[PM/F5: Tài liệu ôn thi] Part C: Decision-making techniques

Part C sẽ ôn lại 5 dạng bài tập quan trọng môn Performance Management (F5) với chủ đề Decision-making techniques

1. Tổng quan:

Topic	Question types	Question index
		MCQ	Case
Decision-making           techniques	1. Relevant cost analysis	1,2	3
	2. Cost volume profit analysis	4,5,6
	3. Limiting factors	7,8,9	10
	4. Pricing decisions	11,12	13
	5. Dealing with risk and uncertainty in decision‐making	14,15
Reference: BPP ACCA F5 - Performance Management StudyText

2. Dạng bài chi tiết:

2.1. Dạng 1: Relevant cost analysis

Ref: Tóm tắt kiến thức Dạng 1: Relevant cost analysis

Câu 1:

Question: Which of the following terms would not normally be used to describe a relevant cost for a decision?

A. Incremental 
B. Future
C. Material
D. Cash

Answer: C (Ref: F5 BPP - page.34)

Câu 2:

Question: Drippy is producing a list of relevant cash flows regarding a decision she has to make. She is considering launching a new type of USB memory stick that guarantees better protection to the host computer.   

Drippy manages many existing products and has a standing arrangement with a technology magazine for advertising space entitling her to advertise each month.  The contract has just been signed and covers the next twelve months.  Payment is made in the month following an advert appearing.  Drippy is going to use the magazine to advertise her exciting new USB stick.

Is the cost of the advertising space best described as a:

A. Sunk cost
B. Historic cost
C. Relevant cost
D. Committed cost

Answer: D

It could be argued that it is also a sunk cost but the better and more exact description is that it is a committed cost as the cash has not yet been actually paid over. 

Câu 3:

Question: GDP Co specialises in refurbishing the inside of yachts and has been asked to quote, on a relevant cost basis, for the refurbishment of a yacht called Bow. The refurbishment will start in one week’s time. GDP Co has spent $100 obtaining the following information about the refurbishment:

Materials

The material required will be:

• 20m of upholstery fabric  
• 10m of teak wood for the flooring.

The cheapest source for the upholstery fabric would be from an overseas supplier at a cost of $85/m. GDP Co buys most of its fabric from overseas and pays $400 per month to a shipping company as a retainer and then $7.50/m for each metre transported.

GDP Co has 5m of teak wood in inventory which cost $100/m and could be sold at a 5% discount on original cost. This teak is left from a previous job and is stained dark mahogany.

The colour of the stain required for Bow, tan, is lighter and the costs of sanding and staining the teak are:

• sanding $14/m
• staining $4.50/m
• reset of staining machine, arising after each staining job is completed $80.

To ensure the colour of the teak is consistent, all the teak for one job is stained at the same time, and the staining cost is the same irrespective of the age of the teak. The cost of purchasing new teak is $110/m. New teak can be stained the correct colour for Bow with no preparation.

Non‐current assets

A new galley will be required. This can be purchased for $4,500 and the fitting costs will be $2,000. Alternatively, the existing galley can be refurbished. The materials for refurbishment will cost $4,000, and 40 hours of semi‐skilled labour will be employed specifically for the refurbishment at a cost of $15/hr. The fitting costs of the refurbished galley will be 10% less than a new galley.

Labour

100 hours of skilled will be required for the upholstery and flooring work. Skilled labour is paid the market rate of $25/hour and is currently fully employed on another job, where they earn a contribution of $6/hour. Alternatively, new skilled labour could be employed, but the new workers will require training at a cost of $14/hour for the first 10 hours they are working.

Other costs

It is factory policy to add $2,200 per week to a project, for the duration of the project. This is to cover:

Factory rates	$500
Plant and equipment depreciation	$700
Interest on long term loan to purchase plant and equipment	$400
Profit element	$600

1.  What are the figures to be included in the quote for the upholstery fabric and galley?

$_______ upholstery fabric

$_______ galley

2.  What figure should be included in the quote for the teak wood?
A. $1,220
B. $1,140
C. $1,225
D. $1,145

3. What cost should be included in the quote for the skilled? 

$_______ skilled labour 

Guidance:

Step 1: Determine relevant costs required.

