Question

Assume that a firm, StableCo, faces a 0.4% chance of filing for bankruptcy per month. Over the course of 25 years, what is the probability that StableCo will file for bankruptcy?

Answer 1

The question requires calculating the probability of StableCo filing for bankruptcy over 25 years with a known monthly probability. The calculation involves using the complement rule to find the probability of not filing for bankruptcy each month and exponentiating this over 300 months, before subtracting from one to find the chance of at least one bankruptcy filing.

Step-by-step explanation:

The question asks for the probability that StableCo will file for bankruptcy over the course of 25 years, given a monthly bankruptcy probability of 0.4%. To solve this, we can use the complement rule, which states that the probability of an event not occurring is 1 minus the probability of the event occurring. The event occurring in any given month is independent of it occurring in any other month, so we multiply the probabilities across all months to get the probability of the company never filing for bankruptcy, and then subtract from 1.

First, let's calculate the probability that StableCo does not file for bankruptcy in any given month. This is 1 - 0.4%, or 0.996.

Since there are 12 months in a year, 25 years would have 300 months (25 years * 12 months/year). We need to calculate (0.996)^300, the probability the company does not file for bankruptcy over 300 months. Finally, we subtract this value from 1 to find the probability that the company will file for bankruptcy at least once during that 25-year period.

Answer 2

The probability that StableCo will file for bankruptcy over the course of 25 years is 9.53%.

Step-by-step explanation:

We have the probability of StableCo still operates normally in the business in one year is: 100%-0.4% = 99.60%.

So, the cumulative probability of StableCo still operates normally in the business for 25 years: 99.6% ^25 = 90.47%.

=> The probability that StableCo will file for bankruptcy over the course of 25 years = 100% - the cumulative probability of StableCo still operates normally in the business for 25 years = 100% - 90.47% = 9.53%.

So, the answer is 9.53%.