Sample Spaces

1. Suppose S is a uniform sample space with N elements. If E is any possible come and ω is the probability function for S evaluate ω(e).

2. Define a probability function on the set A = {1, 2, 3} such that A is not a uniform sample space.

3. Given the sample space B = {a, b, c} and probability function ω on B. If ω(a) = 0.3, ω({a, b}) = 0.8 then find ω(b) and ω(c).

4. Suppose that only 30% of a birds hatchlings survive their first year. If a bird hatches 7 chicks, what is the probability exactly 3 will survive their first year? What is the probability at most 3 will survive?

Tom is making calls door to door in a neighborhood of 45 houses to give out gift cards for a new supermarket. He leaves a gift card only on those calls for which the door is answered. On any call the probability of the door being answered is 40%.

a) Find the probability that Tom gives away at most 2 gift cards in the first 5 calls.

b) Given that he has given away exactly 2 gift cards on his first 5 calls, find the probability that Tom will give away the 5th gift card on the 10th call.

c) Find the expected total number of cards given out when he is done.

Top Toys is planning a new radio and TV advertising campaign. A radio commerical costs $300 and a TV ad costs $2000. A total budget of $20,000 is allocated to the campaign. However, to ensure that each medium will have at least one radio commercial and one TV ad, the most that can be allocated to either medium cannot exceed 80% of the total budget. It is estimated that the first radio commerical will reach 5000 people, with each additional commercial reaching only 2000 more people. For TV, the first ad will reach 4500 people, and each additional ad an additional 3000 people. How should the budgeted amount be allocated between radio and TV?

2. Tom is making calls door to door in a neighborhood of 45 houses to give out gift cards for a new

supermarket. He leaves a gift card only on those calls for which the door is answered. On any call the probability of the door being answered is 40%.

1. a) Find the probability that Tom gives away at most 2 gift cards in the first 5 calls.

2. b) Given that he has given away exactly 2 gift cards on his first 5 calls, find the probability that Tom

   will give away the 5th gift card on the 10th call.

3. c) Find the expected total number of cards given out when he is done.

Case Background

A sole proprietor (the owner) has established a service business specializing in recruitment for businesses needing specialized Tool Industry staff. The trail balance at the end of the first three months of operations is provided below. Part of the service is to train people before they are placed with companies. The owner has asked, you, the accountant for HR, to prepare the answers to the questions below considering the notes provided.

Trial Balance

Notes

1. The owner issued a cheque for $2,000 for insurance for the next three month after discovering there was no insurance in place. The cheque has not been recorded as a reduction of cash to-date. There is no insurance expense for the first three months.

2. The equipment must be depreciated for three months. The equipment has a service life of 5 years and monthly depreciation is estimated to be $833 a month.

3. Recorded revenue of $5,000 is unearned and was an advance from a client. This revenue will be earned in the next three months.

4. Salaries of $15,000 were paid in the first three months. However, $1,000 of salaries should be accrued as employees earned these salaries but will not be paid until the 4th month.

5. The owner provided services of $2,500, which were not invoiced or billed to clients in the 3rd month but were earned in accordance with the Revenue Principle.

6. Interest expense (Debit) needs to be recorded at the end of three months. The amount is $750 and should be recorded as a liability in Interest Payable (Credit) on the balance sheet. None of the $50,000 note has been paid to lenders yet. This note will be paid back at the end of 5 years.

7. Supplies of $1,500 must be expensed to Cost of Goods Sold (i.e., moved out of inventory) and a new accrual of Accounts Payable should be established for $2,000 for supplies ordered at the end of the 3rd month, and not booked to-date.

Questions

1. Which inventory system (perpetual or periodic) would provide the most cost-benefit to the owner?

Question 1.1
C Ltd makes two products, Alpha and Beta. The following data is relevant for year 3:
Material M
£2 per unit
Material N
£3 per unit
Direct labour is paid £10 per hour.
Production overhead cost is estimated to be £200,000, which includes £25,000 for depreciation of property and equipment. Production overhead cost is absorbed into product costs using a direct labour hour absorption rate.
Each finished unit requires:
Alpha Beta

Material M 12 units   12 units

Material N 6 units   8 units

Direct labour 7 hours   10 hours


The sales director has forecast that sales of Alpha and Beta will be 5,000 and 1,000 units, respectively, during year 3.
The selling prices will be:
Alpha £182 per unit

Beta   £161 per unit

She estimates that the inventory at 1 January, year 3, will be 100 units of Alpha and 200 units of Beta. At the end of year 3 she requires the inventory level to be 150 units of each product.
The production director estimates that the raw material inventories on 1 January, year 3, will be 3,000 units of material M and 4,000 units of material N.
At the end of year 3 the inventories of these raw materials are to be:
M: 4,000 units
N: 2,000 units
The finance director advises that the rate of tax to be paid on profits during year 3 is likely to be 30%. Selling and administration overhead is budgeted to be £75,000 in year 3, which includes £5,000 for depreciation of equipment.

