Tom Adams has received a job offer from a large investment bank as a clerk to an
ID: 2640100 • Letter: T
Question
Tom Adams has received a job offer from a large investment bank as a clerk to an associate banker. His base salary will be $50,000. He will receive his first annual salary payment one year from the day he begins to work. In addition, he will get an immediate $10,000 bonus for joining the company. His salary will grow at 4.4 percent each year. Each year he will receive a bonus equal to 10 percent of his salary. Mr. Adams is expected to work for 25 years.
What is the present value of the offer if the discount rate is 9 percent?
Using the growing annuity formula I did:
r = .044 r = .09 C = 50000 bonus: 10,000 50000*.1 = 5000
50000/(.09/.044) (1-(1+.044)/(1+.09))^25 + 10000 = PV = 727,075.38
I am not sure if I am correct?
Explanation / Answer
You have correct information with you .
Your formula is not correct.
Now, plugging the values in the formula and getting PV of the salary:
PV = C {[1/(r – g)] – [1/(r – g)] × [(1 + g)/(1 + r)]t}
PV = $50,000{[1/(.09 – .044)] – [1/(.09 – .044)] × [(1 + .044)/(1 + .0.09)]^25}
PV = $717,075.38
Next year bonus is correct. Bonus =5000
Since bonus is based upon salary, so bonus will also increase with the increase in salary.
Therefore, PV of bonus would be:
PV = C {[1/(r – g)] – [1/(r – g)] × [(1 + g)/(1 + r)]t}
PV = $5,000{[1/(.09 – .044)] – [1/(.09 – .044)] × [(1 + .044)/(1 + .0.09)]^25}
PV = $71,707.54
Total PV of the offer would be = PV of salary + Pv of bonus + Bonus paid today
= $717,075.38+ $71,707.54 + $10,000
=$798,782.92