In: Finance
You’ve just joined the investment banking firm of Dewey, Cheatum, and Howe. They’ve offered you two different salary arrangements. You can have $6,100 per month for the next two years, or you can have $5,100 per month for the next two years, along with a $25,000 signing bonus today. Assume the interest rate is 7 percent compounded monthly. |
a. | If you take the first option, $6,100 per month for two years, what is the present value? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) |
b. | What is the present value of the second option? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) |
a. First option
No. of periods = 2*12 = 24 months
Annual interest rate = 7%, compounded monthly
so, monthly interest rate = rm = 7%/12
This is an annuity with a cash flow of $6100 per month for 24 months
C = 6100, no. of periods = n = 24, monthly rate = rm = 7%/12 = 0.00583333333333333
The present value of an annuity can be calculated using the below formula:
PVAnnuity = (C/rm)*[1-(1+rm)-n]
PVAnnuity = (6100/(7%/12)) * [1-(1+(7%/12))-24]
PVAnnuity = 1045714.28571429*0.130288079225785 = 136244.105704678
Answer -> Present value of first option = $136244.11
b. Second option
In the second option, there is an amount that is paid today and also, there is an annuity, with monthly cash flow of $5100 for 24 months. Present value of this option will be the sum of C0 and the present value of the annuity
Amount paid today as signing bonus = C0 = $25000
Annuity -> C = 5100, rm = 7%/12, n = 24
PVannuity = (5100/(7%/12))*[1-(1+(7%/12))-24] = 874285.714285714*0.130288079225785 = 113909.006408829
Total present value of the second option = C0 + PVAnnuity = 25000 + 113909.006408829 = 138909.006408829
Answer -> Present value of the second option = $138909.01