A factory has a buffer with a capacity of 4 m³ for temporarily storing waste produced by the factory. Each week the factory produces k m³ waste with a probability p_k, where p₀=1/8, p₁=1/2, p₂=1/4 and p₃=1/8. If the amount of waste produced in one week exceeds the remaining capacity of the buffer, the excess is specially removed at a cost of 30 per m³. At the end of each week there is a regular opportunity to remove the waste from the storage at a fixed cost of 25 and a variable cost of 5 per m³. The following policy is used. If at the end of the week the storage buffer contains more than 2 m³, the buffer is emptied; otherwise, no waste is removed. Determine the ling-run average cost per week. You need to define the states and the transition probability matrix well first.

The table shows the investment projected net cash inflows of the two projects over the coming 5 years.

Year	Project A	Project B
1	$200000	$120000
2	$200000	$130000
3	$200000	$150000
4	$200000	$200000
5	$200000	$240000

Initial investment of $500000 and discount rate at 18% per year under each project.

Discount factors for Year 1 to Year 5 as follows:

Year 1	0.8475
Year 2	0.7182
Year 3	0.6086
Year 4	0.5158
Year 5	0.4370

1. Find the payback period in years for each project. (please show step clearly)
2. Finish an evaluation for project A and project B using net present value at the above discount rate for year 1 to year 5.
3. Which one of projects is the best investment for the business? Explain your reason clearly.

Suppose you will receive payments of $8,000, $2,000, and $8,000 in 1, 4, and 9 year(s) from now, respectively. What is the total present value of this stream of payments if the interest rate is 9%? Enter your response below rounded to 2 decimal places.

1. An aluminum ring of radius 5.00 cm and resistance 3.00 × 10–4 O is placed on top of a long air-core solenoid with 1 000 turns per meter and radius 3.00 cm, as shown in the sketch below. Over the area of the end of the solenoid, assume that the axial component of the field produced by the solenoid is half as strong as at the center of the solenoid. Assume the solenoid produces negligible field outside its cross-sectional area. The current in the solenoid is increasing at a rate of 270 A/s. (a) What is the induced current in the ring? At the center of the ring, what are (b) the magnitude and (c) the direction of the magnetic field produced by the induced current in the ring?

2. The square loop in the sketch shown below is made of wires with total series resistance 10.0 O. It is placed in a uniform 0.100-T magnetic field directed perpendicularly into the plane of the paper. The loop, which is hinged at each corner, is pulled as shown until the separation between points A and B is 3.00 m. If this process takes 0.100 s, what is the average current generated in the loop? What is the direction of the current?

3. In the sketch shown below, the bar magnet is moved toward the loop. Is Va – Vb positive, negative, or zero? Explain.

When Patey Pontoons issued 4% bonds on January 1, 2018, with a face amount of $580,000, the market yield for bonds of similar risk and maturity was 5%. The bonds mature December 31, 2021 (4 years). Interest is paid semiannually on June 30 and December 31. (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided.)Required: 5. What is the amount related to the bonds that Patey will report in its balance sheet at December 31, 2018?
6. What is the amount related to the bonds that Patey will report in its income statement for the year ended December 31, 2018? (Ignore income taxes.)
7. Prepare the appropriate journal entries at maturity on December 31, 2021.

1) A 5‐year T‐Note with the face value of $10,000 pays 4% coupon rate. If the current interest rate is 1%, what is the price for this bond? (Set up the relevant equation to solve.

1.

A monopolist has average cost AC = .2Q - 4 + 100/Q and marginal cost MC = .4Q - 4. Market demand is Q = 44 - P, implying that the firm’s marginal revenue is MR = 44 - 2Q. Its profit-maximizing output is

a. 92

b. 46

c. 40

d. 20

2.

Consider the same monopoly situation as in the previous question. The firm’s profit will be

a. 760

b. 660

c. 830

d. 380