A quarterly cash-flow forecast has already been completed:

Year 3 Quarter 1 Quarter 2 Quarter 3 Quarter 4 £ £ £ £
Receipts:
196,000
224,000
238,000
336,000
Payments:
Materials
22,000
37,000
40,000
60,000
Direct wages
100,000
110,500
121,000
117,000
Overhead
45,000
50,000
70,000
65,000
Taxation
5,000
Machinery purchase

The company's balance sheet at 1st January year 3 is expected to be as follows:
£ £ £
Non-current assets:
Cost
Depreciation
NBV
Land
50,000
50,000
Building and Equipment
400,000
75,000
325,000
450,000
75,000
375,000
Current assets:
Inventories
Raw materials
20,000
Finished goods
15,000
35,000
Receivables (Debtors)
25,000
Cash at bank
10,000
70,000
less Current liabilities:
Payables
9,000
Taxation
5,000
14,000
Working Capital
56,000
431,000
Financed by:
Share capital
350,000
Retained earnings
81,000
431,000
Required:
You are required to prepare the company's budgets for year 3 including a budgeted Income Statement for the year and a Balance Sheet at 31 December, year 3.
Page | 2
Question 1.2
The budgeted balance sheet data of Umbago Ltd is as follows:
Balance sheet as at 1st March £ £ £
Non-Current assets:
Cost
Depreciation
NBV
Land and Building
500,000
500,000
Machinery and Equipment
124,000
84,500
39,500
Motor vehicles
42,000
16,400
25,600
666,000
100,900
565,100
Current Assets
Stock of raw materials (100 units)
4,320
Stock of finished goods (110 units)a
10,450
Debtors (January £7,680, February £10,400)
18,080
Cash and Bank
6,790
39,640
Less current liabilities
Creditors (raw materials)
3,900
Working Capital
35,740
600,840
Financed by:
Ordinary share capital (fully paid £1 per share)
500,000
Share premium
60,000
Profit and loss account
40,840
600,840
a The stock of finished goods was valued at marginal cost
The estimates for the next four-month period are as follows:
March April May June
Sales (units)
80
84
96
94
Production (units)
70
75
90
90
Purchase of raw materials (units)
80
80
85
85
Wages and variable overheads @ £65 per unit
£4,550
£4,875
£5,850
£5,850
Fixed overheads
£1,200
£1,200
£1,200
£1,200
The company intends to sell each unit for £219 and has estimated that it will have to pay £45 per unit for raw materials. One unit of raw material is needed for each unit of finished product.
All sales and purchases of raw materials are on credit. Debtors are allowed two months' credit and suppliers of raw materials are paid after one month's credit. The wages, variable overheads and fixed overheads are paid in the month in which they are incurred.
Page | 3
Cash from a loan secured on the land and building of £120,000 (at 7.5% interest rate) is due to be received on 1st May. Machinery costing £112,000 will be received in May and paid for in June.
The loan interest is payable half yearly from September onwards. An interim dividend to 31 March of £12,500 will be paid in June.
Depreciation for the four months, including that on the new machinery, is:
Vehicle and equipment
£15,733 Motor vehicle
£3,500
The company uses the FIFO method of stock valuation. Ignore taxation.
Required:
a) Calculate and present the raw materials budget and finished goods budget in terms of units, for
each month from March to June inclusive.
b) Calculate the corresponding sales budget, the production cost budgets and the budgeted closing
debtors, creditors and stocks in terms of value.
c) Prepare and present a cash budget for each of the four months.

d) Prepare a master budget, i.e. Budgeted trading profit and loss account, for the four months to 30
June, and budgeted balance sheet as at 30 June
e) Advise the company about possible ways in which it can improve its cash management.
Total 35 Marks
(questions from ACCA Managerial Finance exam)
Page | 4

A public school district is investigating whether to purchase a new school bus to take over the rural-most route in the district. They have two options:

A modern, eco-friendly bus complete with seat belts and air conditioning, will have a first cost of $95,000, cost savings (in terms of fuel efficiency and maintenance costs) of $20,000/year the first year, and decreasing by $1000 per year thereafter (so $19,000 the second year, 18,000 the third year, etc…). It’s estimated that the salvage value will be $8,000 at the end of its 20 year life.

A more basic bus will have a first cost $70,000, cost savings of $14,000 per year decreasing by $500 per year each year thereafter (so $13,500 the second year, $13,000 the third year, etc.).It is estimated that the salvage value will be $5000 at the end of its 20-year life.

Assume that the school district also has the option to stay with their current fleet (so the do nothing option is also available).

A) Use Benefits to Costs analysis to determine which of the options, if any, would be most economical for the school district if their MARR is 5%.

B) Compute the value of X- i.e., the first cost of the modern bus- that makes the two alternatives in this example equally desirable:

C) In this problem only the economic consequences were evaluated. Do you think this type of decision is only economic, or are there other factors that could/would/should be considered? Briefly discuss…

(if using excel please provide code)

) A public school district is investigating whether to purchase a new school bus to take over the rural-most route in the district. They have two options:

A modern, eco-friendly bus complete with seat belts and air conditioning, will have a first cost of $95,000, cost savings (in terms of fuel efficiency and maintenance costs) of $20,000/year the first year, and decreasing by $1000 per year thereafter (so $19,000 the second year, 18,000 the third year, etc…). It’s estimated that the salvage value will be $8,000 at the end of its 20 year life.

A more basic bus will have a first cost $70,000, cost savings of $14,000 per year decreasing by $500 per year each year thereafter (so $13,500 the second year, $13,000 the third year, etc.).It is estimated that the salvage value will be $5000 at the end of its 20-year life.

Assume that the school district also has the option to stay with their current fleet (so the do nothing option is also available).

A) Use Benefits to Costs analysis to determine which of the options, if any, would be most economical for the school district if their MARR is 5%.

B) Compute the value of X- i.e., the first cost of the modern bus- that makes the two alternatives in this example equally desirable:

C) In this problem only the economic consequences were evaluated. Do you think this type of decision is only economic, or are there other factors that could/would/should be considered? Briefly discuss…

(if using excel please post code)