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Tom Adams has received a job offer from a large investment bank as a clerk to an associate banker. His base salary will be $59,000. He will receive his first annual salary payment one year from the day he begins to work. In addition, he will get an immediate $15,000 bonus for joining the company. His salary will grow at 3.9 percent each year. Each year he will receive a bonus equal to 10 percent of his salary. Mr. Adams is expected to work for 20 years. What is the present value of the offer if the discount rate is 10 percent?

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Answer:

Present value of the offer = $739,018.03

Explanation:

The cash flows described in the question from end of year 1 to end of year 20 represent a growing annuity for  20 years. The present value of a growing annuity is calculated as follows:

PV= [tex]\frac{P}{i-g}*[1-[\frac{1+g}{1+i}]^n][/tex]

where P = the annuity payment in the first period

          i = interest rate per period that would be compounded for each period

         g = growth rate

         n = number of payment periods

P in the 1st year = the base salary of $59,000 + the 10% bonus of $5,900 = $64,900; g is 3.9% ;i=0.1 and n = 20

Present value of the offer = 15,000 received immediately + PV of the growing annuity

= [tex]15,000+\frac{64,900}{0.1-0.039}*[1-[\frac{1+0.039}{1+0.1}]^2^0][/tex]=739,018.03

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