Ken is offered a choice of two salary packages: Package 1 is commission of 20% on all sales. Package 2 is commission of 10% on all sales, plus a monthly salary of $1,000. If Ken expects to make monthly sales of $30,000, under which package would he earn more money? (Show your calculations). At which monthly sales level would it make no difference which package he chooses? (Show your calculations).
Salary packages can play a crucial role in an individual’s financial well-being. When faced with multiple options, it’s essential to evaluate them carefully to make an informed decision. In this scenario, Ken is presented with two salary packages – one based solely on a commission percentage and the other combining a commission with a fixed monthly salary. We will analyze these options to determine which one would be more financially lucrative for Ken and identify the sales level at which the choice becomes irrelevant.
Package 1 – 20% Commission on All Sales: In Package 1, Ken’s earnings are solely dependent on his sales performance. He is offered a 20% commission on all his sales. To calculate his monthly earnings under this package, we’ll multiply his expected monthly sales by the commission rate.
Earnings in Package 1 = 20% of $30,000 = 0.20 * $30,000 = $6,000
Package 2 – 10% Commission on All Sales + $1,000 Monthly Salary: Package 2 combines a 10% commission on all sales with a fixed monthly salary of $1,000. To determine Ken’s earnings under this package, we’ll calculate both components and sum them up.
Commission in Package 2 = 10% of $30,000 = 0.10 * $30,000 = $3,000 Monthly Salary in Package 2 = $1,000
Total Earnings in Package 2 = Commission + Monthly Salary = $3,000 + $1,000 = $4,000
Comparing the two packages, we find the following:
In Package 1, Ken’s monthly earnings are $6,000.
In Package 2, Ken’s monthly earnings are $4,000.
Therefore, under Ken’s expected monthly sales of $30,000, Package 1, with a 20% commission on all sales, is the more lucrative option as it offers him $6,000 compared to Package 2’s $4,000.
Determining the Sales Level at Which the Choice Becomes Irrelevant:
Now, let’s determine the point at which Ken’s earnings would be the same under both packages. We’ll use the variable “X” to represent this sales level.
In Package 1, Ken’s earnings are given by 20% of X, and in Package 2, his earnings are given by 10% of X plus a fixed $1,000 monthly salary.
Mathematically, we can express this as:
0.20X = 0.10X + $1,000
Solving for X:
0.20X – 0.10X = $1,000
0.10X = $1,000
X = $1,000 / 0.10
X = $10,000
So, at a monthly sales level of $10,000, Ken’s earnings would be the same under both packages. Below this level, Package 2 would be more favorable due to the fixed $1,000 monthly salary, while above this level, Package 1 with its higher commission rate would be the better choice.
When evaluating salary packages, it’s essential to consider your expected performance and financial goals. In Ken’s case, for monthly sales of $30,000, Package 1 with a 20% commission on all sales is the more lucrative choice. However, if Ken expects his monthly sales to drop to $10,000 or below, then Package 2, with its $1,000 fixed monthly salary, becomes a more attractive option. This analysis highlights the importance of understanding the specifics of compensation packages to make the best decision for one’s financial well-being.
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