are expected to increase 8% per year. COGS expense is expected to be of $9,780,000 during the first year. Thereafter, COGS is expected to remain at a constant percentage of Sales. Because operating efficiency is expected to improve each year, SG&A expense is expected to remain at $3,750,000 for each of the five years of the project. At the end of the project’s five-year life, production will cease, and the manufacturing facility will be sold for an estimated $4,500,000. At that time, Inventory, Accounts Receivable and Accounts Payable will return to their pre-project levels.

If the project is implemented, it will likely increase sales of the company’s existing complimentary products. The net impact of those sales is expected to be a $2,225,000 annual increase in pre-tax profits.

Your employer’s tax rate is 21%. The firm has 5 million shares of common stock outstanding. The firm requires a 11% rate of return on capital projects of this risk.

Prepare a discounted cash flow analysis to determine whether your employer should implement this capital project. Your analysis should reveal answers to each of the following questions. Clearly label all cells. Highlight the cells that answer the following questions:

1. What is the initial investment amount (Year 0)?
2. What are the total cash flows each year (Years 1-5)
3. What is the NPV?
4. What is the IRR?

1. Firm A has a beta of 5 and estimated cost of equity of 7%. Firm B has a beta of 0.7 and estimated cost of equity of 6%. What is the assumed market return and risk-free rate?

Show work and formula by hand-only. Do not use Excel.

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 2.2 years, and standard deviation of 0.7 years.

If you randomly purchase 3 items, what is the probability that their mean life will be longer than 1 years? (Give answer to 4 decimal places.)

You have a portfolio with $15,000 invested in Stock A with a beta of 2.5, $25,000 invested in stock B with a beta of 0.7, and $10,000 invested in Stock C with a beta of 1.0. If the risk-free rate is 2% and the market risk premium is 6%, what is the required return of the portfolio?