Note: Chi phí chìm (sunk costs) không phải là chi phí liên quan vì chi phí này đã thực sự phát sinh trong quá khứ, nó không phải là chi phí tương lai

Chi phí khấu hao (depreciation and amortisation costs) không là chi phí liên quan vì nó không gây ảnh hưởng tới dòng tiền

Chi phí cam kết (committed costs) không là chi phí liên quan vì mặc dù các chi phí này sẽ phát sinh trong tương lai nhưng là không thể tránh được, nó đã được cam kết bởi các quyết định trước đó. Do đó, nó không phải là chi phí gia tăng, phát sinh trực tiếp do quyết định S

Step 2: Determine the requirements and conditions of relevant costs required.

Step 3: Calculating the relevant costs

Labour relevant cost

• If work can be done in idle time => relevant cost = 0
• If labour is fully required => relevant cost is the additional payments required (overtime or additional payment)
• If labour is fully required and no other sources of labour could be used => relevant cost is contribution ignored + direct labour cost

Material relevant cost

• If inventory is unavailable in the warehouse => relevant cost is replacement cost (buy a new one)
• If inventory is available in the warehouse and not used regularly => relevant cost is scrap value
• If inventory is available in the warehouse and used regularly => relevant cost is higher of value in other use and scrap value

Machinery relevant cost

• Incremental cost of using the machine.
• Opportunity cost when using the machine and forgone other use

Answer: 

As we can see, obtaining information cost is sunk cost and $400 shipping fee per month is committed cost. So, the relevant cost excludes 2 of them.

1.    $1,850 upholstery fabric

       $6,400 galley

Step 1: Determine relevant costs required.

There are 2 relevant costs: 

• Material relevant cost: Upholstery fabric
• Machinery relevant cost: Galley

Step 2: Determine the requirements and conditions of relevant costs required

	Requirements	Conditions
Upholstery fabric	20m	Must be bought from overseas
Galley	A new galley required	Buying a new one; or Refurbishing the existing one

Step 3: Calculating the relevant costs

The Upholstery fabric is unavailable in warehouse and must be bought from overseas. So all of 20m have the relevant cost including the cost of it ($85/m) and the transportation fee ($7.50/m). 

🡪 The relevant cost of Upholstery fabric = $85 × 20 + $7.50 × 20 = $1,850  

The relevant cost of Galley is:

The cost of the new one = Cost + Fitting cost = $4,500 + $2,000 = $6,500

The cost of refurbishment = Cost of materials + Labour cost = $4,000 + 40 x $15 = $6,400

🡪 The relevant cost of Galley are $6,400

2.    A

Step 1: Determine relevant costs required.

There is material relevant cost:  Teak wood

Step 2: Determine the requirements and conditions of relevant costs required

	Requirements	Conditions
Teak wood	10m	- 5m are available in inventory; and - 5m have to be bought

Step 3: Calculating the relevant costs

There are 5m of Teak wood available in warehouse and not used regularly. So the relevant cost of them is the higher between value in other use (use on this project) and scrap cost (100 x(1-5%) = $95/m).

The other 5m unavailable in warehouse must be bought.

If the teak in inventory is used, the relevant cost is sale proceeds lost plus the cost of sanding = $95 + $14 = $109. While the cost of purchasing new teak is $110/m.

All the teak needs staining and the machine resetting.

Relevant cost = 5 × $109 + 5 × $110 + $4.50 × 10 + $80 = $1,220

3.    $2,640 skilled labor

Step 1: Determine relevant costs required.

There is labor relevant cost:  Skilled labor

Step 2: Determine the requirements and conditions of relevant costs required

	Requirements	Conditions
Skilled labor	100 hours	- Using skilled labors in the company; or - Employing new skilled labors

Step 3: Calculating the relevant costs

The relevant cost of Skilled labors is the lower between the cost of using available workers and employing new workers.

