Question

A small firm has developed a new machine to manufacture steel canisters. The machine is a considerable improvement over the ones currently available in the market in terms of size and noise suppression. If the company’s management decides to manufacture this new machine, it is almost certain that the larger firms in the industry will copy the design and take the majority of the market through price competition. As such, management is also considering the possibility of entering into a partnership agreement with one of the larger firms on a 50-50 arrangement on profit and cost distribution to minimize their exposure or simply selling the design for the new machine to one of the larger firms for P10,000,000. Management feels that the decision depends mostly on expected profit in the first year of production if they pursue the manufacturing of the machine. The costs of setting up the production lines and marketing the new machine are estimated to be P25,000,000. The variable cost of the machine is about P1,000,000 per machine, and the firm plans to sell the machine for P1,500,000. To simplify the analysis, the company is assuming that there will be no demand or that the market demand will be either 50 or 75 machines.

What would be the investment choices given the following criteria:

- Maximin

- Maximax

- Minimax regret

What would be the investment choice if each state of nature would be given an equal probability of occurrence?

Answer 1

First, let’s create the table. The decision that the firm needs to make is partnership or production.

In case of partnership the setup cost is P 10 million. However sharing the profit and cost, means that profit per machine will be (1.5 -1.0)/2 = P 0.25 million. Hence in case of 0 demand the total cost is P 10 million. In case of 50 demand, the profit is (50*0.25 - 10) = 2.5 and in case of 75 demand the profit is (75*0.25 – 10) = 8.75. (All figures are in millions of P)

Similarly in case of production, the setup cost is P 25 million. However the profit per machine is P 0.5 million. In case of 0 demand there will a loss of P25 million, in case of 50 demand there will be a profit of (50*0.5 – 25) = 0 and in case of 75 demand there will a profit of (75*0.5 – 25) = 12.5.

Now let’s draw the payoff table

Maximin: we shall choose the best among the worst expectation. The worst payoff in each decision is loss of 25 million and loss of 10 million. The best option is to choose the loss of 10 million. In other words, through maximin we shall choose partnership with other company

Maximax: we shall choose the best among the best expectation. The best expectation among the two decisions are profit of 8.75 and profit of 12.5. The best among these is 12.5 and hence we shall choose production through maximax approach.

Minimax regret: For this we need to use the regret table. The regrets are calculate for each column. For the best option we use 0. As if we choose this then there is no regret. However, in case if we decide otherwise then the difference between the best possible option and chosen option is the regret. Using the regret table we have maximum regret as 3.75 and 15. Among the two we shall choose the minimum. Hence through minimax regret approach we shall choose partnership.