Question

The Heaton Electronics Company produces SD memory cards in sizes ranging from 2GB to 32GB. The management team are looking at options for growing the company in the future. The company has identified three options for growth.

• Keep the product range the same but increase the factory capacity to produce more of the products
• Expand the product range to include larger memory cards (up to 124 GB)
• Invest in new technology for manufacturing cards with extremely large memory sizes.

The management team believe that the profit (after investment) over the next three years will depend on whether the demand for the larger memory card sizes grows slowly, moderately or at a rapid rate. The potential profit under each market condition is shown below

Table: Potential profit (in £millions)

	Growth in the demand for larger memory cards
Option	Slow	Moderate	Rapid
Increase the factory capacity	2.0	1.3	1.2
Expand the product range up to 124 GB	1.3	1.5	1.6
Invest in new technology	0.8	2.5	3.8

Part a)

i) What is the best decision using the Maximax rule?

ii) What is the best decision using the Maximin rule?

[2 marks]

Part b)

What is the best decision using the Minimax Regret rule (show your working, include your opportunity losses in your answer)

[4 marks]

Part c)

The company decide to use a Hurwicz criterion of alpha (  ) = 0.6. Calculate the best decision using the Hurwicz criterion. (show your working in your answer)

[4 marks]

Part d)

Are the company being optimistic or pessimistic using an alpha of 0.6 for the Hurwicz criterion? Briefly explain your answer.

[2 marks]

Part e)

The company narrow down the choice to either expanding the product range or investing in new technology. Both projects generate cash flow at different stages of the project. The cash flow generated at each stage is shown below. Using a discount rate (r) of 2.5%, calculate the Net Present Value (NPV) for both projects and determine the best decision based on the NPV.

Table: Cash flow comparison for two projects

	Cash Flow
Year	Invest in New Technology	Expand Product Range
0	-1.4	-0.5
1	1.0	0.7
2	4.2	1.4

[6 marks]

Answer 1

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	Growth in the demand for larger memory cards
Options	Slow	Moderate	Rapid	Maximum	Minimum
Increase the factory capacity	2.0	1.3	1.2	2.0	1.2
Expand the product range upto 124 GB	1.3	1.5	1.6	1.6	1.3
Invest in new technology	0.8	2.5	3.8	3.8	0.8

Part (a)

i) Maximax = Max ( 2.0 , 1.6 , 3.8 ) = 3.8

Thus, according to Maximax criteria, Investing in a new technology is the best decision.

ii) Maximin = Max ( 1.2 , 1.3 , 0.8 ) = 1.3

Thus, according to Maximin criteria, Expand the product range upto 124 GB is the best decision.

Part (b)

For Minimax Regret , a regret matrix is needed. Thus, a regret matrix is obtained by deducting each value of the table from maximum cell value of it's corresponding column. for eg : For

	Growth in the demand for larger memory cards
Options	Slow	Moderate	Rapid	Maximum
Increase the factory capacity	0	1.2	2.6	2.6
Expand the product range upto 124 GB	0.7	1	2.2	2.2
Invest in new technology	1.2	0	0	1.2

Therefore, Minimax = Min ( 2.6 , 2.2 , 1.2 ) = 1.2

Therefore, according to Minimax regret criteria, Investing in a new technology is the best decision.

Part (c)

Hurwicz = Max * + Min * ( 1 - )   , where = 0.6

	Growth in the demand for larger memory cards
Options	Slow	Moderate	Rapid	Maximum	Minimum	Hurwicz
Increase the factory capacity	2.0	1.3	1.2	2.0	1.2	1.68
Expand the product range upto 124 GB	1.3	1.5	1.6	1.6	1.3	1.48
Invest in new technology	0.8	2.5	3.8	3.8	0.8	2.6

Max (Hurwicz) = 2.6

Thus, according to Hurwicz criteria, Investing in a new technology is the best decision.

Part (d)

Since the = 0.6 > 0.5 , the company is having an optimistic approach towards the project.

Part (e)

r = 0.025

For Invest in new technology,

NPV1 = -1.4 * ( 1+r )^0 + 1 * ( 1+r )^1 + 4.2 * ( 1+r )^2 = 3.573 units.

For Expand product range,

NPV2 = -0.5 * ( 1+r )^0 + 0.7 * ( 1+r )^1 + 1.4 * ( 1+r )^2 = 1.5155 units.

Since NPV1 > NPV2, the company should proceed with Invest in new technology option as per the NPV