The existing skilled labour can be used costing ($25 + $6) × 100 = $3,100

OR new labour can be hired and trained costing $25 × 100 + $14 ×10 = $2,640

🡪 The labour relevant cost = $2,640

2.2. Dạng 2: Cost volume profit analysis

Ref: Tóm tắt kiến thức Dạng 2: Cost volume profit analysis

Câu 4:

Question: A company produces and sells a single product. Budgeted sales are $2.4 million, budgeted fixed costs are $360,000 and the margin of safety is $400,000. What are budgeted variable costs?

A. $1.640 million
B. $1.728 million
C. $1.968 million
D. $2.040 million

Answer: C

Margin of safety (unit) = Budgeted sales units – Breakeven sales units

🡪  Breakeven sales units = $2,400,000 - $400,000 = $2,000,000

Sales revenue at BEP	=	Fixed cost
		C/S ratio

🡪  C/S ratio = $360,000/ $2,000,000 = 18%

🡪 Variable costs = (1-18%) x Sales = 82% x $2,400,000 = $1,968,000

Câu 5:

Question: Edward sells two products with selling prices and contributions as follows:

	Product F	Product G
Selling price	$40	$20
Contribution	$10	$4
Budgeted sales units	150,000	100,000

Edwards’s fixed costs are $1,400,000 per year.

What is Edwards’s current breakeven revenue to the nearest $?

A. $100,000 
B. $200,000 
C. $5,600,000 
D. $5,894,737

Answer:

The breakeven revenue (BER) = Fixed costs / Average CS ratio 

BER = $1,400,000/0.2375 (W1) = $5,894,737

W1: 

	Product F	Product G	Total
Budget revenue	$6,000,000	$2,000,000	$8,000,000
Contribution	$2,000,000	$2,000,000	$4,000,000
C/S	0.25	0.2
Average C/S			0.2375

Câu 6:

Question: A company makes and sells a single product. When sales per month are $6.8 million, total costs are $6.56 million. When sales per month are $5.2 million, total costs are $5.44 million. There is a step cost increase of $400,000 in fixed costs when sales are $6.0 million, but variable unit costs are constant at all levels of output and sales.

What is the breakeven point for sales revenue per month?

A. $6.0 million
B. There are two breakeven points: $5.64 million and $6.36 million
C. $5.64 million only
D. $6.36 million only

Guidance: 

(*) Because there are two levels of fixed costs, there must be two breakeven points.

In this case, you need to calculate the variable and fixed costs effectively using the high-low method.

Answer: B

Because there is a step cost increase of 400,000 in fixed costs when the sales are $6.0mil. So we have the total cost excluding the step cost increase at the level of sales $6.8mil are:

The total cost at $6.8mil (excluding $400,000) = $6,560,000 - $400,000 = $6,160,000

The high-low method:

🡪  Variable costs = 45% Sales 🡪 Contribution = 55% Sales 🡪 C/S ratio = 55%

At the level of sales are $5.44 mil:

Fixed cost = Total cost – Variable cost = $5,440,000 – (45% x 5,200,000) = $3,100,000

At the level of sales are $6.8mil:

Fixed cost = Total cost – Variable cost = $6,560,000 – (45% x 6,800,000) = $3,500,000

2.3. Dạng 3: Limiting factors

Ref: Tóm tắt kiến thức Dạng 3: Limiting factor analysis

Câu 7:

Question: A linear programming model has been formulated for two products, A and B, manufactured by J co.  

Which TWO of the following statements about linear programming are true?

A. J Co can use linear programming if it starts to manufacture another product, C.
B. J Co would not need to use linear programming if there was not a demand constraint.
C. J Co should ignore fixed costs when making decisions about how to utilise production capacity in the short run, using linear programming.  
D. Linear programming models can be used when there is an experience curve, once the steady state has been reached

Answer: C, D

The first statement is not true: linear programming is only suitable when there are two

products.

The second statement is not true: there needs to be more than one limiting factor, but it is not essential for one of these two to be the level of demand.

