An international company appoints a 30-year Harvard MBA as its new president on a 5-year contract at a salary of $450,000. The salary is to increase each year by 9%. On the first day of the job, a serious past misconduct is discovered about the incumbent. The board of directors therefore decides to

Question

An international company appoints a 30-year Harvard MBA as its new president on a 5-year contract at a salary of $450,000. The salary is to increase each year by 9%. On the first day of the job, a serious past misconduct is discovered about the incumbent. The board of directors therefore decides to fire him the same day. However, as stipulated in the employment contract, he must be paid the present value of the salaries along with a golden handshake in the sum of $500,000. If i = 10%, how much is he paid?

Accepted Answer

The analysis period is 5 years. We can draw a cashflow diagram either from the president’s viewpoint or the company’s. The answer will be independent of the viewpoint considered. Fig. 4.10 shows the company’s diagram with cashflows as costs. The president’s initial salary of $450,000 increases at 9% per year. So the value of A1 is $450,000, and g= 9% = 0.09. The P-value of the salaries plus the $500,000 golden handshake is the total payment to the fired president.

There are two ways to determine the P-value of the salaries. In one, we determine the present value of [latex]A_{1}[/latex],[latex] A_{2}[/latex], …, and [latex]A_{5}[/latex] individually using the basic relationship [latex]F=P(1+i)^{n}[/latex] , and add them. In the second approach, we exploit the geometric series the cashflows form, using the equation derived in this section. Let us opt for the equation approach.

With [latex]i=0.10[/latex] and g = 0.09, i ≉ g, and hence Equation (4.7) is applicable. This equation will yield the P-value of [latex]A_{1}[/latex],[latex] A_{2}[/latex], …/ [latex]A_{5}[/latex] at period 0. With n = 5, the P-value of the future salaries is:

[latex]A_{1} \frac{1-(1+g)^{5} (1+i)^{-5} }{i-g}[/latex]

[latex]=450,000\frac{1-(1+0.09)^{5} (1+0.10)^{-5} }{0.10-0.09}[/latex]

[latex]=450,000\frac{1-(1.5386 imes 0.6209)}{0.01}[/latex]

[latex]=450,000 imes 4.4683[/latex]

[latex]=\$2,010,749[/latex]

Total payment = P - value of salaries + golden handshake

[latex]=\$2,010,749+\$500,00[/latex]

[latex]=\$2,510,749[/latex]

The “sacked” president is thus paid $2,510,749.

Question 4.5: An international company appoints a 30-year Harvard MBA as i...

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