Under which of the following cases may a percentage change be computed?
a. The trend of the amounts is decreasing but all amounts are positive.
b. There is no amount in the base year.
c. There is a negative amount in the base year and a negative amount in the subsequent year.
d. There is a negative amount in the base year and a positive amount in the subsequent year.
The correct answer and explanation is :
The correct answer is:
a. The trend of the amounts is decreasing but all amounts are positive.
Explanation:
A percentage change is typically computed using the formula:
[
\text{Percentage Change} = \left( \frac{\text{New Value} – \text{Old Value}}{\text{Old Value}} \right) \times 100
]
To properly calculate a percentage change, the denominator (Old Value or Base Year Value) must be a meaningful reference point. Let’s analyze each case:
- Option (a): The trend of the amounts is decreasing but all amounts are positive.
- This is a valid case for computing a percentage change. Even though the values are decreasing, as long as they remain positive, division is possible, and the percentage change can be calculated normally.
- Option (b): There is no amount in the base year.
- If the base year amount is zero, the denominator in the percentage change formula becomes zero. Division by zero is undefined, making it impossible to compute a valid percentage change.
- Option (c): There is a negative amount in the base year and a negative amount in the subsequent year.
- While mathematically possible, percentage changes involving negative values can be misleading. A percentage decrease or increase assumes a reference point that can logically grow or shrink, but negative numbers complicate this interpretation.
- Option (d): There is a negative amount in the base year and a positive amount in the subsequent year.
- The percentage change formula would involve division by a negative base value, leading to a result that does not provide meaningful insight. Transitioning from a negative to a positive value suggests a fundamental shift rather than a relative change.
Thus, only option (a) allows for a meaningful percentage change calculation.