A company has to decide whether to invest money in the development of a microbio

Question

A company has to decide whether to invest money in the development of a microbiological product. The company’s research director has estimated that there is a 60% chance that a successful development could be achieved in two years. However, if the product had not been successfully developed at the end of this period, the company would abandon the project, which would lead to a loss in present value terms of $3 million. Present value is designed to take the company’s time preference for money into account. In the event of a successful development a decision would have to be made on the scale of production. The returns generated would depend on the level of sales which could be achieved over the period of the product’s life. For simplicity, these have been categorized as either high or low. If the company opted for large volume production and high sales were achieved, then net returns with a present value of $6 million would be obtained. However, large-scale production followed by low sales would lead to net returns with a present value of only $1 million. On the other hand, if the company decided to invest only in small-scale production facilities then high sales would generate net returns with a present value of $4 million and low sales would generate net returns with a present value of$2 million. The company’s marketing manager estimates that there is a 75% chance that high sales could be achieved.

C) There is some debate in the company about the probability that was estimated by the research director. Assuming that all other elements of the problem remain the same, determine how low this probability would have to be before the option of not developing the product should be chosen.

Present Value of net returns

New owner’s utility

-$3m

0

$0m

0.6

$1m

0.75

$2m

0.85

$4m

0.95

$6m

1.0

Present Value of net returns

New owner’s utility

-$3m

0

$0m

0.6

$1m

0.75

$2m

0.85

$4m

0.95

$6m

1.0

Explanation / Answer

60% chance successful in 2 years otherwise -- Larger production high sales -- 6 m profit

-- Large production low sales -- 1 million return

-- low production high sales -- 4 million return

-- low production low sales -- 2 million return

Prob for high sales =0.75 and low sales = 0.25

40% chance loss of 3 million

Since expected value of utility is negative, not advisable to start with the project

-------------------------------------------------

Let us assume p and q instead of 0.6 and 0.4

When p <0.7843before the option of not developing the product should be chosen.

Present Value of net returns Successful Not successful Larger production Small production Large sales Small sales Net probability New owner’s utility Utility * prob -$3m 0.6 0.4 0.5 0.5 0.75 0.25 0.4 -3 -1.2 $0m 0 0 0 $1m High prod and low sales (0.3)(0.5)(0.25) 0.075 0.6 0.045 $2m Low prod and low sales (0.6)(0.5)(0.25) 0.075 0.75 0.05625 $4m Low prod and high sales (0.6)(0.5)(0.75) 0.225 0.85 0.19125 $6m High prod and high sales (0.6)(0.5)(0.75) 0.225 0.95 0.21375 1 1 -0.69375

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