Question

a company is considering making a new product. estimate the probability that the new product is successful is 0.75. if it is successful it will generate $240,000 in revenue. if it is not successful, it would not generate any revenue. the cost to develop the product is $196,000. use profit (revenue - cost) and expected value to decide whether the company should make this product. which of the following did your solution include? p = $240,000 - $196,000 = $44,000. the expected value is a weighted average of each possible value weighted by its probability. ev = ($44,000)(0.75)+($ - 196,000)(0.25) = $ - 16,000. the expect average profit is $ - 16,000. the company should not make the product.

Explanation:

Step1: Calculate profit if successful

If successful, revenue is $240000$ and cost is $196000$. Profit $P$ if successful is $P = 240000 - 196000=\$44000$.

Step2: Define probabilities

Probability of success $p_1 = 0.75$, probability of failure $p_2=1 - 0.75 = 0.25$. Profit if failure is $- 196000$ (as cost is incurred and no revenue).

Step3: Calculate expected value

The expected - value formula for a discrete random variable is $EV=p_1\times\text{Profit}_1 + p_2\times\text{Profit}_2$. Substitute values: $EV=(44000)\times(0.75)+(-196000)\times(0.25)$.
$EV = 44000\times0.75-196000\times0.25=33000 - 49000=-\$16000$.

Answer:

The expected value is a weighted average of each possible value weighted by its probability.
$EV=(44000)(0.75)+(-196000)(0.25)=-\$16000$
The expect average profit is $-\$16000$
The company should not make the product.