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 $111,000 per year for the next two years, or you can have $40,000 per year for the next two years, along with a $25,000 signing bonus today. The bonus is paid immediately, and the salary is paid at the end of each year. Required: (a) If the interest rate is 7 percent compounded monthly, what is the present value of the first arrangement? (b) If the interest rate is 7 percent compounded monthly, what is the present value of the second arrangement?

Answer 1

Note: Though the compounding of the rate is monthly but the salary is paid per year, hence we need to calculate Effective annual rate (EAR)

The formula to calculate Effective annual rate (EAR) when the compounding is monthly

EAR = ((1+i/n)^n) - 1

((1+(7%/12)^12)) - 1

((1+(0.005833333)^12)) - 1

1.072290080 - 1

7.2290081%

Option 1

As per given data, The salary is paid at the end of each year.

Present Value of annuities = Annuities * [ 1- ( 1+r)^-n]/ r

111000 * ((1-(1.072290081)^-2) /0.072290081)

111000 * ((1-(0.869711920) /0.072290081)

111000 * 1.80229538

$200054.79

Option 2

You can use the PV function in excel

PV(rate,NPER,PMT,FV,TYPE)

rate 7.2290081%, NPER 2, PMT 40000

PV(7.2290081%,2,40000)

72091.82

To this we can the bonus paid immediately

72091.82+25000

$97091.82

Note: I have not rounded any intermediate calculation