The third statement is correct: fixed costs do not change and do not need to be considered.

The fourth statement is correct: a steady state being reached means that variable costs are constant.

Câu 8:

Question: A company has the following production planned for the next four weeks. The figures reflect the full capacity level of operations. Planned output is equal to the maximum demand per product.

The direct labour force is threatening to go on strike for two weeks out of the coming four. This means that only 2,160 hours will be available for production, rather than the usual 4,320 hours.

If the strike goes ahead, which product or products should be produced if profits are to be maximised?

Guidance: 

Step 1: Determine limiting factor

Step 2: Calculating contribution per unit of limiting factor

Step 3: Establish the optimal production plan

Answer:

Step 1: Determine limiting factor

There are only 2,160 labour hours will be available for production. So, labour hours are the limiting factor.

Step 2: Calculating contribution per unit of limiting factor

If there are only 2,160 labour hours will be available for production, the company should produce Product A and Product D. Product C and Product D should not be produced.

Therefore, make all of 400 product D. Then, 1,360 hours (2,160 hours – 800 hours) remaining can be used to produce product A. The number of product A produced are 227 products.

Câu 9:

Question: A jewellery company makes rings (R) and necklaces (N). 

The resources available to the company have been analysed and two constraints have been identified:

 Labour time 3R + 2N < 2,400 hours                            Machine time 0.5R + 0.4N < 410 hours 

The management accountant has used linear programming to determine that R = 500 and N = 400.   Which of the following is/are slack resources?

1. Labour time available 
2. Machine time available 
   A. 1 only 
   B. 2 only 
   C. Both 1 and 2 
   D. Neither 1 nor 2

Answer: A

If the values for R and N are substituted into the constraints:

Labour required = (3 × 500) + (2 × 400) = 2,300 hours which is less than what is available so there is slack.

Machine time required = (0.5 × 500) + (0.4 × 400) = 410 hours which is exactly what is available and so there is no slack.

Câu 10:

Question: 

COMESTIC CO (12/10 AMENDED)

The Cosmetic Co is a company producing a variety of cosmetic creams and lotions. The creams and lotions are sold to a variety of retailers at a price of $23.20 for each jar of face cream and $16.80 for each bottle of body lotion. Each of the products has a variety of ingredients, with the key ones being silk powder, silk amino acids, and aloe vera. Six months ago, silk worms were attacked by disease causing a huge reduction in the availability of silk powder and silk amino acids. The Cosmetic Co had to dramatically reduce production and make part of its workforce, which it had trained over a number of years, redundant. 

The company now wants to increase production again by ensuring that it uses the limited ingredients available to maximize profits by selling the optimum mix of creams and lotions. Due to the redundancies made earlier in the year, the supply of skilled labour is now limited in the short term to 160 hours (9,600 minutes) per week, although unskilled labour is unlimited. The purchasing manager is confident that they can obtain 5,000 grams of silk powder and 1,600 grams of silk amino acids per week. All other ingredients are unlimited. The following information is available for the two products:

	Cream	Lotion
Material required: Silk powder (at $2.20 per gram)	3 grams	2 grams
Silk amino acids (at $0.8 per gram)	1 gram	0.5 grams
Aloe vera (at $1.40 per gram)	4 grams	2 grams
Labour required: Skilled ($12 per hour)	4 minutes	5 minutes
Unskilled (at $8 per hour)	3 minutes	1.5 minutes

Each jar of cream sold generates a contribution of $9 per unit, whilst each bottle of lotion generates a contribution of $8 per unit. The maximum demand for lotions is 2,000 bottles per week, although demand for creams is unlimited. Fixed costs total $1,800 per week. The company does not keep inventory although if a product is partially complete at the end of one week, its production will be completed in the following week. 

