You\'ve just joined the investment banking firm of Dewey, Cheatum, and Howe. The

Question

You've just joined the investment banking firm of Dewey, Cheatum, and Howe. They've offered you two different salary arrangements. You can have $193,000 per year for the next two years, or you can have $75,000 per year for the next two years, along with a $40,000 signing bonus today. The bonus is paid immediately, and the salary is paid at the end of each year.

(a)

If the interest rate is 9 percent compounded monthly, what is the present value of the first arrangement?

(b)

If the interest rate is 9 percent compounded monthly, what is the present value of the second arrangement?

Explanation / Answer

a) Present value of the first arrangement:

let PV of the salary paid at the end of the first year is P1.

Here,

rate of interest = 9% p.a = 9%/12 per month = 0.09/12 per month (as the interest is being compounded monthly)

Future value of the salary at the end of the first year = $193000

Therefore using the formula for compound interest,

193000 = P1 (1 + 0.09/12)12 , where 193000 is the future value of P1 at the end of one year when interest has been compounded monthly.

=> 193000 = P1 x 1.0938

=> P1 = $176449

Similarly the PV (P2) of the salary at the end of th second year could be calculated from the folloing equation:

193000 = P2 (1 + 0.09/12)24

=> 193000 = P2 x 1.1964

=> P2 = 193000/1.1964 = $161317

So under the first arrangement the present value of the salary

= $176449 + $161317 = $337,766

b) Present value of the second arrangement:

Here the signing bonus of $40000 is being paid today.

let PV of the salary paid at the end of the first year is P1.

Here,

rate of interest = 9% p.a = 9%/12 per month = 0.09/12 per month (as the interest is being compounded monthly)

Future value of the salary at the end of the first year = $75,000

Therefore using the formula for compound interest,

75,000 = P1 (1 + 0.09/12)12 , where 75,000 is the future value of P1 at the end of one year when interest has been compounded monthly.

=> 75,000 = P1 x 1.0938

=> P1 = $68,568

Similarly the PV (P2) of the salary at the end of th second year could be calculated from the folloing equation:

75000 = P2 (1 + 0.09/12)24

=> 75000 = P2 x 1.1964

=> P2 = 75,000/1.1964 = $62,688

So under the second arrangement the present value of the salary

= $68,568 + $62,688 = $131,256

Present Value of the bonus and the salaries under the second arrangement = $40,000 + $131,256 = $171,256

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