Let's break down the problem:

1. Initial drop of 40%:

   • If the stock starts at $100 and drops by 40%, it loses 40% of its value.
   • The loss is:
     $40\% \text{ of } 100 = 0.40 \times 100 = 40$
   • After the drop, the stock is worth: $100 - 40 = 60$

2. Subsequent increase of 75%:

   • After the drop, the stock is now worth $60.
   • A 75% increase on $60 is: $75\% \text{ of } 60 = 0.75 \times 60 = 45$
   • After the increase, the stock is now worth: $60 + 45 = 105$

Thus, the stock's value after these changes is $105, which is higher than where it started.

Final Answer:

• The value of the stock is higher than where it started.
• If the stock started at $100, it is now worth $105.

Would you like further details or clarifications on any part of this?

Here are 5 follow-up questions related to this topic:

1. What happens if a stock drops by 50% and then increases by 50%? Will the value be the same?
2. How does the order of percentage changes affect the final value of a stock?
3. What is the formula for calculating percentage change over multiple periods?
4. How do you calculate the total percentage change from successive increases and decreases?
5. If a stock increases by 100% after dropping 50%, what will be its final value?

Tip: When a percentage decrease is followed by a percentage increase, the increase is always calculated on a smaller base, making it harder to fully recover from large drops.