Briarcliff Stove Company is considering a new product line to supplement its range line. It is anticipated that the new product line will involve cash investment of $700,000 at time 0 and $1.0 million in year 1. After tax cash inflows of $250,000 are expected in year 2, $300,000 in year 3, $350,000 in year 4, and $400,000 each year thereafter through year 6. Though the product line might be viable after year 6, the company prefers to be conservative and end all calculations at that time.

a) If the required rate of return is 15 percent, what is the net present value of the project? Is it acceptable?

b) Calculate Accounting Rate of Return

c) What is the project’s payback period?

d) What is the project’s profitability index?

e) What would be the case if the required rate of return was 10 percent?

The manager of a paint supply store wants to determine whether the mean amount of paint contained in 1-gallon cans purchased from a nationally known manufacturer is actually 1 gallon. You know from the manufacturer’s specifications that the standard deviation of the amount of paint is 0.02 gallon. You select a random sample of 50 cans, and the mean amount of paint per 1-galllon can is 0.995 gallon.

a. At the .05 level of significance, is there evidence that the mean amount is different from 1.0 gallon? Show all steps! Draw the normal curve and insert all information given.

b. Compute the p-value and interpret its meaning. Show all steps!

c. Construct a 95% confidence interval estimate of the population mean amount of paint. Show all steps! d. Compare the results of (a) and (c). What conclusions do you reach? Show all steps!

Consider the solution of the differential equation y′=−3yy′=−3y passing through y(0)=0.5y(0)=0.5.

A. Sketch the slope field for this differential equation, and sketch the solution passing through the point (0,0.5).

B. Use Euler's method with step size Δx=0.2Δx=0.2 to estimate the solution at x=0.2,0.4,…,1x=0.2,0.4,…,1, using these to fill in the following table. (Be sure not to round your answers at each step!)

C. Plot your estimated solution on your slope field. Compare the solution and the slope field. Is the estimated solution an over or under estimate for the actual solution?
A. over
B. under

D. Check that y=0.5e−3xy=0.5e−3x is a solution to y′=−3yy′=−3y with y(0)=0.5y(0)=0.5.

The manager of a paint supply store wants to determine whether the mean amount of paint contained in 1-gallon cans purchased from a nationally known manufacturer is actually 1 gallon. You know from the manufacturer’s specifications that the standard deviation of the amount of paint is 0.02 gallon. You select a random sample of 50 cans, and the mean amount of paint per 1-galllon can is 0.995 gallon.

1. At the .05 level of significance, is there evidence that the mean amount is different from 1.0 gallon? Show all steps! Draw the normal curve and insert all information given.
2. Compute the p-value and interpret its meaning. Show all steps!
3. Construct a 95% confidence interval estimate of the population mean amount of paint. Show all steps!
4. Compare the results of (a) and (c). What conclusions do you reach? Show all steps and graphs
   

There is an unknown charge  Q  at the origin.  From a location 0.40 m from the origin along the y axis, I launch a charged particle in the x direction with a speed of 15 m/s, and it goes in a circle.  The particle’s charge is 1.0×10^-6 C and its mass is 0.20 kg.

(a) [15 pts.] What is the charge Q?

(b) [4 pts.] If I launched the particle at 20 m/s, instead of 15 m/s, would it come back or would it escape and get infinitely far away?  Would the path it follows be a circle?

(c) [8 pts.] What is the minimum speed I could launch the particle with in order for it to escape to infinity?

(d) [3 pts.] If I launch the particle with the speed from part (c), is there a particular direction I have to launch it at in order for it to escape, or would any direction do?  If there is a particular direction, what is it?

At Brokerage firms, Customer satisfaction (dependent variable) is thought to be a function of speed of transactions and the size of the company (independent variables). Using excel determine the additional satisfaction rating that a customer derives from working with a large (L) company. Enter the increase in the satisfaction rating below.

(Note: ignore the p-value associated with customer size for this analysis.)

Your task is to value Shake Shack's (SHAK’s) stock. Shake Shack's dividends two, four, and five years from now are expected to be, respectively, $3.25, $4.10, and $4.50. (Shake Shack has announced that it’ll not pay any dividends at t=1 and t=3, instead using nearly all free cash to add restaurants across the country.) Across years 6 and 7 and 8, dividends will grow by 7%/year. The dividends are projected to grow, after that, at a constant rate of 3% forever. SHAK has a debt-to-equity ratio (in market-value terms) of 1.0. The yield to maturity on SHAK's bonds averages 4% and the company's tax rate is 30%. If the risk-free rate is 2.2%, the market risk premium is 6%, and SHAK's equity beta is 1.25, what should the stock sell for today based on a discounted valuation of its projected dividends?

(9 pts) Engineers must consider the breadths of male heads when designing motorcycle helmets. Men have head breadths that are normally distributed with a mean of 6.0 in and a standard deviation of 1.0 in. (The next page has a copy of cdf values for the standard normal distribution.) a) If one male is randomly selected, find the probability that his head breadth is less than 6.2 in.






b) Find the probability that 100 randomly selected men have a mean head breadth that is less than 6.2 in. State any rule/assumption or result to justify your answer.








c) A production manager for Safeguard Helmet Company plans an initial run of 100 helmets. Seeing the result from part b), the manager reasons that all helmets should be made for men with head breadths less than 6.2 in., because they would fit all but a few men. What is wrong with that reasoning?