Required 

a) On the graph paper provided, use linear programming to calculate the optimum number of each product that the Cosmetic Co should make per week, assuming that it wishes to maximise contribution. Calculate the total contribution per week for the new production plan. All workings must be rounded to two decimal places. (10 marks) 
b) Calculate the shadow price for silk powder and the slack for silk amino acids. All workings must be rounded to two decimal places. (5 marks) 

Guidance:

Step 1: Define variables

Step 2: Establish objective function

Step 3: Establish constraints

Step 4: Establish coordinates to plot lines representing the inequalities

Step 5: Draw the graph

Step 6: Find the optimal solution using an iso-contribution line

Answer:

a)    Total contribution per week = 17,514.34

Step 1: Define variables

Let x = number of jars of face cream to be produced

Let y = number of bottles of body lotion to be produced 

Let C = contribution

Step 2: Establish objective function

The objective is to maximise contribution (C) 

Face cream contribution (x) = $9.00 per unit 

Body lotion contribution (y) = $8.00 per unit Maximise C = 9x + 8y, subject to the constraints below.

Step 3: Establish constraints

Silk powder: 3x + 2y ≤ 5,000 

Silk amino acids: 1x + 0.5y ≤ 1,600 

Skilled labour: 4x + 5y ≤ 9,600 

Non-negativity constraints: x, y ≥ 0 

Maximum demand for body lotion: y ≤ 2,000

Step 4: Establish coordinates to plot lines representing the inequalities

Silk powder: 3x + 2y x 5,000

If x = 0, y = 2,500

If y = 0, x = 1,666.7

Silk amino acids: 1x + 0.5y x 1,600

If x = 0, y = 3,200

If y = 0, x = 1,600

Skilled labour: 4x + 5y x 9,600

If x = 0, y = 1,920

If y = 0, x = 2,400

Also, plot the line y = 2,000 (maximum weekly demand for body lotion).

Step 5: Draw the graph

Step 6: Find the optimal solution using an iso-contribution line

C = 9x + 8y

If C = (8 x 800) = 6,400, then:

If y = 0, 9x = 6,400

Therefore x = 711.11

By moving the iso-contribution line out across the graph, it is clear that the optimal solution lies as point C, the intersection of the constraints for skilled labour and silk powder.

Solving the simultaneous equations for these constraints:

4x + 5y = 9,600 x 3

3x + 2y = 5,000 x 4

12x + 15y = 28,800 (1)

12x + 8y = 20,000 (2)

Subtract (2) from (1):

7y = 8,800

y = 1,257.14

If y = 1,257.14 and;

4x + 5y = 9,600

The 5 x 1,257.14 + 4x = 9,600

Therefore x = 828.58

The optimal solution is therefore to make 828.58 jars of face cream and 1,257.14 bottles of body lotion.

	$
Contribution
Face cream: 828.58 units x unit contribution of $9.00	7,457.22
Body lotion: 1,257.14 units x unit contribution of $8.00	10,057.12
	17,514.34

b)    Shadow price = $1.83 per gram

       Slack = 142.85 gram

Shadow price for silk powder: 

The shadow price for silk powder can be found by solving the two simultaneous equations that intersect at point C on the graph in part (a). The shadow price is the increase in value which would be created by having one additional unit of limiting factor. For this reason, we must add one more hour to the equation for silk powder.

4x + 5y = 9,600 x 3

3x + 2y = 5,001 x 4

12x + 15y = 28,800 (1)

12x + 8y = 20,004 (2)

Subtract (2) from (1):

7y = 8,796

y = 1,256.57

3x + (2 x 1,256.57) = 5,001

x = 829.29

C = (9 x 829.29) + (8 x 1,256.57) = $17,516.17

Original contribution = $17,514.34

The shadow price for silk powder is, therefore, $1.83 per gram.

Slack for amino acids:

Each unit of face cream requires 1 gram of silk amino acids and each unit of body lotion requires 0.5 grams of amino acids.

(828.58 x 1) + (0.5 x 1,257.14) = 1,457.15 grams used

Grams available = 1,600 grams

Therefore slack = 142.85 grams

2.4. Dạng 4: Pricing decisions

Ref: Tóm tắt kiến thức Dạng 4: Pricing decisions - Phần 1

  Pricing decisions - Phần 2

Câu 11:

Question: Which of the following statements regarding market penetration as a pricing strategy is/are correct? 

