Question

Today is your first day at the investment banking firm of Dewey, Cheatum and Howe. They have offered you a choice between two different compensation arrangements. You can have a salary of $95,000 per year for the next two years, or you can have a salary of $84,000 per year for the next two years and a signing bonus $20,000 that is paid 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 8 percent compounded monthly, which compensation program do you prefer? Explain why. If the interest rate is 18 percent compounded monthly, which compensation program do you prefer? Explain why. do not use excel or a calculator to solve

Answer 1

Option 1
Salary of 95000 per year
Monthly Salary = P = 95000/12
Interest Rate = r = 8% = 0.08/12
Number of months = n = 24
Present Value of future salary payments = P/(1+r) + P/(1+r)² +....+ P/(1+r)ⁿ = P[1- (1+r)^-n]/r = (95000/12)[1- (1+0.08/12)^-24]/(0.08/12) = $175041.80

Option 2
Salary of 84000 per year
Monthly Salary = P = 84000/12
Interest Rate = r = 8% = 0.08/12
Number of months = n = 24
Present Value of future salary payments = P/(1+r) + P/(1+r)² +....+ P/(1+r)ⁿ = P[1- (1+r)^-n]/r = (84000/12)[1- (1+0.08/12)^-24]/(0.08/12) = $154773.81
Signing Bonus = $20000
Present Value of future salary + bonus = $174773.81

Hence, option 1 is better. This is because a lumpsum is received initially and there is no effect of discounting on this lumpsum.

Interest Rate = 18%

Option 1
Salary of 95000 per year
Monthly Salary = P = 95000/12
Interest Rate = r = 18% = 0.18/12
Number of months = n = 24
Present Value of future salary payments = P/(1+r) + P/(1+r)² +....+ P/(1+r)ⁿ = P[1- (1+r)^-n]/r = (95000/12)[1- (1+0.18/12)^-24]/(0.18/12) = $158574.04

Option 2
Salary of 84000 per year
Monthly Salary = P = 84000/12
Interest Rate = r = 8% = 0.18/12
Number of months = n = 24
Present Value of future salary payments = P/(1+r) + P/(1+r)² +....+ P/(1+r)ⁿ = P[1- (1+r)^-n]/r = (84000/12)[1- (1+0.18/12)^-24]/(0.18/12) = $140212.84
Signing Bonus = $20000
Present Value of future salary + bonus = $160212.84

In this scenario, option 2 is better