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 $85,000 per year for the next two years, or you can have $74,000 per year for the next two years, along with a $20,000 signing bonus today. The bonus is paid immediately, and the salary is paid in equal amounts at the end of each month.If the interest rate is 7 percent compounded monthly, what is the PV for both of the options?

Answer 1

Answer:

The correct answer for 1st option is $158,206.95 and for 2nd option is $157,733.11.

Explanation:

According to the scenario, the given data are as follows:

1st option

Payment ( PMT ) = $85,000

Interest rate (I) = 7%

Time (N) = 2 years

So, the effective rate of interest can be calculated as :

R = $((\frac{1+\frac{7}{100} }{12})^{12} -1)$

R = 7.2290%

Present value can be calculated by using following formula:

P = PMT x (((1-(1 + r) ^- n)) / i)

Hence, present value of 1st option can be calculated as:

PV = 85000×((1-(1 + 7.229%) ^- 2) / 7%)

PV = $158,206.95

Now, present value of 2nd option can be calculated as:

Payment = $74,000

Bonus = $20,000

So, PV = 74000×((1-(1 + 7.229%) ^- 2) / 7%)

PV = 137,733.11

Bonus (add) = $20,000

Total PV = $157,733.11

Hence, the present value for 1st option is $158,206.95 and for 2nd option is $157,733.11.