1. It is useful if significant economies of scale can be achieved.
2. It is useful if demand for a product is highly elastic. 
   A. 1 only 
   B. 2 only 
   C. Neither 1 nor 2
   D. Both 1 and 2

Answer: D

Penetration pricing involves setting a low price when a product is first launched in order to obtain strong demand.

It is particularly useful if significant economies of scale can be achieved from a high volume of output and if demand is highly elastic and so would respond well to low prices.

Câu 12:

Question: A product has a prime cost of $12, variable overheads of $3 per unit, and fixed overheads of $6 per unit.

Which pricing policy gives the highest price?

A. Prime cost + 80% 
B. Marginal cost + 60%
C. TAC + 20%
D. Net margin of 14% on selling price

Answer: C

Prime cost + 80% = 12 × (1.8) = $21.6

MC + 60% = 15 × (1.6) = $24.00

TAC + 20% = 21 × (1.2) = $25.20

Net margin would mean 21 × 100/86 = $24.40

Câu 13:

Question: 

BELTON PARK RESORT

Belton Park Resort is a new theme park resort located in the country of Beeland. The resort is made up of a theme park, a hotel, and an indoor water park. The resort opened two months ago and is already very popular.

As all theme parks in Beeland are required, by law, to shut down in the colder month of January because of the risk of accidents, Belton Park Resort must decide whether to shut down the whole resort or just the theme park. It could choose to keep open the hotel and/or the water park.

Since Belton Park Resort has not been open for long, there is limited historical data available about costs and revenues.

However, based on the last two months, the following average monthly data is available:

Hotel

Number of rooms	120
Average room rate per night	$100
Average occupancy rate per month	90%
Average nightly spend on ‘extras’ per room	$20
Average nightly spend on ‘extras’ per room*	60%

Water park

Number of visitors per month	12000
Admission price per visitor	$21
Average spend on ‘extras’ per visitor	$12
Contribution margin for ‘extras’*	60%

*‘Extras’ includes anything purchased by the customer not included in the room rate or admission price.

Management estimates that, for January, the average room rate per night would need to decrease by 30% and the admission price for the water park by 20%. With such reductions, it is estimated that an occupancy rate of 50% would be achieved for the hotel and that the number of visitors to the water park would be 52% lower than current levels. The average nightly spend on ‘extras’ per room of $20 at the hotel and $12 per customer at the water park is expected to remain unchanged.

The running costs for the hotel and water park for each of the last two months are as follows:

	Notes	Hotel	Water park
		$	$
Staff costs	1	120,000	75,600
Maintainance costs	2	14,600	6,000
Power costs	3	20,000	18,000
Security costs	4	13,600	8,000
Water costs	5	12,900	12,100

Notes:

(1) Staff costs

Permanent staff

Included in the staff costs for the hotel are the salary of $30,000 per annum for the hotel manager and $24,000 per annum for the head chef. These are both permanent members of staff who are paid for the full year regardless of their working hours. 

The water park employs one permanent member of staff, the manager, on a salary of $24,000 who is also paid for the full year regardless of his working hours.

Temporary staff

The remaining staff costs relate to temporary staff who are only paid for the hours they work. If the hotel stays open in January, half of these staff members will continue to work their current hours because their jobs are largely unaffected by guest occupancy rates. However, the other half of the staff will work proportionately fewer hours to reflect the 50% occupancy rate in January as opposed to the 90% occupancy rate of the last two months. 

At the water park, the temporary staff’s working hours will fall according to the number of visitors, hence a fall of 52% would be expected for January.

(2) Maintenance costs

Maintenance is undertaken by a local company, ‘Techworks’, which bills Belton Park Resort for all work carried out each month. If the hotel and water park are closed, Techworks will instead be paid a flat fee for the month of $4,000 for the hotel and $2,000 for the water park.

(3) Power costs

Electricity 

Belton Park Resort pays a fixed monthly charge for electricity of $8,000 for the hotel and $7,000 for the water park, all year round. 

