9.1. Obtain the total periodic payments of a loan of 16,000€ and 3 years term, with the following conditions:

a. Adjustable interest rate.
Annual adjustment period: 1 year.
Type of loan: Semi-annually constant principal repayments over 3 years.
Nominal interest rate for the 1st period: 3%
Interest rates for the remaining periods: the index rate plus 0.5 percentage points.

The index rate take the following values for the other periods:

ir = 0.05 ; ir = 0.045

Find the periodic payments to be made.

b. Monthly constant payments over each adjustment period.
Annual adjustment period: 1 year.

Nominal interest rate for the 1st period : 5%.
Remaining periods: index rate plus 0.3 percentage points.
The index rates take the following values for each of the periods:

ir = 0.06 ; ir = 0.04

Find the periodic payments to be made.

c. Adjustable interest rate.
Annual adjustment period: 1 year.
Type of loan: quarterly constant principal repayments over 3 years.
Nominal interest rate for the 1st period: 7%
Interest rates for the remaining periods: the index rate plus 0.2 percentage points.

The index rates take the following values for the other periods:

ir = 0.035 ; ir = 0.05

Find the periodic payments to be made.

SciTools Incorporated, a company that specializes in scientific instruments, has been invited to make a bid on a government contract. The contract calls for a specific number of these instruments to be delivered during the coming year. The bids must be sealed (so that no company knows what the others are bidding), and the low bid wins the contract. SciTools estimates that it will cost $5000 to prepare a bid and $95,000 to supply the instruments if it wins the contract. On the basis of past contracts of this type, SciTools believes that the possible low bids from the competition, if there is any competition, and the associated probabilities are those shown in the table below. In addition, SciTools believes there is a 30% chance that there will be no competing bids.

Based on the data in the table above, SciTools will limit its choices for bids to $115,000, $120,000, and $125,000.

a) Draw a decision tree for this scenario

b) Solve this decision tree using EMV

c) Draw the risk profiles for all decision strategies

d) Draw the cumulative risk profile for this scenario. Is there dominance?

e) Construct a tornado diagram for this scenario, if we assume the following ranges for the

variables:

a. Probability of no competing bids: 0 to 0.6

b. Cost to supply the instruments: $85,500 to $105,400

c. Bid cost: $4,500 to $5,500

What is the best mechanical pencil lead size (i.e. 0.5, 0.7 etc) and lead type (I.e. Hb etc) for engineering drawing (isometric and orthogonal) ?

*MiniTab Is Required for this question** Suppose that a precise measuring device for new hair growth has been developed and is used in the experiment described in exercise 1922. The percentages of new hair growth for the 30 pairs of men involved in the experiment were recorded. Do these data allow the chemist to conclude that drug B is more effective?

Drug A   Drug B
3.5   7.1
2.4   6.6
4.2   4.2
1.1   1.0
2.9   2.7
2.8   4.1
5.6   8.3
4.8   8.8
0.8   0.8
3.6   3.4
2.0   1.8
5.6   6.9
4.3   6.8
7.1   7.9
3.8   6.2
3.6   3.5
4.2   7.3
2.8   2.7
6.1   9.5
3.7   6.2
4.0   6.7
3.5   6.8
3.1   3.0
6.0   9.0
5.3   8.4
2.6   4.1
4.8   4.8
2.2   1.8
4.2   5.6
0.8   2.2

Analyze the following items on the balance sheet for your base company that would be

important to an investor, and discuss whether your company’s performance related to these

items appeared to be improving, deteriorating, or remaining stable. Justify your answer.

October

1. S. Erickson invested $5 0,000 cash, a $16,000 pool equipment, and $12,000 of office equipment in the company.

2. The company paid $4,000 cash for five months’ rent.

3. The company purchased $1,620 of office supplies on credit from Todd’s Office Products.

5. The company paid $4,220 cash for one year’s premium on a property and liability insurance policy.

6. The company billed Deep End Co $4,800 for services performed in installing a new pool

8. The company paid $1,620 cash for the office supplies purchased from Todd’s Office Products on October 3.

10. The company hired Julie Kruit as a part-time assistant for $136 per day, as needed.

12. The company billed Deep End Co another $1,600 for services performed.

15. The company received $4,800 cash from Deep End Co as partial payment on its account.

17. The company paid $750 cash to repair pool equipment that was damaged when moving it.

20. The company paid $1,958 cash for advertisements published in the local newspaper.

22.The company received $1,600 cash from Deep End Co. on its account.

28. The company billed Happy Summer Corp $6,802 for consulting services performed.

31. The company paid $952 cash for Julie Kruit’s wages for seven days’ work.

31. S. Ericksonwithdrew $3,500 cash from the company for personal use.

November

1. The Company reimbursed S. Erickson in cash for business automobile mileage allowance (Ericksonlogged 1,500 miles at $0.32 per mile).

