The owners of a small manufacturing concern have hired a vice president to run the company with the expectation that she will buy the company after five years. For the first $150,000 of profit, the v ...

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The owners of a small manufacturing concern have hired a vice president to run the company with the
expectation that she will buy the company after five years. For the first $150,000 of profit, the vice
president's compensation is a flat annual salary of $50,000 plus 60% of company profits. Beyond the
first $150,000 in profits, the vice president's compensation is the salary she receives at $150,000 profit
plus 10% of company profits in excess of $150,000.
On the following graph, use the purple points (diamond symbols) to plot the vice president's salary as
a function of annual profit, for the profits levels of $0, $50,000, $100,000, $150,000, $200,000,
$250,000, and $300,000.
For any profit level below $150,000, the vice president earns a base salary of $50,000 plus 60% of the
profit. Thus, for a profit level of zero, the vice president
earns $50+(60%×$0)=$50.00 $50+60%×$0=$50.00 thousand. Similarly, for a profit level of
$50,000, the vice president's compensation
is $50+(60%×$50)=$80.00 $50+60%×$50=$80.00 thousand. Compensation for profit levels of
$100,000 and $150,000 can be calculated in the same way.
At profit levels above $150,000, the vice president earns 10% of those profits plus the compensation
she earned for the first $150,000 in profit. Thus, for a profit level of $200,000, the vice president
earns $50+(60%×$150)=$140.00 $50+60%×$150=$140.00 (in thousands), or the
compensation (including base salary) from the first $150,000 in annual company profit
plus 10%×($200?$150) 10%×$200?$150 (in thousands), since she receives 10% of the $50,000
of annual profit in excess of the $150,000 profit threshold. Therefore, the vice president
earns $140.00+10%×($200?$150)=$145.00 $140.00+10%×$200?$150=$145.00 (in
thousands) when annual company profit is $200,000. The vice president's compensation can be
calculated in the same way for the remaining levels of annual company profit.
Annual
Compan
y Profit Percenta
ge
Earned
By Vice
Presiden
t Base
Salary Total Vice President Compensation
($,
thousan
ds) ($,
thousan
ds) ($, thousands)
$0 60% $50 $50+(60%×$0)=$50.00 $50+60%×$0=$50.00
$50 60% $50 $50+(60%×$50)=$80.00 $50+60%×$50=$80.00
$100 60% $50 $50+(60%×$100)=$110.00 $50+60%×$100=$110.00
$150 60% $50 $50+(60%×$150)=$140.00 $50+60%×$150=$140.00
$200 10% $50 $140.00+10%×($200?
$150)=$145.00 $140.00+10%×$200?$150=$145.00
$250 10% $50 $140.00+10%×($250?
$150)=$150.00 $140.00+10%×$250?$150=$150.00
$300 10% $50 $140.00+10%×($300?$150)=$155.00

The vice president has the option to purchase the company after five years. The purchase price for the
company is set at 4 times earnings (profit), computed as average annual profitability over the next five
years. In five years, the company is expected to be worth $10 million.
On the following graph, use the green points (triangle symbols) to plot the vice president's expected
profit from buying the company, for average annual profitabilit