Gas 

The gas charges relate to heating and include a fixed charge of $2,200 per month for the hotel and $1,500 per month for the water park. The remainder of the gas charges is based solely on usage and would be expected to increase by 50% in January because of the colder weather. 

(4) Security costs 

If the hotel and water park close, no changes will be made to the current arrangements for security whilst the premises are empty. 

(5) Water costs 

It is estimated that water costs for the hotel would fall to $6,450 for the month if it remains open in January. However, the water costs for the water park would be expected to remain at their current level. If the hotel and water park were closed, all water would be turned off and no charges would arise. 

Required: 

Calculate the incremental cash flows, for the month of January (31 days), if Belton Park Resort decides to keep open: 

    i.   the hotel; 
    ii.  the water park. 

In each case, state whether it should remain open or should close. 

Guidance:

Step 1: Calculate revenue (Cash inflows)

Step 2: Calculate costs (Cash outflows)

Step 3: Calculate profit or loss (Incremental cash flows)

• If a project has positive incremental cash flows (Cash inflows > Cash outflows), the company should open it.
• And if it has negative incremental cash flows (Cash inflows < Cash outflows), it should be closed.

Answer:

Calculate the incremental cash flows and state whether the projects should remain open or should close.

Step 1: Calculate revenue (Cash inflows)

The Hotel:

Step 2: Calculate costs (Cash outflows)

Step 3: Calculate profit or loss

The Hotel:

Incremental cashflows = Cash inflows – cash outflows = $152,520 - $121,583 = $30,937

The Water park:

Incremental cashflows = Cash inflows – cash outflows = $138,240 - $65,678 = $72,562

🡪 Both of them should stay open because the incremental cash flows are both positive.

2.5. Dạng 5: Dealing with risk and uncertainty in decision‐making

Ref: Tóm tắt kiến thức Dạng 5: Risk and Uncertainty - Phần 1

  Risk and Uncertainty - Phần 2

Câu 14: 

Question: A company is considering the development and marketing of a new product.  Development costs will be $2m.  There is a 75% probability that the development effort will be successful, and a 25% probability that it will be unsuccessful. If development is successful and the product is marketed, it is estimated that:

	Expected profit	Probability
Product very successful	$6.0m	0.4
Product moderately successful	$1.8m	0.4
Product unsuccessful	($5.0m)	0.2

What is the expected value of the project? 

A. ($0.41m) 
B. $2.12m 
C. $1.59m 
D. $0.41m

Answer:

(W1) EV =   ($6m × 0.4) + ($1.8m × 0.4) – ($5m × 0.2) =   $2.12m

(W2) EV   =   ($2.12m × 0.75) + ($Nil × 0.25) = $1.59m

Net benefit:   $1.59m – $2m = ($0.41m)

Câu 15:

Question: Shuffles is attempting to decide which size of fork‐lift truck to buy to use in its warehouses.   There are three grades of the truck, the A series, B series, and the C series.    The uncertainty faced is the expected growth in the on‐line market it serves, which could grow at 15%, 30%, or even 40% in the next period.    

Shuffles has correctly produced the following decision table and has calculated the average daily contribution gained from each combination of truck and growth assumption.

Decision table		Type of truck
		A series	B series	C series
Growth rate	15%	$2,400	$1,800	$3,600
	30%	$1,400	$1,900	$4,500
	40%	$4,900	$2,800	$3,900

Based upon the scenario information, if the probabilities of the given growth rates are 15%: 0.4, 30%: 0.25, and 40%: 0.35, which truck would the risk‐neutral buyer purchase?

Answer: C Series

Expected value calculations: 

A Series:  ($2,400 × 0.4) + ($1,400 × 0.25) + ($4,900 × 0.35) = $3,025 

B Series:  ($1,800 × 0.4) + ($1,900 × 0.25) + ($2,800 × 0.35) = $2,175 

C Series:  ($3,600 × 0.4) + ($4,500 × 0.25) + ($3,900 × 0.35) = $3,930

 

Author: Quang Dung