2. The company received $5,630 cash from Underground Inc. for consulting services performed.

5. The company purchased office supplies for $1,325 cash from Todd’s Office Products.

8. The company billedSlides R Us $7,568 for services performed.

13. The company agreed to perform future services for Henry’s Pool and Spa Co. No work has been performed.

18. The company received $2,802 cash from Happy Summer Corp as partial payment of the October 28 bill.

22. The company donated $450 cash to the United Way in the company’s name.

24. The company completed work and sent a bill for $4,800toHenry’s Pool and SpaCo.

25. The company sent another bill to Happy Summer Corp for the past-due amount of $ 4 000.

28. The company reimbursed S. Erickson in cash for business automobile mileage(1,300 miles at $0.32 per mile).

30. The company paid cash to Julie Kruit for 14 days’ work.

30. S. Erickson withdrew $1,500 cash from the company for personal use

December

2. Paid $1,200 cash to West Side Mall for Splashing Around’s share of mall advertising costs.

3. Paid $350 cash for minor repairs to the company’s pool equipment

4. Received $4,800 cash from Henry’s Pool and Spa Co. for the receivable from November.

10. Paid cash to Julie Kruit for six days of work at the rate of $136 per day.

14. Notified by Henry’s Pool and Spa Co. that Splashing Around’s bid of $ 10,000 on a proposed project has been accepted. Henry’s paid a $ 6,500 cash advance to Splashing Around

15. Purchased $1,400 of office supplies on credit from Todd’s Office Products.

16. Sent a reminder to Slides R Us to pay the fee for services recorded on November 8.

20. Completed a project for Underground Inc and received $6,545 cash.

22–26 Took the week off for the holidays.

28. Received $4,500 cash from Slides R Us on its receivable.

29. Reimbursed S. Erickson for business automobile mileage (500 miles at $0.32 per mile).

31. S.Erickson withdrew $ 2,500 cash from the company for personal use.

Adjusting Entries

The following additional facts are collected for use in making adjusting entries prior to preparing

financial statements for the company’s first three months:

a. The December 31 inventory count of office supplies shows $1800 still available.

b.Three months have expired since the 12-month insurance premium was paid in advance.

c. As of December 31, Julie Kruit has not been paid for four days of work at $136 per day.

d.The pool equipment, acquired on October 1, is expected to have a four-year life with no salvage value.

e. The office equipment, acquired on October 1, is expected to have a five-year life with no salvage value.

f.Three of the five months’ prepaid rent has expired

just the adjusting entries journalized.

A cylindrical can is to be built to occupy a volume of 5000m3. The top and bottom of the cylinder cost $500/m2, wheras the cost to build the wall of the cylinder is $300/m2. Also, the top of the cylinder is to have a circular hole that will occupy 1/4 of the top area. Find the dimensions, to 2 decimal places, of the cylinder to minimize the cost. What is the cost, rounded to the nearest hundred, to build the cylinder?

A model of a plane is built to a scale of 1/14 and is tested in a wind tunnel.

If the plane is designed to travel at 800 km/h at an altitude of 5 km, determine the required density of the air in the wind tunnel so that the Reynolds and Mach numbers are the same. Assume the temperature is the same in both cases and the speed of sound in air at this temperature is 340 m/s. ρp = 0.7364 kg/m3 at an altitude of 5 km.

A Pharmaceutical company produces three drugs: A, B, and C. It can sell up to 500 kg of each drug at the following prices (per kg):

Drug Sales price

A $10

B $15

C $25

The company can purchase the raw material at $7 per kg. Each kg of raw material can be used to produce either one kg of Drug A or one kg of Drug B. Assume cost of these operations is negligible. For a cost of $4 per kg processed, Drug A can be converted to 0.7 kg of Drug B and 0.3 kg of Drug C. For a cost of $5 per kg processed, Drug B can be converted to 0.9 kg of Drug C. Formulate this problem as a spreadsheet model and use Solver to determine the number of kgs of the raw material to purchase to make Drug A and Drug B, and the number of kgs of Drugs A and B to further process in order to maximize profit from selling the drugs subject to producing more than using each drug and max sales constraints.

Hint: Each operation in this problem has one input and one or more outputs, whereas each operation in the Production Process problem in Session 10 had one output but 1 or more inputs.   So in this problem, instead of "Production of 1 unit of" on the top, put the "Usage of 1 unit of" on the top, and put kgs of each drug to be produced on the left.   Consider the raw material to make Drug A different from that to make Drug B (call them RM1 and RM2). Instead of labour, there is cost.

Problem 6 (Inference via Bayes’ Rule)
Suppose we are given a coin with an unknown head probability θ ∈ {0.3,0.5,0.7}. In order to infer the value θ, we experiment with the coin and consider Bayesian inference as follows: Define events A1 = {θ = 0.3}, A2 = {θ = 0.5}, A3 = {θ = 0.7}. Since initially we have no further information about θ, we simply consider the prior probability assignment to be P(A1) = P(A2) = P(A3) = 1/3.
(a) Suppose we toss the coin once and observe a head (for ease of notation, we define the event B = {the first toss is a head}). What is the posterior probability P(A1|B)? How about P(A2|B) and P(A3|B)? (Hint: use the Bayes’ rule)
(b) Suppose we toss the coin for 10 times and observe HHTHHHTHHH (for ease of notation, we define the event C = {HHTHHHTHHH}). Moreover, all the tosses are known to be independent. What is the posterior probability P(A1|C), P(A2|C), and P(A3|C)? Given the experimental results, what is the most probable value for θ?
(c) Given the same setting as (b), suppose we instead choose to use a different prior probability assignment P(A1) = 2/5,P(A2) = 2/5,P(A3) = 1/5. What is the posterior probabilities P(A1|C), P(A2|C), and P(A3|C)? Given the experimental results, what is the most probable value for θ?